**Global Understanding of Accretion and Ejection around Black Holes**

Editor

**Santanu Mondal**

MDPI ' Basel ' Beijing ' Wuhan ' Barcelona ' Belgrade ' Manchester ' Tokyo ' Cluj ' Tianjin

*Editor* Santanu Mondal Theoretical Astrophysics Indian Institute of Astrophysics Bangalore India

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This is a reprint of articles from the Special Issue published online in the open access journal *Galaxies* (ISSN 2075-4434) (available at: www.mdpi.com/journal/galaxies/special issues/Accretion and Ejection around Black Holes).

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### **Contents**


### **Chandra B. Singh, David Garofalo and Benjamin Lang**


### **About the Editor**

### **Santanu Mondal**

Santanu Mondal is a Ramanujan Fellow at the Indian Institute of Astrophysics. He completed his Ph.D. in 2015 from Indian Centre for Space Physics, India. He was a Kreitman Fellow at the Ben-Gurion University of the Negev, Israel and FONDECYT Fellow at the Universidad de Valparaiso, Chile. He is also a life member of Astronomical Society of India. He was a visiting scientist of NASA/GSFC in 2014 and MPIA, Garching in 2017. His works include theory and observation of accretion-ejection flows around black holes, numerical simulation of the Fermi Bubbles, and the imaging of galaxy clusters.

### **Preface to "Global Understanding of Accretion and Ejection around Black Holes"**

Black holes are one of the most interesting and fascinating objects in the universe, not because of their name, but because of their activity. They produce enormous amount of radiation from the accretion disks surrounding them and also a large amount of mechanical energy as jets. These make them important objects in the universe. However, their importance is recognized only recently in the long history of astronomy and astrophysics. In the early 1960s, the discovery of quasars was a trigger for the start of studying accretion disks. Accretion disks are now known in various compact objects, low mass black holes, ultraluminous X-ray sources, including active galactic nuclei, etc. These objects also produces jets occasionally in the relativistic and sub-relativistic limit.

The content of this book includes different aspects of accretion and ejection flows around black holes of all scales. The radiation coming from the disk and jet varies in a broad range from radio to gamma rays. However, their origin, spectral behaviour, linking with timing properties, and (anti)correlation between different bands are still lacking proper physical explanation. Therefore, we put the focus of discussion of this book related to the theory of accretion-ejection flows and its application to explain observations from different ground- and space-based observatories.

We hope the articles in this book will serve as a reference for astronomers in this field and interested astronomers from some other fields.

I thank all the contributing authors for making this Special Issue possible. I gratefully acknowledge the MDPI/Galaxies editorial and publication team for their constant support and effort for making this issue successful. My special thanks go to Ms. Queens Cui, the Managing Editor of this journal. Finally, I thank my colleagues, family, and my wife Suparna Mandal for their constant support during the COVID pandemic period, during which the majority of this issue was completed.

> **Santanu Mondal** *Editor*

### *Editorial* **Global Understanding of Accretion and Ejection around Black Holes**

**Santanu Mondal**

Indian Institute of Astrophysics, II Block Koramangala, Bangalore 560034, India; santanu.mondal@iiap.res.in

Accretion and ejection around compact objects, mainly around black holes, both in low mass, and supermassive, is rich and has been studied exhaustively. However, the subject is expanding and growing rapidly after the launch of different space-based satellites and ground-based telescopes in multiwavelength bands, leaving a range of questions on accretion and ejection mechanisms. The proper understanding of the underlying physical mechanisms responsible for observational evidence is still lacking for several reasons. For instance, different phenomena are studied as a separate system, the hydrodynamics of one component ignores the other, spectral properties ignore timing properties or vice versa, and there is not enough instrumental resolution to decipher small scale physics.

With the advent of high-resolution satellite observations, it is possible to look at the problems globally as a complete package in a more consistent way. Recently, many new low mass black hole candidates have been discovered; however, very little is known about those systems, e.g., mass, spin parameter, orbital period. The study in the spectrotemporal domain also needs proper understanding of spectral state change, quasi periodic oscillation (QPO) frequency evolution, hardness intensity diagram, and line emissions. Therefore, it is a good time to take a break, recapitulate what has been carried out, what is ongoing, and what can be carried out in the future with upcoming missions, both from a theoretical and observational perspective, bringing together experts across the electromagnetic spectrum to gain new insights into the physical process of accretion.

This special issue covers both theoretical and observational aspects of accretion and ejection around both low mass and supermassive black holes. The papers published in this Special Issue provide novel, interesting phenomenological and theoretical contributions to this mainline topic. There is a range of questions related to the underlying physical processes which are responsible for the observed variabilities. This Issue puts some light on those basic questions and provide a roadmap for the resolution. For example, the physical picture of luminous active galactic nuclei (AGN) with powerful jets has been several decades-old problems in high-energy astrophysics. One of the fundamental problems is that to produce such powerful jets strong magnetic fields are to be transported from the accretion disk to the black hole horizon. This gives rise to greater disk thickness, which in turn decreases the radiative efficiency of the disk. Ref. [1] pointed out that recent numerical simulations have been partially successful to address the issue and much work is needed to single out the physical processes. They provided a road map for a resolution that counterrotating black holes with thin disks should be further explored in new simulations.

In addition, for a class of AGNs where the radiation is dominated by the accretion disk and its corona are known as Seyfert galaxies. This class of AGNs shows variability in different timescales in their observed lightcurve and emitted spectra, however, the physical origin of which is highly illusive, most importantly when the question comes on the origin of the inner hot corona and its geometrical and thermodynamical properties. Ref. [2] studied a well-known source Mrk 335 using several models including both physical and phenomenological and inferred the origin of variability from the basic accretion flow parameters. Authors suggested that the cooling and viscosity are important to make the corona variable, similar to low mass black hole candidates (LMBHCs, ref. [3]), which

**Citation:** Mondal, S. Global Understanding of Accretion and Ejection around Black Holes. *Galaxies* **2022**, *10*, 64. https://doi.org/ 10.3390/galaxies10030064

Received: 13 April 2022 Accepted: 20 April 2022 Published: 27 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

actually depends on the variation of the mass accretion rate (ref. [4,5]). The matter which is falling onto a black hole can be isothermal or adiabatic depending on the radiation mechanisms taken into account. Ref. [6] studied the Bondi accretion onto a supermassive black hole for the variable adiabatic index of the flow using Paczy´nski–Wiita potential. Earlier, a detailed study of accretion processes with varying the polytropic index was also done by ref. ([7,8] and others).

The other class of AGNs of which the radiation is mainly dominated by the jets is called blazars and radio-loud AGN. In their high activity state jet is the dominating contributor to the observed features, however, the disk can also contribute when the jet activity is low or moderate ref. [9]. Therefore, distinguishing the central engine responsible for the variabilities in these objects is one of the front line topics. Refs. [10–12] studied these issues and related variability properties in this special issue. Apart from continuum modeling, line emission is crucial to understand the gaseous outflows from these systems. This indeed helps us to understand the role of the Eddington luminosity, mass accretion rates, and the geometry of the flow in originating variable line profiles (see ref. [13] in this context and references therein), the wind/outflow velocities, and also from which region these lines are originating. Ref. [14] addressed some of these issues for quasars.

If we look at the black holes of small scales, they too show variability in their spectrotemporal domain, including QPOs, jet/outflows, the signature of magnetic field etc. Refs. [15,16] studied low LMBHCs, XTE J1908+094 and V404 Cygni, and determined their mass accretion rates, corona radii etc. Ref. [16] estimated the equipartition magnetic field strength of V404 Cygni source during the outburst phase and estimated the value of 900 Gauss. The authors did not find any QPO frequency in their power density spectra. They suggested that the absence of QPOs is due to the non-satisfaction of resonance condition (see ref. [17]).

It is to be noted that the mass of the central compact objects is hardly known, therefore, estimating its value is important to estimate different length scales of the flows correctly. Refs. [2,15] estimated the masses of the AGN and LMBHC from their spectral fitting, which agree with the dynamical mass measurement of the sources.

In addition to the fluid dynamics, one can also find the geodesic orbit of particles in black string spacetime geometry. Ref. [18] studied the same and found that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits.

To summarize, the papers compiled in this Special Issue presented interesting results and gave useful insights onto the accretion-ejection processes around black holes. Furthermore, the articles on this Issue also put light on what can be carried out using future observations.

**Funding:** S.M. acknowledges Ramanujan Fellowship research grant #RJF/2020/000113 from SERB-DST, Govt. of India.

**Institutional Review Board Statement:** Not Applicable.

**Informed Consent Statement:** Not Applicable.

**Data Availability Statement:** This paper does not include any data as it is a review article on the papers published in the Special Issue titled the same as the title of the article.

**Conflicts of Interest:** The author declares no conflict of interest.

### **References**


### *Article* **Isolating an Outflow Component in Single-Epoch Spectra of Quasars**

**Paola Marziani 1,\* , Alice Deconto-Machado <sup>2</sup> and Ascension Del Olmo <sup>2</sup>**


**Abstract:** Gaseous outflows appear to be a universal property of type-1 and type-2 active galactic nuclei (AGN). The main diagnostic is provided by emission features shifted to higher frequencies via the Doppler effect, implying that the emitting gas is moving toward the observer. However, beyond the presence of blueshift, the observational signatures of the outflows are often unclear, and no established criteria exist to isolate the outflow contribution in the integrated, single-epoch spectra of type-1 AGN. The emission spectrum collected the typical apertures of long-slit spectroscopy or of fiber optics sample contributions over a broad range of spatial scales, making it difficult to analyze the line profiles in terms of different kinematical components. Nevertheless, hundred of thousands of quasars spectra collected at moderate resolution demand a proper analysis of the line profiles for proper dynamical modeling of the emitting regions. In this small contribution, we analyze several profiles of the HI Balmer line H*β* from composite and individual spectra of sources radiating at moderate Eddington ratio (Population B). Features and profile shapes that might be traced to outflow due to narrow-line region gas are detected over a wide range of luminosity.

**Keywords:** active galactic nuclei; optical spectroscopy; ionized gas; broad line region

#### **Citation:** Marziani, P.;

Deconto-Machado, A.; Del Olmo, A. Isolating an Outflow Component in Single-Epoch Spectra of Quasars. *Galaxies* **2022**, *10*, 54. https://doi.org/10.3390/ galaxies10020054

Academic Editor: Santanu Mondal

Received: 15 February 2022 Accepted: 17 March 2022 Published: 24 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

### **1. Introduction**

Type-1 active galactic nuclei (AGN) are characterized by the presence of broad and narrow optical and UV lines (for introductions, see, e.g., [1–6]). Spectra show a mind-boggling variety of broad emission line profiles not only among different objects but also among different lines in the spectrum of the same object. Sulentic [7] carried out measurements of spectral shifts and asymmetries exhibited by the broad lines relative to the narrow ones, proposing an empirical classification scheme for the broad HI Balmer line H*β*. Among the classes identified by Sulentic [7], two stand out: AR,R and AR,B, where AR means red-ward asymmetric, and the letter after the comma indicates either a shift of the line peak toward red or blue.

Fast forward more than 30 years, type-1 quasars are now being contextualized on the basis of the main sequence (MS) trends (e.g., [1,8,9]). Type-1 AGNs have been grouped into two main populations, Population A and B, defined on the basis of Balmer line widths (more specifically of H*β*: FWHM H*β* . 4000 km s−<sup>1</sup> for Population A; FWHM H*β* & 4000 km s−<sup>1</sup> for Population B [1,10] at low and moderate luminosity log *L* . 46 (erg s−<sup>1</sup> )). The classification of the quasar population along MS has its main physical foundation on systematic differences in Eddington ratio [11]: Population A sources typically have *L*/*L*Edd & 0.2, with extreme Population A sources reaching *L*/*L*Edd& 1 [12], values close to the expected theoretical limit for super-Eddington accretion rate [13–15]. Usually, Pop. B sources present lower values of the Eddington ratio when compared with the ones of Pop. A. The governing parameter of the MS itself appears to be an Eddington ratio convolved with the effect of orientation (e.g., [16,17]).<sup>1</sup>

Sources showing prominent H*β* red asymmetries (i.e., AR,R according to Sulentic [7]) are classified as belonging to Population B [10,11]. The red asymmetry itself can be considered as a defining feature of Population B sources, hinting at the presence of a "very broad component" (VBC) at the line base [18–23]. The physical properties of the region associated with VBC are largely undetermined (e.g., [24]) but the general consensus is that the region is located at the innermost radii of the broad line region (BLR), closest to the central continuum source. This inference follows from the deduction of a velocity field dominated by virial motions, at least for several population B sources [25,26]. The dynamical conditions of the "very broad line region" (VBLR) are the subject of current debate [27]. Two main alternatives have been proposed: infall and obscuration [28], or gravitational and transverse redshift [27,29–33]. Both mechanisms are, however, still consistent with a virial velocity field as the main broadening factor.

Gaseous outflows appear to be ubiquitous in type-1 AGN, although their traceability and their kinetic power varies greatly along the main sequence [34,35]. The signature of outflows in the optical and UV spectra is provided by the blueshift of emission lines with respect to the rest frame, under the assumption that the shift is due to a Doppler effect on the wavelength of lines emitted by gas moving toward us and that the receding side of the flow is mainly hidden from view (e.g., [36]). While there is unambiguous evidence of outflows from the emitting regions of quasars radiating at high Eddington ratios, the situation is by far less clear for Pop. B where the accretion rate is modest, as implied by a Eddington ratio . 0.2. High-resolution X-ray and ultraviolet (UV) observations of the prototypical Population B source NGC 5548 reveal a persistent ionized outflow traced by UV and X-ray absorption and emission lines [37]. However, the CIV emission line profile lacks strong evidence of such an outflow also because of the prominent red line wing merging with HeII*λ*1640 [38].

In this short note, we address the very specific issue of the origin of sources showing a blueshift at the peak of the H*β* emission line, e.g., of the AR,B classification. The focus is on the H*β* line because the line is a singlet, and its peak is isolated from other contaminants, offering a clear view of its broad and narrow components. The [OIII]*λλ*4959,5007 lines recorded along with H*β* help assess the nature of the H*β* line profile. In addition, the narrow, high-ionization [OIII]*λ*5007 emission lines are known to be affected by outflows, as indicated by the frequent blueward asymmetries and even systematic shifts [39–43]. Section 2 presents the data used in this work, which comprise a set of composite spectra covering a wide range in luminosity and redshift, for which H*β* and [OIII]*λλ*4959,5007 emissions have been covered with optical and IR spectroscopic observations. Details on how the spectral analysis was performed are shown in Section 3. The main results come from the profile comparison of H*β* and [OIII]*λ*5007 (Section 4) and are briefly analyzed in terms of the physical conditions of the line emitting gas, as well as of the dynamical parameters of the outflow (Section 5).

### **2. Data**

The data analyzed in this paper refer to the most widely populated spectral type of Population B, B1, defined by FWHM H*β* in the range of 4000–8000 km s−<sup>1</sup> [44]. Median composite spectra covering the H*β* range were computed over spectral type B1 sources belonging to two samples of low-to-moderate redshift and luminosity [44,45], and one sample of intermediate *z* and high luminosity [46]. The [44] composites are based on the individual observations of Marziani et al. [47] that involved 97 B1 spectra. The [45] composites are SDSS spectra in the redshift range of 0.4–0.7, covering both MgII*λ*2800 and H*β*. The radio-quiet B1 composite was computed over 179 spectra, while CD and FR-II composites involved 16 and 23 spectra, respectively. The [46] B1 composite included 22 high-luminosity, Hamburg ESO (HE) quasars. Median composites were constructed from continuum-normalized (at 5100 Å) spectra, after a determination of the heliocentric redshift based on [OII]*λ*3727 or a narrow component of H*β*, two low-ionization narrow line that provide the best estimators of the systemic redshift of the host galaxy [48]. The accurate redshift correction allowed for the preservation of the spectral resolution of the individual

spectra. The [45] composites should, therefore, have a resolving power *λ*/*δλ* ∼ 2000. The resolving power is only slightly lower for [44], *λ*/*δλ* ∼ 1000. The HE ISAAC near-IR observations were all collected with a narrow slit (0.6 arcsec) that yielded *λ*/*δλ* ∼ 1000, comparable to the spectra of the samples observed with optical spectrometers. The main physical properties associated with the composite spectra are summarized in Table 1, where the first column lists an identification code, and the following columns list the redshift range and the median values of bolometric luminosity, black hole mass *M*BH, and the Eddington ratio *L*/*L*Edd. In addition to the composite spectra, the spectra of two quasars of extreme luminosity at intermediate redshift (Deconto-Machado et al. 2022, in preparation) provide examples of two opposite cases: One where a prominent outflow signature is detected (Q0029+079), and one in which there is no obvious evidence of outflow (HE0001-2340). The last two lines of Table 1 consider composites for core-dominated (CD) and Fanaroff– Riley (FR) sources belonging to spectral type B1 from the [45] sample. These two composite were defined to address the somewhat controversial issue of the mild-ionized outflow presence among radio-loud, jetted AGN.<sup>2</sup> The data of Table 1 confirm that the empirical selection of spectral type B1 corresponds to the selection of modest *L*/*L*Edd radiators. At the higher redshift and luminosity, *L*/*L*Edd appears somewhat higher (*L*/*L*Edd ≈ 0.3) because of the preferential selection of higher *L*/*L*Edd for a fixed black hole mass in flux limited surveys [51].


*a* : Black hole mass computed from the H*β* scaling law provided by Vestergaard and Peterson [52], using the H*β* full profile FWHM. Applying the average correction suggested for spectral type B1 would lower the mass by a factor 0.64 and increase the *L*/*L*Edd ratio by the inverse of this factor. *<sup>b</sup>* Bolometric correction assumed a factor 10; *<sup>c</sup>* Bolometric correction assumed a factor 4, as appropriate for very high luminosity sources following Netzer [53].

### **3. Analysis**

The non-linear multicomponent fits were performed using the SPECFIT routine from IRAF [54]. This routine allows a simultaneous minimum-*χ* <sup>2</sup> fit of the continuum approximated by a power law and the spectral line components yielding FWHM, peak wavelength, and intensity of all line components. In the optical range, we fit the H*β* profile as well as the[OIII]*λλ*4959,5007 emission lines and the FeII multiplets accounted for by a scaled and broadened template [55]. The details of multi-component analysis has been provided in several previous papers (e.g., [56]) and will not be repeated here. Suffice to say that the broad profiles of Pop. B sources can be successfully modeled with two Gaussians: (1) one narrower, unshifted or slightly shifted to the red; and (2) one broader, with FWHM <sup>∼</sup> 10,000 km s−<sup>1</sup> , and shifted by few thousands km s−<sup>1</sup> to the red [57]. This model accounts for the AR,R profile type. In addition to the model decomposition, we measured

several parameters on the full broad profile [58]. The definitions of the centroids and of the asymmetry index *A*.*I*. are reported below for convenience:

$$c(\frac{i}{4}) = \frac{v\_{\text{r,B}}(\frac{i}{4}) + v\_{\text{r,R}}(\frac{i}{4})}{2}, i = 1, 2, 3; \frac{i}{4} = 0.9,\tag{1}$$

where the radial velocities are measured with respect to the rest frame at fractional intensities *<sup>i</sup>* 4 for each value of the index *i* on the blue and red side of the line with respect to the rest frame.

$$A.I.(\frac{1}{4}) = \frac{v\_{\rm r,B}(\frac{1}{4}) + v\_{\rm R}(\frac{1}{4}) - 2v\_{\rm r,P}}{v\_{\rm r,R}(\frac{1}{4}) - v\_{\rm r,B}(\frac{1}{4})}.\tag{2}$$

Note that the *A*.*I*., unlike the centroids, is defined as a shift with respect to the line peak radial velocity *v*r,P (*v*r,P is measured with respect to rest frame; a suitable proxy is provided by *c*(0.9)).

### **4. Results**

### *4.1. Broad* H*β*

Figure 1 shows the continuum-subtracted spectra and their models for the [44–46] composite spectra (top, middle and bottom panel, respectively). The measurements of the broad H*β* line parameters are reported in Table 2. For each spectrum, Table 2 lists the normalized flux *F* of the H*β* full broad profile (H*β*BC + H*β*VBC+ H*β*BLUE), its equivalent width *W* H*β* in Å, and the normalized fluxes of H*β*BC and H*β*VBC separately. The following columns report several parameters for the H*β* blue-shifted excess with respect to the standard Population B decomposition involving only H*β*BC and H*β*VBC: normalized flux, equivalent width, peak shift, FWHM, and skew. The last columns yield the normalized flux and the equivalent width of the FeII*λ*4570 emission blend, as defined by Boroson and Green [55]. The equivalent width values correspond roughly to the normalized flux so that they are reported only for the main features. The normalized fluxes can be approximately converted into luminosities by multiplying them by the luminosity values reported in Table 1 divided by the bolometric correction and by 5100, i.e., by the wavelength in Å at which the continuum was normalized. Table 3 reports FWHM, A.I., and centroids as defined in Section 3 for the *broad* H*β* profile (H*β*BC + H*β*VBC+ H*β*BLUE i.e., without considering the narrow (H*β*NC) and semi-broad (H*β*SBC) components associated with narrow-line region emission). Only at the highest *L* blueshifted emission with a broad profile (H*β*BLUE) is detected in the H*β* profile: In this case, the H*β*BLUE contribution is .5% of the total line luminosity for the [46] composite and reaches about 1/3 of the total line luminosity in the admittedly extreme Q0029 case. In no case, however, was H*β*BLUE able to create a significant shift to the blue close to the line base: red asymmetry dominates and even the Q0029 H*β* broad profile is "symmeterized" toward the line base, with a centroid at <sup>1</sup> 4 peak intensity close to 0 km s−<sup>1</sup> .

**Figure 1.** Analysis of the H*β* + [OIII]*λλ*4959,5007 region for [44] (**top**), [45] (**middle**), and [46] (**bottom**) B1 composite spectra. Continuum subtracted spectra are shown in the rest frame, over the range 4550–5300 Å (left panel), with an expansion around [OIII]*λ*5007 (right panels). Thin solid lines: continuum-subtracted spectrum; dashed magenta line: model spectrum; thick black line: H*β* broad component; red thick line, H*β* very broad component; thin smooth black lines: narrow components of H*β* and [OIII]*λ*5007; blue lines: blue shifted components. Green lines trace the scaled and broadened FeII emission template. The lower panel show the observed minus model residuals in radial velocity scale.


#### **Table 2.** Broadline properties measurements.

*a* : In units of Å; *<sup>b</sup>* : in units of km s−<sup>1</sup> . *c* skew as reported by the SPECFIT routine; it is equal to the conventional definition of skew [59] + 1.

**Table 3.** H*β* profile properties measurements.


*a* In units of km s−<sup>1</sup>

### *4.2.* [OIII]*λ5007 and* H*β Narrow-Line Emission*

.

Table 4 summarizes the measurements of the components associated with the narrowline region (NLR) emission, i.e., narrow and semi-broad components of H*β* and [OIII]*λ*5007 (H*β*NC, [OIII]*λ*5007NC, and H*β*SBC and [OIII]*λ*5007SBC), for which normalized flux, equivalent width, shift, and FWHM are reported. The skew parameter is reported only for semi-broad components, as the narrow components are assumed to be symmetric Gaussian, within a few tens km s−<sup>1</sup> from the rest frame [48].

The [44] composite shows a broad + narrow component profile that is very well represented by three Gaussians: the symmetric unshifted H*β*NC, unshifted H*β*BC and the H*β*VBC with a significant shift to red. A small blue-shifted excess appears at the interface between H*β*NC and H*β*BCand has been modeled by an additional Gaussian. Its intensity is so low that a very good fit with no significant worsening in the *χ* 2 can be achieved also without it. Most notably, the [OIII]*λ*5007 profile (enlarged in the right panel) is also fairly symmetric: A small centroid blueshift ∼ −<sup>50</sup> km s−<sup>1</sup> is detected only at <sup>1</sup> 4 peak intensity (Table 5, where the [OIII]*λ*5007 full profile parameters are reported as in Table 3 for H*β*). The relatively large shift reported for [OIII]*λ*5007SBC is compensated by a red-ward skew (Figure 1, right panel on top row). In this case, the decomposition [OIII]*λ*5007NC- [OIII]*λ*5007SBC is especially uncertain, and a more reliable measurement is provided by the centroid.

*Galaxies* **2022**, *10*, 54


**Table 4.** Narrow line measurements.

: In units of Å; *b* : in units of km s−1 . *c* skew as reported by the SPECFIT routine; it is equal to the conventional definition of skew [59] + 1.

*a*


**Table 5.** [OIII]*λ*5007 profile measurement.

*a* : In units of km s−<sup>1</sup> .

The [45] composite spectrum appears as a "goiter" at the top of the H*β*BC broad profile. The [OIII]*λ*5007 profile is also fairly asymmetric, and it can be modeled by a narrower, almost unshifted component and a skewed Gaussian displaced to the blue by ≈ −<sup>500</sup> km s−<sup>1</sup> . The top of the H*β* profile is well fit by assuming two components with the same shift, width, and asymmetry of the model components' [OIII]*λ*5007 line. The consistency between the model of H*β*SBC and [OIII]*λ*5007SBC provides evidence that the H*β* blueshifted, and the skewed component is associated with a NLR outflow. The [46] composite can be equally modeled with the same skewed and blueshifted component for H*β* and [OIII]*λ*5007. However, this model would require an implausibly strong [OIII]*λλ*4959,5007 emission. The fit shown in the bottom panel of Figure 1 assumes a broader component for H*β* emission.

At very high luminosity (Figure 2), a prominent outflow is apparently absent in one Pop. B H*β* profile (HE0001) but very prominent in another (Q0029). If the classification of Q0029 as a Population B source is correct, the model of the blue "goiter" at the side of the H*β* profile implies a strong contribution of blueshifted emission with a broad profile. The [OIII]*λ*5007 profiles are also different: the equivalent width *W* is higher and the shift is lower in the case of HE0001, where no significant H*β* outflow is detected. By all means, the properties of Q0029 appear more extreme. We predict that this source will show extreme CIV blueshift, with an amplitude of several thousands km s−<sup>1</sup> .

**Figure 2.** *Cont*.

**Figure 2.** Analysis of the H*β* + [OIII]*λλ*4959,5007 region for two high-luminosity, high-*z* quasars belonging to the B1 spectral type. The top one, HE0001-234, shows no appreciable evidence of blueshift, while the bottom one (HB89) 0029+073 requires a stronger blue shifted excess for [OIII]*λλ*4959,5007 and an even stronger and broader one to fit H*β*. Color coding of the components is the same as in the previous Figure. The shaded area identifies a spectral region affected by atmospheric absorptions

The [OIII]*λ*5007 shift and the A.I. become more negative, and the equivalent width decreases with increasing luminosity. This is a pure luminosity effect that proceeds in the same sense of the effect of an increasing Eddington ratio in sample covering the full span of *<sup>L</sup>*/*L*Edd<sup>∼</sup> <sup>10</sup>−<sup>2</sup> <sup>−</sup> 1, and it can be interpreted as a result of NLR evolution with redshift [35].

### *4.3. Jetted Sources*

The CD and FR-II composites from the [45] sample (Figure 3) show that the [OIII]*λ*5007 blueshifted and skewed component is not detected in H*β*, implying that the intensity ratio is [OIII]*λ*5007/H*β* 1 for this component. In addition, the [OIII]*λ*5007 profile for the FR-II composite spectrum is much more symmetric than that of the CD composite, for which its A.I. and centroid shifts are more consistent with the RQ composite of the same sample. This systematic difference may arise because of the different viewing angles expected for CD (seen almost pole on) and FR-II sources (seen at a viewing angle ≈ 40–60 [60]).

**Figure 3.** *Cont*.

### **5. Discussion**

The analysis performed above has been focused on sources radiating at relatively modest *L*/*L*Edd (Population B) but covering a wide range of redshifts (0 . *z* . 3) and luminosities. Significant outflow features have been detected in NLR, as traced by H*β* and [OIII]*λλ*4959,5007 blue shifted components. At high luminosity, significant blueshifts are found not only in the [OIII]*λλ*4959,5007 lines but also with a broader profile, hinting at an association with BLR emission.

### *5.1. How Important Is the Outflow Component?*

The present analysis relies on the important assumption that the Population B profile at H*β* low-*z* and luminosity is not significantly affected by any outflowing gas. Reverberation mapping campaigns in the early 2000s provided evidence that the main broadening mechanism is indeed provided by a virial velocity field of gas orbiting around a point-like mass. More recent works point toward a more complex situation ([61–63] Bao et al., 2022, in preparation), although the main inference from velocity-resolved reverberation mapping studies for the sources with the red H*β* asymmetry is that the velocity field is predominantly virial, with the frequent detection of infall motions. The detection of infall is based on the shorter time delay of the red wing and not on the response of the line core.

### *5.2. Identifying an Outflow Component*

The H*β* profile of Population B presents a clear inflection between H*β*BC and H*β*NC that can be explained on the basis of the expected radial emissivity of H*β* [64]. The identification of an outflow component may be achieved by considering the following options:


semi-broad component is applicable to the H*β* profile, then it is likely that the outflow is mainly associated with NLR emission.

• Even modest centroid blueshift in the broad profile of H*β* at fractional intensity <sup>3</sup> 4 or 0.9, the outflow might involve BLR emission. In this case, H*β*BLUE corresponds to the prominent blueshifted emission of the CIV line observed at high luminosity [56]. The detection of H*β*BLUE is made more difficult by the CIV/H*β* ratio expected to be 1.

### *5.3. Location and Physical Nature of the Outflow*

Even in case of modest accretion rate, the outflow can be radiatively driven [65]. The ratio between the radiation and gravitation force can be written as *a*rad/*a*grav ≈ 7.2 *L*/*L*Edd *N* −1 c,23 where *<sup>N</sup>*c,23 is the Hydrogen column density in units of <sup>10</sup><sup>23</sup> cm−<sup>2</sup> (e.g., [66]). For *L*/*L*Edd ∼ 0.1, the gas of moderate common density *N*c,23 ∼ 0.1 could be accelerated to *a*rad/*a*grav ∼ 10 (c.f. Equation (6) of Netzer and Marziani [65]) [67]. The first underlying assumption is that all of the photon's momentum in the ionizing continuum is transferred to the line-emitting gas. The second assumption is that the gas is optically thick relative to the ionizing continuum, and this condition is more easily verified if the ionization parameter is low, implying that the low column density gas located farther out from the AGN continuum source might be preferentially accelerated. This might explain why we see a signature due to a semi-broad component in H*β*, H*β*SBC, which is in turn associated with the [OIII]*λ*5007 semi-broad component, likely at the inner edge of NLR, and it may be the main signature of outflow in low *L*/*L*Edd sources.

Regarding BLR, at low luminosity, there is no signature of outflow, if our interpretation of the profile is correct. For Population B sources, however, the observed spectrum can be explained by the locally optimized cloud (LOC) scheme, in which a range of ionization parameters, density, and column density is assumed, and the emerging spectrum is set by the parameters at which lines are emitted most efficiently [68,69]. This is to say that there might be always gas as "light" as needed for an outflow; however, the outflow may not produce a significant signature in the emission line spectrum. A powerful outflow at a modest Eddington ratio may become possible only at high luminosity (e.g., [70–72]), as predicted from wind theory and confirmed by observations [56,73–75].

### *5.4. The Fate of the Outflowing Gas: No Feedback Effects at Low L*

The mass outflow rate at a distance *r* can be written as follows if the flow is confined to a solid angle of Ω of volume <sup>4</sup> 3 *πr* 3 Ω 4*π* : *M*˙ ion <sup>o</sup> = *ρ* Ω*r* <sup>2</sup>*v*<sup>o</sup> = *M*ion o *<sup>V</sup>* Ω*r* <sup>2</sup>*v*<sup>o</sup> ∝ *Lv*o*r* −1 [76]; it implies *M*˙ ion <sup>∼</sup> <sup>30</sup>*L*44*v*o,1000*<sup>r</sup>* −1 1kpc *Z* 5*Z* −<sup>1</sup> *n* −1 3 , where the mass of ionized gas can be directly estimated from the line luminosity: *<sup>M</sup>*ion <sup>∼</sup> <sup>1</sup> · <sup>10</sup><sup>7</sup> *<sup>L</sup>*44 *Z* 5*Z* −<sup>1</sup> *n* −1 3 . <sup>3</sup> The lowluminosity cases [44,45] imply that the outflow velocity is *v*o,1000 ∼ 1 from the peak shift of [OIII]*λ*5007SBC, and the [OIII]*λ*5007SBC luminosity is log *L*[OIII] ∼ 42. Assuming *<sup>Z</sup>* <sup>≈</sup> <sup>1</sup>*<sup>Z</sup>* as appropriate for Population B sources [27], *<sup>M</sup>*ion <sup>∼</sup> <sup>5</sup> · <sup>10</sup>5*<sup>n</sup>* −1 3 and *M*˙ ion <sup>∼</sup> 0.15*r* −1 1kpc*n* −1 3 . By the same token, the thrust and kinetic power can be written as *Mv*˙ <sup>∼</sup> 1.9 · 1035*L*44*v* 2 o,1000*r* −1 1kpc *Z* 5*Z* −<sup>1</sup> *n* −1 3 and *<sup>e</sup>*˙ <sup>∼</sup> <sup>10</sup>43*L*44*<sup>v</sup>* 3 o,1000*r* −1 1kpc *Z* 5*Z* −<sup>1</sup> *n* −1 3 , which become *Mv*˙ <sup>∼</sup> <sup>1</sup> · <sup>10</sup>34*<sup>r</sup>* −1 1kpc*n* −1 3 and *<sup>e</sup>*˙ <sup>∼</sup> <sup>5</sup> · <sup>10</sup>41*<sup>r</sup>* −1 1kpc*n* −1 3 . Even assuming that we are observing a flow at *<sup>r</sup>* <sup>∼</sup> <sup>10</sup> pc, the kinetic power is *<sup>e</sup>*˙ . <sup>10</sup><sup>44</sup> erg s−<sup>1</sup> , a factor ≈ 100 below the bolometric luminosity and ≈ 1000 the Eddington luminosity of the [45] case. The emitting gas might be beyond or at the limit of the black hole sphere of influence given by *r* ≈ *GM*/*σ* 2 ? ≈ <sup>8</sup> · <sup>10</sup>19*M*9,/*<sup>σ</sup>* 2 ?,400 cm, where *σ*? is the velocity dispersion associated with the bulge of the host galaxy in units of 400 km s−<sup>1</sup> . At this radius, the escape velocity is expected to be *<sup>v</sup>*esc <sup>∼</sup> <sup>500</sup> km s−<sup>1</sup> for a <sup>10</sup><sup>9</sup> <sup>M</sup> black hole. It is, therefore, doubtful whether the outflowing gas might be even able to escape from the sphere of influence of the black hole. Even less likely, the outflowing gas might "wreak havoc" galaxy-wide in the bulge and the disk of

the host due to the small amount of gas masses involved in the outflow, and due to the escape velocity that can be as high as *v*esc & 1000 km s−<sup>1</sup> in the inner regions of a massive spheroid or in a giant spiral such as the Milky Way [77].

The scenario might radically change at high luminosity: considering the [46] composite, the velocity of [OIII]*λ*5007SBC is higher by a factor ≈ 2, and the line luminosity is higher by a factor ∼ 10, implying a 20-, 40-, and ∼100-fold increase over the [45] case in mass flow, thrust, and kinetic power, respectively. In the [46] case, the kinetic power would be comparable to the Eddington luminosity. An even more powerful outflow is expected for Q0029.

### **6. Summary and Conclusions**

The analysis of outflow signatures carried out in the present paper has been focused on three samples of type-1 AGN covering a wide range of luminosity.

The detection of different kinematic components in single epoch profiles is a complicated issue. The apertures and slit widths used in ground-based observation add up the emission from the AGN continuum, BLR, NLR, and host galaxy, which are associated with widely different spatial scales. The case of Population B sources of spectral type B1 is particularly well-suited to analyze the presence of an outflow component in the Balmer H*β* line for sources that are radiating at modest Eddington ratios.

Generally speaking, the detection of significant systematic blueshifts in the centroid measurements can be taken as a signature of outflow. If the blueshift/blue asymmetry is confined at the top of the H*β* line and the H*β* narrow emission can be modeled as [OIII]*λ*5007 assuming a semi-broad and a narrow component with a similar parameter, then the evidence of the outflow (the "goiter" in the line profile) remains confined to the NLR. However, if the H*β* centroid at <sup>3</sup> 4 or at lower fractional intensity is also blue shifted, it is likely that a BLR outflow is being detected. Low column density gas can be driven into an outflow by radiation forces. Blueshifts in the line core can be, therefore, straightforwardly interpreted by an outflow component, without invoking binary BLR, in turn pointing toward sub-parsec binary black holes. Other spectral types along the MS have been identified as frequently involving binary black hole candidates [78,79].

The estimates of mass flow, thrust, and kinetic power are highly uncertain because of the lack of spatially resolved data. This situation might be changing soon with the development of integral-field spectrographs. Nonetheless, even when maximizing the coarse estimates reported above, it is unlikely that the thrust and the kinetic power (only <sup>∼</sup> <sup>10</sup>−<sup>2</sup> the Eddington luminosity as derived for the [44,45] samples) might have a strong impact on the host galaxy's evolution and not to mention the possibility of driving the black hole mass—bulge correlation (e.g., and references therein [80]). Even if the [OIII]*λ*5007 samples only emission from mildly ionized gas and the mass flow might be dominated by the higher-ionization gas, for low luminosity AGNs such as the prototypical Population B Seyfert-1 NGC 5548, kinetic luminosity remains a very small fraction of the Eddington luminosity [37,81]. The situation is expected to change at the "cosmic noon" at redshifts in the range of 1–2, when the most luminous quasars are observed, and of which the [46] composite provides a representative spectrum.

**Author Contributions:** P.M. wrote most of the paper; A.D.-M. contributed to the analysis of spectra. A.D.-M. and A.D.O. Both contributed with suggestions and critical reading. All authors have read and agreed to the published version of the manuscript.

**Funding:** Funding for the Sloan Digital Sky Survey has been provided by the Alfred P. Sloan Foundation and the U.S. Department of Energy Office of Science. The SDSS web site is http://www.sdss.org. (accessed on 14 February 2022). SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute

for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data could be made t available upon request.

**Acknowledgments:** A.D.M. and A.D.O. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the project PID2019-106027GB-C41 and the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). A.D.M. acknowledges the support of the INPhINIT fellowship from the "la Caixa" Foundation (ID 100010434). The fellowship code is LCF/BQ/DI19/11730018.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Abbreviations**

The following abbreviations are used in this manuscript:


### **Notes**


### **References**


### *Article* **Non-Thermal Emission from Radio-Loud AGN Jets: Radio vs. X-rays**

**Elena Fedorova 1,\* , Bohdan Hnatyk <sup>1</sup> , Antonino Del Popolo 2,3 and Anatoliy Vasylenko <sup>4</sup> and Vadym Voitsekhovskyi <sup>1</sup>**


**Abstract:** We consider the sample of 55 blazars and Seyferts cross-correlated from the Planck all-sky survey based on the Early Release Compact Source Catalog (ERCSC) and Swift BAT 105-Month Hard X-ray Survey. The radio Planck spectra vs. X-ray Swift/XRT+BAT spectra of the active galactic nuclei (AGN) sample were fitted with the simple and broken power law (for the X-ray spectra taking into account also the Galactic neutral absorption) to test the dependencies between the photon indices of synchrotron emission (in radio range) and synchrotron self-Compton (SSC) or inverse-Compton emission (in X-rays). We show that for the major part of the AGN in our sample there is a correspondence between synchrotron and SSC photon indices (one of two for broken power-law model) compatible within the error levels. For such objects, this can give a good perspective for the task of distinguishing between the jet base counterpart from that one emitted in the disk+corona AGN "central engine".

**Keywords:** blazars; active galactic nuclei; X-rays; jets; synchrotron emission; inverse-Compton emission

### **1. Introduction**

The blazars are the radio-loud AGN with one jet directed along the line-of-sight to the observer (i.e., AGN type 0). Due to the jet alignment, an observer can see near pure jet base emission at the AGN center, as the emission of the disk+corona «central engine» is usually significantly weaker than the jet base one, and almost not visible in the blazar's X-ray spectrum. This makes blazars especially interesting when we intend to investigate the properties of the jet base emission. Here, we consider the dependence between the direct synchrotron emission of a jet base in the radio wave range and its inverse Compton (IC) or synchrotron self-Compton (SSC) emission in X-rays. Taking into account that nonblazar radio loud (RL) AGN have the same non-thermal component in their spectra, this dependence can open some possibilities to distinguish between nuclear (disk+corona) and jet base components in their high energy spectra extrapolating some parameters of the jet base synchrotron radio spectra to IC/SSC ones.

The jet base is of the order of a percent of pc in size. It is composed of ultra-relativistic plasma, either electron-positron (usually referred to as leptonic) or electron-proton (referred to as hadronic); the composition of this plasma is still being debated. Plasma particles are ejected at relativistic bulk velocity from an AGN central region and being accelerated at shock fronts inside the jet, emit synchrotron radiation visible at a wide range of wavelengths from radio to ultraviolet or even higher.

**Citation:** Fedorova, E.; Hnatyk, B.; Popolo, A.D.; Vasylenko, A.; Voitsekhovskyi, V. Non-Thermal Emission from Radio-Loud AGN Jets: Radio vs. X-rays. *Galaxies* **2022**, *10*, 6. https://doi.org/10.3390/ galaxies10010006

Academic Editor: Santanu Mondal

Received: 29 November 2021 Accepted: 30 December 2021 Published: 4 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Depending on the peak frequency *ν<sup>S</sup>* of the Synchrotron power (of peak intensity) *νS*F(*νS*) two classes of BL Lacs were introduced in [1]: low-frequency peaked BL Lacs (LBL) and high-frequency peaked BL Lacs (HBL). In [2], similar classification was introduced to the sample of all blazars: low Synchrotron peaked blazars (LSP, *<sup>ν</sup><sup>S</sup>* <sup>≤</sup> <sup>10</sup><sup>14</sup> Hz), intermediate Synchrotron peaked blazars (ISP, <sup>10</sup><sup>14</sup> <sup>≤</sup> *<sup>ν</sup><sup>S</sup>* <sup>≤</sup> <sup>10</sup><sup>15</sup> Hz), and high Synchrotron peaked blazars (HSP, *ν<sup>S</sup>* > 10<sup>15</sup> Hz) (see also discussion in [3–5]).

In addition to the dominant non-thermal jet-driven emission, accretion-driven thermal disk radiation, Comptonised by a hot ∼100 keV corona to power-law X-ray emission, can also make a significant contribution to the overall X-ray flux in some cases (3C120, 3C273, etc.) [2,6,7]. Signatures of such a disk+corona contribution in X-ray spectra are expected from LSP blazars in which IC/SSC jet components are dominant. Some ISP blazars with the intersection of falling synchrotron and rising IC/SSC spectra in the X-ray band (similarly to IBL S5 0716+714) are also promising candidates for the investigation of a jet-disk+corona interplay in X-ray band [2,8].

As it was shown in [9], the jet synchrotron and X-ray IC/SSC spectra are interconnected because they are produced by the same leptonic cosmic ray population. In particular, there is a relationship between photon indices in radio-band Γ*<sup>R</sup>* and X-ray band Γ*X*.

In our work, we investigate how this dependency manifest itself in radio and X-ray spectra of the sample of radio loud AGN created from the cross-correlation of the Swift BAT 105-Month Hard X-ray Survey (https://swift.gsfc.nasa.gov/results/bs105mon/ Accessed on 10 June 2020) and the Planck Early Release Compact Source Catalog (ERCSC, [10]) (http://www.sciops.esa.int/index.php?project=planck&page=Planck\_Legacy\_Archive Accessed on 15 June 2020). For this purpose, we use the 24–240 GHz Planck spectra and the Swift/XRT+BAT spectra of the same objects in X-rays and compare the photon indices.

The organisation of this paper is as follows. In the Section 2, we analyse the nonthermal MWL emission of AGN jets. In Section 3, we describe our AGN sample and spectral fitting procedure. In Section 4, we discuss an interconnection of radio and X-ray spectra of considered AGN and in Section 5 we draw out our conclusions.

### **2. Spectral Energy Distribution of Radio Loud AGN**

Accelerated particles—cosmic-ray electrons and positrons (hereafter electrons)—of the jet in the most cases are distributed over the energies *E* > *E<sup>m</sup>* (Lorentz factor *γ* = *E*/*mec* <sup>2</sup> > *γm*) following a single power-law dependency *N*(*E*) ∝ *E* −*p* exp(−*E*/*Ecut*) of the injected electron spectrum with the spectral index *p* and an exponential cut-off at *E* ∼ *Ecut* [9,11]. Such distribution of ultra-relativistic electrons (*γ<sup>m</sup>* 1) generates a two-hump spectrum consisting of the low-frequency synchrotron component and the high-frequency component due to inverse-Compton scattering (IC) of synchrotron photons (synchrotron-self-Compton SSC) or external low energy photons (CMB and other background radiation) by the same electron population [12]. In Figure 1, the two-hump spectra of two LSPs (3C279 and 3C273) and two HSPs (Mrk 421 ans Mrk 501) blazars are presented. In 3C273 case, the thermal contribution of the accretion disk in the optical-UV band is also visible.

The fast radiation cooling of the high energy relativistic electrons (if present) results in the broken power law spectrum of the final emitting electrons with the spectral index *p* + 1 for *γ* > *γc*. For such a two-segment power law electron spectrum the corresponding synchrotron spectrum for the slow cooling case (*γ<sup>c</sup>* > *γm*) is the four-segment power law *F<sup>ν</sup>* ∝ *ν* <sup>−</sup>*<sup>α</sup>* with the spectral indices *<sup>α</sup><sup>s</sup>* (the photon index <sup>Γ</sup>*<sup>s</sup>* <sup>=</sup> *<sup>α</sup><sup>s</sup>* <sup>+</sup> 1) equal to <sup>−</sup>2.0, <sup>−</sup>1/3, (*p* − 1)/2, and *p*/2 for *ν* < *νa*, *ν<sup>a</sup>* < *ν* < *νm*, *ν<sup>m</sup>* < *ν* < *νc*, and *ν* > *νc*, correspondingly. Here *ν<sup>a</sup>* is the self-absorption frequency, *ν<sup>m</sup>* is the frequency of synchrotron emission of electrons with minimum Lorenz factor *γ* = *γm*, *ν<sup>c</sup>* is the same for electrons at the edge of fast cooling with *γ* = *γ<sup>c</sup>* and the typical case *ν<sup>a</sup>* < *ν<sup>m</sup>* < *ν<sup>c</sup>* with the weak self-absorption regime *ν<sup>a</sup>* < *ν<sup>c</sup>* is considered [9]. Synchrotron frequencies *ν<sup>i</sup>* (*i* = *a*, *m*, *c*) are radiated by electrons with *γ<sup>i</sup>* via *γ* 2 -scattering of virtual photons with gyrofrequency *ν<sup>g</sup>* = *ωg*/2*π* = *eB*/(2*πmec*) in magnetic field *B*: *ν<sup>i</sup>* ∼ *γ* 2 *i νg*.

**Figure 1.** Two-hump multi-wavelength spectra of LSP (3C279 and 3C273) and HSP (Mrk 421 ans Mrk 501) blazars. In 3C273 case the thermal contribution of disk in optical-UV band is also visible. Credit: A.E. Wehrle/M.A. Catanese/J.H. Buckley/Whipple Collaboration.

In the case of IC/SSC emission, the real photons of background (IC) or newly generated synchrotron (SSC) radiation are *γ* 2 -scattered by the relativistic electrons and characteristic frequencies of the SSC spectra are dependent on ones of synchrotron spectra *ν IC ij* ∼ *γ* 2 *i νj* . Therefore, the profiles of the SSC spectra are similar to the synchrotron ones and for the considered above case *ν<sup>a</sup>* < *ν<sup>m</sup>* < *ν<sup>c</sup>* the four-segment power law spectrum has the spectral indices *αIC* (the photon index Γ*IC* = *αIC* + 1) equal to −1.0, −1/3, (*p* − 1)/2, and *p*/2 for *ν* < *ν IC ma*, *ν IC ma* < *ν* < *ν IC mm*, *ν IC mm* < *ν* < *ν IC cc* , and *ν* > *ν IC cc* , correspondingly [9].

The multi-wavelength spectral energy distributions of blazars (BL Lacs and FSRQs) clearly demonstrates the two-hump shape (Figure 2, taken from [4]). As it is discussed in detail in [4], at low frequencies *<sup>ν</sup>* <sup>&</sup>lt; *<sup>ν</sup><sup>t</sup>* up to the self-absorption frequency <sup>10</sup><sup>11</sup> <sup>≤</sup> *<sup>ν</sup>t*/*Hz* <sup>≤</sup> <sup>10</sup><sup>12</sup> in the radio band a reasonable approximation of all observable spectra corresponds to power law with *α<sup>R</sup>* = −0.1 or photon index Γ*<sup>R</sup>* = 0.9. In log(*νLν*) − log *ν* representation where *L<sup>ν</sup>* is the spectral luminosity, the peak frequency *ν<sup>S</sup>* of the synchrotron emission determines the mentioned above classes (LSP, ISP, and HSP) of blazars. At frequency *νcut*,*<sup>S</sup>* the transition to the IC-dominated emission takes place. In a similar way, the peak frequency *ν<sup>C</sup>* determines Compton-dominated hump and at *νcut*,*<sup>C</sup>* Compton-dominated emission decays. Between limiting frequencies *ν<sup>t</sup>* and *νcut*,*C*, the two-segment power law approximations for synchrotron humps (photon indices Γ<sup>1</sup> and Γ2) and for IC/SSC humps (photon indices Γ<sup>3</sup> and Γ<sup>4</sup> = Γ2) are presented and analysed in [4]. In Figure 2, the hump parameters are indicated for the FSRQs with 44 < log(*Lγ*/*erg s*−<sup>1</sup> ) < 45. From Table 1, in [4], it follows that interconnection between synchrotron radio-spectra at frequencies *ν<sup>t</sup>* < *ν* < *ν<sup>S</sup>* and IC/SSC X-ray spectra at frequencies *ν* > *νcut*,*<sup>S</sup>* as signatures of emission produced by common cosmic-ray electron population is visible in some cases. Namely, in the cases of FSRQs with 44 < log(*Lγ*/*erg s*−<sup>1</sup> ) < 47 the photon indices Γ<sup>1</sup> ≈ 1.5, while 1.4 < Γ<sup>3</sup> < 1.75 and IC/SSC X-ray emission dominates for *<sup>ν</sup>* <sup>&</sup>gt; *<sup>ν</sup>cut*,*<sup>S</sup>* <sup>≈</sup> <sup>10</sup><sup>16</sup> Hz. There are also promising sources among BL Lacs with 46 < log(*Lγ*/*erg s*−<sup>1</sup> ) < 48 for which 1.5 < Γ<sup>1</sup> < 1.65 while 1.45 <sup>&</sup>lt; <sup>Γ</sup><sup>3</sup> <sup>&</sup>lt; 1.62 and IC/SSC X-ray emission dominates for *<sup>ν</sup>* <sup>&</sup>gt; *<sup>ν</sup>cut*,*<sup>S</sup>* <sup>≈</sup> <sup>6</sup> <sup>×</sup> <sup>10</sup><sup>15</sup> Hz.

**Figure 2.** Spectral parameters of the two-hump multi-wavelength spectra for the new phenomenological Fermi blazar sequence, substantiated in [4]. Upper, middle and lower parts of the figure show the spectra of FSRQs, BL Lacs, and all sources, correspondingly. Different colours indicate different bins of the log(*Lγ*/*erg s*−<sup>1</sup> ). Characteristic frequencies and photon indices are presented for FSRQs case with 44 < log(*Lγ*/*erg s*−<sup>1</sup> ) < 45. See detail in the text. Figure taken from [4].

### **3. The AGN Sample and Spectral Fitting**

This research includes all the Swift/XRT+BAT datasets available in public data archive HEASARC for the objects of the sample identified as beamed AGN<sup>1</sup> .

However, other sources identified these objects as BL Lacs (Table 1), FSRQs (Table 2), and Seyferts 1 (Table 3). In these Tables we show the source type, coordinates, and redshift following the SIMBAD data<sup>2</sup> and the neutral hydrogen absorbing column in the Galaxy following [13].


**Table 1.** Sub-sample of BL Lac type blazars.


**Table 2.** Sub-sample of FSRQ type blazars.

The Planck spectra within the frequency range 24 to 240 GHz were taken from the Early Release Compact Source Catalog (ERCSC) of compact sources observed by Planck during the 2009–2010 whole sky coverage. These Planck spectra are publicly available on the HEAVENS webpage<sup>3</sup> .

The Swift/XRT spectra were obtained using the observations made by UK Swift Science Data Centre (UKSSDC) at the University of Leicester<sup>4</sup> . We have used single-pass centroid with the maximum of 10 attempts and 6 arcmin search radius.

The Swift/BAT spectra were obtained from the Swift BAT 105-Month Hard X-ray Survey official webpage<sup>5</sup> .

To perform the spectra fitting the XSPEC package of the NASA HeaSoft version 6.27.2 software for astronomical data processing and analysis<sup>6</sup> was applied.


**Table 3.** Sub-sample of Seyfert 1 type AGN.

To fit the spectra in the both radio and X-ray range (here we include also the neutral hydrogen absorption in our model) we use the simple or broken power-law model taking into account that the flattering frequency *ν<sup>t</sup>* due to the self-absorption may be located in the Planck range and the dip frequency *νcut*,*<sup>S</sup>* of the transition from synchrotron to IC component may be located in the Swift range or higher (Figure 2). So, if the self-absorption frequency *ν<sup>t</sup>* falls into the Planck range 24 GHz < *ν<sup>t</sup>* < 240 GHz, the two-segment power law approximation results in two photon indices: Γ1,*<sup>l</sup>* < 1 for *ν* < *ν<sup>t</sup>* and Γ1,*<sup>h</sup>* > 1 for *ν* > *ν<sup>t</sup>* .

In a similar way, simple power law X-ray Swift spectra with 2 > Γ<sup>3</sup> ≈ Γ<sup>1</sup> > 1 are expected for the LSP and some IPS blazars with *<sup>ν</sup>cut*,*<sup>S</sup>* <sup>≤</sup> <sup>10</sup><sup>17</sup> Hz, i.e., below the Swift range. Otherwise, the two-segment power law approximation of X-ray spectra will results in two photon indices: Γ3,*<sup>l</sup>* > 2 for *ν* < *νcut*,*<sup>S</sup>* and 2 > Γ3,*<sup>h</sup>* > 1 for *ν* > *νcut*,*S*. If *hνcut*,*<sup>S</sup>* exceeds the Swift/BAT range (175 keV) two photon indices: Γ3,*<sup>l</sup>* ≥ 2 for *E* < *Ebr* and Γ3,*<sup>h</sup>* ≥ Γ3,*<sup>l</sup>* for *E* > *Ebr* describe the falling part of the synchrotron spectra of HPS blazars.

In Table 4, we show the best-fit model parameters to the Planck and Swift/XRT+BAT spectra of the sample of 55 blazars and Seyferts. The models used to fit them were:


We explain the details of our Planck spectra fitting and data statistics in the Appendix A. In columns 2–4 of the Table 4, we show the best-fit photon indices and break energies for the Planck spectra of the objects shown in the first column; in the last three columns we show the photon indices and the break energies for the X-ray (Swift/XRT+BAT) spectra. If the difference between the simple power-law and broken power-law is statistically significant (i.e., the null-hypothesis probability P*null* < 10% where the null-hypothesis corresponds to the simple power-law model) we show the best-fit broken power-law model parameters. If there is not such difference between these two models in sense of *χ*-statistics and values of parameters, we show the simple power-law photon index only.


**Table 4.** The best-fit model parameters for the Planck and Swift/XRT+BAT spectra.


**Table 4.** *Cont.*

### **4. AGN Sample: Interconnection of Radio and X-ray Spectra**

As we can see from the Table 4 33 of 55 AGN have at least one of the photon indices in the model of Planck spectrum coincident with one of the photon indices of the X-ray spectral model. In total, 23 AGN of this subsample follow the pattern when the single Γ<sup>1</sup> or the upper Γ1,*<sup>h</sup>* photon index of the Planck spectrum coincides within the error levels with the single Γ<sup>3</sup> or lower Γ3,*<sup>l</sup>* photon index of the X-ray spectrum, i.e., in both radio and X-ray ranges we see the lower segments of the synchrotron and IC/SSC components.

Such a situation we observe for S5 0212+735, PKS0312-770, PKS 2331-240, PKS0537- 441, PMN J0623-6436, 3C 309.1, 4C +31.63, 4C +32.14, 4C +50.11, 4C +73.18, PKS 1329-049, PKS 2005-489, PKS 2227-088, PKS 0405-12, PKS 0426-380, PKS 0528+134, PKS 0723-008, B2 0552+39A, S5 1039+81, S5 1803+784, B1921-293, B2 2023+33, PMN J1508-4953, and others. In total, 8 objects of this subsample follow the pattern when the single Γ<sup>1</sup> or the upper Γ1,*<sup>h</sup>* photon index of the Planck spectrum coincides within the error levels with the upper Γ3,*<sup>h</sup>* photon index of the X-ray spectrum, i.e., PKS 1143-696, PG1222+216, 3C 273, 3C 279, and others. Three objects have both upper and lower photon indices of the Planck spectrum coincident with the X-rays ones: PKS 0537-286, [HB 89] 2230+114 and 3C 380; such a situation can be interpreted as if we can see the Γ1,*l*,*<sup>h</sup>* and Γ3,*l*,*<sup>h</sup>* segments in the both Planck and Swift spectra. However, for some of them, namely 3C 273, [HB 89] 2142-758, etc., the values of the lower photon indices are below 1, what can be interpreted for the radio range as a sign of the self-absorption (see Figure 1 for the 3C273 case).

The subsample with no correspondence between the photon indices is also quite significant and consists of 22 blazars. There can be different explanations for each of these objects. For instance, as shown in [14], the single synchrotron zone model is inappropriate for 3C 454.3. Mrk 501 is the HSP blazar for which we see the lower part of synchrotron hump in the Planck spectrum and the upper one in X-rays. The IC/SSC spectrum of Mrk 501 is situated above the energies we consider here (see Figure 1). Similarly, to explain the 4C +49.22 spectral properties the two-zone SSC model is needed [15]. PKS 1830-21 is a gravitationally lensed blazar and its spectra thus can be distorted by the influence of a lensing object [16]. The classification type of PKS 0521-36 is not surely BL Lac, there are some signs of a Broad Line Radio Galaxy (BLRG) also [17], and thus the accretion disk/corona counterpart in its X-ray spectrum can be quite significant. S5 0716+714 is an ISP blazar for which the significant part of the Planck spectrum lies in the self-absorbed zone and in X-rays we see a dip-like intersection of synchrotron and SSC spectra at *E<sup>b</sup>* ≈ 6 keV [8].

### **5. Conclusions**

In the simple one-zone model of multi-wavelength radiation of radio-loud AGN the observable two-hump spectra with *<sup>ν</sup>Lν*-maxima in low-energy (∼10−<sup>1</sup> <sup>−</sup> <sup>10</sup><sup>4</sup> eV) and high-energy (≥10<sup>7</sup> eV) bands can be naturally explained by the non-thermal synchrotron and IC/SSC emission of relativistic leptons, accelerated at relativistic shocks, and during magnetic field reconnections in relativistic jets. Typical power-law spectra of accelerated leptonic cosmic-rays result in similar predicted slopes or photon indices of low-energy radio and high energy X-ray and *γ*-ray emission. Meantime, in some radio-loud AGN Comptonised thermal X-ray luminosity of accretion disk+corona complex can be comparable to the non-thermal X-ray jet luminosity. Joint analysis of radio and X-ray spectra of such AGN open a possibility to disentangle jet and disk+corona contributions and to clarify the radiative processes in AGN. We carry out a comparative analysis of Planck radio spectra and Swift /XRT+BAT X-ray spectra for the sample of 55 beamed AGN (Blazars and Seyferts 1) from the Swift BAT 105-Month Hard X-ray Survey. For 33 of 55 AGN we confirm predicted by one-zone model coincidences of the photon indices of radio and X-ray spectra. As expected, comparison of radio and X-ray data can help to disentangle jet and disk+corona contribution in case of LSP and some of ISP radio-loud AGN, in which transition from synchrotron to IC/SSC dominant contribution take place in sub-keV region.

**Author Contributions:** Conceptualization, E.F., B.H. and A.D.P.; methodology, E.F., B.H. and V.V.; software, E.F. and A.V.; investigation, writing—original draft preparation, E.F., B.H., A.D.P. and V.V.; writing—review and editing, A.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Sample of AGN is available from the authors.

**Acknowledgments:** We are grateful to the anonymous reviewer for very attentive and helpful comments and suggestions that helped us significantly improve the quality of the manuscript. We acknowledge reusing of figure 6 from article The Fermi blazar sequence of G. Ghisellini et al., MNRAS 2017, 469, 255–266.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A. Planck Spectral Models**

The Planck spectra were fitted using the two models:


The results of our fitting are shown in the Table A1. In several exclusive cases when the both models mentioned above gave the fits with the *χ*/d.o.f. > 2.0 we tried to apply the more complicated model, namely, the three-segment broken power-law one, with the three different photon indices and two breaks. These cases are marked by upper digits in the Table A1 and described in details below the Table. To estimate the statistical significance of our models, we suppose the simplest one of them, i.e., the single power-law as a nullhypothesis. Using the Fisher test (*ftest* in the XSPEC) we calculated the null-hypothesis probability for every object of the sample; these probabilities are shown in the last column of the Table A1.


**Table A1.** The model parameters for the Planck spectra.


**Table A1.** *Cont.*

If the null-hypothesis probability is less than 50% we consider the alternative model (i.e., broken power-law one) as the best-fit one. Otherwise, *Pnull* > 50% means that the single power-law fit is adequate and the broken power-law fit is excessively and statistically indistinguishable from the power-law one.

In case when the double broken power-law model was applied ( AGN 3C 273, PKS 0402-362 and FBQS J1159+2914) we have calculated for it two "null-hypothesis" probabilities; one for the single power-law null hypothesis and the second one considering the broken power-law model as a null-hypothesis.

There are the comments 1, 2 and 3 to the Table:

1. *bkn2po* <sup>Γ</sup>1,*<sup>l</sup>* = 0.96 <sup>±</sup> 0.01, E*b*<sup>1</sup> = 3.8\*10−<sup>4</sup> eV, <sup>Γ</sup>1,*<sup>i</sup>* = 1.76 <sup>±</sup> 0.02, E*b*<sup>2</sup> = 10−<sup>3</sup> eV and Γ1,*<sup>h</sup>* = 1.88 ± 0.05; *χ* <sup>2</sup>/*d*.*o*. *f* . = 4.2/4; with P*Null* = 3% of the *bknpo* model relatively to *bkn2po* one and P*Null* < 10−4% relatively to the power-law one;

2. *bkn2po* <sup>Γ</sup>1,*<sup>l</sup>* = 0.7 <sup>±</sup> 0.1, E*b*<sup>1</sup> = 2.5 <sup>±</sup> 0.3\*10−<sup>4</sup> eV, Γ1,*<sup>i</sup>* = 1.13 ± 0.08, E*b*<sup>2</sup> = 6.0 ± 0.6\*10−<sup>4</sup> eV, Γ1,*<sup>h</sup>* = 1.45 ± 0.05 and *χ* <sup>2</sup>/*d*.*o*. *f* . = 9.2/3; with P*Null* = 15% of the *bknpo* model relatively to *bkn2po* one and P*Null* = 0.1% relatively to the power-law one;

3. *bkn2po* <sup>Γ</sup>1,*<sup>l</sup>* = 0.4 <sup>±</sup> 0.5, E*b*<sup>1</sup> = 1.9 <sup>±</sup> 0.1\*10−<sup>4</sup> eV, <sup>Γ</sup>1,*<sup>i</sup>* = 3.4 <sup>±</sup> 0.8, E*b*<sup>2</sup> = 2.3 <sup>±</sup> 0.2\*10−<sup>4</sup> eV, Γ1,*<sup>h</sup>* = 1.13 ± 0.07 and *χ* <sup>2</sup>/d.o.f. = 7.9/4; with P*Null* = 18% of the *bknpo* model relatively to *bkn2po* one and P*Null* = 34.7% relatively to the power-law one.

### **Appendix B. X-ray Spectral Models**

The Swift/XRT+BAT spectra were fitted using the two models:


column density *NH*. The lower fitting values for *N<sup>H</sup>* were set to the Galactic absorption values for particular object shown in the Tables 1–3. In the Table A2 we show the absorption excesses relatively to those values.

The results of our fitting are shown in the Table A2. To estimate the statistical significance of our models, we have performed the same as for the Planck spectra, namely we suppose that the simplest model of two, i.e., the single power-law is the null-hypothesis. Using the Fisher test we have calculated the null-hypothesis probability P*Null* for every object of our sample; these probabilities are shown in the last column of the Table A2. We have determined the best-fit model in the same way as we did for the Planck spectra.


**Table A2.** The model parameters for the Swift spectra.


**Table A2.** *Cont.*

<sup>∗</sup> 10<sup>19</sup> cm−<sup>2</sup> ; ∗∗ keV.

### **Notes**


### **References**


### *Article* **Promise of Persistent Multi-Messenger Astronomy with the Blazar OJ 287**

**Mauri J. Valtonen 1,2,\* , Lankeswar Dey 3,\* , Achamveedu Gopakumar <sup>3</sup> , Staszek Zola <sup>4</sup> , S. Komossa <sup>5</sup> , Tapio Pursimo <sup>6</sup> , Jose L. Gomez <sup>7</sup> , Rene Hudec 8,9 , Helen Jermak <sup>10</sup> and Andrei V. Berdyugin <sup>2</sup>**


**Abstract:** Successful observations of the seven predicted bremsstrahlung flares from the unique bright blazar OJ 287 firmly point to the presence of a nanohertz gravitational wave (GW) emitting supermassive black hole (SMBH) binary central engine. We present arguments for the continued monitoring of the source in several electromagnetic windows to firmly establish various details of the SMBH binary central engine description for OJ 287. In this article, we explore what more can be known about this system, particularly with regard to accretion and outflows from its two accretion disks. We mainly concentrate on the expected impact of the secondary black hole on the disk of the primary on 3 December 2021 and the resulting electromagnetic signals in the following years. We also predict the times of exceptional fades, and outline their usefulness in the study of the host galaxy. A spectral survey has been carried out, and spectral lines from the secondary were searched for but were not found. The jet of the secondary has been studied and proposals to discover it in future VLBI observations are mentioned. In conclusion, the binary black hole model explains a large number of observations of different kinds in OJ 287. Carefully timed future observations will be able to provide further details of its central engine. Such multi-wavelength and multidisciplinary efforts will be required to pursue multi-messenger nanohertz GW astronomy with OJ 287 in the coming decades.

**Keywords:** BL lacertae objects; OJ 287; supermassive black holes; accretion discs; gravitational waves; jets

### **1. Introduction**

Supermassive black hole (SMBH) binary systems are expected to be common in the Universe [1–7]. Inspiral gravitational waves from SMBH binaries with total mass &10<sup>9</sup> *<sup>M</sup>* and orbital periods between months and years should lie in the nanohertz (nHz) microhertz range [8–10]. The routine detection of nHz gravitational waves (GWs) from SMBH binary systems is the primary goal of rapidly maturing Pulsar Timing Array (PTA) experiments [11–13]. The eventual detection of nHz GW sources will complement the

**Citation:** Valtonen, M.J.; Dey, L.; Gopakumar, A.; Zola, S.; Komossa, S.; Pursimo, T.; Gomez, J.L.; Hudec, R.; Jermak, H.; Berdyugin, A.V. Promise of Persistent Multi-Messenger Astronomy with the Blazar OJ 287. *Galaxies* **2022**, *10*, 1. https://doi.org/ 10.3390/galaxies10010001

Academic Editor: Santanu Mondal

Received: 2 December 2021 Accepted: 19 December 2021 Published: 22 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

vibrant field of GW astronomy, inaugurated by the routine detections of hectohertz GWs from stellar-mass black hole (BH) binaries by the LIGO-Virgo collaboration [14,15]. This collaboration also heralded the era of multi-messenger GW astronomy by the observations of hectohertz GWs from a binary neutron star merger (GW170817) and its electromagnetic (EM) counterparts (EM170817) [16,17]. The eventual detection of continuous nHz GWs from individual SMBHBs and observations of their electromagnetic (EM) counterparts can make profound contributions to the emerging field of multi-messenger GW astronomy [10,18]. EM observations in recent years have suggested the existence of many candidate binary SMBH systems with varying orbital periods (e.g., OJ 287 with 12 yr period [19]; 3C 66B with 1 yr period in the radio [20] but also see [21,22]; SDSS J1201+3003 identified from a tidal disruption event optical lightcurve [23]; PG1302-102 identified in the optical Catalina transient survey [24] see also [25]; and see, for example, Charisi et al. [26], who found 33 further quasars with statistically significant periodic variability). Some of these systems and candidates are in the nHz GW regime which should be detectable in GWs by the PTA consortium during the SKA era [27–29]. However, none of these systems had as detailed modeling and testable predictions as OJ 287, and no lightcurve has had the very long-term coverage that was obtained for OJ 287.

Persistent multi-wavelength electromagnetic observations will be crucial to pursue multi-messenger GW astronomy with OJ 287 in the coming decades. In what follows, we provide a brief introduction to the binary black hole (BBH) central engine description for OJ 287 and discuss the context and the need to pursue a variety of electromagnetic observations. These efforts should allow us to place tight observational constraints on the various aspects of the BBH central engine description for OJ 287 that will be crucial for pursuing multi-messenger GW astronomy with OJ 287. We now describe briefly our BBH description for OJ 287 and ongoing multi-wavelength observational campaigns on the source.

### *1.1. OJ 287 and Its BH Binary Central Engine Description*

The bright blazar OJ 287 (RA: 08:54:48.87, Dec: +20:06:30.6), situated at a redshift of *z* = 0.306, was first discovered as a radio source during the course of the Ohio sky survey in the 1960s [30]. However, the optical light curve of OJ 287 goes all the way back to the year 1888 as it had been unintentionally photographed often in the past due to its proximity to the ecliptic plane [19,31]. Interestingly, the optical light curve of OJ 287, extending over 130 years, exhibits unique quasi-periodic high-brightness flares (outbursts) with a period of ∼12 years [19,32,33]. Further, the blazar shows a long-term variation in its apparent magnitude with a period of ∼60 years [32] (see Figure 1).

**Figure 1.** Optical lightcurve of OJ 287 between 1888 and 2021. The figure includes a large number of previously unpublished data points by two of the authors (R.H., S.Z.). All point have been transformed to the V-band, including data in Laine et al. [34].

In 1982, the binary nature of OJ 287 was recognized by Aimo Sillanpää, while constructing historical light curves for the quasars in the Tuorla–Metsähovi variability survey which had begun two years earlier [35]. It was obvious that the next major outburst was about to happen and the blazar monitoring community was alerted. This first OJ 287 campaign was fruitful [36,37]. A more detailed explanation of the binary BH (BBH) scenario was subsequently proposed to explain the quasi-periodic flares in OJ 287 by associating them with increased accretion flow to the primary BH. This was due to the accretion disk perturbations of the secondary BH during its pericenter passages in an orbit which lies in the disk plane [19]. Moreover, a notable prediction of the model was that OJ 287 should show an outburst again in the autumn of 1994. This was verified by the second campaign called OJ-94 [38].

In 1994, Lehto & Valtonen [39] recognized that the flares in OJ 287 were not exactly periodic, and that the systematics of the past flares are better understood if the flares are double-peaked and the two peaks are separated by ∼1–2 years. This led to the proposal of a new SMBHB central engine model (LV96 model hereafter) for OJ 287 where a supermassive secondary BH is orbiting the more massive primary BH in a relativistic eccentric orbit with a redshifted orbital period of ∼12 years and where the orbital plane is inclined with respect to the accretion disk of the primary at a large angle. In this model, the double-peaked flares occur due to the impacts of the secondary BH on the accretion disk of the primary BH twice during each orbit. The third campaign carried out by the OJ-94 group verified the flare on October 1995. It came within the narrow two-week time window of the prediction [40,41].

Each impact releases hot bubbles of gas from both sides of the disk which then expand and cool down until they become optically thin [39,42]. At this point, bremsstrahlung radiation from the entire volume becomes observable causing the optical brightness of the blazar to increase rapidly [43]. The resulting flare can last for a few weeks and should reach its peak within the course of a few days.

The LV96 BBH central engine model of OJ 287 with subsequent fine-tuning of the orbital and disk parameters has been very successful in explaining the past observed optical flares, including many which have been discovered in historical data since 1994. See Dey et al. [33] for a collection of flare light curves. Moreover, this model has accurately predicted the time of arrival of future flares expected during the years 2005, 2007, 2015, and 2019 which triggered new observing campaigns [32,33,44–46]. The 2005 flare came a week ahead of the orbital schedule calculated by Sundelius et al. [44] and corrected for the astrophysical time shift between the disk impact and the flare by LV96 [47,48]. The latest prediction of the 2019 *Eddington flare* was successfully observed with the *Spitzer space telescope* [34] which showed that the orbital times are now known with the accuracy of ±4 h.

The model also predicted that the excess emission during the impact flares is unpolarised, and it has the bremsstrahlung spectrum at <sup>∼</sup><sup>3</sup> <sup>×</sup> <sup>10</sup><sup>5</sup> K. At the time (in the spring of 1995 when the model was constructed) it was only known that during the rapid brightening of the 1983 flare the polarisation decreased with rising flux: the first point at ∼16.5 mJy in the V-band had polarisation of 8.2% while the peak at ∼33 mJy had polarisation of 0.8% and the four points measured around the peak had the average polarisation of 4% [36]. This is exactly what is expected if the excess emission is unpolarised. The same trend was seen again in 2007 and 2015 [49,50]. In 1984, 1994, 1995, 2005 and 2019 the polarisation measurements were not obtained for the primary peak, partly due to seasonal and weather restrictions.

The spectral slope over a wide range of frequencies was measured during the 2005 flare and the expected spectral index of *α<sup>ν</sup>* ∼ −0.2 was found. It is quite different from the usual spectral index of *α<sup>ν</sup>* ∼ −1.3 over the same spectral range [51,52]. The spectral index *α<sup>ν</sup>* ∼ −0.2 was confirmed during the 2015 and 2019 flares. The complete change in the nature of emission in the flare as compared with the usual out-of-flare emission excludes the possibility that the flares are somehow related to Doppler boosting variations in a turning jet [53,54].

As an example, the 2015 flare was observed by the Swift observatory [55]. The first observation prior to the flare on JD 2457354 found the flux 1.92 mJy in the UV channel M2. Almost simultaneously it was observed in several optical bands, including the V-band, where the flux was recorded as 5.67 mJy [56]. The highest M2 flux value in this set of Swift observations was recorded on JD 2457360.65: it was 5.55 mJy, while the nearly simultaneous V-flux (about 0.5 d earlier) was 10.0 mJy [57]. Our R-band magnitude 13.36 on JD 2457360.65 is in agreement with this V-flux. We take the first observations as the base level, and obtain the flare contributions in M2 and V-bands of 3.63 mJy and 4.33 mJy, respectively. The spectral index between these two wavebands becomes *α<sup>ν</sup>* ∼ −0.2, the bremsstrahlung value for the temperature in question.

The observation of the bremsstrahlung optical flare during early September 2007 confirmed the highly-relativistic nature of the binary BH in OJ 287. This is because the BBH model would have predicted the arrival of OJ 287's impact flare on Earth around early October 2007 if the effects of GW emission had been ignored while describing the relativistic trajectory of the secondary BH in the blazar [46,49]. Thereafter, the observation of the *GR centenary flare* during November-December 2015 was used to constrain the dimensionless Kerr parameter of OJ 287's primary BH [33,50]. The updated BBH parameters of the OJ 287 system, determined using post-Newtonian (PN) equations of motion, are given below: primary BH mass *<sup>m</sup>*<sup>1</sup> <sup>=</sup> 18.35 <sup>×</sup> <sup>10</sup>9*<sup>M</sup>*, secondary BH mass *<sup>m</sup>*<sup>2</sup> <sup>=</sup> <sup>150</sup> <sup>×</sup> <sup>10</sup>6*<sup>M</sup>*, primary BH Kerr parameter *χ*<sup>1</sup> = 0.38, orbital eccentricity *e* = 0.657, and orbital period (redshifted) *p* = 12.06 years [33]. We now describe the various EM observational campaigns that allowed us to extract additional astrophysical details of the BBH central engine description for the blazar.

### *1.2. Multi-Wavelength Emission of OJ 287 and Previous and Ongoing Monitoring Campaigns*

OJ 287 has been the target of intense multi-wavelength coverage and monitoring in recent decades. Early optical observations first revealed very bright high-states reaching up to ∼12 mag. Dedicated optical monitoring campaigns [58–60] and the addition of photographic plate data dating back to the late 19th century [31] then revealed that bright optical maxima recur semi-periodically. These observations led to first suggestions of the presence of a binary SMBH in OJ 287 [19] and its later confirmation in subsequent campaigns, as mentioned above [48,61]. An ongoing optical monitoring program of OJ 287 combines optical data taken at multiple ground-based observatories and provides coverage at sub-daily cadence except for epochs when OJ 287 is unobservable due to its proximity to the Sun [33,62]. Figure 1 shows the optical lightcurve of OJ 287 from late 19th century to the present epoch. Based on the latest optical high-state discovered in this program in late 2015 and interpreted as a binary impact flare [50], a new broad-band radio—X-ray monitoring program of OJ 287 was initiated and is described below. Most of the time, the optical emission of OJ 287 is dominated by synchrotron emission from the jet, as known from SED modeling [63] and high levels of polarization [64]. However, it shows a decrease in polarization, expected in the binary SMBH model, at epochs where an additional thermal bremsstrahlung contribution from the disk impacts contributes to the emission, for example, [49]. Optical polarimetric monitoring of OJ 287 was carried out during the epoch 2016–2017 following changes in polarization and led to the interpretation of the 2016–2017 optical high-state as a binary after-flare [61].

Based on the faintness of its optical Balmer lines from the broad-line region (BLR; [65,66]), OJ 287 is classified as a BL Lac object. Given its spectral-energy distribution (SED), it is of LBL type (low-frequency-peaked blazar; [67]). Optical emission lines from the narrow-line region (NLR) like [OIII]*λ*5007 are only faintly present [66].

As a blazar, OJ 287 is a bright radio emitter [30] with a structured, relativistic jet [68–70] that is highly polarized [71]. On average, the jet is pointing close to our line of sight [68,72], but it shows large swings in its position angle [73,74] that can be understood in the context of the binary SMBH model [75].

OJ 287 was first detected in the *γ*-ray regime with the CGRO/EGRET satellite observatory [76] and shows repeated flaring in the Fermi *γ*-ray band for example, [63,72,77] along with more quiescent epochs not detected by Fermi. The first very-high energy (VHE; *E* > 100 GeV) detection was obtained in 2017 with VERITAS [78]; an observation triggered by the measurement of an exceptionally bright X-ray outburst (Figure 2) discovered with Swift in the course of the dedicated long-term, multi-frequency monitoring program MOMO (Multiwavelength Observations and Modelling of OJ 287; [79,80]).

**Figure 2.** X-ray (0.3–10 keV) lightcurve of OJ 287 obtained in the course of the MOMO program with Swift between 2015 December and 1 March 2020. Two bright outbursts were discovered in 2016–2017 and 2020. Adopted from Komossa et al. [81].

OJ 287 is a bright and variable X-ray emitter observed with most major X-ray observatories and first detected with the Einstein satellite [82]. The X-ray spectrum of OJ 287, based on XMM-Newton observations between 2005 and 2020 (energy range: 0.3–10 keV), is characterized by a super-soft (low-energy) synchrotron component and a hard (high-energy) inverse Compton (IC) component [83]. The synchrotron component dominates the X-ray outburst states [80]. High-energy emission up to 70 keV was detected with NuSTAR with an unusually soft power-law spectrum of photon index Γ<sup>X</sup> = 2.4 accompanying the 2020 outburst [80]. OJ 287 shows an X-ray jet extended by 2000 [84].

Starting in late 2015, OJ 287 has been the target of the dedicated multi-wavelength monitoring program MOMO [79–81,83,85] (see the review by Komossa et al. [86]). MOMO is aimed at characterizing the blazar properties and facets of the binary SMBH in detail. The program employs multiple frequencies in the radio band between 2–40 GHz obtained with the Effelsberg observatory, UV–optical Swift data in 6 filters, and the Swift X-ray band (0.3–10 keV). The monitoring cadence is as short as 1–4 days. Additional deeper observations with multiple ground and space-based observatories are triggered in the case of exceptional outburst or low-states discovered with Swift and/or in the radio band. The community is alerted in form of *Astronomer's Telegrams* about particular states of OJ 287 (ATel #8411, #9629, #10043, #12086, #13658, #13702, #13785, and #14052). MOMO is the densest multi-wavelength monitoring program of OJ 287 involving X-rays, with >1000 datasets so far taken, providing spectra, broad-band SEDs, and lightcurves, during all activity states of OJ 287 [81,86].

Some of the main results of the program MOMO are as follows: Two bright outbursts were identified in the course of MOMO in 2016–2017 and 2020 (Figure 2); the brightest so far recorded in X-rays [79–81]). These outbursts were non-thermal in nature, and they are consistent [80] with after-flares predicted by the binary SMBH model, when disk impacts of the secondary lead to the triggering of new jet activity of the primary SMBH. OJ 287 has turned out to be one of the most spectrally variable blazars in the X-ray regime (Figure 3) with power-law spectral indices as steep as Γ<sup>X</sup> = 3 [81,83]. Supersoft synchrotron emission dominates the outburst states. Another key features of the MOMO lightcurve is a pronounced, symmetric UV–optical deep fade in November–December 2017 (Figure 3) of still unknown nature [80,81]. Structure function analyses of Swift data between 2015– 2020 has revealed characteristic break times of 4–39 days depending on activity state and waveband [81]. Discrete correlation analysis between UV, optical and X-ray bands during the same epoch shows lags and leads in X-rays w.r.t. the UV, attributed to an IC component, where external Comptonization is favored over synchrotron-self-Compton emission [81,86].

The MOMO program continues as OJ 287 nears its next predicted binary SMBH impact flare. Results obtained so far including >1000 broad-band SEDs will serve as a useful data base to identify new activity states of OJ 287 driven by blazar variability in comparison to binary-driven activity, and allow detailed modelling of the broad-band emission from the radio to the high-energy regime at each epoch. We now take a closer look at the present description of the primary BH accretion disk and propose a detailed scenario to describe the outcome of secondary BH impact with the disk.

**Figure 3.** Multi-wavelength X-ray–optical lightcurve of OJ 287 taken with Swift since December 2015. The majority of data was obtained during the MOMO program. Panels from top to bottom: Observed X-ray flux in the band (0.3–10) keV in units of 10−<sup>11</sup> erg/s/cm<sup>2</sup> , X-ray powerlaw photon index Γx, Swift UVOT UV and optical fluxes (corrected for Galactic extinction) in units of 10−<sup>11</sup> erg/s/cm<sup>2</sup> . Every year, observations are interrupted by ∼3 months when OJ 287 is in close proximity to the Sun such that Swift cannot observe. Selected epochs are marked in color: (1) The epoch near the 2015 binary impact flare, (2) the bright 2016–2017 outburst, (3) the 2017 optical-UV deep fade, and (4) the 2020 April outburst. Epochs (2) and (4) were interpreted as possible binary after-flares. Epochs like the deep fade in 2017 (feature 3) and the new low-state in September 2020 can be used to obtain host galaxy imaging of OJ 287 when the blazar emission itself is least disturbing. Adopted from Komossa et al. [81].

### **2. Accretion Disk in OJ 287**

Our binary model of OJ 287 is based on the interpretation of the huge optical flares as impacts of a secondary black hole on accretion disk of the primary. While the emission level of OJ 287 is between 1 and 2 mJy in the optical V-band most of the time, the emission rises to 13 mJy (in the 2015 flare) or similar values in the peaks that we interpret as impact flares, that is, they represent an order of magnitude increase in the optical flux. The increase occurs on the time scale of a day or so which is about a fraction of 0.0002 of the 12 yr (9 yr redshift corrected) binary orbital period. This implies that the emission region in the source responsible for these huge flux variations, cannot be greater than one light day in size. Most of the work on the binary black hole model has concentrated on the orbit of the secondary. However, it is equally important that we also find out the basic properties of the accretion disk from the way the disk reacts to the impacts, and how these one-light-day emission regions are activated.

In the original binary black hole model of Lehto & Valtonen [39] the disk was taken as a standard disk with two parameters, viscosity *α* and accretion rate *m*˙ . Fixed values were given for these parameters. When more impacts were observed later, both in the future and in the past historical light curve, it became possible to solve the values of these parameters together with the orbit solution. Altogether it is a 9 parameter problem which has a unique solution as soon as the exact times of 10 flares are known. Mathematically it is equivalent to a ninth order equation which has nine unique roots. The method of solution is iterative, similar to the Newton-Raphson algorithm [46]. From the detailed study of the 2015 flare, the values of the two standard parameters were determined to be *α* = 0.26 and *m*˙ = 0.08 in Eddington units.

In the model of Lehto & Valtonen [39], a spherical bubble of hot plasma is released from the disk by the impact. Ivanov et al. [42] later demonstrated that actually two bubbles are released, one on each side of the disk. Therefore each impact is detectable via a radiating bubble on the front side of the disk. The model further specified that the bubble expands isotropically and therefore retains its spherical shape. The simulation of Ivanov et al. [42] casts doubt on whether this is true at an early stage of the bubble, but this was not considered important, as the bubble becomes optically thin only at a later time, which results in the observed great increase in brightness.

Valtonen et al. [87] noted that the maximum brightness of the 2015 flare should have been 26 mJy in the standard model. The fact that the peak value was only half of this value is most easily explained if the bubble is compressed along the line of sight. Thus it appears necessary that the expansion of the bubble is not completely unconstrained, but that it is influenced possibly by the general magnetic fields in the disk. In that case, it would be interesting to know what happens to the flux of the bubble from the very beginning if its expansion is constrained all the way. From Ivanov et al. [42] one could conclude that initially the expansion is more jet-like, a flow perpendicular to the disk rather than a gentle release of bubbles. Ivanov et al. [42] called them fountains. In the following we consider what difference this makes to the impact flare light curve.

### **3. Anisotropically Expanding BH Impact Generated Bubbles**

According to Lehto and Valtonen (LV in the following, [39]), the compressed plasma inside the accretion disk, following the impact, bursts out of the disk with the speed *vperp* = (6/7)*vsec* (LV Equation (7)) and the time to come out of the disk is *τdyn* = *h*/*vperp* (LV Equation (8)), where *vsec* is the speed of the secondary black hole at the impact and *h* is the semi-height of the disk. The flux from this bubble follows *S* ∼ *e f f Vbubble* (LV Equation (14)), if the bubble is fully transparent. The quantities *e f f* and *Vbubble* are the free-free emissivity and the volume of the bubble, respectively. However, we see only the fraction 1/*τ* of the bubble, where *τ* is its optical depth. Here *τ* = *de f f T* −1 , if *d* is the geometrical depth and *T* the temperature of the bubble. Therefore the flux goes as

$$S\_{\rm seen} \sim \varepsilon^{ff} V\_{\rm bubble} / \left( d \varepsilon^{ff} T^{-1} \right) . \tag{1}$$

We can substitute *T* ∼ *V* −1/3 *bubble* in adiabatic expansion which means that

$$S\_{\rm seen} \sim V\_{\rm bubble}^{2/3}/d \,. \tag{2}$$

We can put *Vbubble* ∼ *r* <sup>2</sup>*d*, where *<sup>r</sup>* is the bubble radius (*<sup>d</sup>* <sup>∼</sup> *<sup>r</sup>* in spherical geometry). The adiabatic expansion speed *v* ∼ *T* 1/2 <sup>∼</sup> *<sup>V</sup>* −1/6 *bubble* and

$$d \sim vt \sim V\_{bubble}^{-1/6} t \,. \tag{3}$$

Now, we have to specify the geometry of the bubble: For a tube of fixed radius seen end-on, *<sup>V</sup>bubble* <sup>∼</sup> *dr*<sup>2</sup> , *r* = *constant*, or *Sseen* ∼ *d* <sup>−</sup>1/3, and since *<sup>d</sup>* <sup>∼</sup> *<sup>d</sup>* <sup>−</sup>1/6*t*, it follows that *d* ∼ *t* 6/7. Thus

$$S\_{\text{seen}} \sim t^{-2/7}.\tag{4}$$

Flux drops with time roughly as *Sseen* ∼ *t* −1/3 .

For a tube of fixed depth seen end-on, *<sup>V</sup>bubble* <sup>∼</sup> *dr*<sup>2</sup> , *d* = *constant* or *Sseen* ∼ *r* 4/3, and since *r* ∼ *r* <sup>−</sup>1/3*t*, it follows that *<sup>r</sup>* <sup>∼</sup> *<sup>t</sup>* 4/3 . Thus

$$S\_{\text{seen}} \sim t^{16/9}.\tag{5}$$

Flux increases with time nearly as *Sseen* ∼ *t* 2 (cf. Figure 2 in [87]) For standard spherical bubbles of radius *r* the corresponding relation is [43]

$$S\_{\rm seen} \sim V\_{\rm bubble}^{2/3} / r \sim r \sim t^{2/3}. \tag{6}$$

Table 1 lists the disk impacts between 1971 and 2031. The first two columns come from [33], the numbers from the third column onwards are derived in the next section.

**Table 1.** Times of disk impacts and bremsstrahlung flares as well as the radii of the *H<sup>α</sup>* bubbles, impact speed on the disk, the delay of the *H<sup>α</sup>* flare and the time of the *H<sup>α</sup>* flare


In the spring of 2005, there was a major flare, 6.6 mJy at 2005.12, one of the biggest deviations from the standard binary black hole model during years 1996–2010 [44,45,88]. Figure 4 shows the observations (monthly averages) from 2005, prior to the main flare in October of that year. The disk impact occurred at 2005.11 (9 February 2005). With a time translation such that 3 December 2021 corresponds to 9 February 2005, we generate a predicted light curve for the 2021/22 season. For the values appropriate for 2005 and 2021 impacts, which take place at the same radial distance from the center, *τdyn* ∼ 20 days. The flaring related directly to the disk impact should start around 23 December 2021, and the flares should be recognizable as bremsstrahlung flares in the optical—UV region, with no counterpart in radio nor X-rays. The on-going and planned observational campaigns should be able to provide excellent constraints on our detailed modeling. So far, the period of early December 2021 was covered with Swift in the ongoing MOMO project and with ground-based optical observations. The optical–UV low-state detected in 2–14 December implies a small shift in the onset of the flare (work in preparation).

**Figure 4.** The optical light curve of OJ 287 during 2005 in V-band mJy units. Plot shows the monthly averaged data points for the early part of 2005 while the latter part, with faster variability, has 3 day averaged data points. The dashed curve is the theoretical line based on present work and Valtonen et al. [87]. Additionally, the theoretical curve provides the expected light-curve of OJ 287 during 2021–2022 and we mark its epochs on the upper x-axis while employing the time shift of the SMBH binary central engine description Dey et al. [33]. This is motivated by the fact that the secondary BH impact distances from the center should be roughly the same during 2005 and 2021. The first big flare during 2022 is not expected to be visible from any Earth-based facility while the secondary peak may become barely visible by early September 2022.

We now move on to explore other observational implications of the expanding impact bubble. This requires an extension of LV96 [39], where the brightness evolution of the bubbles was terminated at the epoch when the bremsstrahlung flares emerge. However, at a later stage when the bubbles have cooled enough, they may become visible again as hydrogen line flares. In what follows, we study the timing of these proposed *Hα* flares, and connect them with one epoch when the hydrogen lines were seen to be exceptionally bright, by a factor of ten above the normal.

### **4. Possible Spectroscopic Implications of the Evolving BH Impact Generated Bubbles**

After the bremsstrahlung flare the radiating bubble cools until it falls below the jet continuum level and is not observed any more [87]. However, at a later time, the bubble has cooled enough to become an *HII* region. This may appear as a sudden increase of the strength of the Balmer lines for a limited period of time. At the end of 1984, Sitko & Junkkarinen [65] observed such an increased line flux, approximately a factor of ten higher than normal [66]. To our knowledge, this was a unique occasion when such an *Hα* flare has been seen. Therefore it is tempting to associate this epoch with the dying moments of one the bubbles that had generated a bremsstrahlung flare at an earlier time.

In order to estimate when the bubbles left over from disk impact may reach the *Hα* stage, we calculate the required increase in the bubble radius until its temperature has dropped to 10<sup>4</sup> K. Using Table 3 of Dey et al. [33] and Table 1 of Valtonen et al. [87], and assuming an adiabatically expanding bubble, we obtain the radii of the bubbles listed in column 3 of Table 1. In Valtonen et al. [87] the expansion speed of the bubble is given as ∼*vrel*/4 where *vrel* is the speed at which the secondary impacts the accretion disk. In fact, the expansion speed value *vrel*/4.6 is used in the following since it gives the correct timing for the 1984 *Hα* flare, 1984.98 [65]. This value is well within the uncertainty of the expansion speed, extracted from the numerical simulations by Ivanov et al. [42]. These values are given in column 4 of Table 1, while column 5 gives the time of the expansion up to this stage. In column 6 we give the estimated time of the beginning of the *Hα* flare.

The epochs of observation in the line monitoring program of Nilsson et al. [66] and in the program by some of the present authors at the *Nordic Optical Telescope* (T.P.) as well at the *Rozhen Telescope* of Bulgarian Academy of Sciences (S.Z.) are given in Table 2.


**Table 2.** The epochs of the line monitoring program.

The expected flares in the time span and close to these observations were at 2007.42, 2008.33, 2016.80 and 2021.21. In the first two cases, the observational epochs were too early by 0.16 and 0.05 yrs, respectively, in order to catch the beginning of the flares. The last two were too early by 0.54 yr and too late by 0.61 yr. Therefore, if the *Hα* flares started as expected, we would not have seen them, even if the flares lasted several months.

In order to calculate the line flux, we proceed as follows. The emissivity of the Balmer *Hβ* line may be taken as

$$
\varepsilon\_{H\beta} = 8.3 \times 10^{-26} \, n^2 \, \text{erg} \, \text{cm}^{-3} \, \text{s}^{-1} \,, \tag{7}
$$

where *n* is the number density of Hydrogen atoms. We calculate the line flux using the density for the 1984 line flare, *<sup>n</sup>* <sup>=</sup> 3.2 <sup>×</sup> <sup>10</sup><sup>8</sup> and the bubble radius 3250 AU from Table 1. The result is

$$S\_{H\not\!\!\!=} = 2.2 \times 10^{-15} \text{ erg s}^{-1}.\tag{8}$$

Sitko & Junkkarinen [65] find *<sup>S</sup>H<sup>β</sup>* <sup>∼</sup> 1.2 <sup>×</sup> <sup>10</sup>−<sup>15</sup> erg s−<sup>1</sup> , but state the value as uncertain. The more certain *<sup>S</sup>H<sup>α</sup>* <sup>=</sup> <sup>24</sup> <sup>×</sup> <sup>10</sup>−<sup>15</sup> erg s−<sup>1</sup> , divided by some number of order of 10 [65] takes us close to the above estimate. The radius and the number density are different in 2024 than in 1984, but the different factors practically cancel each other. Therefore we expect the 1984 *Hα* line flare to repeat itself in 2024.

### **5. Explaining Observed Gamma Ray Flares**

Here, we will distinguish the classical gamma-ray regime, as observed by the Fermi satellite, with many gamma flares detected (typically in the *E* ∼ 100 MeV regime); and the VHE emission (*E* > 100 GeV) that this Section mostly focuses on. At VHE, OJ 287 was only detected once, by VERITAS. The VERITAS observation was triggered by the Swift detection of an exceptional X-ray high-state in the course of the MOMO program [79,80]. Otherwise, OJ 287 is monitored in gamma-rays with Fermi, with many large and small flares.

Classical gamma ray flares have been reported many times in OJ 287 [77,78]. For example, the 2009 classical flare coincides with the last of the predicted tidal flares following the 2007 bremsstrahlung flare [45] while the 2017 VHE flare came soon after the last of the predicted tidal flares following the 2015 bremsstrahlung flare [89]. We can predict the next VHE gamma ray flare following the same principles.

In order to study the orbital phase of the 2017 VHE flare in our model, we have calculated the response of the OJ 287 accretion disk to the 2013 secondary crossing, using a disk of 146,880 particles. The particles leaving the disk are counted, and the time (*time*1) and distance (*r*) from the center are noted down. Assuming a constant transit speed to the jet (taken to be at *r* = 3000 AU), the jet reaction time (*time*2) is calculated. Figure 5 corresponds to the transit speed of *c*/6 in the observers frame which equals to 0.22*c* in the OJ 287 frame. This transit speed value fits best with the two observed light curve peaks at 2016.2 and 2016.8. The present calculation differs from Pihajoki et al. [89] in that the surface density of the disk follows Lehto & Valtonen [39] rather than a uniform density which was used in Pihajoki et al. [89]. Pihajoki et al. [89] also did not take the transit time into account, so that it would have to be done collectively for all particles for a comparison with observations. Note that the second peak becomes stronger when a realistic surface density model is used, in agreement with observations.

**Figure 5.** Simulation of the response of the accretion disk to the crossing of the secondary black hole through the disk before the 2015 bremsstrahlung flare. Particles which escape the disk are counted, and they are placed on the time axis assuming that the particle contributes to the light curve after traveling the distance of ∼15,000 AU with a constant speed of 0.22*c* where *c* is the speed of light. The exact value of travel distance depends on the radial distance from the center where the particle is released from the disk. The particle count in each time box (*time*2) is turned into a magnitude, assuming that the relation between the particle number and the total brightness in each box is linear. The first flare in observations at the end of 2015 is different (impact flare) and is not modeled by this process.

The tidal flares of the light curve of OJ 287 following the 2005 and 2022 bremsstrahlung flares were calculated by Pihajoki et al. [89]. No time transformation was applied so that the plots in Figure 4 of Pihajoki et al. [89] are for *time*1, as defined above. Using the same transit speed of particles to the jet as above we should add 1.0 yr to the time axis. For the 2005 impact the two main flares in the predicted light curve are at 2007.4 and 2008.6. Even though these are placed at the summer period of few or no observations (OJ 287 is close the sun at the beginning of August), a strong brightening of the source was observed in the following autumn (both 2007 and 2008) which agrees with the tidal flare explanation. The interpretation of the light curve is made complicated by the fact that the bremsstrahlung flare of 2007.7 falls in the same time interval as the tidal flare [48].

As to the 2022 case, the predicted light curve has maxima at 2023.5 and 2024.2 [89]. Note that the nature of the simulation by Pihajoki et al. [89] is such that the tidal flares appear to get weaker with time. This is an artifact of the simulation technique which does not replace the escaped particles by new ones in the disk. Because of practically the same impact distance in 2005 and 2022, the tidal responses should be rather similar. We therefore expect that VHE gamma rays would again be detectable in the spring of 2024. The prediction cannot be more precise until we see the corresponding flare starting in the optical region. Further, we expect to see such flare again in the X-ray regime, as in 2017 when the very bright X-ray flare detected with Swift triggered the VHE observation. Given the ongoing monitoring program with Swift with very dense coverage and >1000 SEDs already obtained for example, [80,81], very detailed timing and comparison with the 2017 flare will then be possible. This ongoing project, or any X-ray monitoring with future X-ray missions, can then also be used to trigger new VHE observations.

In addition, OJ 287 observations can reveal interesting astrophysical information when it enters low luminosity state and this is what we focus on in the next section.

### **6. Optical Multicolor Photometry at Minimum Light**

From time to time, the brightness of OJ 287 falls to a very low light level. It is hard to predict when these times will happen again, even though it is thought that the low light level may be associated with the secondary moving in front of the primary [90]. The absolute minimum light observed so far took place in the spring of 1989. In Figure 6 we replot the observations [90], and fit smooth curves through them. When the brightness of the AGN falls towards the brightness of the host galaxy, the color of OJ 287 is expected to change gradually from the typical jet color to the color of the host galaxy as the fade proceeds. Takalo et al. [90] conclude that at the brightness level V = 17.4, the host galaxy contributes at least half of the brightness of the source. Using the usual conversion V − K = 3.2, Kcorrection and evolution correction of 0.6 and the distance modulus m − M = 41, this implies the absolute K-band magnitude of *M<sup>K</sup>* = −26.8 ± 0.3 [91].

**Figure 6.** The observations of the 1989 fade of OJ 287 with the *Nordic Optical Telescope* and the *Jacobus Kapteyn Telescope* at La Palma, with 2*σ* errorbars. Here we plot the magnitudes in three filters B, V and R: the I band data were too few to show a significant variation. The lines are fifth order polynomial fits through the data points. We note that the dip on 18 May was deepest in the B band and less deep going to longer wavelengths. There is a possible time delay in the sense that the dip starts from longer wavelengths and happens later at shorter wavelengths. At 37 GHz the minimum took place on 3 May 1989.

Using surface photometry in the K-band with the *Nordic Optical Telescope* Nilsson et al. [92] find *K* = −14.65 ± 0.6, leading to *M<sup>K</sup>* = −25.85 ± 0.6 with the Kcorrection −0.5, which is somewhat, but not significantly, fainter than the value measured by the color method. However, this may not be the total brightness of the host. It is well known that galaxies of this brightness category have extensive haloes which contribute as

much as one magnitude to the host. For example, the absolute K-magnitude of NGC 4889 is *M<sup>K</sup>* = −25.4 [93] (using m − M = 34.7 and V − K = 3.2) measured out to roughly the same 30 kpc linear distance as the surface photometry of OJ 287 in Nilsson et al. [92] while its total magnitude out to 100 kpc distance is about *M<sup>K</sup>* = −26.8 [94]. Typically the outer envelope contributes about 0.8 magnitudes to the total brightness [95–97]. Actually, if taken to the redshift of *z* = 0.3, NGC 4889 would probably appear very much like the OJ 287 host. Even the estimated mass of its central black hole is practically the same as the primary BH mass in OJ 287 [94].

We also note that the color photometry method is more likely to capture the faint halo light than the surface photometry method since the latter is seriously influenced by the high background light level generated by the fringes of the strong point source in the center [98]. The signal-to-noise ratio is better at longer wavelengths than in the traditional optical range which may be the reason why it is difficult to get a host magnitude measurement in the shorter wavelength bands below the infrared K-band [92]. For example, the *Hubble Space Telescope* image gives the range from *M<sup>K</sup>* = −24.7 to *M<sup>K</sup>* = −26.3, converted from the I-band to the K-band in the usual way [98]. The magnitude of the i-band image taken at *Gran Telescopio Canarias* corresponds to *M<sup>K</sup>* = −25.2 ± 0.3 [92].

It is interesting to see where this magnitude by multicolor method places OJ 287 in the black hole mass—host galaxy mass diagram. Considering that OJ 287 is at a much higher redshift than galaxies normally displayed in this diagram [99] and that the correlation is redshift dependent [100], we find that OJ 287 follows almost exactly the well established correlation (Figure 7).

**Figure 7.** The galaxy sample of Saglia et al. [99] with three additional galaxies in the black hole mass vs. galaxy stellar mass diagram (stars), while the position of OJ 287 is given as a solid square. The dashed line represents the correlation found by Portinari et al. [100] for galaxies in the upper-right hand part of the graph around redshift 0.5.

When do we expect to be able to repeat the host galaxy brightness measurement by the photometric method? It depends on the reason behind the fade. At the time, in 1989, the secondary was near apocentre of its orbit, and the major axis of the orbit was close to perpendicular to the disk. This configuration minimizes the tidal perturbation of the disk by secondary. The next time a similar configuration arises is around 2032 (see Figure 8).

Takalo et al. [90] suggests that during the fade the secondary moves between us and the primary, and this causes a temporary misalignment of the jet, leading to decreased Doppler boosting that shows up as a fade. This is a sensible proposition as we may find as follows: Suppose the secondary passes within 100 AU of the jet. Then the jet is gravitationally deflected by ∼4 ◦ . Using the parameters from Hovatta et al. [101], and adding 4 ◦ to the viewing angle, we find that the jet becomes fainter by about 3 magnitudes. That is, if we have the normal V-band magnitude ∼15, in the fade it may drop to ∼18 which is actually what happened during the 1989 fade. We cannot perform a more detailed calculation since we do not know the inclination of the orbit of the secondary. This proposition could be studied further, as the jet swinging back and forth should appear also in radio maps, with the proper delay for each frequency, as well as in optical polarisation with a small delay. A

comparison of optical and radio light curves at the fades should also establish the relative positions of the radio and optical cores in the jet. The 1989 fade suggests that they lie close to each other.

We may ask when this configuration repeats itself. Figure 8 and its caption lists such times. Since the optical emission region is in the jet a little way from the center, the times given by the model are about half-a-year earlier than the response in the optical emission. The 1998 and 2008 fades were discussed in Pietilä et al. [102] and Valtonen et al. [88] while the 2020.05 alignment, with the same response time as in 1989, would place the fade in the summer period of 2020 when we had no observations (Figure 8).

**Figure 8.** Temporal evolution of the angular separation between the primary jet in OJ 287 and the line joining the primary and secondary BHs. The separation is calculated assuming that the jet precession follows the disk model of Dey et al. [75]. Minimum separation angle occurs at 1980.73, 1988.95, 1997.61, 2008.45, 2020.05, and 2031.85.

Obviously, a fade would be a good time to repeat the surface photometry study of the host, too. In addition, epochs of very faint intrinsic emission from this blazar (jet) can be used to trigger host galaxy imaging because the central point source and its point spread function (PSF) is least affecting the host measurements at such epochs. For instance, in November 2017 and September 2020 such optical–UV low-states were identified in Swift monitoring (Figure 3) and new ones will be detected in the course of the ongoing MOMO program as well as in ground-based optical monitoring campaigns.

### **7. The Radio Jet**

OJ 287 has a prominent radio jet which is known for its large swings in the position angle in the sky [73]. These swings are well understood if they result from the variations in the orientation of the inner accretion disk, and if these variations are translated into the direction of the jet [74,75]. Actually, these large swings were predicted by Valtonen et al. [88] before they were observed. The high resolution data at 86 GHz is compared with a theory line in Figure 9 (see Dey et al. [75] for details). A 3.4 yr delay is found between the change of the disk axis and the direction of the jet. This is because the point at which the jet position angle is measured is typically 200 microarcsec from the radio core, and it takes some time to transit the information of the disk orientation change to this distance in the jet. The actual jet speed in OJ 287 is discussed for example, in Valtonen et al. [103]. In this case we find the relativistic Γ ∼ 7. This is somewhat lower than the values measured by other methods. For example, Savolainen et al. [104] give Γ ∼ 9.3, Jorstad et al. [68] find Γ ∼ 16.5, and Hovatta et al. [101] find Γ ∼ 15.4. Anyway, our Γ ∼ 7 is close enough, and gives further support for the model. If the disk model was not accurate, or if the principles of jet-disk connection were not valid, there is no reason why the value coming out of this model would be anywhere near the values obtained via quite different methods.

**Figure 9.** The position angle of the radio jet in 86 GHz observations (points) compared with the model line. The best-fit parameters are taken from Table 1 of Dey et al. [75] and we have used the disk model to calculate the theoretical model line. The viewing angle varies with time but is typically similar to the value found in Hovatta et al. [101]. The delay time between the change of the jet direction at its origin and the appearance of the change in 86 GHz observations is 3.4 yr.

The region of the jet which we observe depends on the frequency because the resolution of the global VLBI maps is proportional to the observing frequency. Unfortunately, this technique cannot be extended as far as the optical frequencies. However, some information about the jet may be obtained by monitoring of optical polarization. Valtonen et al. [105] demonstrate that the optical polarization angle is a good proxy for the position angle of the radio jet. A big position angle jump occurred in 1995 in the optical polarization while a similar jump took place in 2009 in 15 GHz radio maps. Figure 10 shows how the optical polarization is modeled by our swinging jet model. The time delay is one quarter of the 86 GHz delay, so the distance of the region emitting in optical should be closer to the center by the same amount.

**Figure 10.** The annually averaged optical position angles of OJ 287 (points) together with the same jet model as in the radio jet observations. Note that the position angle has large fluctuations after the time of large optical flares, 1983/84 and 1994/95. The model parameters are the same as for the radio flares, except that time delay is 0.92 years, that is, the optical emission region is closer to the center than the observed radio jet region at 86 GHz. This region cannot be resolved in optical observations.

In the high resolution map from April/May 2014 [70], the 86 GHz component C2 at 90 microarcsec from the center has the position angle −8 ± 45◦ . The latter component more or less coincides with the point in the jet where our model places the optical emission region (Figure 11). The innermost component C1b at 40 microarcsec lies at the position angle 13 ± 10◦ , interestingly close to the theoretically calculated position angle the secondary jet at the position angle 14.6 ± 4 ◦ of Dey et al. [75] (see Figure 11). Below, we explore other possibilities of searching for observational evidence of the secondary black hole.

**Figure 11.** The distance and position angle PA of radio components in the Radioastron VLBI map by Gomez et al. [70] with error bars. The 22 GHz data are used when available. The component J1 comes from 15 GHz observations. Superposed are the theoretical positions of the corresponding components at two epochs (stars and triangles) in the spin model [74,75]. The position of the expected secondary jet is also marked (cross). Its position angle is independent of epoch.

### **8. On the Presence of Secondary BH Accretion Disk**

The mass ratio of the two black holes in the OJ 287 binary is 122. Thus for the same *m*˙ and *α*, the primary disk should be 122 times brighter. However, if the mass accretion rate is 122 times greater in the secondary than in the primary, both disks could be equally bright. This would put the brightness of the secondary over the Eddington limit, which may be possible at least in some accretion disk models [106]. It is well known that tidal perturbations increase the accretion flow considerably, see, for example, Sillanpää et al. [19].

We may use Sundelius et al. [45] and Pihajoki et al. [89] to estimate the accretion rate to the secondary. In these simulations one particle represents ∼100 solar mass of gas and the gas is accreted at the average rate of ∼5 particles per year, that is, the mass accretion rate is about <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>2</sup> solar mass per year. This is approximately the mass contained within the Bondi-Hoyle accretion radius for the secondary, and much of it is likely to remain bound to the secondary when it leaves the disk. At what rate this matter is accreted to the black hole itself is another problem: it may well be that only some fraction of the gaseous envelope around the secondary black hole finds its way to the center before it suffers another collision with the disk. On the other hand, the steady state accretion rate of the primary is much lower, ∼0.6 solar mass per year [87]. Thus the higher accretion rate to the secondary may compensate for its lower mass, in which case the secondary may not be all that much fainter than the primary.

However, the secondary is truncated by tides which may reduce its optical emission below the brightness of the primary, since the optical emission is associated primarily with larger radii in standard disk models. The accretion by the secondary is also not steady, and its brightness may vary considerably depending on the epoch of observation. Not seeing it at one epoch does not mean that it could not be seen at all.

At present, there are several ways by which the secondary could show up. In spectral observations there could be extra lines that match the redshift of the secondary at that particular instant in time. Because of the high orbital speed, these lines would be found quite far apart from the primary redshift in the spectrum. For example in November 2021 the secondary should have had redshift 0.38, in contrast to 0.307 in the primary. However, the relative redshift changes constantly, and moreover, the secondary spends a great deal of time behind the accretion disk and cannot be seen. After the 3 December crossing to the far side of the disk we should not see it for another ten years, and even after that only briefly. This is because precession now lines up the secondary orbit such that the pericenter is towards us, and the secondary spends only about 1/10 of its orbital time in the pericenter part of the orbit.

Table 2, column 4, gives the expected wavelengths (in angstroms) of the secondary *Hβ* or *Hα* lines (the latter in square brackets). During the periods when the secondary should be behind the disk, we give the line for the opposite viewing direction, since we cannot be absolutely sure that we have identified the viewing direction correctly. Our interpretation in this respects relies heavily on Takalo et al. [90]. These values are in curved brackets, and refer to *Hα*. In Figure 12, we show the theoretically calculated redshift of the secondary BH.

**Figure 12.** The redshift of the secondary black hole as a function of time. Two inclination values are shown: 90◦ (edge-on) and 50◦ . The model does not specify the inclination. The shaded regions are the time intervals when the secondary is in front of the accretion disk and thus visible to us. The identification of the "front side" is based on taking the secondary to be in front of us during the 1989 deep fade [90].

Among the VLT data, there is only one epoch where the expected secondary line would be within the observed wavelength range, and no line is seen. However, in this case we would need to have had the viewing direction wrong. Thus there is nothing in the VLT spectra that excludes the possibility of secondary lines in our current model. In the NOT and Rozhen spectra we are in the right wavelength region for *Hβ*, and the NOT spectra are taken at the time when we should see the secondary lines (see Figure 13). We do not see any of them. In fact, only a single primary line is detected weakly. Thus this non-detection does not give strong observational limits.

The second way to find signs of the secondary is to look for the jet of the secondary. It may arise as soon as a new accretion disk has formed after a disk impact. Since the new accretion disk is formed from the material pulled out of the primary accretion disk, its axis should share the orientation of the axis of the mean disk of the primary. This is in contrast to the primary jet, which wobbles considerably around the axis of the mean disk under the influence of the companion [75]. A search for radio emission in a constant direction at the position angle ∼15◦ may reveal an indication of such a jet. The length of the jet should scale with the mass of the black hole, so that the secondary jet may be a factor ∼122 shorter than the primary jet [107,108]. In the primary jet the outermost component J1 at 15 GHz is found at 3400 microarcsec from the center; thus the secondary jet may be expected in the scale of ∼30 microarcsec. This is the scale which has just been reached at VLBI [70] and will be studied in coming years.

Additionally, some of the flares may arise in the secondary jet rather than in the primary jet. They could be recognized for their short variability time scale. However, since the secondary jet is expected to represent only a fraction of the flux of the primary jet, the fast variations would appear at a low amplitude, consistent with Valtaoja et al. [109] who found 1–10% peak-to-peak amplitude variations during the 1983/84 flaring season, with a 15.7 min period. Pihajoki et al. [89] find that variations down to 3.5 d may be associated with the primary while the variability of the secondary could be faster by at least a factor of 122, depending on the secondary spin. For a maximally spinning secondary the 15.7 min period may arise [110]. It is the period of the innermost stable orbit about the secondary black hole in the jet reference frame.

Since the secondary disk is likely to overflow its Roche lobe, we may also find interesting X-ray emission from the ring in the primary disk where the overflow stream terminates, akin to X-ray binaries. It is also worth searching for the direct accretion disk signature of the primary in the SED including a strong disk contribution in X-rays persistently detected in AGN with SMBHs of that mass.

**Figure 13.** Optical spectra of OJ 287 taken at the *Nordic Optical Telescope*. The continuum has been fitted with a low-order polynomial and subtracted and the spectra have been shifted in vertical direction for clarity. The positions of *λ*4861 H*<sup>β</sup>* and *λ*50006 [OIII] at the redshift of OJ 287 are indicated by vertical lines. The red curve below shows the positions of prominent atmospheric emission lines. Apparent deep absorption structures in the spectrum are telluric lines. The epochs are (from top to bottom): 12 February 2010, 23 October 2010, 18 November 2010, 4 January 2011, 17 January 2011, 1 October 2011, 11 February 2011, 23 April 2011, 7 May 2011, 16 November 2011, 19 February 2012, 27 December 2012, and 6 March 2013.

### **9. Are There More OJ 287-like Systems?**

The remaining lifetime of the OJ 287 black hole binary before a merger is 10<sup>4</sup> yr. Comparing this with the merger time scale of <sup>10</sup><sup>7</sup> yr, there is only a chance of <sup>∼</sup>10−<sup>3</sup> to catch the system at this late stage of evolution. Is this a problem? It depends on the parent population of OJ 287-like systems. As an order of magnitude estimate, it has been deduced that there are something like 10<sup>4</sup> binary black hole systems in the sky in the OJ 287 brightness category [111]. If this is the parent population, some ten of them would be found in the final stages of merger [112].

How could we find other OJ 287-like systems? We define an OJ 287-like binary black hole system such that it shows repeated bremsstrahlung flares due to the impacts on the accretion disk. The main requirement is that the mass ratio of the two black holes is rather large, so that the smaller black hole does not disrupt the accretion disk entirely in the process [51]. This is not very restrictive as large galaxies act as attractors of mergers with smaller galaxies, and together with the black hole mass-galaxy mass correlation this produces typically unequal pairs of black holes.

OJ 287 is a blazar with a jet pointing nearly toward us which increases its brightness many-fold, by about 3 magnitudes by our estimate above. The jets of other similar systems would likely point in some other direction. Thus it is unlikely that other OJ 287-like systems are found in lists of brightest radio sources, such as the Ohio Survey which gives the initial to the name of OJ 287.

However, if such a source is discovered through the repeated bremsstrahlung flares, it will take time before enough flares are seen to solve the orbit. In the case of OJ 287 we

are lucky that the source lies in the ecliptic zone which has been frequently photographed over 130 yrs. No such luck can be expected for the other OJ 287-like systems. It is also rather likely that these other systems contain smaller binary components by mass than OJ 287, with weaker bremsstrahlung flares. While other candidate binary black hole systems have been identified in recent years (review by [113]), none of them were explained by involving optical bremsstrahlung flares, and none of them so far has the dense polarimetry monitoring that OJ 287 has seen. Thus we may find more OJ 287-like systems, but not before full-sky monitoring programs have been operational for some time. We now briefly list GW aspects of our description for OJ 287.

### **10. Pulsar Timing Array Response to nHz GWs from OJ 287's SMBH Binary Engine**

The above listed observational campaigns in many electromagnetic observational windows clearly point to the presence of a nHz GW emitting SMBH binary in OJ 287. Therefore, it is important to develop prescriptions to model the expected pulsar timing array (PTA) response to nHz inspiral GWs from systems like OJ 287 [10]. The fact that the orbital eccentricity and primary BH spin can substantially influence the BH binary orbital evolution, as demonstrated in [33,114], prompted us to employ an improved version of GW phasing approach to model temporally evolving GW polarization states from such systems [115–117]. This is required as the PTA relevant GW-induced pre-fit pulsar timing residual, namely PTA response to inspiral GWs, induced by an isolated GW source at a given epoch *t* may be written as [118]

$$R(t) = \int\_0^t \left[ h(t' - \tau\_P) - h(t') \right] dt',\tag{9}$$

where *τ<sup>P</sup>* is the geometric time delay in the solar system barycenter (SSB) frame of the underlying millisecond pulsar while *t* and *t* 0 are the SSB relevant coordinate time variables. Further, *h*(*t*) provides the effective GW strain induced by an isolated source at an epoch *t* and depends on the intrinsic parameters of the GW source like the total mass, spin values, orbital eccentricity and angles that specify its sky location, as detailed in [116]. In other words, PTA response of a pulsar to inspiral GWs from OJ 287 like system at a time *t* depends not only on the strength of the inspiral GWs at the SSB at *t* but also on the GW amplitude at location of the pulsar at time *t* − *τP*. This is another reason why we need to employ PN approximation to track the orbital evolution and the resulting GW polarization states while modeling PTA response to inspiral GWs from SMBH binaries [116].

In an ongoing effort, we are modeling temporally evolving quadrupolar order *h*(*t*) from comparable mass BH binaries inspiraling along PN-accurate eccentric orbits under the influence of dominant order spin-orbit interactions due to the primary BH spin. This is being done by adapting and extending the GW phasing efforts of Damour et al. [115], Susobhanan et al. [116]. It may be recalled that this approach usually employs Kepleriantype parametric solution to model the conservative dynamics of SMBH binaries in eccentric orbits. Thereafter, the effects of GW emission are incorporated by adapting the method of variation of constants, as detailed in [115]. In practice, we invoke the arguments of energy and angular momentum balance that lead to differential equations for orbital frequency and eccentricity with the help of orbital averaged PN-accurate far-zone energy and angular momentum fluxes [117].

In Figure 14, we plot the expected PTA response of PSR J0751 + 1807 to inpsiral nHz GWs associated with our SMBH binary central engine description for OJ 287 as detailed in [33]. The plot is based on Equation (9) where we have employed quadrupolar order *h*(*t*) expression for spinning BH binaries in eccentric orbits from Königsdörffer & Gopakumar [119] while the orbital parameters are as detailed in Dey et al. [33]. The sharp features depend on the orbital eccentricity and pulsar distance and provide unique signatures of the expected PTA response to nHz GWs from such SMBH binaries. Unfortunately, the expected timing residuals are substantially below what we can achieve with the current timing campaigns on PSR J0751 + 1807. However, it should

be possible to find and time milli-second pulsars with such exquisite timing precision during the SKA era [29]. Therefore, it should be possible to monitor persistent inspiral GWs from SMBH binaries like OJ 287 during the SKA era. This development should naturally allow us to pursue persistent multi-messenger GW astronomy with crucial inputs from the ongoing, planned and proposed multi-wavelength electromagnetic observations of OJ 287. This is because such observational campaigns should allow us to constrain various astrophysical parameters of the binary BH central engine description for the unique blazar OJ 287.

**Figure 14.** Timing residuals induced by inspiral GWs from OJ 287's SMBH binary on a typical PTA pulsar PSR J0751 + 1807. We let the pulsar distance to be 1.4 Kpc [120] while SMBH binary parameters as listed in Section 1.1 with its luminosity distance to be 1.6 Gpc. Timing of milli-second pulsars with SKA are expected to achieve similar timing residuals.

### **11. Discussion**

This article emphasizes the importance of continuing monitoring of OJ 287 at all wavelengths of the electromagnetic spectrum as well as in gravitational waves. Even though the binary orbit has now been solved [33] and confirmed [34], there are many aspects of the system which still need verification and from which we can learn interesting astrophysics.

(1) The confirmation of the 2022 optical flare: This flare does not appear in any of the simple schemes that have been proposed over the years as alternatives to the LV96 binary black hole model. Difficult as it is to observe from the ground, we should just be able to observe the tail end of this flare. Polarisation observations play an important role here since the tail end of the flare should very highly polarised [36,50,59].

(2) The detection of the signals from the 3 December 2021 disk impact: This is energetically a huge event which has at previous times been studied only by occasional photometric measurements. This time we expect a full coverage from optical polarisation to X-rays which are the expected key indicators of the impact. So far, in ongoing MOMO/Swift and ground-based monitoring observations, OJ 287 was found in a low-state in early December 2021 (Komossa et al., and Zola et al., in prep.). The timing of the impact also depends on the detailed model, which will be improved after the 2021/22 observing season.

(3) The *Hα* flares: This has been caught only once, accidentally by Sitko & Junkkarinen [65]. Later spectroscopic surveys, some of which are reported in this paper for the first time, have not been equally lucky. Now we give a rather precise prediction for the *Hα* flare which follows the 3 December 2021, disk impact.

(4) The secondary black hole: The secondary black hole has never been directly detected. One of the problems is the short separation between the two black holes in the sky, typically 10 microarcseconds, depending on its orbital phase in an eccentric orbit. It will be several years before this resolution is achieved in radio VLBI. However, an attempt was made to detect the secondary by its spectral lines, but so far we only report a null result. It is a difficult task due to the high background level of the jet component. New attempts

should be made during periods of low light level. Here we have made a prediction when such occasions may arise.

(5) Radio jet of the secondary: Even though the immediate surroundings of the secondary are hard to resolve, the current resolution in radio VLBI should be just enough to see the jet. A strong radio component was recently reported [70] at the expected position of the secondary jet [75]. It remains to be seen if this component behaves as expected. One problem is that the current direction of the primary jet is not very far from the suspected secondary jet. However, if the primary jet behaves according to our models [75], the primary jet will move away from the secondary jet, and the identification becomes more clear. Thus the continuing radio VLBI monitoring of OJ 287 is essential.

(6) Radio jet of the primary: The radio jet of OJ 287 has been mapped in radio VLBI since the 1980s. The origin of the jet and its connection to the central black hole and its accretion disk are still open problems. In the LV96 binary black hole model it is possible to calculate the direction of the spin axis of the primary as well as the normal to the innermost disk. They follow each other more or less [75], with the disk normal showing a little more short time scale wobble than the spin axis. If we make the reasonable assumption that the initial jet direction is determined either by the spin axis (spin model) or the disk normal (disk model), we obtain a unique model for the jet which wobbles predictably. When projected onto the sky, we obtain position angles at any point in time, and since the resolution at higher frequencies is better than at lower frequencies in the global VLBI, we get snapshots of the jet at different distances from the center. After solving for the unknown viewing angles, we get a full picture of the bulk flow in the jet.

(7) Optical polarisation angle: It is usually assumed that the optical emission arises in the jet closer to the black hole than the radio emission. We have applied the same model for the optical polarisation that works for the radio position angle, and find that the region of optical emission is about four times closer to the central black hole than the inner 86 GHz emission knot. It is interesting also that the optical polarisation gives the direction of the innermost jet. This is not surprising since the jet has been found to have helical magnetic field geometry [70]. When compressed along the jet axis in shock fronts, the field lies practically perpendicular to the jet axis and the polarisation is lined up with the jet. It is important to continue regular polarisation monitoring programs to learn more about the inner jet.

(8) Optical fades: The times of low light level in the jet are useful also for the detection of the host galaxy. The absolute magnitude of the host has been measured by surface photometry out to ∼30 kpc from the galaxy center, beyond which it is difficult to measure any light above the background generated by the bright point source, the AGN itself. Its brightness measured out to this distance is among the highest ever detected, and therefore it is likely that the total brightness of OJ 287 host is also among the highest. The brightness may also be measured by multicolor photometry at low light, because the color of the host is expected to be very different from the color of the jet. Thus the combined color of the source becomes more and more like galaxy colors when the source fades. This method suggests a brightness increase by one magnitude if the outer envelope of the host galaxy is included.

(9) High-energy emission and broad-band SEDs: Very dense, simultaneous X-ray–UV– optical monitoring has allowed us to identify the latest binary after-flares in 2017 and 2020, based on the brightest X-ray flares so far discovered from OJ 287 and other arguments [80]. Ongoing monitoring will reveal new outstanding X-ray–UV outbursts. Spectroscopy, SED modelling, cross-correlation analyses and structure function analyses [81,86] will allow us to probe in detail the binary and outburst physics across the electromagnetic spectrum, and will allow to search for an accretion disk contribution of the secondary at select epochs. Ongoing high-energy monitoring could also serve as trigger criterion for new VHE observations.

(10) Very high energy gamma rays: VHE gamma rays have been detected in OJ287 only once. This occurred after the two big tidal flares which followed the 2015 impact flare. Even though we do not know the mechanism which produced this event, it may useful

to monitor OJ 287 again after the tidal flares which follow the 2022 impact flare. More frequent monitoring would be also useful to see if the two phenomena are really connected.

(11) Fast variability: The shortest time scale of periodic or quasi-periodic variability that may be associated with the primary jet is 3.5 days. This has been seen in many occasions. The time scale of variability should be ∼122 times shorter in the secondary jet, due to the smaller mass of the secondary by this factor, or it could be even as low as ∼15.7 min if the secondary spins much faster than the primary. Thus the study of fast variability in radio, optical and X-rays may reveal details of the secondary jet which are otherwise hard to recover.

(12) Pulsar Timing Array: It will be important to develop accurate and efficient algorithms to model the expected PTA signals from SMBH binaries like OJ 287. Further, data analysis approaches that can efficiently look for such nHz GW sources in the PTA datasets of SKA era will need to be developed [10]. Additionally, it will be desirable to search for milli-second pulsars close to the Sky location of OJ 287 as they are expected to be more sensitive to inspiral GWs from OJ 287. Investigations should be pursued to figure out the possibility of tracking the trajectory of secondary BH during the ngEHT era.

(13) It has been argued that OJ 287 may produce a few muon neutrinos with energies more than 100 TeV in instruments like IceCube-Gen2 during ten years of Fermi flaring epochs, influenced by the modeling of the 2017 flare of TXS 0506 + 056 [121,122]. The neutrino studies will be an important part of multi-messenger astronomy with OJ 287 in the coming decades.

**Author Contributions:** M.J.V. and L.D. have been responsible for the main design of this article as well as for theoretical developments. L.D. and A.G. were in charge of the gravitational wave part, S.Z. of optical photometry, S.K. of the MOMO project and X-ray parts, T.P. and S.Z. of optical spectroscopy, R.H. of historical magnitude measurements, H.J. and A.V.B. of optical polarimetry and J.L.G. of radio mapping. All authors have read and agreed to the published version of the manuscript.

**Funding:** L.D. and A.G. acknowledge the support of the Department of Atomic Energy, Government of India, under project identification # RTI 4002. A.G. is grateful for the financial support and hospitality of the Pauli Center for Theoretical Studies and the University of Zurich. S.Z. acknowledge the grant NCN 2018/29/B/ST9/01793. R.H. acknowledges support by GACR grant 13-33324S and by the MSMT Mobility project 8J18AT036.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Kari Nilsson for a valuable contribution in data reduction and producing one of the figures. We also appreciate the help that Vilppu Piirola has provided and continues to provide in optical polarisation observations of OJ 287. We also thank Gene Byrd and Shirin Haque for reading the manuscript and for valuable inputs.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


### *Article γ***-ray Flux and Spectral Variability of Blazar Ton 599 during Its 2021 Flare**

**Bhoomika Rajput \* and Ashwani Pandey**

Indian Institute of Astrophysics, Block II Koramangala, Bangalore 560034, India; ashwanitapan@gmail.com **\*** Correspondence: bhoomikarjpt2@gmail.com

**Abstract:** Blazars are known to emit exceptionally variable non-thermal emission over the wide range (from radio to *γ*-rays) of electromagnetic spectrum. We present here the results of our *γ*-ray flux and spectral variability study of the blazar Ton 599, which has been recently observed in the *γ*-ray flaring state. Using 0.1–300 GeV *γ*-ray data from the *Fermi* Gamma-ray Space Telescope (hereinafter *Fermi*), we generated one-day binned light curve of Ton 599 for a period of about one-year from MJD 59,093 to MJD 59,457. During this one year period, the maximum *γ*-ray flux detected was 2.24 <sup>±</sup> 0.25 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ph cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> at MJD 59,399.50. We identified three different flux states, namely, epoch A (quiescent), epoch B (pre-flare) and epoch C (main-flare). For each epoch, we calculated the *γ*-ray flux variability amplitude (F*var*) and found that the source showed largest flux variations in epoch C with F*var* ∼ 35%. We modelled the *γ*-ray spectra for each epoch and found that the Log-parabola model adequately describes the *γ*-ray spectra for all the three epochs. We estimated the size of the *<sup>γ</sup>*-ray emitting region as 1.03 <sup>×</sup> <sup>10</sup><sup>16</sup> cm and determined that the origin of *<sup>γ</sup>*-ray radiation, during the main-flare, could be outside of the broad line region.

**Keywords:** galaxies; active; galaxies–quasars; individual (Ton 599)

### **1. Introduction**

Blazars are the jetted subclass of the Active Galactic Nuclei (AGNs) that are understood as AGNs with very small viewing angles to the line of sight [1,2]. Blazars emit broadband electromagnetic radiation that ranges from radio to extremely high *γ*-ray energies. The jets of blazars are highly Doppler boosted, resulting in flux variations over the entire accessible electromagnetic wavebands. Flat spectrum radio quasars (FSRQs) and BL Lacertae (BL Lacs) objects are the two subclass of blazars. The difference between these subclasses is determined by the equivalent width (EW) of the emission lines in their optical spectra, with FSRQs having EW > 5 Å and BL Lacs having EW < 5 Å [3]. A more physical criterion for distinguishing between FSRQs and BL Lacs was proposed by [4] which is based on the ratio of broad line region (BLR) luminosity (*LBLR*) to Eddington Luminosity (*LEdd*). FSRQs have the value *<sup>L</sup>BLR*/*LEdd* <sup>&</sup>gt; <sup>5</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> , whereas BL Lacs have the value *<sup>L</sup>BLR*/*LEdd* <sup>&</sup>lt; <sup>5</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> .

The broad-band spectral energy distributions (SEDs) of blazars comprise of two humps; the low energy hump and the high energy hump. The low energy hump peaks at optical/UV/X-ray region and the high energy hump peaks at MeV/GeV/TeV region [5–7]. The genesis of the low energy hump is well understood through synchrotron emission mechanism of the relativistic electrons, while the high energy hump originates through inverse Compton (IC) emission process [6]. Based on the position of the synchrotron peak frequency (*νsyn*), blazars are further classified as low synchrotron peaked (LSP; *νsyn* < 10<sup>14</sup> Hz), intermediate synchrotron peaked (ISP; 10<sup>14</sup> Hz < *νsyn* < 10<sup>15</sup> Hz) and high synchrotron peaked (HSP; *νsyn* > 10<sup>15</sup> Hz) blazars.

Due to the Doppler boosting in blazars' jets, the observed emission *Sobs* relative to the emission in the co-moving frame *Sint* is defined as e.g., [8]

$$S\_{\rm obs} = S\_{\rm int} \delta^q \tag{1}$$

Flux and Spectral Variability of Blazar Ton 599 during Its 2021 Flare. *Galaxies* **2021**, *9*, 118. https://doi.org/ 10.3390/galaxies9040118

**Citation:** Rajput, B.; Pandey, A. *γ*-ray

Academic Editor: Santanu Mondal

Received: 15 November 2021 Accepted: 10 December 2021 Published: 13 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

where *q* = 3 + *α* for a moving compact source and *q* = 2 + *α* for a stationary jet [9]. *α* is the spectral index which is defined as *f<sup>ν</sup>* ∝ *ν* −*α* . *δ* is the Doppler boosting factor which is described as *δ* = 1/Γ(1 − *β*cos*θ*), where Γ is bulk Lorentz factor (Γ = 1/(1 − *β* 2 ) 1/2), *β* is the speed of jet in units of the speed of light and *θ* is the viewing angle between observer's line of sight and jet's axis. The observed time is also shortened by the effect of Doppler boosting by a factor *δ* −1 . These two consequences of the Doppler boosting increase the chances of observed variations in blazars over a wide range of wavelengths and make them the brightest objects in the extragalactic sky.

The study of flux variability is a valuable tool for determining the size of the emission zone in blazars. Blazars exhibit variability over a wide range of timescales, from few minutes to several years, across the full wavelength range i.e., from radio to *γ*-rays [10–14]. The variability in blazars can be explained by the shock-in-jet model [15]. In this scenario, the inhomogeneities in the jet flow produce relativistic shocks. These shocks travel through the jet plasma at relativistic speed and accelerate the particles. The other scenario is the magnetic reconnection, which is responsible for the rapid variations in blazar jets and has been investigated extensively in recent years [16–19]. Within the reconnection region, magnetic reconnection possibly enables small-scale ultra-relativistic flow, also called jet-injet scenario [16,19,20]. The ultra-relativistic motion of small plasmoids causes additional Doppler boosting and results in very short and bright flares.

The launch of *Fermi* Telescope in 2008 gave us an unprecedented opportunity to explore the *γ*-ray regime in blazars. Using *Fermi* data at *γ*-ray energies, flux doubling time scales have been detected as short as few minutes in both FSRQs and BL Lacs [14,21–23]. Causality considerations in these circumstances point to highly compact *γ*-ray emission zones in blazars' jets. The detection of *γ*-ray photons with energy greater than 10 GeV in FSRQs leads to the conclusion that the *γ*-ray emission region should be located at outside the cavity formed by the broad emission line (BLR) [24]. Otherwise, pair production on UV photons emitted by (BLR) clouds should severely attenuate the *γ*-ray photons. Despite several studies, the physics of *γ*-ray variability in blazars is still a captivating subject of research.

Ton 599 (4FGL J1159.5 + 2914; [25]) is an FSRQ, located at redshift z = 0.725 [26] with R.A. = 11*h*59*m*31.8*<sup>s</sup>* and Dec. = +29◦14043.800. Ton 599 is a strongly polarized and a highly optically violent variable quasar [27]. It was first detected in high energy *γ*rays by the Energetic Gamma Ray Experiment Telescope (EGRET) in the second EGRET catalogue [28] and later by the *Fermi* Large Area Telescope (*Fermi*-LAT) [29]. The correlation study between radio and *γ*-ray bands was carried out by [30] for this source to put the constraints on *γ*-ray emission region in parsec-scale jets. In 2017, for the first time, Ton 599 went through a protracted flaring condition spanning the full electromagnetic spectrum. During this flare, the maximum *<sup>γ</sup>*-ray flux observed was 1.26 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ph cm−<sup>2</sup> s −1 [31]. The detailed study of *γ*-ray flux variability during this flare was carried out by [31,32]. A multiwavelength study and the broad-band SED modelling of this flare was conducted by [33] using a two-component leptonic emission model. An EC mechanism with a dusty torus (DT) photon field producing seed photons was identified to be responsible for the GeV emission in this study. Ton 599 recently displayed a bright flare from July to September 2021, allowing us to investigate its *γ*-ray emission process and its consequences during this source's flaring condition.

In this paper, we describe the *γ*-ray analysis performed on the source Ton 599 utilising data collected over a one-year period from September 2020 to August 2021, with the goal of constraining the *γ*-ray emission region in blazars. The data used in this study is presented in Section 2. Section 3 describes the *γ*-ray light curve, followed by results in Section 4 and discussion in Section 5. Section 6 presents a summary of the results.

### **2.** *γ***-ray Observations and Data Reduction**

In this work, we used the *γ*-ray observations of Ton 599 taken by the *Fermi*-LAT for a period of ∼1 year, from 2020 September to 2021 August (MJD: 59,093–59,457). *Fermi*-LAT is a pair-conversion *γ*-ray telescope that can detect *γ* rays with energies ranging from 20 MeV to more than 1 TeV. It has a large field of view of about 2.4 sr and scans the full sky in every 3 h, covering 20% of the sky at any time [34]. We used the package ScienceTools v1.2.23 with the instrument response function P8R3\_SOURCE\_V3<sup>1</sup> for our analysis. We used the latest LAT Pass 8 data in the energy range 100 MeV to 300 GeV, where the photon-like events are classified as 'evclass = 128, evtype = 3'. The region of interest (ROI) is specified as a circle with a radius of 10◦ and is centred on the *γ*-ray position of the source. We used a maximum zenith angle of 90◦ to remove *γ*-ray contamination from the earth's limb. The latest isotropic model 'iso\_P8R3\_SOURCE\_V3\_v1' and the Galactic diffuse emission model 'gll\_iem\_v07' were used to analyze the data. The recommended condition '(DATA QUAL > 0)&&(LAT CONFIG= = 1)' was then used to construct the required good time intervals. Over the time period of interest, an unbinned likelihood analysis is performed to generate the 1-day binned *γ*-ray light curve of Ton 599. In the light curve, the source was considered to be detected if the test statistics (TS) > 9, which corresponds to a 3*σ* detection [35]. Our final one-day binned *γ*-ray light curve contains 256 confirmed measurements of Ton 599.

### **3.** *γ***-ray Light Curve**

The one-day binned *γ*-ray light curve of Ton 599 from 2020 September to 2021 August (MJD: 59,093–59,457) is shown in Figure 1. For the entire period of the light curve, we estimated the average *<sup>γ</sup>*-ray flux which was found to be 0.43 <sup>±</sup> 0.36 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ph cm−<sup>2</sup> s −1 . Based on the average *γ*-ray flux, we visually identified three different flux states, namely, quiescent state, pre-flaring state, and the main flaring state, which were labelled as epoch A, epoch B, and epoch C, respectively. The duration of these epochs are marked by vertical lines in Figure 1 and the details of these epochs are given in Table 1. We classified epoch A as a quiescent epoch since the flux was lower than the average flux for the whole time span. During epochs B and C, the flux increased 2–3 times than the average flux, so we classified these epochs as flaring epochs. Over the whole time span of the light curve, the value of the flux was maximum during the flaring epoch C. The value of the maximum flux was determined to be 2.24 <sup>±</sup> 0.25 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ph cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> at MJD 59,399.50.

**Table 1.** The epochs considered for the *γ*-ray light curve study are listed in the table below. Here, *N*, *x*¯, and *Fvar* denote the total number of data points, the average *γ*-ray flux, and the fractional variability amplitude, respectively, for the epoch. The *γ*-ray flux is in the units of 10−<sup>6</sup> ph cm−<sup>2</sup> s −1 .


**Figure 1.** One-day binned *γ*-ray light curve of Ton 599 (**upper panel**) with the TS values corresponding to each flux value (**lower panel**) . The vertical black lines refer to the quiescent epoch (Epoch A), whereas vertical blue lines refer to the *γ*-ray flaring epochs (Epoch B and Epoch C). In the upper panel the horizontal cyan line represents the average flux from September 2020 to August 2021.

### **4. Results**

### *4.1. γ-ray Flux Variability*

We used the fractional variability amplitude (*Fvar*) to characterize the flux variability properties of Ton 599. The *Fvar* is commonly used to quantify the intrinsic variations in blazar light curves and is defined as, e.g., [12,36,37]

$$F\_{\text{var}} = \sqrt{\frac{S^2 - \overline{\sigma\_{err}^2}}{\mathfrak{x}^2}} \tag{2}$$

In the above equation *S* 2 is the sample variance and *σ* 2 *err* is mean square error. These are defined as

$$S^2 = \frac{1}{N-1} \sum\_{i=1}^{N} (\mathbf{x}\_i - \bar{\mathbf{x}})^2 \tag{3}$$

and

$$
\overline{\sigma\_{err}^2} = \frac{1}{N} \sum\_{i=1}^{N} \sigma\_{err,i}^2 \tag{4}
$$

Here *N* is the total number of data points in the light curve and *x*¯ is the arithmetic mean of the light curve.

The uncertainty in *Fvar* is given by the following equation

$$err(F\_{var}) = \sqrt{\left(\sqrt{\frac{1}{2N}} \frac{\overline{\sigma\_{err}^2}}{\overline{\pi}^2 F\_{var}}\right)^2 + \left(\sqrt{\frac{\overline{\sigma\_{err}^2}}{N} \frac{1}{\overline{\pi}}}\right)^2} \tag{5}$$

For each epoch, we calculated the value of *Fvar* separately by considering the average flux (*x*¯) and the data points (*N*) within the epoch only. The values of *N*, *x*¯, and *Fvar* for each epoch are listed in Table 1. The errors calculated using Equation (5) are given in Table 1. For epoch A, the error in the value of *Fvar* is relatively large which also indicates that it is a quiescent state. We considered the source to be variable in epochs if *Fvar* > 3 × *err*(*Fvar*). According to our criteria for variations, the source was not variable in epoch A (quiescent state), while significant *γ*-ray flux variations were noticed during epochs B and C with *Fvar* values of 22% and 35%, respectively.

### *4.2. γ-ray Spectral Fitting*

We modeled the *γ*-ray spectrum of Ton 599 for each epoch to investigate the inherent distribution of electrons that causes the *γ*-ray emission during the epoch. We used the power-law (PL) and the log parabola (LP) models to fit the *γ*-ray spectra of Ton 599 using the maximum likelihood analysis. The PL model is defined as follows [38]:

$$\frac{dN(E)}{dE} = N\_\circ \left(\frac{E}{E\_\circ}\right)^\Gamma \tag{6}$$

where *N*◦ is the prefactor (normalization of the energy spectrum), *E*◦ is the pivot energy (∼523.51 MeV) given in the 4FGL catalog, and Γ is the photon index, while, the LP model is given by

$$\frac{dN(E)}{dE} = N\_\circ \left(\frac{E}{E\_b}\right)^{-\alpha - \beta \ln\left(\frac{E}{E\_b}\right)}\tag{7}$$

In this equation *N*◦ is the normalization, *E<sup>b</sup>* is the pivot energy (same as in PL), *α* is photon index at *E<sup>b</sup>* and *β* is the curvature index that defines the curvature of the spectrum around the peak.

For each epoch, the model fitted *γ*-ray spectra of Ton 599 is shown in Figure 2, and the values of best fitted model parameters are given in Table 2. In Figure 2, the uncertainties are large at higher energies because of relatively low photon counts at these energies.

**Table 2.** Details of the PL and LP model fits for the three epochs. Here, *γ*-ray flux is in the units of 10−<sup>6</sup> ph cm−<sup>2</sup> s −1 .


To determine whether the *γ*-ray spectrum has a curvature or not, and which model (LP or PL) best describes the *γ*-ray spectrum of Ton 599, we calculated *TScurve* (curvature of the test statistics) [38], which is defined as:

$$TS\_{curve} = \mathcal{Z}(\log L\_{LP} - \log L\_{PL}) \tag{8}$$

In the above equation, *L* represents the likelihood function. The value of *TScurve* for each epoch is given in Table 2. We employed the *TScurve* > 16 threshold (i.e., 4*σ* level; [35]) to determine the presence of statistically significant curvature in the *γ*-ray spectrum. We found that the LP model best describes the *γ*-ray spectra of Ton 599 for all three epochs.

**Figure 2.** *γ*-ray spectrum for the epochs (**A**–**C**). The name of the epoch is mentioned in each plot.

### *4.3. Location of the γ-ray Emission Region*

To determine the size of the *γ*-ray emitting region, the flux doubling time scale is usually estimated, e.g., [31,39]. We calculated the flux doubling time scale for the one-day binned *γ*-ray light curve during the main-flaring epoch (epoch C) of Ton 599 as follows:

$$F(t\_2) = F(t\_1) \times 2^{\Delta t/\tau\_d} \tag{9}$$

In the above expression, *F*(*t*1) and *F*(*t*2) are the flux values at times *t*<sup>1</sup> and *t*<sup>2</sup> respectively, ∆*t* = *t*<sup>2</sup> − *t*<sup>1</sup> and *τ<sup>d</sup>* represents the flux doubling time.

We found a flux doubling timescale of ∼13.2 h during the epoch C for the blazar Ton 599. Using the flux doubling time scale, we estimated the size of the *γ*-ray emitting region for Ton 599 using the following expression:

$$r \le c\tau\_d \delta / (1+z) \tag{10}$$

A gamma-ray Doppler factor of delta = 12.5 was calculated for Ton 599 by [40] using the multiwavelength data and the known radio Doppler factors with the assumption that the observed boosted emission is from the SSC model. This value is consistent with the lower limits (10.75 and 13.45) of delta obtained for the two bright flares of Ton 599 by [32]. Using *<sup>δ</sup>* = 12.5, the size of the *<sup>γ</sup>*-ray emission region is estimated to be 1.03 <sup>×</sup> <sup>10</sup><sup>16</sup> cm.

According to [41], the location of the *γ*-ray emission region with respect to the central super massive black hole (SMBH) can be approximated by using the relation R = r/*φ*, where r is the size of the *γ*-ray emitting blob and *φ* is the jet opening angle.

An intrinsic opening angle of 0.58◦ (∼0.01 radian) was determined for Ton 599 by [42]. They estimated the jet opening angles for Fermi detected AGNs using 15.4 GHz Very Long

Baseline Array (VLBA) observations following two different methods: (a) by analyzing transverse jet profiles in the image plane and (b) by model fitting the data in the (u, v) plane. Using these values of *r* and *φ*, the location of the *γ*-ray emitting region for Ton 599 was found to be at 1.03 <sup>×</sup> <sup>10</sup><sup>18</sup> cm from the SMBH.

### **5. Discussion**

In this section we give our interpretation of the findings of above-mentioned analyses, as well as a discussion of them.

### *5.1. γ-ray Flux Variability*

In the *γ*-ray band, blazars exhibit remarkable flux variability. For all the three epochs of the source Ton 599, we estimated the flux variability amplitude using one-day binned light curves. We found that during the main-flaring epoch (epoch C), the source showed largest variations with *Fvar* = 0.35 ± 0.03. During the pre-flaring epoch (epoch B), the source was also variable with *Fvar* = 0.22 ± 0.04 and during the quiescent epoch (epoch A), the source was not significantly variable (*Fvar* = 0.36 ± 0.12) within the error bar. During the main-flare (epoch C), the source showed a maximum flux of 2.24 <sup>±</sup> 0.25 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ph cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> at MJD 59,399.50, which is larger than the maximum flux observed during the 2017 flare [31]. We found that the photon index value is 1.99 ± 0.10 during the main-flaring epoch (epoch C), when flux is highest, harder than the 4FGL value of 2.19 ± 0.01.

The observed *γ*-ray variability in the blazars could be attributed to both intrinsic and extrinsic factors. The distribution of relativistic electrons responsible for the emission is one of the intrinsic effects. These relativistic electrons, which can be accelerated to a Lorentz factor of up to 10<sup>6</sup> , are responsible for non-thermal emission from blazar jets via synchrotron or inverse Compton emission processes. The distribution of these relativistic electrons and seed photon responsible for the inverse Compton emission process (synchrotron self Compton (SSC); [15,43] and external Compton (EC); [44,45]) are the intrinsic factors that cause short-term variability in jets. Extrinsic factors, such as the moving blob's high bulk Lorentz factor (Γ) ∼ 50, are in addition to intrinsic factors. Though the large bulk Lorentz factor is a favourable explanation in the case of BL Lacs, because the seed photons come from inside the jets and produce *γ*-rays through inverse Compton. On the other hand, the seed photons in FSRQ, emanate from outside the jets and produce *γ*-rays. However, pair-production through dense broad line region (BLR) can attenuate *γ*-ray emission. As a result, in the case of FSRQs, the large bulk Lorentz factor that causes *γ*-ray variability is not a plausible explanation [46]. The *γ*-ray flux variability in blazars jets can be explained by the magnetic reconnection (jet-in-jet) scenario, in which the mini jets generated in the jets can have a large bulk Lorentz factor and they can produce *γ*-ray flux variability on short time scale [16,19].

### *5.2. γ-ray Spectra*

For each epoch, we modelled the *γ*-ray spectra of Ton 599 using the power law and the log parabola models. We used the *TScurve* value to determine the best fitted model. Based on the *TScurve* value, we found that the LP model best describes the *γ*-ray spectra of Ton 599 during all the three epochs indicating that the GeV *γ*-ray spectrum of Ton 599 is curved.

FSRQs usually have a curved GeV *γ*-ray spectrum, e.g., [47–49]. Several theories have been proposed, in the literature, to explain the curved *γ*-ray spectra of FSRQs. The attenuation of *γ*-ray photons by pair-production (inside the BLR) could explain the curved *γ*-ray spectrum [50]. A viable scenario for defining the curve in the *γ*-ray spectrum is the Klein-Nishina effect on the inverse Compton scattering of BLR photons through relativistic electrons present in the jet [51]. However, several investigations conducted to locate the *γ*-ray emission region discovered that the observed *γ*-ray spectra in FSRQs are not caused by IC scattering of BLR photons and that the *γ*-ray emission site is located outside the BLR [19,52]. The curved *γ*-ray spectra of FSRQs could also be explained by the curved energy distribution of the electrons emitting the radiation [53,54].

### *5.3. Location of the γ-ray Emitting Region*

We calculated the minimum *γ*-ray flux doubling timescale of 13.2 h during epoch C for Ton 599. Using this minimum doubling timescale, we estimated the size of the *γ*-ray emitting region as 1.03 <sup>×</sup> <sup>10</sup><sup>16</sup> cm. We have also identified the location of the *<sup>γ</sup>*-ray emitting blob to be at a distance of 1.03 <sup>×</sup> <sup>10</sup><sup>18</sup> cm from the SMBH. The size of the BLR for TON 599 was estimated as <sup>∼</sup>(2.11–2.45) <sup>×</sup> <sup>10</sup><sup>17</sup> cm by [32]. So, the location of the *<sup>γ</sup>*-ray emitting blob, found in this work, is outside of the BLR. During the 2017 *γ*-ray flare of this source, using two component leptonic model, Ref. [33] found that the seed photons for the GeV emission produced by the dusty torus (DT) and the GeV emitting region is located outside of the BLR. Our results are consistent with the findings of [33].

### **6. Summary**

We investigated the *γ*-ray flux and spectral variability of the blazar Ton 599 during MJD 59,093 to MJD 59,457. For our study, we have chosen three epochs of different flux states: quiescent, pre-flaring, and main-flaring. The outcomes of the analysis of these epochs are summarised below.


**Author Contributions:** Conceptualization, B.R.; Data curation, B.R. and A.P.; Formal analysis, B.R.; Investigation, B.R.; Project administration, A.P.; Resources, B.R.; Visualization, B.R.; Writing—original draft, B.R.; Writing—review & editing, A.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data used in this work is publicly available from the Fermi-LAT data archive https://fermi.gsfc.nasa.gov/ssc/data/access/, accessed on 1 September 2021.

**Acknowledgments:** We thank the anonymous referees for their constructive comments, which helped us to improve the manuscript. This publication made use of data from the *Fermi* Gamma-ray Space Telescope, which accessed from the Fermi Science Support Center. We also acknowledge the use of High Performance Computing Facility (Nova cluster) at Indian Institute of Astrophysics.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Note**

<sup>1</sup> https://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/, accessed on 1 September 2021.

### **References**


### *Article* **The Radiative Newtonian 1** < *γ* ≤ **1.66 and the Paczy ´nski–Wiita** *γ* = **5/3 Regime of Non-Isothermal Bondi Accretion onto a Massive Black Hole with an Accretion Disc**

**Jose M. Ramírez-Velásquez 1,**<sup>∗</sup> **, Leonardo Di G. Sigalotti <sup>2</sup> , Ruslan Gabbasov <sup>3</sup> , Jaime Klapp <sup>4</sup> and Ernesto Contreras <sup>5</sup>**


**Abstract:** We investigate the non-isothermal Bondi accretion onto a supermassive black hole (SMBH) for the unexplored case when the adiabatic index is varied in the interval 1 < *γ* ≤ 1.66 and for the Paczy´nski–Wiita *γ* = 5/3 regime, including the effects of X-ray heating and radiation force due to electron scattering and spectral lines. The X-ray/central object radiation is assumed to be isotropic, while the UV emission from the accretion disc is assumed to have an angular dependence. This allows us to build streamlines in any desired angular direction. The effects of both types of radiation on the accretion dynamics is evaluated with and without the effects of spectral line driving. Under line driving (and for the studied angles), when the UV flux dominates over the X-ray heating, with a fraction of UV photons going from 80% to 95%, and *γ* varies from 1.66 to 1.1, the inflow close to the gravitational source becomes more supersonic and the volume occupied by the supersonic inflow becomes larger. This property is also seen when this fraction goes from 50% to 80%. The underestimation of the Bondi radius close to the centre increases with increasing *γ*, while the central overestimation of the accretion rates decreases with increasing *γ*, for all the six studied cases.

**Keywords:** black hole evolution; supermassive black hole; accretion of matter; galaxies: evolution; galaxies: nuclei

### **1. Introduction**

Observations of giant elliptic galaxies provide firm evidence of the presence of supermassive black holes (SMBHs) in their centres [1,2], which accrete matter from the surroundings and liberate enormous amounts of energy that affect their environments from pc to Mpc scales (see [3] for spherically symmetric black holes with quantum corrections). In particular, the mass accretion rate onto these SMBHs, which is a key quantity to understand the galactic evolution, is usually estimated using Bondi accretion theory [4]. However, semi-analytic calculations and numerical simulations based on the Bondi accretion model do not provide information about the flow transport down to pc and sub-pc scales and the mass accretion rates (e.g., [5–8]). Since active galactic nuclei (AGNs) evolve concomitantly with their host galaxies, they affect each other. For example, good evidence for this kind of feedback has been provided by observations of AGN-starbursts [9]. On the other hand, the energy released during accretion onto a SMBH can hinder further accretion and drive the gas away, which in turn self-regulates the galaxy growth [10].

**Citation:** Ramírez-Velásquez, J.M.; Sigalotti, L.D.G.; Gabbasov, R.; Klapp, J.; Contreras, E. The Radiative Newtonian 1 < *γ* ≤ 1.66 and the Paczy ´nski–Wiita *γ* = 5/3 Regime of Non-Isothermal Bondi Accretion onto a Massive Black Hole with an Accretion Disc. *Galaxies* **2021**, *9*, 55. https://doi.org/10.3390/galaxies 9030055

Academic Editor: Dimitris M. Christodoulou

Received: 11 May 2021 Accepted: 9 August 2021 Published: 11 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

An earlier study on the structure of X-ray-irradiated accretion discs in AGNs was considered by the authors of [11]. They found that the irradiated region above and below the disc consists of a region which is supported by the radiation pressure where the UV flux is created and a warmer thin layer above this region, which is optically thin to the UV radiation. In the last years, studies of flows in AGNs with the inclusion of radiation source terms have become progressively more consistent [12–17]. All of these studies were able to compute cooling and heating functions, which are important to produce the correct opacities in these environments, and new methodologies were proposed to properly include the coupling between matter and radiation. Winds and accretion processes are of primary importance to improve our understanding of the feedback between the galaxy and its guest SMBH [18–23] and therefore on the galactic evolution [24–27]. Photoionization calculations of radiative forces due to spectral lines (i.e., [15]) have also shown the importance of a proper treatment of the coupling between matter and radiation along with the influence of the non-LTE effects (i.e., [28]).

Much effort has been devoted to study the dynamical evolution of the system in terms of the accretion rates onto a SMBH from the numerical solution of the hydrodynamics equations, where a common assumption has been to fix the boundary conditions at infinity as it is indeed required by the classical Bondi solution. However, an inconvenience with this approach is that when exploring the dynamics close to the black hole, this boundary conditions may fail to represent the finiteness of the spatial region under study. Several calculations of accretion processes with an ideal equation of state with different values of the adiabatic index (*γ*; in full symmetric and axisymmetric configurations in relativistic contexts e.g.; [29–35]) show it playing an important role in the estimation of the mass supply in cosmological simulations [21,36,37], and so does the exploration of the effects of varying the adiabatic index on the AGN accretion dynamics. In this paper we extend the analysis of [38] and present solutions for the radial Mach number and density profiles along with the critical points of transonic solutions for the radiative, radial accretion of matter in the potential well of a SMBH for adiabatic indices in the range 1.1 ≤ *γ* ≤ 1.66. It is found that variations of the adiabatic index may change the whole dynamics of the system as well as the mass supply. The methodology employed is detailed in Section 2 and the results are described in Section 3. A catalogue of pure absorption lines for 1.1 ≤ *γ* ≤ 1.66 is given in Section 4. Estimates of the Bondi radius and mass accretion rate as functions of the adiabatic index are given in Section 5. Finally, Section 6 summarizes the relevant conclusions.

### **2. Non-Isothermal Radial Bondi Accretion**

Under the effects of irradiation by X rays, the accretion flow onto the central SMBH is described by the mass and momentum conservation laws

$$\frac{d\rho}{dt} = -\rho \nabla \cdot \mathbf{v}\_{\prime} \tag{1}$$

$$\frac{d\mathbf{v}}{dt} = -\frac{1}{\rho}\nabla p + \mathbf{g} + \mathbf{F}^{\text{rad}},\tag{2}$$

where *ρ* denotes the density, **v** the velocity field, *p* the gas pressure, **g** the gravitational acceleration due to the SMBH, **F** rad = (*F<sup>r</sup>* , *F<sup>θ</sup>* = 0, *F<sup>φ</sup>* = 0) the radiation force per unit mass, and *d*/*dt* = *∂*/*∂t* + **v** · ∇ the material time derivative. Using spherical coordinates and assuming that the angular components of the velocity vanish (i.e., *v<sup>θ</sup>* = *v<sup>φ</sup>* = 0), Equation (2) can be written as

$$\frac{\partial v\_r}{\partial t} + v\_r \frac{\partial v\_r}{\partial r} = -\frac{1}{\rho} \frac{\partial p}{\partial r} - \frac{\partial}{\partial r} \psi\_{\text{grav}}(r) + \frac{\partial}{\partial r} \psi\_{\text{rad}}(r), \tag{3}$$

for the radial velocity component, where *v<sup>r</sup>* = *vr*(*r*, *θ*, *φ*), *p* = *p*(*r*, *θ*, *φ*), *M*BH is the mass of the SMBH, and *ψ*rad(*r*) is a function defined below. If we further assume azimuthal symmetry (i.e., *∂*/*∂φ* = 0) and perform the analysis for a fixed angle *θ*0, such that *vr*(*r*, *θ*, *φ*) = *vr*(*r*, *θ*0) = *v<sup>r</sup>* and *p*(*r*, *θ*, *φ*) = *p*(*r*, *θ*0) = *p*, the above equation becomes

$$\frac{d\mathcal{H}(r)}{dr} = p\frac{d}{dr}\left(\frac{1}{\rho}\right) - \frac{\partial v\_r}{\partial t},\tag{4}$$

where

$$\mathcal{H}(r) = \frac{p}{\rho} + \frac{1}{2}v\_r^2 - \psi\_{\text{grav}}(r) - \psi\_{\text{rad}}(r) \tag{5}$$

is the Bernoulli function H(*r*), *ψ*grav = (*GM*BH)/*r* and *ψ*rad = −*C*(*r*)/*r* are the gravitational and radiation potentials, respectively. Compared to the analysis of [38], a radial dependence is now assumed for the term *C* in the definition of the radiation potential. For simplicity the accretion disc is assumed to be flat, Keplerian, geometrically thin and optically thick. The pressure is related to the density by means of an ideal equation of state

$$p = \frac{k\_B \rho T}{\mu m\_p} = p\_\infty \mathfrak{p}^\gamma,\tag{6}$$

where *k<sup>B</sup>* is the Boltzmann constant, *T* is the gas temperature, *µ* is the mean molecular weight, and *m<sup>p</sup>* is the proton mass. Here *γ* is varied in the range 1 ≤ *γ* < 5/3 and *ρ*˜ ≡ *ρ*/*ρ*∞, where *p*<sup>∞</sup> and *ρ*<sup>∞</sup> are the values of the pressure and density at infinity, respectively. The sound speed is defined according to

$$c\_s^2 = \frac{\gamma p}{\rho}.\tag{7}$$

The radiative contributions in Equations (2) and (4) are here implemented using the strategies used by [13,39–41] (hereafter P07). Although the radiation field from both the disc and the central black hole are modelled as in P07 by adding a radiation force in the momentum equation, there are important differences with P07 that are worth commenting. For instance, in P07 the analysis is based on time-dependent, axisymmetric simulations with *γ* = 5/3, while our analysis consists of steady-state calculations along radial streamlines for fixed *θ* and varying values of the adiabatic index in the interval 1 . *γ* < 5/3. These calculations have been designed to serve as initial conditions for fully three-dimensional simulations of accretion discs [42]. As in P07, the disc is assumed to emit only UV light (i.e., *f*disc = *f*UV) and the central SMBH to emit only X-rays (i.e., *f*? = *f*<sup>X</sup> = 1 − *f*disc) so that the disc and central luminosities are given by *L*disc = *f*disc*L* and *L*? = *f*?*L*, respectively, where *L* is the total accretion luminosity. The radial component of the radiation force is approximated according to the relation (e.g., P07)

$$F\_{r\_{\rm rad}}(r, \theta\_0) = \frac{\sigma\_T L}{4\pi r^2 c m\_p} [f\_\star + 2 \cos \theta\_0 f\_{\rm disk} (1 + M(r, t))] \,\tag{8}$$

where *c* is the speed of light in vacuum, *σT*/*m<sup>p</sup>* is the mass scattering coefficient for free electrons, *θ*<sup>0</sup> is some fixed and constant polar angle measured from the rotational axis of the disk, and *t* is the optical depth

$$t = \frac{(\sigma\_T / m\_p) \rho v\_{\rm th}}{|dv\_r / dr|},\tag{9}$$

where *v*th is the thermal velocity (set using a temperature of 25,000 K), *dvr*/*dr* is the velocity gradient along the radial direction, and *M*(*r*, *t*) is the so-called force multiplier [43], defined by

$$M(r,t) = kt^{-\alpha} \left[ \frac{(1+\tau\_{\text{max}})^{(1-\alpha)} - 1}{\tau\_{\text{max}}^{(1-\alpha)}} \right],\tag{10}$$

where *α* = 0.6 is the ratio of optically thick to optically thin lines. According to [44], the parameter *k* is given by the minimun between

$$k = 0.03 + 0.385 \exp\left(-1.4 \xi^{0.6}\right),\tag{11}$$

and

$$\log k = \begin{cases} -0.383, & \text{for } \log T \le 4, \\ -0.630 \log T + 2.138, & \text{for } 4 < \log T \le 4.75, \\ -0.870 \log T + 17.528, & \text{for } \log T > 4.75, \end{cases} \tag{12}$$

which is based on detailed photoionization calculations performed using the XSTAR code (P07), while *τ*max = *tη*max with

$$\log \eta\_{\text{max}} = \begin{cases} 6.9 \exp\left(0.16 \xi^{0.4}\right), & \text{if } \log \xi \le 0.5, \\ 9.1 \exp\left(-7.96 \times 10^{-3} \xi\right), & \text{if } \log \xi > 0.5. \end{cases} \tag{13}$$

where *ξ* is the photoionization parameter. The parameter *η*max defined by Equation (13) is used to determined the maximum force multiplier, i.e., *M*max = *k*(1 − *α*)*η α* max. The local X-ray flux

$$\mathcal{F}\_X = \frac{L\_\star}{4\pi r^2} \exp(-\tau\_X),\tag{14}$$

is used to estimate the photoionization parameter *ξ* = 4*π*F*X*/*n*, where

$$
\pi\_{\mathbf{X}} = \int\_0^r \kappa\_{\mathbf{X}} \rho dr,\tag{15}
$$

is the X-ray optical depth, evaluated between the centre (*r* = 0) and a radius *r* in the accreting flow, and *n* = *ρ*/(*µmp*) is the number density of the accreting gas. The absorption coefficient *κ<sup>X</sup>* is set to 0.4 g−<sup>1</sup> cm<sup>2</sup> for all values of *ξ*.

The *γ* = 5/3 regime of non-isothermal Bondi accretion is modelled using the Paczy ´nski– Wiita (PW) potential [45,46]

$$
\psi\_{\rm grav} = \frac{GM\_{\rm BH}}{r - R\_s}'\tag{16}
$$

where *R<sup>s</sup>* = 2*GM*BH/*c* 2 is the gravitational radius of the black hole. While this pseudo-Newtonian potential does not obey the Poisson equation, it has become a standard tool because it accurately models the general relativistic accretion of matter onto a nonrotating SMBH. In particular, this form of the potential reproduces the radii of a marginally stable Keplerian orbit (*r* = 3*Rs*) and of a marginally bound orbit (*r* = 2*Rs*) as predicted by Einstein's gravity in the Schwarzschild metric [46].

Under the assumption of steady-state motion, Equations (4) and (5) can be combined to produce after a few algebraic steps the integral equation

$$\int \frac{d}{dr} \left( \frac{\mathcal{M}^2 \tilde{c}\_s^2}{2} + \frac{\tilde{\rho}^{(\gamma - 1)}}{\gamma - 1} - \frac{1}{\mathfrak{x}} + \frac{I\_{\text{tot}}^{\text{rad}}|\_{\theta = \theta\_0}(\mathfrak{x})}{\mathfrak{x}} \right) dr = 0,\tag{17}$$

where

$$\infty \equiv \frac{r}{r\_B}, \quad \mathcal{E}\_\mathbf{s} \equiv \frac{c\_\mathbf{s}}{c\_\infty} = \not{\mathfrak{p}}^{(\gamma - 1)/2}, \quad \mathcal{M} \equiv \frac{v\_r}{c\_\mathbf{s}} \,\tag{18}$$

and

$$l\_{\rm tot}^{\rm rad}|\_{\theta = \theta\_0}(\boldsymbol{\pi}) = l\_{\rm Edd}^{\rm rad} f\_{\rm rad}|\_{\theta = \theta\_0}(\boldsymbol{\pi}). \tag{19}$$

Here *C*|*θ*=*θ*<sup>0</sup> (*x*) = *GM*BH*l* rad tot |*θ*=*θ*<sup>0</sup> (*x*),

$$r\_B = \frac{GM\_{\rm BH}}{c\_{\infty}^2} \,\prime \tag{20}$$

is the Bondi radius, *c* 2 <sup>∞</sup> = *γp*∞/*ρ*∞, M is the Mach number, *l* rad Edd = *L*/*L*Edd with *<sup>L</sup>*Edd <sup>=</sup> <sup>4</sup>*πcGM*BH*mp*/*σ<sup>T</sup>* being the Eddington luminosity, *<sup>σ</sup><sup>T</sup>* <sup>=</sup> 6.6524 <sup>×</sup> <sup>10</sup>−<sup>25</sup> cm<sup>2</sup> is the Thomson cross section, and *f*rad|*θ*=*θ*<sup>0</sup> (*x*) is the radiative force parameter given by the relation

$$f\_{\rm rad}|\_{\theta=\theta\_0}(\mathbf{x}) = f\_\star + 2\cos\theta\_0 f\_{\rm disk} [1 + M(\mathbf{x}, t)].\tag{21}$$

Although the force multiplier is an explicit function of *x* and *t*, for simplicity hereafter we omit the *x*-dependence and write it as *M*(*t* = *τ*).

Equation (17) can be integrated to give

$$\rho^{(\gamma - 1)} \left( \frac{\mathcal{M}^2}{2} + \frac{1}{\gamma - 1} \right) = \frac{1}{\mathfrak{x}} - \frac{l\_{\text{tot}}^{\text{rad}}|\_{\theta = \theta\_0}(\mathfrak{x})}{\mathfrak{x}} + \frac{1}{\gamma - 1}. \tag{22}$$

This equation describes the non-isothermal (*γ* > 1), steady-state accretion along a radial streamline for a fixed angle *θ* = *θ*<sup>0</sup> when the effects of radiation emission due to electron scattering and spectral discrete lines with appropriate boundary conditions at infinity and ionization changes due to temperature corrections are considered. A sketch showing the geometry of the system is displayed in Figure 1, where a radial streamline at a meridional angle *θ*<sup>0</sup> is shown. In terms of the above assumptions and the normalized parameters (18), Equation (1) becomes

$$
\alpha^2 \mathcal{M} \mathfrak{gl}^{(\gamma+1)/2} = \lambda\_\prime \tag{23}
$$

where *λ* is the accretion parameter given by

$$
\lambda = \frac{\dot{M}\_B}{(4\pi f\_{\text{solid}})r\_B^2 \rho\_{\infty} c\_{\infty}},
\tag{24}
$$

which determines the accretion rate for given boundary conditions and mass of the SMBH. In this expression, 4*π f*solid = R sin *θdθdφ* is the solid angle covered by the streamline at the polar angle *θ*<sup>0</sup> (see Figure 1). When *f*solid = 1 (full solid angle), Equation (24) reduces to the classical accretion parameter. However, for a *θ*0-dependent force *f*solid << 1. This dependence is important only for the final calculation of *M*˙ *<sup>B</sup>* = *λ*(4*π f*solid)*r* 2 *B ρ*∞*c*∞, which is fixed once the value of *θ*<sup>0</sup> is chosen. Replacing *ρ*˜ from Equation (23) into Equation (22), the radiative-radial Bondi problem reduces to solving the equation

$$\mathbf{g}(\mathcal{M}) = \Lambda f(\mathbf{x}), \quad \text{with} \quad \Lambda = \lambda^{2(1-\gamma)/(\gamma+1)}, \tag{25}$$

where *χ* rad tot |*θ*=*θ*<sup>0</sup> = 1 − *l* rad tot |*θ*=*θ*<sup>0</sup> , *λ* = *χ* rad tot | 2 *θ*=*θ*<sup>0</sup> *λ*cr, and

$$\lg(\mathcal{M}) \quad = \; \mathcal{M}^{2(1-\gamma)/(\gamma+1)} \Big( \frac{\mathcal{M}^2}{2} + \frac{1}{\gamma-1} \Big)\_{\cdot} \tag{26}$$

$$f(\mathbf{x}) = \mathbf{x}^{4(\gamma - 1)/(\gamma + 1)} \left( \frac{\chi\_{\text{tot}}^{\text{rad}}|\_{\theta = \theta\_0}}{\mathbf{x}} + \frac{1}{\gamma - 1} \right),\tag{27}$$

$$
\lambda\_{\rm cr} = \frac{1}{4} \left( \frac{2}{5 - 3\gamma} \right)^{(5 - 3\gamma)/[2(\gamma - 1)]} \quad . \tag{28}
$$

**Figure 1.** Model geometry. (**a**) Integration is performed along a radial streamline for a fixed meridional angle *θ*0. (**b**) The full angular dependence can be obtained by integrating along different radial streamlines.

For this case Equations (17)–(27) remain the same with the only change being the substitution of *x* by *x* − *x<sup>s</sup>* , where *<sup>x</sup><sup>s</sup>* <sup>=</sup> *<sup>R</sup>s*/*rB*. Here we take *<sup>R</sup>s*/*r<sup>B</sup>* <sup>=</sup> 1.75 <sup>×</sup> <sup>10</sup>−<sup>5</sup> for the calculations of Figure <sup>2</sup> and 2.18 <sup>×</sup> <sup>10</sup>−<sup>6</sup> for the rest of the calculations. The radiative Bondi-like problem then reduces to solving Equations (25)–(28) for the Mach number, M, as a function of radius. On the other hand, it must be noticed that the PW potential, in addition to reproducing the innermost stable circular orbit and the marginally bound orbit, also accounts for a non-vanishing critical radius for *γ* = 5/3, in contrast to the purely Newtonian radial accretion, for which

$$\mathbf{x}\_{\text{crit}} = \mathbf{x}\_{\text{s}} + \sqrt{\frac{2\chi\_{\text{total}}^{\text{rad}}\mathbf{x}\_{\text{s}}}{\mathfrak{Z}}},\tag{29}$$

✡

where now the factor *χ* rad total (>0) appears, which is not present in [38,47].

**Figure 2.** (**Left**) Angular dependence of the UV emission for models *M*1,2,3 and *M*? 1,2,3. The horizontal black solid line at *χ* rad tot = 0 mark the transition from type 5 to types 1 and 2 solutions. (**Right**) Mach number as a function of radius for model *M*? 1 and *γ* = 1 (analytical solution; orange curves), *γ* = 1.1 (numerical solution from [38] with *ψ*rad = −*C*/*r*; gray curves, and this work with *C* = *C*(*r*); green curves), *γ* = 3/2 (blue curves), *γ* = 1.55 (black curves), *γ* = 1.66 (magenta curves) and *γ* = 5/3 (non-radiative (NR), with *<sup>x</sup><sup>s</sup>* <sup>=</sup> 2.5 <sup>×</sup> <sup>10</sup>−<sup>3</sup> ; red curves). The thick solid curves represent supersonic inflow (*x* < *xs*) and outflow (*x* > *xs*) solutions, while the dashed lines represent inflow and ourflow subsonic solutions.

✑

The angular variation of the UV emission, *χ* rad tot , for models with and without the force multiplier is shown in the top panel of Figure 2. Model *M*<sup>1</sup> has *f*? = 0.5 and *f*disc = 0.5, model *M*<sup>2</sup> has *f*? = 0.2 and *f*disc = 0.8, while model *M*<sup>3</sup> has *f*? = 0.05 and *f*disc = 0.95, with *M*(*τ*) = 0 so that both types of radiation can be evaluated in detail. Models *M*? 1 , *M*? 2 , and *M*? 3 differ from the preceding models in that *M*(*τ*) 6= 0. For different fractions of *f*?, *f*disc, and position *x*, we estimate the critical angles for which a transition from type 5 to type 1 and 2 solutions is allowed<sup>1</sup> . This plot, which corresponds to *ρ*˜ = 0.001, *x* = 3, and *γ* = 1.55, is an example of the complexity of the system. In particular, *M*? 2 (green line with empty squares) and *M*? 3 (red line with full triangles) have physical transonic solutions for *θ* > *π*/8, while model *M*? 1 (blue line with empty circles) does not admit solutions for which *χ* rad tot < 0, and so this flow can be seen in any angular direction. The transition for *M*? 2 occurs at a lower angle than for *M*? 3 , meaning that we should find more collimated streamlines for the *M*? 2 flows than for the *M*? 3 flows. It is interesting to see that model *M*1, for which only electron scattering is present (*M*(*τ*) = 0) and *f*? = *f*disc = 0.5, behaves like model *M*? <sup>1</sup> with no transition to the unphysical region where *χ* rad tot < 0. As the fraction of disc photons increases (i.e., from *f*disc = 0.8 to 0.95), critical angles for which unphysical type 5 solutions occur (for *θ* phase *M*2,3 < *π*/8) are found even when only electron scattering is dominating.

In both sets of models *M*1,2,3 and *M*? 1,2,3, the radiation acceleration depends on the ionization parameter defined as

$$\mathfrak{F} = \frac{(f\_{\star}L)\exp\left(-\tau\_{\mathbf{X}}\right)}{n r^{2}},\tag{30}$$

where *<sup>L</sup>* <sup>=</sup> 7.45 <sup>×</sup> <sup>10</sup><sup>45</sup> erg s−<sup>1</sup> , which is appropriate for a <sup>10</sup>8*<sup>M</sup>* SMBH accreting at an efficiency of 8%. The gas density is *n*(*x*) = (*ρ*∞*ρ*˜(*x*))/(*µmp*) cm−<sup>3</sup> , with *ρ*<sup>∞</sup> = 10−<sup>20</sup> gr cm−<sup>3</sup> , *µ* = 0.7, and the optical depth *τ<sup>X</sup>* is integrated using Equation (15) with *κ<sup>X</sup>* = 0.4 g −1 cm<sup>2</sup> . The physical parameters for all models computed in this study are listed in Table 1 (a full analysis of the angular dependence is beyond the scope of the present work, and will be presented in a forthcoming paper). In all cases we choose *θ*<sup>0</sup> = *θ* phase acc . The fractions *f*? and *f*disc in Table 1 are exactly the same used by P07, which comply with observational results from [49,50].

**Table 1.** Parameters of the accretion models.


(a) *<sup>M</sup>*(*t*) <sup>6</sup><sup>=</sup> <sup>0</sup> (yes) and *<sup>M</sup>*(*t*) = <sup>0</sup> (no). (b) The values of *<sup>γ</sup>* <sup>=</sup> {1.1, 1.2, 1.3, 13/9, 3/2, 1.53, 1.55, 1.63, 1.65, 1.66}. (c) The angle *θ* phase acc is given in terms of *θ* phase, i.e., *θ* phase acc = 1.1*θ* phase. All models *M*? <sup>∗</sup> and *<sup>M</sup>*<sup>∗</sup> shared the same angle.

The bottom panel of Figure 2 shows the dependence of the Mach number of the inflow and outflow transonic solutions with the normalized radial distance from the black hole for model *M*? 1 and various characteristic values of the adiabatic index, namely *γ* = 1 (full analytical solution; orange curves), *γ* = 1.1 (numerical solution from [38] with *ψ*rad = −*C*/*r*; gray curves, and this paper with *ψ*rad = −*C*(*r*)/*r*; green curves), *γ* = 3/2 (blue curves), *γ* = 1.55 (black curves), *γ* = 1.66 (magenta curves), and *γ* = 5/3 (red curves). Note that the latter curves correspond to the PW model with no radiation, i.e., with *f*? = *f*disc = 0. The intersection of curves of the same colour define the position of the sonic point (*xs*). The thick solid curves for *x* < *x<sup>s</sup>* represent supersonic inflow solutions, while those at larger radii (i.e., *x* > *xs*) represent supersonic outflow solutions. The dashed curves at radii *x* > *x<sup>s</sup>* are subsonic inflow solutions and those for *x* < *x<sup>s</sup>* are subsonic outflow solutions. The Mach number profiles are shown up to radial distances of <sup>≈</sup>10−3.1*r<sup>B</sup>* from the centre. It is evident from this figure that isothermal (*γ* = 1) inflow occurs at slightly higher values of Macc(*r*) than its non-isothermal counterparts. As the adiabatic index is increased the accretion rate occurs at relatively smaller values of the Mach number everywhere and closer to the central source so that the region of supersonic accretion involves progressively smaller central volumes as *γ* increases. In contrast, the isothermal outflow takes place at much lower Mach numbers compared to the non-isothermal cases. These differences are clearly expected to influence the rates for non-isothermal accretion. As the adiabatic index is increased above *γ* = 3/2 the outflow close to *x* = 10−<sup>3</sup> becomes supersonic only when *γ* = 1.66 and keeps subsonic for all values <1.66. In the interval 0.01 . *x* . 0.1, the outflow proceeds supersonically for all non-isothermal cases (*γ* > 1) with a small dependence of the Mach number on *γ*, while towards larger *x*(&0.2) the outflow becomes more supersonic as the adiabatic index is increased.

### **3. Results**

The Mach number as a function of distance from the source is shown in the top panel of Figure 3 for model *M*? 1 and varied *γ*. The solid curves depict the inflow solutions, while the dotted lines with arrows correspond to the outflow solutions. In all cases, the complete subsonic and supersonic solutions are shown. The position of the sonic point, *x*crit, is defined by the intersection between the inflow and the outflow solutions. When matching the subsonic portion of the solution at *x* ≤ *x*crit with the supersonic one at *x* > *x*crit, we then obtain the "Bondi-outflow" solution. The difference with the Parker solution is the location of the integration limits in the Bernoulli equation. In the Bondi problem they are located at infinity, while in the Parker problem they are located at the base of the wind. For all models, the Bondi outflows are always depicted by dotted lines with small arrows pointing out of the system. On the other hand, when matching the subsonic part of the solution at *x* > *x*crit with the supersonic one at *x* ≤ *x*crit, we then obtain the "Bondi-inflow" solution. Increased values of *γ* produce slower inflows and faster outflows everywhere, while the position of the sonic point is shifted towards smaller radii. The left panel of Figure 4 shows a close comparison of the Mach number profiles between the Newtonian *γ* = 1.66 case with spectral line forces (gray curves) and the *γ* = 5/3 case with *M*(*τ*) = 0 (orange curves). For *M*(*τ*) 6= 0 the inflow and outflow Mach number profiles essentially overlap those for the Newtonian *γ* = 1.66 case with *M*(*τ*) 6= 0 regardless of the radiation field. In spite of differences in the value of *M*(*τ*), the inflow and outflow profiles for both cases look almost identical.

Figure 3 (right panel) displays the Mach number as a function of radius for model *M*? 2 and varied *γ*. Compared to the left panel of Figure 3, we see that increasing the fraction of UV emission (from *f*? = 0.5 to 0.2) increases the inflow Mach number everywhere, while the position of the sonic point is shifted towards larger radii. Consequently, for given *γ*, when the ionizing flux decreases faster inflows are produced everywhere. In particular, at small radii *x* . 0.01 the inflow becomes more supersonic. A similar trend is observed for model *M*? <sup>3</sup> with the weakest X-ray heating (*f*? = 0.05) and the strongest UV emission (*f*disc = 0.95), where the sonic point is moved farther away compared to model *M*? 2 and therefore the supersonic inflow close to the centre occupies a larger volume. A comparison of the right panel of Figure 4 with that of left panel shows that as the UV heating dominates over the X-ray luminosity, the (*<sup>γ</sup>* <sup>=</sup> 5/3) inflow becomes faster than the *<sup>γ</sup>* <sup>=</sup> 1.66 <sup>−</sup> *<sup>M</sup>*? 1 inflow. It is interesting to note that the increase of the UV emission from *f*disc = 0.8 to *f*disc = 0.95 has only mild effects on the inflow and outflow Mach number profiles as well. The Mach number profiles for models *M*<sup>1</sup> and *M*<sup>2</sup> with no force multiplier (i.e., *M*(*τ*) = 0) and varied *γ* are now displayed in Figure 3 (right), respectively. The profiles for model *M*<sup>3</sup> are very similar to those shown in Figure 3 for model *M*2. For model *M*1, where the central X-ray heating is the strongest and no line driving is present, the solution does

not admit type 5 flows regardless of the incident angle. As shown in Figure 3 (bottom) the critical points occur far from the central source between *x* ≈ 0.2 (for *γ* = 1.1) and *<sup>x</sup>* <sup>≈</sup> 0.007 (for *<sup>γ</sup>* <sup>=</sup> 1.66). These distances are relatively similar to those found for model *<sup>M</sup>*? 1 with force multiplier. For *θ*<sup>0</sup> = <sup>3</sup> 8 *<sup>π</sup>* and close to the SMBH (*<sup>x</sup>* <sup>≈</sup> <sup>10</sup>−<sup>3</sup> ), the Mach number ranges from ≈1 (for *γ* = 1.66) to ≈8 (for *γ* = 1.1). When the fraction of UV emission is increased to *f*disc = 0.8, the position of the sonic point is shifted outwards so that the flow becomes supersonic in a larger central volume as can be seen by comparing bottom with top. However, model *M*<sup>2</sup> is characterized by smaller supersonic volumes than model *M*3. Similarly to the cases with force multiplier, as the UV emission is increased, the flow close to the central black hole becomes more supersonic. Moreover, for *γ* = 1.66 models *M*<sup>2</sup> and *M*<sup>3</sup> both exhibit outflows that are slower at large radii (*x* > 1) than their Bondi-inflow counterparts close to the central source, while the inverse is seen to occur for larger *γ*.

**Figure 3.** (**Top**) Radial Mach number profiles of the inflow (solid lines) and outflow (dotted lines with arrows) solutions for model (**a**) *M*? <sup>1</sup> with *M*(*τ*) 6= 0 and (**b**) *M*<sup>1</sup> with *M*(*τ*) = 0, *f*? = 0.5, *f*disc = 0.5, and varied *<sup>γ</sup>* in the interval 1.1 <sup>≤</sup> *<sup>γ</sup>* <sup>≤</sup> 1.66. (**Bottom**) (**c**) *<sup>M</sup>*? <sup>2</sup> with *M*(*τ*) 6= 0 and (**d**) *M*<sup>2</sup> with *M*(*τ*) = 0, *f*? = 0.2, *f*disc = 0.8.

**Figure 4.** Comparison of the Mach number profiles between the Newtonian (*γ* = 1.66) case with spectral line forces and the (*γ* = 5/3) case with *M*(*τ*) = 0.

For all models the density profiles are similar and almost independent of the adiabatic index. In all cases the density increases for *<sup>x</sup>* . 0.1 from <sup>≈</sup>(1−7) to values as high as <sup>≈</sup>10<sup>3</sup> when the UV emission rises from *f*disc = 0.5 to *f*disc = 0.95 for models with *M*(*τ*) 6= 0. In contrast, when *M*(*τ*) = 0 the highest central densities are seen to occur for model *M*<sup>1</sup> with *<sup>ρ</sup>*˜ <sup>≈</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>2</sup> at *<sup>x</sup>* <sup>=</sup> <sup>10</sup>−<sup>3</sup> , while models *M*<sup>2</sup> and *M*<sup>3</sup> with stronger UV emission and weaker central X-ray heating reach central densities of ≈1000 at the same radial distance from the SMBH, respectively. Additionally, in these cases the density profiles show a very little dependence on the adiabatic index. It is clear from the present results that the flow dynamics are sensitive to the radiative process that dominates the environment.

### **4. Catalogue of Pure Absorption Spectral Line Shapes for 1.1** ≤ *γ* ≤ **1.66**

As resolution improves with the emergence of more powerful telescopes, it becomes mandatory to predict the shape of absorption spectral lines as seen by a distant observer. This can be done by imagining a radially falling atom onto the SMBH according to the predictions of models *M*? 1,2,3, which would absorb photons emitted by the inner region at 10 in the rest-frame. Then we use the Doppler-shift formula [51]:

$$w = \frac{w\_0}{\gamma L (1 - \frac{\mathbf{v}(x)}{c} \cos \phi)},\tag{31}$$

where *w* is the angular frequency of an emitted photon with rest-frame frequency *w*<sup>0</sup> as measured by the observer, *γL* is the Lorentz factor, v(*x*) is the velocity of the absorbing atom, and *φ* is the angle between the streamline and the line-of-sight towards the observer, which we set to *φ* = 0. For falling particles we set v(*x*) = −M(*x*)*c*s, where *c*<sup>s</sup> is given by Equation (7)<sup>2</sup> , for values of <sup>≈</sup>360, 420, 430, 440, and <sup>420</sup> km s−<sup>1</sup> . A simple description of the absorption spectrum is given by

$$F\_{\lambda}(\mathbf{x}) = \exp\left\{-A(\mathbf{x})\exp\left[-\frac{\left(\lambda(\mathbf{x}) - \lambda\_0\right)^2}{\sigma^2}\right]\right\},\tag{32}$$

where *ν*0*λ*<sup>0</sup> = *w*0/(2*π*)*λ*<sup>0</sup> = *c*, *σ* is given by 0.1%*λ*(*x*), *c* is the speed of light, and *λ*<sup>0</sup> is the photon wavelength in the rest frame. The intensity of the absorption is modelled by setting *<sup>A</sup>*(*x*) = *<sup>ρ</sup>*(*x*)/*ρ*max, where *<sup>ρ</sup>*(*x*) = *<sup>ρ</sup>*˜(*x*)*ρ*<sup>∞</sup> and *<sup>ρ</sup>*max <sup>=</sup> *<sup>ρ</sup>*˜(*<sup>x</sup>* <sup>=</sup> <sup>3</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> )*ρ*∞. As the particle is getting closer and closer to the black hole, the density increases and the shape of the spectral line tends to have a deeper deep shifted towards the red. Figure 5 depicts the predicted accretion absorption line shape for models *M*? 1 , *M*? 2 , and *M*? <sup>3</sup> with varied values of *γ*. From this figure, it is clear that the most asymmetrical lines are for model *M*? 3 corresponding to *f*? = 0.05, for which the high-energy radiation is weaker making the particle to attain higher velocities and therefore more asymmetry. Telescopes with higher resolutions will be needed to resolve the asymmetry of these lines. As the UV emission dominates over the X-ray heating the absorption lines become broader, while they become narrower with increasing *γ* regardless of the radiation field. For *γ* = 1.1 the symmetry is enough to distinguish which source of radiation is dominant with a resolution of <sup>≈</sup>2500 km s−<sup>1</sup> . However, as *γ* increases this property is lost as changes in the fraction of UV heating from *f*disc = 0.5 to 0.95 cannot be easily distinguished from the shape of the spectral absorption lines.

**Figure 5.** Absorption line shapes as predicted for models *M*? 1 , *M*? 2 , and *M*? <sup>3</sup> with varied adiabatic indices in the range 1.1 ≤ *γ* ≤ 1.66. The solid red lines depict the profiles of a typical absorption line for an atom falling off onto a black hole.

✠

✠

### **5. Estimated Bondi Radius and Mass Accretion with Respect to Conditions at Infinity**

We are now in the position to quantify the ratio between the estimated (*re*) and the true (*rB*) values of the Bondi radius and that between the estimated (*M*˙ *<sup>e</sup>*) and the true (*M*˙ rad) accretion rates when the boundary conditions are not at infinity. These ratios are given as functions of the radial distance from the SMBH by the following relations

$$\frac{r\_{\varepsilon;\{\text{acc,out}\}}(\mathbf{x})}{r\_B} = \left(\frac{\mathbf{x}^2 \mathcal{M}\_{\{\text{acc,out}\}}}{\lambda}\right)^{2(\gamma - 1)/(\gamma + 1)}\,,\tag{33}$$

✠

$$\frac{\dot{M}\_{\varepsilon;\{\text{acc,out}\}}(\mathbf{x})}{\dot{M}\_{\text{rad}}} = \frac{1}{\chi\_{\text{tot}}^{\text{rad}}|\_{\theta=\theta\_0}^2} \left[ \frac{r\_{\varepsilon;\{\text{acc,out}\}}(\mathbf{x})}{r\_B} \right]^{-(5-3\gamma)/[2(\gamma-1)]},\tag{34}$$

respectively, where *χ* rad tot (*θ*, *x*) is the angle- and space-dependent radiative factor. Figure 6 (left) shows the estimated Bondi radii for model *M*? 1 for adiabatic indices between *γ* = 1.1 and 1.66. At small radial distances (*<sup>x</sup>* <sup>=</sup> <sup>8</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> ), model *M*? <sup>1</sup> with *γ* = 1.1 has an estimated Bondi radius of *re*/*r<sup>B</sup>* ≈ 0.50. As the adiabatic index is increased, the ratio *re*/*r<sup>B</sup>* decreases reaching values slightly less than 0.5 for *<sup>γ</sup>* <sup>=</sup> 1.1 and as low as <sup>≈</sup>0.03 for *<sup>γ</sup>* <sup>=</sup> 1.66 at *<sup>x</sup>* <sup>=</sup> <sup>10</sup>−<sup>2</sup> . The same trends are also seen for models *M*? 2 (see Figure 6 (right)) and *M*? 3 as *γ* is increased, except that now the estimated Bondi radii achieve slightly lower values as the radiation field is dominated by the UV emission from the accretion disc. The profiles for model *M*? 3 are very similar to those displayed in Figure 6 with the ratios *re*/*r<sup>B</sup>* achieving slightly smaller values close to the centre. For all models regardless of the adiabatic index the ratio *re*/*r<sup>B</sup>* → 1 at large radii (*x* = 3).

Figure 7 shows the estimated accretion rates for models *M*? 1 , and *M*? 2 , for varied values of *γ*. When the UV emission is increased from *f*disc = 0.8 to 0.95 for model *M*? 3 the trends are almost the same as those in Figure 7 (right) for model *M*? 2 . In all cases, the radiative effects lead to an overestimation of the accretion rates for *x* . 0.1 (model *M*? 1 ) and *x* . 0.12 (models *M*? 2 and *M*? 3 ). The differences between *M*˙ *<sup>e</sup>*(*x*) and *M*˙ rad grow rapidly as we get closer to the central source. However, the rapid growth of the ratio *M*˙ *<sup>e</sup>*(*x*)/*M*˙ rad towards

the centre becomes progressively less steep as *γ* is increased, with *M*˙ *<sup>e</sup>*(*x*)/*M*˙ rad becoming almost flat for *γ* = 1.66. For instance, model *M*? 1 has an accretion rate at *x* = 10−<sup>2</sup> for *γ* = 1.1 that is about 100 times larger than for *γ* = 1.66. A similar difference between both values of *γ* happens when comparing models *M*? 2 and *M*? 3 , where the UV emission from the disc dominates over the incident X-ray flux. The observed large overestimations in the estimated accretion rates make sense because as the closer the accreting matter is to the source of gravitation, the less accurate are the determination of *ρ* and *c*<sup>s</sup> from their values at infinity. However, the authors of [38] found that the level of overestimation of the accretion rates compared to the classical Bondi problem is slightly attenuated when the effects of line driving are ignored (model *M*<sup>1</sup> with *γ* = 1.1). The same is true for higher values of *γ*.

**Figure 6.** (**Left**) Estimated Bondi radii for model *M*? <sup>1</sup> with *<sup>M</sup>*(*τ*) <sup>6</sup><sup>=</sup> 0. (**Right** *<sup>M</sup>*? <sup>2</sup> with *M*(*τ*) 6= 0), *f*? = 0.5(0.2) and *f*disc = 0.5(0.8) for varied values of the adiabatic index in the range 1.1 ≤ *γ* ≤ 1.66. The vertical solid lines mark the position of the sonic point and the symbols on them identify to which inflow solution they correspond to.

**Figure 7.** (**Left**) Estimated accretion rates for model *M*? <sup>1</sup> with *<sup>M</sup>*(*τ*) <sup>6</sup><sup>=</sup> <sup>0</sup> (**Right** *<sup>M</sup>*? <sup>2</sup> with *M*(*τ*) 6= 0), *f*? = 0.5 and *f*disc = 0.5 for varied values of the adiabatic index in the range 1.1 ≤ *γ* ≤ 1.66. The vertical solid lines mark the position of the sonic point and the symbols on them identify to which inflow solution they correspond to.

### **6. Conclusions**

In this paper, we have investigated the non-isothermal Bondi accretion onto a supermassive black hole (SMBH) when the adiabatic index is varied in the interval 1.1 ≤ *γ* ≤ 1.66 by including the effects of X-ray heating and UV emission. The radiation field is modelled using the prescriptions introduced by [13] (P07), where a central SMBH is considered as a source of X-ray heating and a surrounding optically thick, geometrically thin, standard accretion disc as a source of UV radiation. The radiative, non-isothermal radial accretion is solved semi-analytically using a method similar to that developed by the authors of [41]. The X-ray heating from the SMBH is assumed to be isotropic, while the UV emission from the accretion disc is assumed to have an angular dependence. The effects of both types of radiation are studied for different flux fractions (*f*? and *f*disc) and an incident angle

*θ*<sup>0</sup> = *θ* phase acc in the presence and absence of the effects of spectral line driving. The *γ* = 5/3 regime is also explored using the Paczy´nski–Wiita (PW) potential for the case when the effects of line driving are ignored.

The relevant conclusions are summarized as follows:


**Author Contributions:** Conceptualization, J.M.R.-V. and L.D.G.S.; methodology, J.M.R.-V., L.D.G.S. and E.C.; software, J.M.R.-V.; formal analysis, J.M.R.-V., L.D.G.S. and J.K.; validation, J.M.R.-V., L.D.G.S., J.K., R.G. and E.C.; writing—review and editing, J.M.R.-V., L.D.G.S., J.K., R.G. and E.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been partially supported by Yachay Tech under the project for the use of the supercomputer QUINDE I and by UAM-A through internal funds. One of us (J. K.) acknowledges financial support from CONACYT under grant 283151.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The code to reproduce the average h*ξ*i calculations underlying this article are available in Zenodo at doi:10.5281/zenodo.4075323. For the new varying *ξ*, it will be available under request to the corresponding author.

**Acknowledgments:** IMPETUS is a collaboration project between the ABACUS-Centro de Matemática Aplicada y Cómputo de Alto Rendimiento of Cinvestav-IPN, the School of Physical Sciences and Nanotechnology of the Yachay Tech University, and the Área de Física de Procesos Irreversibles of the Departamento de Ciencias Básicas of the Universidad Autónoma Metropolitana–Azcapotzalco (UAM-A) aimed at the SPH modelling of astrophysical flows.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Notes**


### **References**


### *Article* **Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime**

**Sanjar Shaymatov 1,2,3,4,5,\* and Farruh Atamurotov 3,6**


**Abstract:** We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with Ω*r*<sup>ˆ</sup> , Ω*ϕ*<sup>ˆ</sup> , and Ω*ω*<sup>ˆ</sup> in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact extra spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur in the allowed region when particles move along the black string. We find that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. Interestingly we also find that isofrequency pairing of geodesic orbits in the region of parameter space cannot be realized beyond the critical value J*cr* ≈ 0.096 of the conserved quantity of the motion arising from the compact extra spatial dimension.

**Keywords:** isofrequency; geodesic orbits; black string

### **1. Introduction**

In general relativity, black holes are regarded as one of the most interesting and fascinating objects due to their geometric and remarkable gravitational properties. However, the point to be noted is that their existence had been predicted as a potential tool in explaining observational phenomena until the discovery of the gravitational waves detected by LIGO and Virgo scientific collaborations [1,2] and as well as the first direct shadow of supermassive black hole at the center of galaxy 87 by the Event Horizon Telescope (EHT) collaboration [3,4]. These observations opened a qualitatively new stage to reveal black hole's unknown properties and test remarkable nature of the background geometry around black hole's horizon irrespective of the fact that there are still fundamental problems that general relativity faces, i.e., the occurrence of singularity, spacetime quantization, etc. In this framework, the motion of test particles in the strong gravitational field regime has been a productive field of study for several years [5–19]. On the other hand, there is an extensive body of work devoted to understand the nature of radiative inspirals around black holes as a source of gravitational waves and binary systems [20–28].

It is worth noting that experiments and observations always allow to test the nature of the geometry through alternative theories of modified gravity in the strong field regime. The spactime geometry that can depart from the spherically symmetric Schwarzschild black hole was considered by Grunau and Khamesra [29]. This spacetime metric describes a five dimensional black string due to the compact extra dimension added to the well known Schwarzschild metric. Thus, it is one of reasons why this solution is interesting object to

**Citation:** Shaymatov, S.; Atamurotov, F. Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime . *Galaxies* **2021**, *9*, 40. https://doi.org/10.3390/ galaxies9020040

Received: 21 April 2021 Accepted: 25 May 2021 Published: 28 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

investigate its properties. The motion of test particles in the different gravity string models has been investigated thoroughly by several authors [30–35]. Furthermore, the geodesic motion of test particles in the black string spacetime for both rotating and non-rotating cases has been studied in detail [29]. The geodesic motion of colliding particles was also studied in the vicinity of black string spacetime [36].

The theoretical investigation of isofrequency pairing of geodesic circular orbits has been considered in the vicinity of Schwarzschild and Kerr black holes, i.e., the region of the parameter space where such geodesic orbits occur has been discussed by providing an intuitive explanation of their occurrence. The above investigation was addressed by taking an external asymptotically uniform magnetic field in the Schwarzschild spacetime [25]. It turns out that the surface of allowed region where isofrequency pairing orbits occur decreases as a consequence of the presence of the external magnetic field. It was later extended to the spinning particles in the Schwarzschild-de Sitter spacetime [26]. In the present paper, we consider isofrequency pairing of geodesic orbits around black string spacetime geometry, as shown by the line element in [29]. We then study the effect of the compact extra spatial dimension *ω* on the isofrequency pairing of geodesic spiral orbits sharing the same three orbital frequencies.

In this paper, we consider a new frequency Ω*ω*<sup>ˆ</sup> arisen from the compact extra spatial dimension associated with the motion in the extra direction along the black string. Generally, the bound orbits are confined to the interior of a compact special spiral given by *<sup>h</sup>z*1(*<sup>e</sup>* <sup>=</sup> <sup>0</sup>) <sup>≤</sup> *<sup>h</sup><sup>z</sup>* <sup>≤</sup> *<sup>h</sup>z*2(*<sup>e</sup>* <sup>=</sup> <sup>1</sup>); frequencies, in particular, <sup>Ω</sup>*r*<sup>ˆ</sup> and <sup>Ω</sup> <sup>ˆ</sup>*<sup>θ</sup>* are considered as "libration"-type frequencies associated with the radial and longitudinal periods, while Ω*ϕ*<sup>ˆ</sup> is a "rotation"-type frequency. In the case of black string, new frequency Ω*ω*<sup>ˆ</sup> can be defined by a "libration-rotation" type frequency which involves two kinds of type frequencies, as described above. For the sake of clarity, we will further focus on the motion of test particles at the equatorial plane (i.e., *θ* = *π*/2), and hence we omit Ω <sup>ˆ</sup>*<sup>θ</sup>* as it loses its meaning. Then bound geodesic orbits around black string spacetime are respectively characterized by three orbital frequencies, i.e., Ω*r*<sup>ˆ</sup> , Ω*ϕ*<sup>ˆ</sup> , and Ω*ω*<sup>ˆ</sup> associated with the periodic motions. Thus, these orbits are considered as triperiodic orbits around the black string spacetime. In doing so we predict that an infinite number of pairs of such orbits may occur in a region of parameter space around the black string spacetime where physically distinct orbits possessing <sup>E</sup>, <sup>L</sup>, and <sup>J</sup> share the same orbital frequencies associated with <sup>Ω</sup>*ϕ*<sup>ˆ</sup> , Ω*r*<sup>ˆ</sup> , and Ω*ω*<sup>ˆ</sup> , thereby referring to the "isofrequency" bound geodesic orbits synchronized in phase *ϕ* while passing periastra at the same time. Isofrequency pairing of geodesic orbits occuring in the vicinity of black string spacetime may in principle play an important role in an astrophysical scenario in understanding the nature of radiative inspirals around black holes.

The paper is organised as follows: In Section 2 we briefly describe the metric for black string and provide the geodesic equations of motion. We further study the effect of the compact extra dimension on the isofrequency pairing of geodesic spiral orbits in Section 3. We end up with conclusion in Section 4. Throughout the paper we use a system of geometric units in which *G* = *c* = 1.

### **2. The Metric and the Geodesic Equations of Motion**

The metric describing five dimensional black string spacetime with the compact extra spatial dimension *ω* added to the Schwarzschild metric in the Boyer-Lindquist coordinates (*t*,*r*, *θ*, *ϕ*, *ω*) is given by [29]

$$\begin{split} ds^2 &= -\left(1 - \frac{2M}{r}\right)dt^2 + \left(1 - \frac{2M}{r}\right)^{-1}dr^2 \\ &\quad + r^2(d\theta^2 + \sin^2 d\varphi^2) + d\omega^2 \end{split} \tag{1}$$

with *M* being the total mass of black string and *ω* corresponding to the compact extra spatial dimension.

The radial motion of geodesic test particles in the equatorial plane of black string spacetime satisfies the following equation

$$
\dot{\tau}^2 = \mathcal{E}^2 - V\_{eff}(r; \mathcal{L}, \mathcal{J}) \, , \tag{2}
$$

where

$$N\_{eff}(r; \mathcal{L}, \mathcal{I}) = \left(1 - \frac{2M}{r}\right) \left(1 + \mathcal{J}^2 + \frac{\mathcal{L}^2}{r^2}\right),\tag{3}$$

with E = *E*/*m*, L = *L*/*m*, and J = *J*/*m* being the conserved constants per unit mass and related to the particle's specific energy, angular momentum, and conserved quantity arising from *ω*, respectively.

It is well known that bound orbits exist in the case when L > 2 √ 3*M* with 2 √ 2/3 < E < 1 for the Schwarzschild black hole. Whereas, in the case of black string, bound orbits only exist when L > 2 √ 3(1 + J 2 ) 1/2*M* with 2 √ 2(1 + J 2 ) 1/2/3 <sup>&</sup>lt; <sup>E</sup> <sup>&</sup>lt; (<sup>1</sup> <sup>+</sup> <sup>J</sup> 2 ) 1/2 is satisfied, and the motion of particles is then restricted by the turning points being labeled as the periastron *r*<sup>p</sup> and the apastron *r*a, respectively.

We now consider the innermost stable circular orbit (ISCO) for test particles orbiting around black string spacetime. To find radii of the ISCO one needs to solve the following equation

$$W\_{eff}^{\prime\prime}(r; \mathcal{L}, \mathcal{J}) = 0 \,. \tag{4}$$

In our case *rISCO* can be determined implicitly from the condition

6L 2 (*r* − 4*M*) − 4(1 + J 2 )*Mr*<sup>2</sup> = 0 , (5)

with L obtained on solving *V* 0 *e f f*(*r*; L, J ) = 0. Thus, we have the ISCO radius *rISCO* = 6*M* for black string spacetime. It is worth noting that the ISCO is the same in contrast for the Schwarzschild black hole.

The standard condition *Ve f f*(*rp*,L, J ) = *Ve f f*(*ra*,L, J ) = E 2 leads to the specific energy E and angular momentum L of the particle, given in terms of *p* and *e*. Here, *r<sup>p</sup>* = *Mp*/(1 + *e*) and *r<sup>a</sup>* = *Mp*/(1 − *e*) respectively refer to the periastron and the apastron [25]. In between these two turning points lies bound orbits with corresponding specific energy and angular momentum. Note that parameters *p* and *e* respectively measure the size of the orbit and its degree of noncircularity [37]. Then we have

$$\mathcal{L}^2 = \frac{(p - 2 - 2e)(p - 2 + 2e)}{p(p - 3 - e^2)}(1 + \mathcal{J}^2),$$

$$\mathcal{L}^2 = \frac{p^2 M^2}{p - 3 - e^2}(1 + \mathcal{J}^2). \tag{6}$$

Following Cutler et al. [38], we turn to the integration of the geodesic equations in terms of *t*(*r*), *ϕ*(*r*), and *ω*(*r*) coordinates

$$t(r) = \mathcal{E} \int \frac{r dr}{(r - 2M) \left[\mathcal{E}^2 - V\_{eff}(r; \mathcal{L}, \mathcal{J})\right]^{1/2}} \tag{7}$$

$$\varphi(r) = \mathcal{L} \int \frac{dr}{r^2 \left[\mathcal{E}^2 - V\_{eff}(r; \mathcal{L}, \mathcal{I})\right]^{1/2}},\tag{8}$$

and

$$
\omega(r) = \mathcal{I} \int \frac{dr}{\left[\mathcal{E}^2 - V\_{eff}(r; \mathcal{L}, \mathcal{I})\right]^{1/2}}.\tag{9}
$$

Using Equations (6)–(9) and substituting *r*(*χ*) = *Mp*/(1 + *e* cos *χ*) into Equation (3), we then have the following expressions together with *χ* related to the coordinates *t*, *ϕ*, and *ω* as

$$\frac{dt}{d\chi} = \frac{Mp^2[(p-2)^2 - 4e^2]^{1/2}(p - 6 - 2e\cos\chi)^{-1/2}}{(p - 2 - 2e\cos\chi)(1 + e\cos\chi)^2},\tag{10}$$

$$\frac{d\varphi}{d\chi} = \frac{p^{1/2}}{(p - 6 - 2e \cos \chi)^{1/2}} \, \, \, \, \tag{11}$$

$$\frac{d\omega}{d\chi} = \frac{\mathcal{I}M p^{3/2} (p - 3 - \varepsilon^2)^{1/2}}{(1 + \mathcal{I}^2)^{1/2} (p - 6 - 2\varepsilon \cos \chi)^{1/2} (1 + e \cos \chi)^2} \,. \tag{12}$$

The radial period and frequency are defined by [24,25,38]

$$T^{\circ} = \int\_{0}^{2\pi} \frac{dt}{d\chi} \, d\chi \, \, \quad \Omega^{\circ} = \frac{2\pi}{T^{\circ}} \,. \tag{13}$$

The azimuthal frequency of the orbit will then have the form as

$$
\Omega^{\Phi} = \frac{1}{T^{\sharp}} \int\_{0}^{T^{\sharp}} \frac{d\varphi}{dt} dt = \frac{\Delta \varphi}{T^{\sharp}} \,, \tag{14}
$$

with azimuthal phase ∆*ϕ*, which is given by

$$\begin{split} \Delta \boldsymbol{\varrho} &= \int\_{0}^{2\pi} \frac{d\boldsymbol{\varrho}}{d\boldsymbol{\chi}} d\boldsymbol{\chi} = \\ &= \int\_{0}^{2\pi} \frac{\sqrt{p}}{\sqrt{p-6-2e\cos\chi}} d\chi = 4\sqrt{\frac{p}{\varepsilon}} K \left( -\frac{4e}{\varepsilon} \right), \end{split} \tag{15}$$

where *<sup>e</sup>* <sup>=</sup> *<sup>p</sup>* <sup>−</sup> *<sup>p</sup>s*(*e*) = *<sup>p</sup>* <sup>−</sup> <sup>6</sup> <sup>−</sup> <sup>2</sup>*<sup>e</sup>* and *<sup>K</sup>*(*x*) = <sup>R</sup> *<sup>π</sup>*/2 0 *<sup>d</sup>θ*(<sup>1</sup> <sup>−</sup> *<sup>x</sup>* sin<sup>2</sup> *θ*) <sup>−</sup>1/2 is the complete elliptic integral of the first kind.

As a consequence of the presence of the compact extra dimension *ω*, the new frequency can be defined by

$$
\Omega^{\hat{\omega}} = \frac{1}{T^{\hat{\mathbb{P}}}} \int\_0^{T^{\hat{\mathbb{P}}}} \frac{d\omega}{dt} dt = \frac{\Delta \omega}{T^{\hat{\mathbb{P}}}} \, \, \, \, \tag{16}
$$

where ∆*ω* is the new extra phase accumulated over time interval *T r*ˆ .

### **3. Isofrequency Pairing Orbits in Black String Spectime Geometry**

Now we investigate the isofrequency and bound orbits of the particles in the vicinity of the black string spacetime. We consider orbits lying extremely close to the separatrix *e* in order to estimate the divergent quantities of the azimuthal and the new extra phases, the radial period, and their ratio in Equations (14) and (16). Considering the near-separatrix analytic expansions we obtain the corresponding expression for ∆*ω* as

$$
\Delta\omega = \frac{\mathcal{I}\mathcal{M}(3+2\varepsilon-\varepsilon^2)^{1/2}}{(1+\mathcal{I}^2)^{1/2}(1+2\varepsilon)}\sqrt{\frac{(6+2\varepsilon)^3}{e}}
$$

$$
\times \left[1+\mathcal{O}\left(\frac{\varepsilon}{4e}\right)\right]\ln\left(\frac{64e}{\varepsilon}\right). \tag{17}
$$

The previous investigations suggest that the occurrence of isofrequency pairing of geodesic orbits is strongly related to the presence of boundary regions referred as *separatrix* and *circular-orbit duals* (COD), and each and every circular orbit in the open range between the separatrix and singular curve and between the singular curve and COD as well has a dual isofrequency pairing. Note that the existence of the *separatrix* plays an important role for occurrence of these dual orbits in this isofrequency scenario. Considering the singular curve and the circular orbit duals in the particular region of the gravitational object is particularly important, and the COD can also play an important role due to the fact that as a boundary region allowing to keep pairs of isofrequency orbits that exist in this region [24–26].

Let us then study the effect of the compact extra dimension on the occurrence of the isofrequency pairing of geodesic orbits in black string spacetime. Based on the above discussions and Equations (13)–(15) we keep the result for which the range of frequencies of any pairs of orbits on Ω*ϕ*<sup>ˆ</sup> = (*M*/*r* 3 *b* ) 1/2 in the black string is given by

$$
\boldsymbol{\Omega}\_{\varepsilon=0}^{\phi} = 0.062 < \boldsymbol{\Omega}^{\phi} < \boldsymbol{\Omega}\_{\varepsilon=1}^{\phi} = 0.125 \,\text{.}\tag{18}
$$

where we have defined Ω˜ *<sup>ω</sup>*<sup>ˆ</sup> = *M*Ω*ϕ*<sup>ˆ</sup> as a dimensionless parameter.

Further, we determine the values of radial and azimuthal frequencies numerically and tabulate their values in Table 1.


**Table 1.** Values of Ω*r*<sup>ˆ</sup> and Ω*ϕ*<sup>ˆ</sup> are tabulated for different values of eccentricity *e* for isofrequency pairing of geodesic spiral orbits around the black string.

In Table 2, we show numerical values of the frequency Ω˜ *<sup>ω</sup>*<sup>ˆ</sup> of the bound orbits around the black string. As can be seen from Table 2 the value of the frequency Ω˜ *<sup>ω</sup>*<sup>ˆ</sup> arisen from the compact extra spatial dimension is increasing with an increase in the value of the forth conserved quantity J , but the height of the horizontal direction along black string is decreasing for given values of eccentricity *e*. However, numerical analysis leads to the fact that when the value of the fourth conserved quantity attains J*cr* ≈ 0.096 geodesic spiral orbits are not allowed all through to occur around the black string. Thus, the pairs of geodesic circular spiral orbits of particles with the same radial Ω˜ *<sup>r</sup>*<sup>ˆ</sup> , azimuthal Ω˜ *<sup>ϕ</sup>*<sup>ˆ</sup> , and new Ω˜ *<sup>ω</sup>*<sup>ˆ</sup> frequencies occur in the particular region of the gravitational object under this critical value irrespective of the fact that these orbits are physically distinct with different values of conserved quantities (i.e., E, L, and J ). Then the pairs of these spiral orbits of particles with three frequencies associated with (Ω˜ *<sup>r</sup>*<sup>ˆ</sup> , Ω˜ *<sup>ϕ</sup>*<sup>ˆ</sup> , Ω˜ *<sup>ω</sup>*<sup>ˆ</sup> ) would move and oscillates in a cylindrical form along the black string.

It turns out that as a consequence of the decrease in the value of J the above mentioned cylindrical region becomes larger around the black string. It could then play an important role in allowing the particles to move along the black string, thus increasing the amount of isofrequency pairs of geodesic spiral orbits in the region between the *separatrix*, *circular-orbit duals* and *horizontal length hz*, i.e., in the particular region of the black string. Hence, one can keep in mind that there would exist an infinite number of pairs of circular spiral orbits having the same three orbital frequencies around the black string regardless of physically distinct obits with three conserved quantities. As a consequence of the presence of compact extra spatial dimension, the occurrence of isofrequency pairing of spiral orbits would be of particularly importance in understanding and explaining the behavior of black string spacetime and the nature of the radiative inspirals as a source of gravitational waves or binary systems.

**Table 2.** The values of <sup>Ω</sup>*ω*<sup>ˆ</sup> are tabulated for different values of the fourth conserved parameter <sup>J</sup> for isofrequency pairing of geodesic spiral orbits around the black string. The point to be noted here is that *h<sup>z</sup>* corresponds to the horizontal length and will be valid only for the non vanishing compact extra dimension, i.e., *ω* 6= 0.


### **4. Conclusions**

We considered isofrequency pairing of geodesic spiral orbits in the black string spacetime, which recovers the Schwarzschild one in the case of vanishing *ω*. Thus, in an astrophysical scenario, it is worth investigating these geodesic orbits in the vicinity of black string as it allows to test the effects arising from the five dimensions. Our analysis suggests that the compact extra dimension *ω* leads to an increase in the number of pairs of circular spiral orbits. These pairs of orbits having the same three orbital frequencies (i.e., Ω*r*<sup>ˆ</sup> , Ω*ϕ*<sup>ˆ</sup> , and Ω*ω*<sup>ˆ</sup> ) occur in the particular region and oscillate in the cylindrical form around the black string in spite of the fact that they are physically distinct orbits possessing different conserved quantities (i.e., E, L, and J ). Furthermore, we showed that pairs of geodesic spiral orbits are not allowed all through to occur in the black string vicinity in the case when the fourth conserved quantity attains J ≈ 0.096.

The obtained results suggest that an infinite number of pairs of such orbits may occur in the particular region around the black string and it would be particularly important in explaining not only the possibility of occurrence of pairs of geodesic spiral orbits around the black holes, but also the nature of the black string spacetime. These theoretical results and discussions would be useful to the possible interpretation of astrophysical observations, and they could help to provide details of the validity of alternative models to black holes and also explain the nature of the radiative inspirals since isofrequency paring of geodesic spiral orbits can give the same information as such inspiral objects.

In a future work, we would be considering the possible extensions of recent results to the case of rotating black string and studying the effects of the rotation and a compact extra dimension on the specific isofrequency pairing of geodesic orbits. This would be of primary astrophysical importance.

**Author Contributions:** Conceptualization, S.S. and F.A.; investigation, S.S. and F.A.; methodology, S.S. and F.A.; validation, S.S. and F.A.; formal analysis, S.S. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable—no new data generated.

**Acknowledgments:** S.S. acknowledges the support of the Uzbekistan Ministry for Innovative Development. F.A. acknowledges the support of INHA University in Tashkent.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


### *Article* **Study of Accretion Flow Dynamics of V404 Cygni during Its 2015 Outburst**

**Arghajit Jana 1,2,\* , Jie-Rou Shang <sup>3</sup> , Dipak Debnath <sup>2</sup> , Sandip K. Chakrabarti <sup>2</sup> , Debjit Chatterjee 2,4 and Hsiang-Kuang Chang <sup>5</sup>**

	- Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India

**Abstract:** The 2015 Outburst of V404 Cygni is an unusual one with several X-ray and radio flares and rapid variation in the spectral and timing properties. The outburst occurred after 26 years of inactivity of the black hole. We study the accretion flow properties of the source during its initial phase of the outburst using *Swift*/XRT and *Swift*/BAT data in the energy range of 0.5–150 keV. We have done spectral analysis with the two component advective flow (TCAF) model fits file. Several flow parameters such as two types of accretion rates (Keplerian disk and sub-Keplerian halo), shock parameters (location and compression ratio) are extracted to understand the accretion flow dynamics. We calculated equipartition magnetic field *Beq* for the outburst and found that the highest *Beq* ∼ 900 Gauss. Power density spectra (PDS) showed no break, which indicates no or very less contribution of the Keplerian disk component, which is also seen from the result of the spectral analysis. No signature of prominent quasi-periodic oscillations (QPOs) is observed in the PDS. This is due to the non-satisfaction of the condition for the resonance shock oscillation as we observed mismatch between the cooling timescale and infall timescale of the post-shock matter.

**Keywords:** X-rays: binaries—stars individual: (V404 Cygni)—stars:black holes—accretion; accretion disks—shock waves—radiation:dynamics

### **1. Introduction**

Transient black hole candidates (BHCs) have two phases in their lives: the quiescence phase and the outbursting phase. They spend most of their lifetimes in the quiescence phase. A sudden rise in viscosity leads to an outburst when the X-ray intensity rises by a factor of thousands or more that of the quiescence phase. Matter from the companion star accretes to the central black hole, and in this process, gravitational potential energy is converted to heat and radiation. A black hole (BH) X-ray spectrum generally consists of two components: a multi-color blackbody and a hard power-law tail. The multi-color blackbody part is believed to originate from a Shakura-Sunyaev type standard thin disk [1]. The power-law tail is believed to originate from a Compton corona [2,3]. In the two-component advective flow (TCAF) solution, the CENBOL or CENtrifugal pressure supported BOundary Layer [4,5] replaces the Compton corona used in other models, such as disk-corona model [6,7] or evaporated disk in ADAF [8]. In this paper, we used the TCAF solution to study the accretion flow dynamics of V404 Cygni during its first outburst in 2015 after a long quiescent of ∼26 years.

V404 Cygni is one of the most studied black hole X-ray binary systems. It is also known as GS 2023+338. It was first identified as an optical nova in 1938. In 1956, another nova outburst was reported in this system [9]. In 1989, V404 Cygni went through another outburst. The 1989 outburst was discovered by the all sky monitor onboard *Ginga*. It is

**Citation:** Jana, A.; Shang, J.-R.; Debnath, D.; Chakrabarti, S.K.; Chatterjee, D.; Chang, H.-K. Study of Accretion Flow Dynamics of V404 Cygni during Its 2015 Outburst. *Galaxies* **2021**, *9*, 39. https://doi.org/ 10.3390/galaxies9020039

Academic Editors: Yosuke Mizuno and Emilio Elizalde

Received: 10 April 2021 Accepted: 21 May 2021 Published: 25 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

located at RA = 306◦ .01 and Dec = 33◦ .86. After spending ∼26 years in the quiescent state, V404 Cygni went through a short but violent outburst on 15 June 2015. In December 2015, another short activity was observed [10]. The binary system V404 Cygni harbors a black hole of mass 9–12 *M* at the center with a K-III type companion of mass ∼1 *M* [11–13]. The inclination angle of the binary system is ∼67◦ [12,13]. The orbital period of the system is 6.5 days [11]. V404 Cygni is located at a distance of 2.39 kpc, measured by parallax method [14]. V404 Cygni has a high spinning black hole with spin parameters *a* ∗ > 0.92 [15].

The 2015 outburst of V404 Cygni was discovered on 15 June simultaneously by *Swift*/BAT [10] and *MAXI*/GSC [16]. This outburst of the source was extensively observed in multi-wavelength bands, such as in radio [17], optical [18] and X-ray [19,20]. *INTE-GRAL* observation reported multiple X-ray flares during the outburst [19]. Several radio flares were also observed [17]. Extreme variable and rotating jet is observed during the outburst [21–23]. The source showed rapid changes in the spectral properties in a very short time [24]. *INTEGRAL* observation detected *e* <sup>−</sup> − *e* <sup>+</sup> pair annihilation on 20 June 2015 [25]. *FERMI*/LAT detected high energy *γ*-ray jet in the source on 26 June 2015 [26]. King et al. [27] reported detection of emission lines with Chandra-HETG, indicating strong disc wind emission. Motta et al. [24] argued that a slim disk is formed at the inner accretion flow due to the super-Eddington accretion in the source.

In this *paper*, we study the timing and the spectral properties of V404 Cygni with combined *Swift*/XRT and *Swift*/BAT data in the broad energy range of 0.5–150 keV during the initial phase of the 2015 outburst. We have done spectral analysis with the TCAF model-based *fits* file to extract physical flow parameters. The nature of these model-fitted accretion flow parameters allowed us to investigate the physical reasons behind the origin of the several flares and their variability and turbulent features. We have also calculated the equipartition magnetic field and cooling time during the outburst of the source.

The paper is organized in the following way. In Section 2, we briefly discuss the disk structure prescribed by TCAF and the way flow parameters decide on the spectral shape. In Section 3, we discuss the observations and the data analysis procedure. In Section 4, we present the results of our analysis. In Section 5, we make a discussion based on our result, and finally, in Section 6, we summarize our findings.

### **2. TCAF Solution**

TCAF configuration is based on the solution of a set of equations which govern viscous, transonic flows around a black hole [28]. In the TCAF solution, accreting flow consists of two components: (*i*) high viscous, high angular momentum, optically thick and geometrically thin Keplerian disk flow ( . *m*d), (*ii*) low viscous, low angular momentum, optically thin sub-Keplerian halo flow ( . *m*h). The Keplerian disk accretes on the equatorial plane and is immersed within the sub-Keplerian flow. Centrifugal force rises as flow moves close to the black hole and becomes comparable with the gravitational force. Low viscous halo matter is fast-moving and forms an axisymmetric shock at the centrifugal barrier [29]. The post-shock region i.e., CENBOL 'puffed-up', and becomes 'hot'. The Keplerian disk truncates at the shock location. The multi-color black body part of the observed spectrum that is formed by the soft photons is emitted from the Keplerian disk. A fraction of these soft photons are intercepted by the CENBOL. Depending on the temperature and size of the CENBOL, soft photons become hard photons through repeated inverse-Comptonization scattering at the CENBOL. Conversely, a fraction of Comptonized photons is reprocessed at the Keplerian disk and produces a reflection hump. Thus in the TCAF solution, the reflection component is self-consistently incorporated. However, a Gaussian line may be required to add if an iron emission line is present. CENBOL is also considered to be the base of the jets or outflows [30]. Toroidal magnetic flux tubes are responsible for the collimation of jet [31,32]. Oscillation of CENBOL can be triggered when the cooling and heating times inside CENBOL are similar, and the emerging photons produce the quasi-periodic oscillations (QPOs) [33–35] hereafter C15.

Transient BHCs generally show different spectral states during their outbursts. In TCAF, these observed spectral states are controlled by the flow parameters (two types of accretion rates and two shock parameters). A typical outbursting BHC generally goes through spectral state transitions to form a hysteresis loop as follows: hard state (HS) → hardintermediate state (HIMS) → soft-intermediate state (SIMS) → soft state (SS) → softintermediate state (SIMS) → hard-intermediate state (HIMS) → hard state (HS) [36,37]. In the upper panel of Figure 1 (adopted from [38]), we show a cartoon diagram of the above four spectral states under the TCAF solution. In the lower panel, typical spectra of each spectral state correspond to the diagrams are shown. In the cartoon diagrams, brown, light green, dark green, and grey regions represent Keplerian disk, sub-Keplerian halo, CENBOL and jet, respectively. It is to be noted that the cartoon diagram and corresponding spectra are only for illustrative purposes. TCAF model fits file assumes the shock location as the truncation radius of the Keplerian disk ; however, it may not occur all the time. For example, in the HS, a disk may not be formed at all, or in the SS, the shock may not be formed with the negligible sub-Keplerian flow. However, these scenarios are the example of extreme cases. In general, both Keplerian disk and sub-Keplerian halo matters are present in the accretion flow, and the TCAF model fits file covers the most probable parameter space of the system. quasi-periodic oscillations (QPOs) [33–35] hereafter C15. Transient BHCs generally show different spectral states during their outbursts. In TCAF, these observed spectral states are controlled by the flow parameters (two types of accretion rates and two shock parameters). A typical outbursting BHC generally goes through spectral state transitions to form a hysteresis loop as follows: hard state (HS) → hardintermediate state (HIMS) → soft-intermediate state (SIMS) → soft state (SS) → softintermediate state (SIMS) → hard-intermediate state (HIMS) → hard state (HS) [36,37] . In the upper panel of Figure 1 (adopted from [38]), we show a cartoon diagram of the above four spectral states under the TCAF solution. In the lower panel, typical spectra of each spectral state correspond to the diagrams are shown. In the cartoon diagrams, brown, light green, dark green , and grey regions represent Keplerian disk, sub-Keplerian halo, CENBOL and jet, respectively. It is to be noted that the cartoon diagram and corresponding spectra are only for illustrative purposes . TCAF model fits file assumes the shock location as the truncation radius of the Keplerian disk ; however, it may not occur all the time. For example, in the HS, a disk may not be formed at all, or in the SS, the shock may not be formed with the negligible sub-Keplerian flow. However, these scenarios are the example of extreme cases. In general, both Keplerian disk and sub-Keplerian halo matters are present in the accretion flow, and the TCAF model fits file covers the most probable parameter space of the system.

and heating times inside CENBOL are similar, and the emerging photons produce the

*Galaxies* **2021**, *1*, 0 3 of 21

**Figure 1.** In upper panel, cartoon diagrams of four commonly observed spectral states under TCAF solution are shown (adopted from [38]). Brown, light green, dark green and grey region represent Keplerian disk, sub-Keplerian halo, CENBOL and jet, respectively. An outbursting black hole evolves as HS → HIMS → SIMS → SS → SIMS → HIMS → HS. Generally both rising and declining HS and HIMS show monotonically evolving type-C (low frequency) QPOs, and SIMS shows sporadic type-B or type-A QPO. In soft sate these QPOs are absent. Here, EQPO means evolving QPO; SQPO means sporadic QPO; NQPO means no QPO. In the bottom panel, theoretical spectra corresponding to the top paneled spectral states are shown. These spectra are generated using five input parameters (*M*BH in *M*; *m*˙*<sup>d</sup>* in *M*˙ Edd; *m*˙*<sup>h</sup>* in *M*˙ Edd ; *X*<sup>s</sup> in *rs*, *R*), whose values are marked inset. The cartoon diagram and corresponding spectra are only for illustrative purpose. **Figure 1.** In upper panel, cartoon diagrams of four commonly observed spectral states under TCAF solution are shown (adopted from [38]). Brown, light green, dark green and grey region represent Keplerian disk, sub-Keplerian halo, CENBOL and jet, respectively. An outbursting black hole evolves as HS → HIMS → SIMS → SS → SIMS → HIMS → HS. Generally both rising and declining HS and HIMS show monotonically evolving type-C (low frequency) QPOs, and SIMS shows sporadic type-B or type-A QPO. In soft sate these QPOs are absent. Here, EQPO means evolving QPO; SQPO means sporadic QPO; NQPO means no QPO. In the bottom panel, theoretical spectra corresponding to the top paneled spectral states are shown. These spectra are generated using five input parameters (*M*BH in *M*; . *m<sup>d</sup>* in . *M*Edd; . *m<sup>h</sup>* in . *M*Edd ; *X*<sup>s</sup> in *rs*, *R*), whose values are marked inset. The cartoon diagram and corresponding spectra are only for illustrative purpose.

When an outburst is triggered due to lower viscosity and angular momentum, the sub-Keplerian matter moves with free-fall velocity, whereas the Keplerian flow moves in viscous time. Thus, the sub-Keplerian flow dominates the accretion process since it moves faster than the flow in the Keplerian disk. The Keplerian disk is truncated very far away by a large CENBOL. A strong shock (higher *R*) is formed at hundreds of Schwarzschild radius (*r*s) away from the BH. Thus, it is difficult to cool the CENBOL by the Keplerian component. When an outburst is triggered due to lower viscosity and angular momentum, the sub-Keplerian matter moves with free-fall velocity, whereas the Keplerian flow moves in viscous time. Thus, the sub-Keplerian flow dominates the accretion process since it moves faster than the flow in the Keplerian disk. The Keplerian disk is truncated very far away by a large CENBOL. A strong shock (higher *R*) is formed at hundreds of Schwarzschild radius (*r*s) away from the BH. Thus, it is difficult to cool the CENBOL by the Keplerian component. Hard X-ray flux dominates, and a hard state is observed. Compact jet is launched in this

state from the CENBOL [30]. Evolving type-C QPO is produced in this state due to the resonance oscillation of the shock [33].

The source enters the HIMS after HS. The Keplerian disk accretion rate continues to rise and becomes comparable with the sub-Keplerian halo accretion rate. As a result, accretion rate ratio (ARR = . *m*h/ . *m*d) decreases. Due to the rise of the Keplerian disk accretion rate, CENBOL shrinks and becomes cool as the shock moves farther inward. Shock strength decreases as the Compton cooling reduces the post-shock thermal pressure. Further, in this intermediate state, in the presence of jets, mass outflow rate to inflow rate ratio becomes maximum. In this state, evolving type-C QPOs may also be observed.

In the SIMS, the Keplerian rate keeps on increasing, although the sub-Keplerian flow rate started to decrease. This is because more and more sub-Keplerian flow becomes Keplerian by viscous transport. The shock becomes weak in this state. The shock further moves in, and the CENBOL becomes small. The soft X-ray flux increases, and the hard X-ray flux decreases in this state due to rapid rise in . *<sup>m</sup>*<sup>d</sup> and slow decrease in . *m*h. Generally, type-A or type-B QPOs are observed sporadically in this state due to weak oscillation of the CENBOL (type-B) or due to oscillation of shock-less centrifugal barrier (type-A) [34,35]. The time (day) difference between . *<sup>m</sup>*<sup>h</sup> and . *m*<sup>d</sup> peaks gives us rough estimation of the viscous time scale of the source [39,40]. In the SS, the Keplerian disk dominates and completely cools down the CENBOL. The soft X-ray flux dominates over the hard X-ray flux. No shock is formed. As a result, the jet is completely quenched in this state [30,41]. No QPO is produced in the soft state.

The spectral states evolve in the reverse order during the declining phase of the outburst as flow parameters show opposite nature. Starting from the SS to the SIMS transition day, both the Keplerian disk accretion rate and the sub-Keplerian halo accretion rate decreases, although the Keplerian disk rate decreases faster. As a result, ARR increases. As in the SIMS of the rising phase, one may see sporadic type-B or A QPOs in the declining SIMS. In the declining HIMS and HS, evolving type-C QPOs could be seen. Similar to the rising phase, one could observe a compact jet in the HIMS and HS in the declining phase.

TCAF solution is implemented in XSPEC [42] as an additive table model to analyze the spectral properties around the black holes [43,44]. TCAF model has four input flow parameters ( . *m*d, . *m*h, *X*s, *R*) other than mass of the black hole (*M*BH) and normalization (*N*). In the recent years, accretion flow dynamics around several black holes are studied quite successfully using TCAF model [45–48]. Frequencies of the dominating QPOs are predicted from the TCAF model fitted shock parameters [49]. Masses of the black holes are estimated quite successfully from spectral analysis with the TCAF model [49–51]. Jet contribution in the X-rays are also calculated using TCAF solution [52–54].

While fitting with the TCAF model, one must take care of degeneracy. Like any other spectral model, TCAF model is degenerate between different parameters. Thus, one must be very careful while fitting with TCAF model. One must always remember the physical condition of the system. For example, a single spectrum can be fitted with two different set of parameters: ( . *m*<sup>d</sup> = 0.1 . *M*Edd, . *m*<sup>h</sup> = 0.5 . *M*Edd, *M*BH = 10 *M*, *X*<sup>s</sup> = 100 *r*s, *R* = 3.5) and ( . *m*<sup>d</sup> = 0.2 . *M*Edd, . *m*<sup>h</sup> = 0.8 . *M*Edd, *M*BH = 10 *M*, *X*<sup>s</sup> = 10 *r*s, *R* = 4). Clearly, the second set of parameters is unphysical (the Xs can not be low while the the shock is strong and mh is higher than md). Also, one needs to find the parameters with the steppar command to avoid the degeneracy.

### **3. Observation and Data Analysis**

We analyzed *Swift* data for 19 observations between 2015 June 15 (MJD 57,188.77) and 26 June (MJD 57,199.52). We studied the source in 0.5–150 keV energy band with combined XRT and BAT data for five observations (MJD 57,191.01, 57,194.54, 57,197.21, 57,197.33, and 57,198.02). The 15–150 keV BAT data was used for four observations (MJD 57,188.77, 57,193.56, 57,198.15 and 57,199.52) when only BAT observations were available. For the rest of the ten observations, we studied 0.5–10 keV using XRT data.

We used WT mode data for XRT observation. Cleaned event files were generated for XRT using xrtpipeline command. To reduce pile-up effects, we used grade-0 data. For pile-up correction, we chose an annular region around the source. We chose an outer radius of 30 pixels and a varying inner region, depending on the count rate. We extracted spectra for the different inner regions and tested for the pile-up. The piled-up spectra are harder than expected. When increasing the inner region did not alter the spectra, the pile-up had been excluded. A background region is chosen far away from the source at the same axis as the source with an annular of same radii as the source. Then, we obtained *source*, and *background* files using cleaned event files in XSELECT v2.4. A scaling factor was applied to the source and background with backscal task. For an annular of outer radius of *r*<sup>2</sup> and inner radius of *r*1, we used the scaling factor *r*<sup>2</sup> − *r*1. The spectra were re-binned to 20 counts per bin using grppha command. The 0.5–10 keV 0.01 s lightcurves were generated in XSELECT v2.4 using cleaned source and background event files. We followed standard procedures to generate BAT spectra and lightcurves. Detector plane images (dpi) were generated using the task batbinevt. For appropriate detector quality, we used batdetmask task. Noisy detectors were found, and a quality map was obtained using bathotpix. Then batmaskwtevt was run to apply mask weighting to the event mode data. A systematic error was applied to the BAT spectra using batphasyserr. Ray-tracing was corrected using batupdatephakw task. Then a response matrix for the spectral file was generated using batdetmask.

Here, we used the TCAF model-based *fits* file for the spectral analysis. We also used combined diskbb (DBB) and powerlaw (PL) models to get rough estimation about the thermal and the non-thermal fluxes where a reflection component is often required to find the best fits. TCAF model-based fits do not require any additional component for reflection since the reflection component is already incorporated in the model. We required a Gaussian model to incorporate Fe K*α* emission line. We used phabs model for interstellar absorption and pcfabs model for partial absorption. With the TCAF, we extracted physical parameters such as the mass of the black hole (*M*BH) in solar mass (*M*), the Keplerian disk rate ( . *m<sup>d</sup>* ) in Eddington rate ( . *<sup>M</sup>*Edd), the sub-Keplerian halo rate ( . *m<sup>d</sup>* ) in Eddington rate ( . *M*Edd), the shock location (*X*s) (i.e., size of the Compton cloud) in Schwarzschild radius (*r*s) and the shock compression ratio (*R* = *ρ*+/*ρ*<sup>−</sup> with *ρ*<sup>+</sup> and *ρ*<sup>−</sup> are post- and preshock density, respectively). In TCAF, *N* depends on the source's distance and inclination angle and is just a constant factor between the emitted spectra and observed spectra by a given instrument. However, it can vary if any physical processes are present other than the accretion. Since the current version of the TCAF model fits file does not include jets, for instance, a variation of normalization is observed if they are present [52,54]. We first analyzed the spectra after keeping the mass of the black hole as a free parameter. We obtained the mass of the black hole in the range of 9.5–11.5 *M* or the average value of 10.6 *M*. This measured mass range agrees very well with previously reported values by many authors [11,13]. Then, we refitted all the spectra after keeping the mass of the black hole frozen at 10.6 *M*. The result based on the later analysis is presented here.

We achieved best-fittings using steppar command. After obtaining a best-fit based on *χ* 2 *red*(∼1) with TCAF, we ran steppar to verify fitted parameter values. The 'steppar' command ran for pair of parameters . *m*d− . *m*<sup>h</sup> and *X*s−*R*. We also calculated uncertainties with the steppar with 90% confidence. In Figures 2 and 3, 2D-contour plots for two observations (MJD 57,188.77 and 57,189.62) are shown.

*Galaxies* **2021**, *1*, 0 6 of 21

**Figure 2.** 2D confidence contour plot for MJD 57,188.77, for *m*˙ <sup>d</sup> − *m*˙ <sup>h</sup> in the left panel and *X*<sup>s</sup> − *R* in the right panel.**Figure 2.** 2D confidence contour plot for MJD 57,188.77, for . *m*d− . *m*<sup>h</sup> in the left panel and *X*s−*R* in the right panel. **Figure 2.** 2D confidence contour plot for MJD 57,188.77, for *m*˙ <sup>d</sup> − *m*˙ <sup>h</sup> in the left panel and *X*<sup>s</sup> − *R* in the right panel.

**Figure 3.** 2D confidence contour plot for MJD 57189.62, for *m*˙ <sup>d</sup> -*m*˙ <sup>h</sup> in the left panel and *X*<sup>s</sup> − *R* in the right panel. **Figure 3.** 2D confidence contour plot for MJD 57189.62, for . *m*<sup>d</sup> − . *m*<sup>h</sup> in the left panel and *X*<sup>s</sup> − *R* in the right panel.

**Figure 3.** 2D confidence contour plot for MJD 57189.62, for *m*˙ <sup>d</sup> -*m*˙ <sup>h</sup> in the left panel and *X*<sup>s</sup> − *R* in the right panel.

### **4. Results**

observation on MJD 57,191.01.

observation on MJD 57,191.01.

**4. Results** We present the results of spectral and temporal analysis of the source in 0.5–150 keV energy band using combined XRT+BAT or only BAT (in 15–150 keV) or only XRT (in 0.5–10 keV) data. In Figure 4, we show two XRT PDS for observations on MJD 57,191.01 (18 June 2015) and MJD 57,194.54 (21 June 2015). In Figure 5, TCAF model fitted spectrum of combined XRT plus BAT data in the broad energy range of 0.5–150 keV is shown for the **4. Results** We present the results of spectral and temporal analysis of the source in 0.5–150 keV energy band using combined XRT+BAT or only BAT (in 15–150 keV) or only XRT (in 0.5–10 keV) data. In Figure 4, we show two XRT PDS for observations on MJD 57,191.01 (18 June 2015) and MJD 57,194.54 (21 June 2015). In Figure 5, TCAF model fitted spectrum of combined XRT plus BAT data in the broad energy range of 0.5–150 keV is shown for the We present the results of spectral and temporal analysis of the source in 0.5–150 keV energy band using combined XRT+BAT or only BAT (in 15–150 keV) or only XRT (in 0.5– 10 keV) data. In Figure 4, we show two XRT PDS for observations on MJD 57,191.01 (18 June 2015) and MJD 57,194.54 (21 June 2015). In Figure 5, TCAF model fitted spectrum of combined XRT plus BAT data in the broad energy range of 0.5–150 keV is shown for the observation on MJD 57,191.01.

black) and (c) (online red) with exposures of 220 s, 680 s and 160 s, respectively.

black) and (c) (online red) with exposures of 220 s, 680 s and 160 s, respectively.

In Figure 6a, we show the evolution of BAT and XRT fluxes. In Figure 6b–c, we show the variation of the Keplerian disk rate ( *m*˙ <sup>d</sup> ), the sub-Keplerian halo rate ( *m*˙ <sup>h</sup> ) with day (in MJD). In Figure 6d, we show the evolution of accretion rate ratio (ARR = *m*˙ <sup>h</sup> / *m*˙ <sup>d</sup> ). In Figure 7a, we show the variation of the equipartition magnetic field ( *B*eq ) with the day. In Figure 7b–d, we show the variation of the shock location ( *X*<sup>s</sup> ), the shock compression ratio (*R*), and TCAF model normalization with the day. In Figure 8, the time-resolved *Swift*/BAT spectra in the energy range of 15–150 keV for the observation on 15 June 2015 (MJD 57,188.77) are shown. The three spectra are marked as (a) (online green), (b) (online

In Figure 6a, we show the evolution of BAT and XRT fluxes. In Figure 6b–c, we show the variation of the Keplerian disk rate ( *m*˙ <sup>d</sup> ), the sub-Keplerian halo rate ( *m*˙ <sup>h</sup> ) with day (in MJD). In Figure 6d, we show the evolution of accretion rate ratio (ARR = *m*˙ <sup>h</sup> / *m*˙ <sup>d</sup> ). In Figure 7a, we show the variation of the equipartition magnetic field ( *B*eq ) with the day. In Figure 7b–d, we show the variation of the shock location ( *X*<sup>s</sup> ), the shock compression ratio (*R*), and TCAF model normalization with the day. In Figure 8, the time-resolved *Swift*/BAT spectra in the energy range of 15–150 keV for the observation on 15 June 2015 (MJD 57,188.77) are shown. The three spectra are marked as (a) (online green), (b) (online

10−4

−2

0

χ 2

10−3

0.01

keV (Photons cm−2 s−1 keV−1)

0.1

*Galaxies* **2021**, *1*, 0 7 of 21

**Figure 4.** Power density spectra (PDS) of 0.01 s time binned lightcurves of 0.5–10 keV XRT data. The observation date of these PDS are: (**a**) 18 June 2015 (MJD 57,191.01) and (**b**) 21 June 2015 (MJD 57,194.54). **Figure 4.** Power density spectra (PDS) of 0.01 s time binned lightcurves of 0.5–10 keV XRT data. The observation date of these PDS are: (**a**) 18 June 2015 (MJD 57,191.01) and (**b**) 21 June 2015 (MJD 57,194.54). **Figure 4.** Power density spectra (PDS) of 0.01 s time binned lightcurves of 0.5–10 keV XRT data. The observation date of these PDS are: (**a**) 18 June 2015 (MJD 57,191.01) and (**b**) 21 June 2015 (MJD 57,194.54).

Energy (keV) **Figure 5.** TCAF model fitted combined XRT+BAT spectra in the energy range of 0.5–150 keV, observed on MJD 57,191.03. **Figure 5.** TCAF model fitted combined XRT+BAT spectra in the energy range of 0.5–150 keV, observed on MJD 57,191.03. **Figure 5.** TCAF model fitted combined XRT+BAT spectra in the energy range of 0.5–150 keV, observed on MJD 57,191.03.

In Figure 6a, we show the evolution of BAT and XRT fluxes. In Figure 6b–c, we show the variation of the Keplerian disk rate ( . *<sup>m</sup>*d), the sub-Keplerian halo rate ( . *m*h) with day (in MJD). In Figure 6d, we show the evolution of accretion rate ratio (ARR = . *m*h/ . *m*d). In Figure 7a, we show the variation of the equipartition magnetic field (*B*eq) with the day. In Figure 7b–d, we show the variation of the shock location (*X*s), the shock compression ratio (*R*), and TCAF model normalization with the day. In Figure 8, the time-resolved *Swift*/BAT spectra in the energy range of 15–150 keV for the observation on 15 June 2015 (MJD 57,188.77) are shown. The three spectra are marked as (a) (online green), (b) (online black) and (c) (online red) with exposures of 220 s, 680 s and 160 s, respectively.

**Figure 6.** Panel (**a**) shows variation of 0.5–10 keV XRT and 15–150 keV BAT flux with day (MJD). The red (online) triangle represents XRT flux while blue (online) circle represents BAT flux. The fluxes are in the unit of 10−<sup>9</sup> erg cm−<sup>2</sup> s −1 . The variation of (**b**) *m*˙ <sup>d</sup> in *M*˙ Edd and (**c**) *m*˙ <sup>h</sup> in *M*˙ Edd are shown with day (MJD). In panel (**d**) the variation of ARR (=*m*˙ <sup>h</sup>/*m*˙ <sup>d</sup> ) is shown. Blue and red dotted lines represent reported X-ray and Radio flaring activities, respectively. **Figure 6.** Panel (**a**) shows variation of 0.5–10 keV XRT and 15–150 keV BAT flux with day (MJD). The red (online) triangle represents XRT flux while blue (online) circle represents BAT flux. The fluxes are in the unit of 10−<sup>9</sup> erg cm−<sup>2</sup> s −1 . The variation of (**b**) . *m*<sup>d</sup> in . *M*Edd and (**c**) . *m*<sup>h</sup> in . *M*Edd are shown with day (MJD). In panel (**d**) the variation of ARR (= . *m*h/ . *m*d) is shown. Blue and red dotted lines represent reported X-ray and Radio flaring activities, respectively. **Figure 6.** Panel (**a**) shows variation of 0.5–10 keV XRT and 15–150 keV BAT flux with day (MJD). The red (online) triangle represents XRT flux while blue (online) circle represents BAT flux. The fluxes are in the unit of 10−<sup>9</sup> erg cm−<sup>2</sup> s −1 . The variation of (**b**) *m*˙ <sup>d</sup> in *M*˙ Edd and (**c**) *m*˙ <sup>h</sup> in *M*˙ Edd are shown with day (MJD). In panel (**d**) the variation of ARR (=*m*˙ <sup>h</sup>/*m*˙ <sup>d</sup> ) is shown. Blue and red dotted lines represent reported X-ray and Radio flaring activities, respectively.

Day (MJD)

**Figure 7.** The variation (**a**) equipartition magnetic field (*B*eq ) in *Gauss*, (**b**) shock location (*X*s ) in *rs*, (**c**) shock compression ratio (*R*) and (**d**) normalization (*N*) are shown with day (MJD). **Figure 7.** The variation (**a**) equipartition magnetic field (*B*eq ) in *Gauss*, (**b**) shock location (*X*s ) in *rs*, (**c**) shock compression ratio (*R*) and (**d**) normalization (*N*) are shown with day (MJD). **Figure 7.** The variation (**a**) equipartition magnetic field (*B*eq) in *Gauss*, (**b**) shock location (*X*s) in *rs*, (**c**) shock compression ratio (*R*) and (**d**) normalization (*N*) are shown with day (MJD).

.

**Figure 8.** Time resolved BAT spectra for observation on MJD 57,188.77 is shown. The spectra correspond to exposures of (**a**) 220 s, (**b**) 680 s and (**c**) 160 s. **Figure 8.** Time resolved BAT spectra for observation on MJD 57,188.77 is shown. The spectra correspond to exposures of (**a**) 220 s, (**b**) 680 s and (**c**) 160 s.

#### *4.1. Temporal Evolution 4.1. Temporal Evolution*

The 2015 outburst of V404 Cygni is different from other regular outbursts of transient BHCs. It showed rapid changes in a very short timescale in both XRT and BAT count rates. The flux changed significantly in minutes to hours timescales. Several radio and X-ray flares were observed during this epoch. *INTEGRAL* observation revealed 18 X-ray flares during the outburst [19]. Radio flares were also reported during the outburst period [17]. We find that the luminosity was super-Eddington in some observations. On 22 June 2015 (MJD 57,195.41), the XRT flux increased rapidly to 4.61 <sup>×</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> s −1 from 8.2 <sup>×</sup> <sup>10</sup>−<sup>8</sup> erg cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> of the previous observation. This corresponds to the source luminosity, *<sup>L</sup>* ' 3.13 <sup>×</sup> <sup>10</sup><sup>38</sup> erg *<sup>s</sup>* −1 . On 25 June 2015 (MJD 57,198.93), the XRT flux reached at 4.59×10−<sup>6</sup> erg cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> which corresponds to the source luminosity, *<sup>L</sup>* ' 3.12 <sup>×</sup> <sup>10</sup><sup>39</sup> erg s−<sup>1</sup> BAT count rate also increased rapidly within our analysis period. It became maximum on 26 The 2015 outburst of V404 Cygni is different from other regular outbursts of transient BHCs. It showed rapid changes in a very short timescale in both XRT and BAT count rates. The flux changed significantly in minutes to hours timescales. Several radio and X-ray flares were observed during this epoch. *INTEGRAL* observation revealed 18 X-ray flares during the outburst [19]. Radio flares were also reported during the outburst period [17]. We find that the luminosity was super-Eddington in some observations. On 22 June 2015 (MJD 57,195.41), the XRT flux increased rapidly to 4.61 <sup>×</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> s −1 from 8.2 <sup>×</sup> <sup>10</sup>−<sup>8</sup> erg cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> of the previous observation. This corresponds to the source luminosity, *<sup>L</sup>* ' 3.13 <sup>×</sup> <sup>10</sup><sup>38</sup> erg *<sup>s</sup>* −1 . On 25 June 2015 (MJD 57,198.93), the XRT flux reached at 4.59 <sup>×</sup> <sup>10</sup>−<sup>6</sup> erg cm−<sup>2</sup> s <sup>−</sup><sup>1</sup> which corresponds to the source luminosity, *<sup>L</sup>* ' 3.12 <sup>×</sup> <sup>10</sup><sup>39</sup> erg s−<sup>1</sup> . BAT count rate also increased rapidly within our analysis period. It became maximum on 26 June 2015 (MJD 57,198.93) at 4.68 <sup>×</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> s −1 , i.e., luminosity was *<sup>L</sup>* ' 3.18 <sup>×</sup> <sup>10</sup><sup>38</sup> erg s−<sup>1</sup> .

June 2015 (MJD 57,198.93) at 4.68 <sup>×</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> s −1 , i.e., luminosity was *<sup>L</sup>* ' 3.18 <sup>×</sup> <sup>10</sup><sup>38</sup> erg s−<sup>1</sup> . We studied power density spectra (PDS) of 0.01 s binned lightcurve of *Swift*/XRT. We did not find any clear evidence of QPOs during the initial phase of the outburst in *Swift*/XRT PDSs. A weak signature of QPO was observed in the PDS on 18 June 2015 (MJD 57,191.03) (see Figure 4a). The XRT PDS showed an almost flat spectral slope with broad-band noise. The noise decreased as the outburst progressed, during which we found two slopes in the PDS, a steep power-law slope in the lower frequency and a flat slope at a We studied power density spectra (PDS) of 0.01 s binned lightcurve of *Swift*/XRT. We did not find any clear evidence of QPOs during the initial phase of the outburst in *Swift*/XRT PDSs. A weak signature of QPO was observed in the PDS on 18 June 2015 (MJD 57,191.03) (see Figure 4a). The XRT PDS showed an almost flat spectral slope with broad-band noise. The noise decreased as the outburst progressed, during which we found two slopes in the PDS, a steep power-law slope in the lower frequency and a flat slope at a higher frequency. In some PDS, we observed that power diminished very rapidly. We did not find any break in the PDS.

#### higher frequency. In some PDS, we observed that power diminished very rapidly. We did *4.2. Evolution of the Spectral Properties*

not find any break in the PDS. *4.2. Evolution of the Spectral Properties* We have done the spectral analysis using 0.5–150 keV combined *Swift*/XRT and *Swift*/BAT data between 15 and 26 June 2015. Radhika et al. (2016) analyzed the same data set using phenomenological diskbb and powerlaw models [20]. We analyzed the We have done the spectral analysis using 0.5–150 keV combined *Swift*/XRT and *Swift*/BAT data between 15 and 26 June 2015. Radhika et al. (2016) analyzed the same data set using phenomenological diskbb and powerlaw models [20]. We analyzed the data with combined diskbb, and power-law models and have found similar results as in [20]. In general, we used phabs\*pcf\*(diskbb+powerlaw+gaussian) model to estimate thermal and non-thermal fluxes. While analyzing with phenomenological models, we

thermal and non-thermal fluxes. While analyzing with phenomenological models, we did not require a diskbb component regularly. Diskbb component was required only in 9 observations out of a total of 19 observations. During the entire period, PL photon index

did not require a diskbb component regularly. Diskbb component was required only in 9 observations out of a total of 19 observations. During the entire period, PL photon index varied between 0.60 and 2.43, although the PL flux dominated over the DBB flux. We also required a Gaussian for Fe K*α* line emission along with the diskbb+powerlaw model. Detailed results of the phenomenological model fitted spectra are given in Table 1.

In the present paper, our main goal is to study the accretion flow dynamics of the source from spectral analysis with the physical TCAF model. For this purpose, we used phabs\*pcf\*(TCAF+gaussian) model. Detailed results using this model is presented in Table 2. From the spectral analysis in the initial few observations, we obtained very low values of the Keplerian disk rate ( . *<sup>m</sup>*d) while the sub-Keplerian halo rates ( . *m*h) were found to be high (>0.85 . *<sup>M</sup>*Edd). On 19 June 2015 (MJD 57,192.16), . *m*<sup>h</sup> increased to 1.37 . *M*Edd from its previous day value of 0.85 . *M*Edd. After that, it varied within 1.24–1.58 . *M*Edd until the end of our analysis period. On 25 June 2015 (MJD 57,198.02), we observed sudden rise in . *m*<sup>d</sup> from its previous day, i.e., from 0.11 . *M*Edd to 0.15 . *<sup>M</sup>*Edd. Before that, . *m*<sup>d</sup> varied in the range of 0.05–0.12 . *<sup>M</sup>*Edd. After MJD 57,198.02, . *m*<sup>d</sup> was obtained in a narrow range of 0.13–0.16 . *M*Edd (see Figure 6b).

A strong shock (*R* = 2.56) was found far away from the black hole (*X*<sup>s</sup> = 334 *r*s) on the first day (MJD 57,188.77) of our observation (see Figure 7b,c). The shock remained strong for the next five days. After that, the shock was found to move closer to the black hole as the Keplerian disk rate increased. The shock was found at 126 *r*<sup>s</sup> on MJD 57,194.16 with *R* = 1.92. The shock did not move closer than this. After that, shock moved away from the black hole. Again we found that the shock was moving inward after MJD 57,197.21. On the last day of our observation, we found the shock to be located at 143 *r*s.

We added a Gaussian profile and the TCAF solution to incorporate the contribution of the *Fe* emission line in XRT data. Fe-line varied within 6.08 keV and 6.97 keV. In some observations, we required the Fe line width of >1 keV. The source was reported to be partially obscured due to the disk wind and outflow [24,27,55]. We used phabs models for the absorption. We did not freeze *n*<sup>H</sup> at a particular value. Rather, we kept it free. In our analysis, we observed it to vary between 0.54 <sup>×</sup> <sup>10</sup><sup>22</sup> to 1.49 <sup>×</sup> <sup>10</sup><sup>22</sup> cm−<sup>2</sup> . The variable absorption is unlikely due to the interstellar medium, rather it is likely to be associated with the intrinsic absorption of the source. In 11 observations out of total of 19 observations, we required to use pcfabs model to incorporate partial absorption in the XRT data. In some observations, the covering required as high as 95%. In general, it varied between 50% and 95%. For covering absorption, *<sup>n</sup>*<sup>H</sup> varied between 2.2 <sup>×</sup> <sup>10</sup><sup>22</sup> and 28.9 <sup>×</sup> <sup>10</sup><sup>22</sup> cm−<sup>2</sup> .

### *4.3. Time Resolved BAT Spectra*

To study the evolution of spectral nature in short time intervals, we analyzed the time-resolved BAT spectra. Rapid variation of the accretion rates and other physical flow parameters from observation to observation motivated us to make this study. Here, we analyzed time-resolved BAT spectra for four observations on 15 June 2015 (MJD 57,188.77), 18 June 2015 (MJD 57,191.03), 20 June 2015 (MJD 57,193.56) and 26 June 2015 (MJD 57,199.52). We found rapid variation in the BAT spectra within a very short time, even in one observation. In Table 3, TCAF model fitted parameters for time-resolved spectra are presented. For example, on 15 June 2015, within total BAT exposure of 1202 s (Figure 8), we observed the variations of . *m*<sup>d</sup> between 0.041 and 0.057 . *<sup>M</sup>*Edd, and . *m*<sup>h</sup> between 0.82 and 0.88 . *M*Edd. The shock was observed to vary in between ∼326–336 *r*s. Similar rapid variation of the flow parameters ( . *<sup>m</sup>*<sup>d</sup> and . *m*h) were also observed for the remaining three observations.



**Table 1.** DBB+PL Model Fitted Spectral Analysis Results.

In Col. 2, UT dates of the year 2015 are mentioned in dd-mm format. In Cols. 4 & 5, XRT and exposures are mentioned. In Cols. 6 and 7, XRT (0.5–10 keV) and BAT (15–150 keV) fluxes are mentioned. In Cols. 8 and 9, model fitted disk blackbody (DBB) and powerlaw (PL) fluxes are mentioned. All fluxes are in the units of 10−9 erg cm−2 s −<sup>1</sup> . *nH* 1 and *n* 2 H are in the unit of 1022 cm−2 . *n* 1 His Hydrogen column density for interstellar absorption.*nH* 2 is Hydrogen column density for partial covering absorption. The Fe emission line energy and *σ* are mentioned in Col. 15 and 16. Best fitted values of *χ* 2 and degrees of freedom are mentioned in Col. 17 as *χ* 2/*do f* .

*Galaxies* **2021**, *9*, 39



In Col. 2, UT dates of the year 2015 are mentioned in dd-mm format. *n* H and *n* H are in the unit of 1022 cm−2 . *n* H is Hydrogen column density for interstellar absorption.*n* H column density for partial covering absorption. TCAF model fitted/derived parameters are mentioned in Cols. 7–12. The Fe emission line energy and *σ* are mentioned in Col. 13 and 14. Best fitted values of *χ* 2 and degrees of freedom are mentioned in Col. 15 as *χ* 2/*do f* . Note: Mass of the black hole was kept frozen at 10.6 *M* during spectral fitting with the TCAF model

fits file. The average values of 90% confidence ± values obtained using steppar command in XSPEC, are placed as superscripts of fitted parameter values.


**Table 3.** Time Resolved BAT Spectra.

TCAF fitted extracted parameters for time resolved BAT spectra in the energy range of 15–150 keV. Note: First row in each spectra are TCAF model fitted spectral analysis results when entire data exposure including gaps are used. The mass of the BH is frozen at 10.6 *M* during the fitting.

### *4.4. Estimation of Magnetic Field*

Observation of presence of high magnetic field on 25 June 2015 by [56] motivated us to estimate magnetic field strength at the 'hot' Compton cloud region (here CENBOL) for the BHC V404 Cygni during its 2015 outburst. We made some simple assumptions as mentioned below to calculate the equipartition value of the magnetic field. At the shock location, energy conservation leads to the following equation [28],

$$
tau\_+^2 + \frac{1}{2}u\_+^2 = na\_-^2 + \frac{1}{2}u\_-^2. \tag{1}
$$

where, *n* is the polytropic index of the flow, *a* is sound speed, *u* is particle velocity. '+' and '−' signs indicate the values at post- and pre-shock region respectively. The electron number density (*n*e) is given by,

$$m\_{\rm e} = \frac{\dot{m}\_{\rm d} + \dot{m}\_{\rm h}}{4\pi X\_{\rm s} \mu\_{+} H\_{\rm shk} m\_{\rm p}}.\tag{2}$$

For our calculation, we assume CENBOL shape as cylindrical. *m*<sup>p</sup> is the mass of the proton. *H*shk is the shock height. The shock height could be calculated from the TCAF model fitted shock parameters [44] using standard vertical equilibrium [29],

$$H\_{\rm shk} = \sqrt{\frac{n(R-1)X\_s^2}{R^2}}.\tag{3}$$

Now, we can calculate pressure at CENBOL using the following equation,

$$P\_{\rm gas} = \frac{a\_+^2 m\_\text{e} n\_\text{e}}{n}.\tag{4}$$

We consider equipartition magnetic field (*B*eq) as,

$$\frac{B\_{\rm eq}^2}{8\pi} = P\_{\rm rad} + P\_{\rm gas} \tag{5}$$

where, *P*rad is the radiation pressure. The radiation pressure is negligible compared to the gas pressure. Using this equation, we calculated the value of the equipartition magnetic field for this source (see Table 4). We show the variation of the equipartition magnetic field in Figure 7a. We find *B*eq = 97 ± 3 G on our first observation (MJD 57,188.77). Then we found that *B*eq was increasing with the shock moving towards the black hole. *B*eq was maximum on 2015 June 21 (MJD 57194.16) at 923 ± 44 G. On that day, the shock was closest to the black hole.


**Table 4.** Magnetic field and Resonance condition.

Electron number density (*n*e) is in the unit of <sup>×</sup>10<sup>16</sup> cm<sup>3</sup> .

### *4.5. Cooling and Infall Times*

V404 Cygni did not show any strong QPO during its 2015 outburst. Although there are numerous suggestions for the origin of low-frequency QPOs, we believe that these QPOs are generated due to the oscillation of the shock formed in the TCAF solution. This shock oscillates when the resonance condition between cooling and infall time scales is satisfied or when Rankine-Hugoniot conditions are not satisfied to form a stable shock [33–35]. Thus to check if the resonance condition is satisfied or not, we have calculated both cooling and infall time scales during the outburst. Generally, in low mass X-ray binaries, Compton cooling is the primary process of cooling. We also considered the synchrotron cooling since the magnetic field was present.

We calculated both cooling time scales (synchrotron and Compton) during the entire period of our observations and compared that with the infall times. If cooling and infall timescales are roughly comparable, then we may say that the resonance condition for oscillation of the shock is satisfied. For simplicity, here we assume that the matter is moving radially at the post-shock region with speed *u*+. This allowed us to calculate infall time using the following equation,

$$t\_{\rm inf} = \frac{X\_{\rm s}}{\mu\_{+}} \tag{6}$$

Similar to the magnetic field calculation, here we also assume CENBOL as a cylindrical in shape. Now the total thermal energy of electron content within the CENBOL of volume *V* is,

$$E = \gamma\_{\text{e}} m\_{\text{e}} \mathcal{L}^2 V n\_{\text{e} \prime} \tag{7}$$

where *γ*<sup>e</sup> is the Lorentz factor. It is given by, *γ*<sup>e</sup> = 1/ p 1 − *β* 2 e , where *β*<sup>e</sup> = *u*e/*c*, *u<sup>e</sup>* being electron velocity and *c* is the velocity of light. The synchrotron cooling rate is [57],

$$
\Lambda\_{\rm syn} = \frac{4}{3} \sigma\_{\rm T} c \beta\_{\rm e} \gamma\_{\rm e} \,^2 \mathcal{U}\_{\rm B} \,\tag{8}
$$

where *σ*<sup>T</sup> is Boltzman constant. *U*<sup>B</sup> is magnetic energy density and given by, *U*<sup>B</sup> = *B* 2 eq/8*π*. The synchrotron cooling time is given by,

$$t\_{\rm syn} = \frac{E}{\Lambda\_{\rm syn}}.\tag{9}$$

We calculated cooling time due to synchrotron using Equation (9). Note, we use *γ*<sup>e</sup> = 10 for our calculation. We also checked the Compton cooling timescale (*t*Comp). To calculate Compton cooling, we use the same method as described in C15. The Compton cooling timescale is given by Equation (6) of C15,

$$t\_{\rm Comp} = \frac{E}{\Lambda\_{\rm Comp}}.\tag{10}$$

Here, ΛComp is the Compton cooling rate (for more details, see, C15). Here we find that the Compton cooling is much faster than the synchrotron cooling (see Table 4). Thus, the inverse-Comptonization is the primary cooling process. Now if we compare *t*inf with *t*syn or with *t*Comp, in both cases, the ratio deviates largely from unity. It is clear that the resonance condition was not satisfied during the 2015 outburst of V404 Cygni. This indeed verifies the observational fact that there was no prominent signature of type-C low-frequency QPOs during the outburst. The detailed results of our calculation of the magnetic field and two types of cooling time scales are presented in Table 4.

### **5. Discussion**

We study the 2015 outburst of V404 Cygni using *Swift*/XRT and BAT data in the energy band of 0.5–150 keV. We used a total of 19 observations between 15 June 2015 (MJD 57,188.77) and 26 June (MJD 57,199.52) for the timing and spectral analysis. The TCAF model fitted spectral analysis allowed us to understand the nature of this violent outburst from a physical perspective. In the following sub-sections, we discuss our findings from the combined spectral and timing analysis.

### *5.1. Magnetic Field*

A magnetic field is brought in by the accretion flow. The shear, convection, and advection amplify the predominantly toroidal flux tubes. They are expelled from the CENBOL due to the magnetic buoyancy [31,32] in the direction towards the pressure gradient force. If the buoyancy timescale is larger than the shear amplification timescale, then the magnetic flux tubes are amplified within the dynamical timescale; until they reach equipartition where gas pressure matches with the magnetic pressure. In general, the magnetic field is not found to contribute significantly to the accretion disk spectra of black holes as TCAF alone fits the spectral data very well. However, its role is important for the acceleration and collimation of jets and outflow.

Here, we calculated the equipartition magnetic field by equating magnetic pressure with the local gas pressure at the shock location. We found *B*eq = 97 G on the first observation day. After that, it increased gradually with the increase of the accretion rate. We found the maximum value of the magnetic field to be *B*eq = 923 G on 21 June 2015 (MJD 57,194.16). Then, it decreased to 154 G on MJD 57,196.89. Then, we observed that it was varying between 414 and 820 G within our observation. Dallilar et al. calculated the equipartition magnetic field for this source at hot Compton corona to be 461 ± 12 G on 25 June 2015 (MJD 57,198.18) [56]. We found *B*eq = 500 ± 18 G on the same observation day (MJD 57,198.15), which is consistent with the finding of Dallilar et al. (2017).

### *5.2. Power Density Spectra*

No prominent QPOs were observed in the PDS of the Fourier transformed 0.01 c time binned XRT lightcurves in the 0.5–10 keV energy band. The presence of a significant magnetic field may cause turbulence in the accretion disk, which could be responsible for the white noise observed in the PDS. The PDSs were observed to have two slopes: a powerlaw component and a flat component. Powerlaw slope was observed in the lower frequency region while flat slope was observed in the higher frequency. The turbulence could be the reason behind the flat spectrum observed in the XRT PDS. Power in the PDS follows as, *P* ∼ 1/ *f β* , where *f* is the frequency and *β* is powerlaw index. In the most PDS, we found *β* ∼ 0, i.e., flat spectra. It indicates the presence of turbulence in the Keplerian disk. No break was found in power density spectra. This also indicates no or minimal contribution of the Keplerian disk accretion. Precisely, this is found from the spectral analysis.

### *5.3. Absence of QPOs*

We believe that the oscillation of shock is responsible for the QPOs [33]. Generally strong type-C QPOs are observed if the resonance condition is satisfied, i.e., when the infall time of the post-shock matter roughly matches with the cooling time inside the CENBOL. The cooling process could be via inverse-Compton scattering, bremsstrahlung, or synchrotron emission. If the magnetic field is high enough, one can expect the dominance of the synchrotron cooling.

We did not observe any prominent type-C QPOs during the 2015 outburst of V404 Cygni. Non-satisfaction of the resonance condition could be responsible for it. To verify this assertion, we calculated synchrotron and Compton cooling times for this source. We found that the Compton cooling rate is much faster than the synchrotron cooling rate. Thus, the Compton cooling process was the dominant cooling process. We compared Compton cooling time and synchrotron cooling time with the infall time. We found that the infall time and cooling times were not comparable at all (see Table 4). C15 showed that QPO would be generated if the ratio of the infall and the cooling time is between 0.5 and 1.5, i.e., within 50% of unity either way. Since the resonance condition was not satisfied, type-C QPO was not produced.

Huppenkothen et al., 2017 reported of detection of mHz QPO with *Chandra*, *Swift*/XRT and *Fermi* observations [58]. They reported simultaneous detection of 18 mHz QPO with *Swift*/XRT and *Fermi*/GBM. They classified this QPO as a new type of low-frequency QPO. *Chandra*/ACIS observation revealed signatures of 73 mHz and 1.03 Hz QPOs, as well as a QPO at 136 mHz in a single Swift/XRT. They argued that the QPO at 136 mHz is standard type-C QPO. However, they did not seem to be type-C QPOs. However, Radhika et al. also argued that they did not find any clear signature of this QPO [20]. Thus the resonance condition was not behind the origin of these QPOs. Non-satisfaction of the Rankine-Hugoniot conditions at the shock front could be the reason for this type of QPO [34].

### *5.4. Spectral and Temporal Evolution*

V404 Cygni showed complex behavior during the 2015 outburst. We required two absorption models to fit the spectra: phabs model for interstellar absorption and pcfabs for the partial covering absorption. The later absorption may be due to disk wind emission or outflow emission [20,27]. We studied V404 Cygni till MJD 57198. After that, variable dust scattering rings were observed, and the dust halo started to dominate the field of view [59].

Some observations of V404 Cygni could not be fitted with simple disk blackbody and powerlaw models since a significant amount of reflection was present. In the first six observations, the DBB component was not required to fit the spectra (till MJD 57,193.56). After that, it was required occasionally. PL photon indices varied randomly between 0.60 and 2.43. Overall, PL flux dominated over the thermal flux during the entire period of our observation. We often observed a 'hump' region after ∼ 8 keV in the XRT data. This

'reflection hump' was extended up to ∼20 keV in the BAT data. Radhika et al. analyzed 0.5–150 keV combined XRT+BAT data using disk blackbody (diskbb) and PL models and found similar results [20]. Later, they used pexrav [60] model instead of 'PL' model for this reflection. In their analysis, the disk blackbody component was not required in a few observations. They found that photon indices varied randomly between 0.60 and 4.43. Refs. [19,61,62] analyzed *INTEGRAL*/IBIS and *INTEGRAL*/SPI data with Comptonization model in the broad energy range of 20–650 keV. They required an additional cut-off in the energy range of 400–600 keV. They found that the Comptonization temperature was ∼40 keV with seed photon temperature ∼7 keV. This is very high for disk emission. They concluded that this emission could be of different origins, such as synchrotron emission from the jet.

We extracted the physical parameters of the accretion flows from each fit. We first fitted each spectrum by keeping all model input parameters free. We found a variation of *<sup>M</sup>*BH in a narrow range of 9.5–11.5 *<sup>M</sup>* with an average value of 10.6+0.9 <sup>−</sup>1.1 *<sup>M</sup>*. This estimated mass of V404 Cygni agrees well with other reported values in the range of 9–12 *M* [11–13]. We then re-fitted all the spectra by keeping *M*BH frozen at mean value (*M*BH = 10.6 *M*) to extract values of other physical flow parameters during the outburst.

From the variation of the TCAF model fitted flow parameters (i.e., high dominance of . *m<sup>h</sup>* over . *m<sup>d</sup>* , and presence of strong shock (*R* > 2.3) with a large CENBOL), we infer that the source was in the hard state at the beginning of the outburst. High ARR (∼14–22) also indicates this except in one observation made on 18 June 2015 (MJD 57,191.03). From the phenomenological model fittings, the dominance of powerlaw flux also indicates this. On 25 June 2015 (MJD 57,198), we observed that . *m*<sup>d</sup> started to increase rapidly, although other parameters did not change much, leading to the softening of the spectra. At this last phase of our observation, we observed that ARR decreased with an increase in the Keplerian disk rate. During this phase, the source could be in the hard-intermediate state. In general, the spectral state classification is done based on the variation of ARR and the nature of QPO. Due to the absence of QPOs and the ARR's complex behavior, we could not assert the exact state transition day, but the source likely entered in the hard-intermediate state on MJD 57,197.21 when . *m*<sup>h</sup> was found to achieve its maximum rate. After this day, . *m*<sup>d</sup> was found to increase rapidly. However, our classification may not be valid since the source showed rapid fluctuation in a very short timescale [24]. Motta et al. analyzed the time-resolved 0.5–10 keV *Swift*/XRT spectra and found that spectra shape changed in as short as ∼10 s [24].

The 2015 outburst is somewhat similar to the 2003 outburst of H 1743-322. Both outbursts occurred after long quiescence periods. Similar to the 2015 outburst of V404 Cygni, the 2003 outburst of H 1743-322, which also occurred after about 26 years, showed peculiar behavior with several flares and outflow activity. Thus it is possible that a huge amount of matter accumulated at a large pileup radius over a long period of the quiescence phase. With a sudden enhancement of viscosity, the outburst is triggered and leads to a violent and non-settling disk-jet activity [63].

### *5.5. Evolution of the Spectral Properties with Flares*

The present outburst of V404 Cygni did not behave like any other typical outburst of a classical transient black hole. V404 Cygni showed a strong jet associated with several flares. The flares were observed in multi-wavebands, from X-ray, optical, IR to radio [19,64]. Eighteen X-ray flares were reported with the *INTEGRAL* and *SWIFT*/BAT observations between 20 June 2015 (MJD 57,193) and 25 June 2015 (MJD 57198). The magnetic field was the strongest during this phase of the outburst. The magnetic field could be responsible for this flaring activity.

In general, we see a decreasing ARR in an observation immediately after a flare, indicating softening of the spectra (see Figure 6). For example, an X-ray flare was observed on MJD 57,194.31 [19]. This could be due to the high magnetic field on MJD 57,194.16. Immediately after the flare, on MJD 57,194.54, we found that the ARR decreased slightly

from its previous observation (21.6 to 20.2). On 18 June 2015 (MJD 57,191) we observed that the Keplerian disk rate suddenly rose to 0.12 . *M*Edd from 0.06 . *M*Edd within ∼30 mins. This could be associated with the radio flare observed on MJD 57,191.09 with AMI-LA observation [17]. This is expected since a large amount of mass was ejected from the CENBOL during a flare, and inflowing matter rapidly moved inward to fill the vacant space. This led to the softening of the spectrum as the CENBOL size was reduced. However, this was not observed after every flare. It is possible that those flares were not localized, and the disk was unstable. Around MJD 57,198, we found that *B*eq decreased sharply, although *N* increased very rapidly. This could be due to the high magnetic field that produced flare and outflow. This flare and the outflow was responsible for the rapid rise of *N*. Additionally, flaring events could also contribute to the rapid variability. On 21 June 21 2015 (MJD 57,194), the *B*eq was observed to be at an increasing *N*. On the same day, the rapid variation of the spectral properties was observed [65], although the mass accretion rates did not change.

The X-ray jet flux can be calculated based on the deviation of the constancy of the TCAF model normalization [52–54]. However, to calculate jet X-ray flux by this model, we must have at least one observation where the jet's effects were negligible. In that observation, the entire observed X-ray should be contributed only from the inflowing matter of the accretion disk and CENBOL. However, for V404 Cygni, a strong jet was present in all the observations. Thus we were not able to separate the jet X-ray contribution from the total X-ray. Random variation in normalization may be due to a fluctuating magnetic field or unsettling disk, leading to the source's flaring activity.

### **6. Summary**

The first epoch of the 2015 outburst of the Galactic black hole V404 Cygni was unusual and violent. It did not behave like other typical outbursts of Galactic transient black hole candidates. Rapid variations were observed in both spectral and timing properties in very short time scales, ranging from a few minutes to hours. We have used 0.5–150 keV combined *Swift*/XRT and *Swift*/BAT data to study the accretion flow properties of the source. Spectral analysis was done using the TCAF model-based *fits* file in XSPEC. The model fitted/derived flow parameters allowed us to understand the evolution of this violent outburst's accretion flow parameters. We have also calculated the equipartition magnetic field for the outburst. No break is found in the power density spectra, which indicates that the Keplerian disk rate was very low. This is also confirmed from the spectral analysis. The presence of white noise in higher frequencies in the power density spectra indicates a highly turbulent disk. The strong magnetic field could be the reason behind it. It is also responsible for the flares. We find that the Compton cooling process is much faster than the synchrotron cooling process. Since the resonance condition between cooling and infall time scales inside the CENBOL is not satisfied, we did not expect any sharp low-frequency QPO. Indeed the object did not show any signature of prominent type-C QPO.

**Author Contributions:** Conceptualization, S.K.C.; Data curation, A.J.; Formal analysis, A.J.; Methodology, A.J.; Software, D.D. and S.K.C.; Supervision, D.D., S.K.C. and H.-K.C.; Writing—original draft, Arghajit Jana; Writing—review & editing, J.-R.S., D.D., S.K.C., D.C. and H.-K.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data used here, are publicly available.

**Acknowledgments:** This work made use of XRT and BAT data supplied by the UK *Swift* Science Data Centre at the University of Leicester. We acknowledge anonymous referee for his kind suggestion to improve the quality of the paper. A.J. and D.D. acknowledge support from DST/GITA sponsored India-Taiwan collaborative project (GITA/DST/TWN/P-76/2017) fund. Research of D.D. and S.K.C. is supported in part by the Higher Education Dept. of the Govt. of West Bengal, India. D.D. also acknowledges the ISRO sponsored RESPOND project (ISRO/RES/2/418/17-18) fund. D.C. and D.D. acknowledge support from DST/SERB sponsored Extra Mural Research project (EMR/2016/003918) fund. J.-R.S., and H.-K.C. are supported by MOST of Taiwan under grants MOST/106-2923-M-007- 002-MY3 and MOST/107-2119-M-007-012.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Abbreviations**


### **References**


### *Article* **Properties of Faint X-ray Activity of XTE J1908+094 in 2019**

**Debjit Chatterjee 1,2,\* , Arghajit Jana <sup>3</sup> , Kaushik Chatterjee <sup>2</sup> , Riya Bhowmick <sup>2</sup> , Sujoy Kumar Nath <sup>2</sup> , Sandip K. Chakrabarti <sup>2</sup> , A. Mangalam <sup>1</sup> and Dipak Debnath <sup>2</sup>**


<sup>3</sup> Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India; argha0004@gmail.com

**\*** Correspondence: debjit.chatterjee@iiap.res.in

**Abstract:** We study the properties of the faint X-ray activity of Galactic transient black hole candidate XTE J1908+094 during its 2019 outburst. Here, we report the results of detailed spectral and temporal analysis during this outburst using observations from *Nuclear Spectroscopic Telescope Array (NuSTAR)*. We have not observed any quasi-periodic-oscillations (QPOs) in the power density spectrum (PDS). The spectral study suggests that the source remained in the softer (more precisely, in the soft– intermediate) spectral state during this short period of X-ray activity. We notice a faint but broad Fe K*α* emission line at around 6.5 keV. We also estimate the probable mass of the black hole to be 6.5+0.5 <sup>−</sup>0.7 *<sup>M</sup>*, with 90% confidence.

**Keywords:** X-Rays:binaries—stars individual: (XTE J1908+094)—stars:black holes—accretion; accretion disks—shock waves—radiation:dynamics

### **1. Introduction**

Black hole transients (BHTs) are fascinating objects to study. After a long period of quiescence, they show a sudden outburst. The sudden enhancement of viscosity at the piling radius could trigger the outburst [1–3]. The spectral and temporal properties of the source change during the outburst and evolves through the hard state (HS), hard intermediate state (HIMS), soft intermediate state (SIMS), and soft state (SS) [4–6]. Evolution of the state can be seen through hardness intensity diagram (HID) or "q" diagram [7,8] and accretion rate ratio intensity diagram (ARRID; [9,10]). A "failed" outburst is also a commonly known event where the source does not enter the softer spectral states [11–13]. In case of "failed" outbursts, sources do not follow the standard state transition or "q" diagram. The spectral shape varies in different spectral states, mainly due to the relative contribution of the thermal component [14,15] and non-thermal component [16,17].

In Two-Component Advective Flow (TCAF) solution [18,19], the accretion flow consists of two components: high viscous Keplerian flow with high angular momentum and low viscous sub-Keplerian flow with low angular momentum. The sub-Keplerian flow moves towards the black hole almost radially, and it almost stops at the centrifugal barrier and forms an axisymmetric shock [20]. The matter is puffed up beyond the shock and creates a hot electron cloud or Compton corona. This corona is called the CENtrifugal -pressure-supported BOundary Layer (CENBOL). This region intercepts the soft photons coming from the Keplerian disk and emits high-energy photons through inverse-Comptonization. In this way, TCAF can self-consistently explain the accretion dynamics around an accreting black hole. The oscillation of the same shock can explain the observed low-frequency quasi-periodic-oscillations (LFQPOs) [21,22]. The CENBOL is also considered to be the base of jets and outflows [23]. To get an estimation of the physical flow parameters directly from the spectral fit, TCAF model was implemented as an additive table model in XSPEC [24,25]. From spectral fit with the model, we obtain

**Citation:** Chatterjee, D.; Jana, A.; Chatterjee, K.; Bhowmick, R.; Nath, S.K.; Chakrabarti, S.K.; Mangalam, A.; Debnath, D. Properties of Faint X-ray Activity of XTE J1908+094 in 2019. *Galaxies* **2021**, *9*, 25. https://doi.org/10.3390/ galaxies9020025

Academic Editor: Fulai Guo

Received: 27 March 2021 Accepted: 13 April 2021 Published: 16 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

two accretion rate parameters, namely, the Keplerian disk rate (*m*˙ *<sup>d</sup>* ) in Eddington rate (*M*˙ *Edd*), the sub-Keplerian halo rate (*m*˙ *<sup>h</sup>* ) in Eddington rate (*M*˙ *Edd*); two shock or Compton cloud parameters' shock location (*Xs*) in Schwarzschild radius (*rs*), compression ratio (*R*), which is the ratio between post-shock and pre-shock matter densities (*R* = *ρ*+/*ρ*−). One can also obtain the best-fitted value of the mass of the black hole (*MBH* in *M*) and a normalization parameter from each spectral fit. If the mass of the black hole is well known, it could be kept constant during the spectral fitting.

The Galactic black hole (GBH) candidate XTE J1908+094 was discovered on 21 February 2002 by the Proportional Counter Array (PCA) on-board Rossi X-ray Timing Explorer (*RXTE*) [26]. The source spectrum was fitted with an absorbed power-law with photon index (Γ) of 1.55. The power density spectrum did not show any pulsations and exhibited a flat spectrum between 1 mHz and 0.1 Hz. A broad quasi-periodic-oscillation peak at 1 Hz was observed with a power-law break which continued to 4 Hz. A high-energy cutoff at ∼100 keV was also observed using *BeppoSAX* [27]. The source was suggested to be a black hole (BH) candidate from its spectral and timing properties [26–28]. High interstellar absorption (column density, *<sup>N</sup>H*∼2.5 <sup>×</sup> <sup>10</sup><sup>22</sup> cm−<sup>2</sup> ) was reported while fitting the spectrum with a multi-color blackbody, a Comptonization and a broad emission line [28]. The dimensionless spin parameter was also measured to be 0.75 from the broadening of Fe K*α* line [29].

A radio counterpart was discovered at R.A. = 19*h*08*m*53.*s*07, DEC. = +09◦2300500.0 by *Very Large Array (VLA)* [30] which was also consistent with the Chandra observation [31]. Two possible near-infrared (NIR) counterparts were detected [32,33]—one of them is indicated as an intermediate/late-type (A-K) main-sequence companion, while the other is suggested to be a late-type (later than K) main-sequence secondary star [33]. After two similar outbursts in 2002 and early 2003, XTE J1908+094 went through another outburst on 2013 October 26 [34–38]. The 2013 outburst was well-studied in X-rays by *Swift*, *NuSTAR* [39,40]. Although a relativistic broadening of Fe-K*α* line was observed, the spin of the BH could not be constrained due to data quality. A disk reflection contribution was also observed. The source was in the high/soft state during the *NuSTAR* observation. A flare was observed during the studied period. The flare was suggested to be related to the relativistic jet activity. Changes in the corona could be the reason for the flare. Multi-frequency radio and X-ray observation, and radio polarimetry with VLA and AMI-LA during the entire 2013 outburst was done [41]. The source followed the standard hardness-intensity diagram during the outburst. The common behavior of radio jets was also observed, which changes from compact to discrete as the state transits from hard to soft. From the VLBI monitoring of XTE J1908+094, a lateral expansion of resolved, asymmetric jet knots was noticed, which was ejected following the hard- to soft-state transition [42]. The knots are suggested to be the working surface where the ejected materials interacted with the surrounding dense interstellar medium. An external shock formed in this region causes the acceleration of particles, which subsequently diffused outwards over time.

XTE J1908+094 recently showed a "faint" X-ray activity on 2019 April 1 [43]. The source spectrum was fitted with a power-law model with photon index, Γ = 2.3. AMI-LA 15.5 GHz observation on 2019 April 5, detected the radio counterpart of XTE J1908+094 [44]. The obtained spectra on 2019 April 4 from the photon-counting mode of Swift also yield a soft spectrum with high absorption [45]. The source was suggested to be in the soft spectral state while using NICER data on 2019 April 6 and 9 [46].

In this *paper*, we have studied the timing and spectral properties of XTE J1908+094 during its X-ray activity on 2019 April 10 using *NuSTAR* observation of ∼40 ks. The *paper* is organized in the following way. In Section 2, we discuss the observations and the data analysis procedure. In Section 3, we present the temporal and spectral results of our analysis. In Section 4, we carry out the discussion based on our results.

### **2. Observation and Data Analysis**

We processed the *NuSTAR* observation Id 90501317002 (https://heasarc.gsfc.nasa.gov/ cgi-bin/W3Browse/w3browse.pl (accessed on 10 April 2019)) using the nupipeline command of NuSTAR Data Analysis Software (NuSTARDAS) version 1.8.0 (https://heasarc. gsfc.nasa.gov/docs/nustar/analysis/ (accessed on 10 April 2019)) and with the Calibration database (CALDB) version 1.0.2 (http://heasarc.gsfc.nasa.gov/FTP/caldb/data/nustar/ fpm/ (accessed on 10 April 2019)). The spectra and light curves of the source were extracted from the FPMA detectors using a 6000 circle centered at the position of XTE J1908+094. The background region was selected carefully, since the source could have contamination from the nearby bright source GRS 1915+105. The background was chosen as a 6000 radius circle as far away from the XTE J1908+094. The background count rate is less than 2% of the source count rate, indicating that the source is still dominant. We also divided the total ∼40 ks data in three segments of ∼16 ks, ∼10 ks, and ∼12 ks for detailed study. We used XSELECT command filter time for this. The spectra and light curves were then generated using nuproducts. The spectra were re-binned to have 20 counts/s using grppha. The light curves were binned with 100 s time resolution.

For spectral analysis, we used both phenomenological (combined diskbb, powerlaw models) and physical (TCAF based fits file as an additive table model) model in XSPEC version 12.10.1. The hydrogen column density (*NH*) was fixed at 2.5 <sup>×</sup> <sup>10</sup><sup>22</sup> cm−<sup>2</sup> [28]. The multiplicative model, Tbabs was used as an absorption table model considering the vern scattering cross-sections [47] and wilm abundances [48].

### **3. Results**

We studied the 2019 X-ray activity of BHC XTE J1908+094 using *NuSTAR* observation. The source is close to a bright BHC GRS 1915+105. To verify the presence of any contamination due to GRS 1915+105, we studied the source and background count rate variation of XTE J1908+094 (Figure 1). The background count rate was found to be less than 2% of the source count rate. Therefore, we conclude that the X-ray activity of XTE J1908+094 during April 2019 to be "faint" and, yet, the variation observed was inherent rather than due to the nearby sources.

**Figure 1.** Variation of count rates of XTE J1908+094 from *NuSTAR* observation on 10 April 2019. The upper panel (**a**) shows the count rate for the source and the lower panel (**b**) shows the count rate of the background. The! background count is less than 2% of the source counts.

### *3.1. Variability Study from the Light Curve*

We generated the light curve of 100 s time binning of the total 40 ks data to study the variability (Figure 1a). The light curve shows small variability during this period. We also generated the light curves of 14 individual orbits of 0.01 s time binning. The power density spectra (PDS) do not show any quasi-periodic-oscillations (QPOs). This observation contrasted with the 2002 observations of the object where a broad QPO was observed, and the spectrum was harder [49].

We generated light curves of the entire observation in the energy ranges of 3–10 keV and 10–79 keV. The variation in these light curves, along with the hardness ratio (HR; between 10–79 keV and 3–10 keV), are shown in Figure 2. We noticed that the soft photon (3–10 keV) counts always dominate the hard photon (10–79 keV) counts. Both the soft and hard count rates showed coherent periodic variation during the observation. Thus, the HR always remained at low values (∼0.05 to ∼0.15). The soft and the hard count rates and the value of the HR indicate that the source was in the softer spectral regime during our studied period.

**Figure 2.** The variation of (**a**) 3–10 keV count rate, (**b**) 10–79 keV count rate, and (**c**) hardness ratio (HR) with time (in sec). The light curves are binned with a time resolution of 100 s.

### *3.2. Accretion Properties from Spectral Analysis*

We studied the spectral properties with both phenomenological and physical models separately. We first fitted the spectrum of the full observation (∼40 ks) using combined diskbb and powerlaw models (Figure 3a). The inner disk temperature (*Tin*) was obtained as 0.779 keV. The high photon index (Γ∼2.085) indicates a softer spectral state. The fitted spectrum retained a *χ* 2 *red* value of 744/597∼1.246. We noticed a small residual at around 6.5 keV (see Figure 3a). To check the contribution of any Fe-K*α* line in the spectrum, we fitted the spectrum with Tbabs(diskbb+powerlaw+Gaussian) model (Figure 3b). The inner disk temperature (*Tin*) decreased very little (0.645 keV). The photon index also decreased to (Γ∼2.02). We obtained 6.48 keV as the line energy and ∼1 keV as the line width (*σ*) from Gaussian model. The best fitted spectrum gave a *χ* 2 *red* value of 549/594∼0.924. The fit improved with the inclusion of the Gaussian model for the Fe K*α* emission line. We also fitted the spectrum with TCAF fits file along with Gaussian model (Figure 3c). The disk rate was high (*m*˙ *<sup>d</sup>*∼1.699) compared to the halo rate (*m*˙ *<sup>h</sup>*∼0.160). The shock location and compression value were obtained as *Xs*∼49.83 *r<sup>s</sup>* and *R*∼1.1, respectively. These accretion rates and shock parameters, indicating a softer state, also justify the results obtained from the combined diskbb+powerlaw+Gaussian model fitting. The best-fitted spectrum

retained a *χ* 2 *red* value of 562/592∼0.949. The best-fitted spectra using these three different combinations of models are shown in Figure 3. The spectral parameters are listed in Table 1.

**Figure 3.** Unfolded spectra using (**a**) Tbabs(diskbb+powerlaw), (**b**) Tbabs(diskbb+powerlaw+Gaussian), and (**c**) Tbabs(TCAF+Gaussian) with their ratio. The red, green dashed lines are the blackbody and powerlaw model components. The solid black line refers to the combined best fitted spectra. The blue dashed lines are the Gaussian component.

Since a variation can be easily noticed in the light curve of the full observation (Figure 1a), we divided the light curve into three segments of ∼16 ks, ∼10 ks and ∼12 ks and analyzed for detailed study. We fitted these three spectra using two combinations Tbabs(diskbb+powerlaw+Gaussian) and Tbabs(TCAF+Gaussian). The spectral parameters are listed in Table 2. Only TCAF plus Gaussian model fitted spectra are shown in Figure 4.

**Figure 4.** (**a) Best-fitted** spectra for the three segments of the *NuSTAR* observation. The right panel (**b**) shows the *χ* (i.e., (data − model)/error) variations of the three spectra in respective colors.


**Table 1.** Spectral Analysis Results obtained from *NuSTAR* Observation.



### *3.3. Estimation of Inner Disk Radius and Prediction of Mass*

We estimated the mass for XTE J1908-094 from the spectral analysis. From the obtained *χ* 2 *red* values of model 1 and model 2 in Table 1, we suggested model 2 is the best fitted phenomenological model. We considered the fitted disk-normalization (*Ndisk*) to estimate the mass of the BHC XTE J1908+094. We average out the *Ndisk* values obtained from fittings of the three segments of the whole observation (Table 2). The inner radius (*rin*) of the disk and the diskbb normalization (*Ndisk*) are related, as in

$$N\_{disk} = \left(\frac{r\_{in}}{D/10 \text{ kpc}}\right)^2 \cos\theta. \tag{1}$$

*D* is the distance of the system in kpc and *rin* is in km. *θ* is the inclination of the disk in degree. This estimated inner radius from the above equation is subjected to some errors (see [50,51]). The corrected inner radius (*Rin* (km)) is,

$$R\_{\rm in}(\mathbf{km}) \simeq \kappa^2 \mathfrak{F} r\_{\rm in}.\tag{2}$$

*κ* and *ξ* are the hardening factor [51] and inner boundary correction factor [50], respectively. Since the inclination angle of the system is not confirmed, we considered three guess values for the inclination as: *θ*∼30◦ , 50◦ , and 80◦ . The average value of *Ndisk* was 516. We consider the *κ* and *ξ* are 1.7 and 0.41, respectively ([50,51]), and assume the distance of the system to be 10 kpc. We obtained the inner radius (*Rin*) for to be 29 km, 34 km, and 65 km, for the inclination angle 30◦ , 50◦ , and 80◦ , respectively. The inner edge of the disk (*Rin*) is considered to be truncated at the inner most stable circular orbit (ISCO). For a Schwarzschild black hole it is 6*GMBH*/*c* 2 , where *G*, *MBH* and *c* are the Gravitational constant, mass of the black hole and speed of light at vacuum. We obtained the mass for this black hole from the obtained *Rin* values to be 3.2, 3.7, and 7.2 *M*, respectively.

In TCAF, the mass of the BH is an important input parameter. If it is not well known from dynamical or other methods, one can obtain the best-fitted value of the *MBH* from each spectral fit. Here, we obtained the mass of XTE J1908+094 as ∼6.5 *M* from the combined TCAF, and Gaussian model fit when the entire duration of the observation was considered. (Table 1).

### **4. Conclusions**

We studied the spectral and temporal properties of BHC XTE J1908+094 during its renewed X-ray activity using one *NuSTAR* observation in 10 April 2019. The X-ray activity was very faint and mostly dominated by soft photons. No quasi-periodic oscillations (QPOs) were observed in its power density spectra (PDS). The light curves generated in the soft (3–10 keV) and hard (10–79 keV) energy range showed coherent periodic variation. The low value of hardness ratio suggests that the source was in a softer spectral state during the observation.

We analyzed the spectrum using both phenomenological and physical models separately. The high power-law photon index (Γ∼2.23) indicates that the source was either in the soft–intermediate or in soft state. The disk normalization was also relatively high compared to the power-law normalization. Due to the small residual around 6.5 keV, we refitted the spectrum, adding a Gaussian for the contribution of Fe K*α* line emission. A broad Gaussian was obtained with line energy ∼6.48 keV and line width (*σ*) ∼1 keV. The photon index (Γ) decreased to 2.02, suggesting that the source probably was in the soft intermediate state. The presence of a broad width (*σ* ≥ 1) Gaussian line also signifies the spectral state as soft intermediate. While fitting the three segments of the whole observation divided due to the periodic variability, we noticed that the second segment (see, Table 2) showed a slightly harder spectrum than the other two segments (part1 and part3).

We refitted the spectrum using TCAF plus Gaussian model. We noticed an unusually high disk rate (*m*˙ *<sup>d</sup>* <sup>∼</sup> 1.699 *<sup>M</sup>*˙ *Edd*) over the halo rate (*m*˙ *<sup>h</sup>* <sup>∼</sup> 0.160 *<sup>M</sup>*˙ *Edd*). This high amount of hard photon contribution is also noticed in the variation in light curves (see, Figure 2). The obtained shock location (*X<sup>s</sup>* ∼ 49.83 *rs*) and compression ratio (*R* ∼ 1.1) also refer to soft intermediate spectral state. The spectral parameters obtained from the whole observation's partial fitting also suggest that during the mid-segment, when both soft and hard count decreased, the spectrum became harder but remained in the same spectral state. This faint X-ray activity of XTE J1908+094 in 2019 could be due to the sudden enhancement of viscosity and supply of matter from the pile-up radius. This type of behavior was observed in the case of H1743-322 [2] and GX 339-4 [52]. As the supply of residual matter from the previous outburst (2012–2013) was exhausted, the very short-term X-ray activity was also faded.

We also estimated the possible value of the mass of the black hole (*MBH*) from the spectral analysis. During our studied period, the spectra are dominated by the soft photons coming from the disk. The inner radius can be constrained in the soft spectral state from the diskbb normalization (*Ndisk*). Since the other two unknown variables (distance and inclination) are not confirmed for this source, we consider the distance to be 10 kpc and inclination as 30◦ , 50◦ and 80◦ . The corrected inner radius (*Rin*) was obtained as 29 km, 34 km, and 65 km. As the source is found in the soft-intermediate state, the inner radius must be located very close to the ISCO [53]. Considering a Schwarzschild black hole the ISCO is at ∼ 6*GMBH c* <sup>2</sup> or 3 *r<sup>s</sup>* . We obtained the black hole mass of 3.2, 3.7 and 7.2 *M* for those three *Rin*. This result would only be valid for a Schwarzschild black hole. For a Kerr black hole, the inner radius would be located at less than 3 *r<sup>s</sup>* , affecting the prediction of mass from the disk normalization. We could suggest that the system is located at ∼8–10 kpc and is highly inclined (>70◦ ). From the TCAF model fitted spectral fit, we also obtained the mass of the black hole to be ∼6.5 *M*.

### **5. Summary**

We studied the faint outburst of XTE J1908+094 in 2019 using archival *NuSTAR* data. From the timing and spectral study, we conclude that:


**Author Contributions:** Conceptualization, D.C.; Data curation, D.C.; Formal analysis, D.C.; Methodology, D.C. and A.J.; Software, D.D. and S.K.C.; Supervision, D.D., S.K.C. and A.M.; Writing original draft, D.C.; Writing—review and editing, D.C., D.D., A.J., K.C., R.B., S.K.N., S.K.C., A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data used here are publicly available. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA).

**Acknowledgments:** We would like to thank the anonymous referees for their constructive and insightful suggestions. D.C. acknowledges the support of the PDR fellowship, IIA, Bengaluru, Karnataka, India. A.J. acknowledges the support of the Post-Doctoral Fellowship from Physical Research Laboratory, Ahmedabad, India, funded by the Department of Space, Government of India. K.C. acknowledges support from DST/INSPIRE (IF170233) fellowship. R.B. acknowledges support from CSIR-UGC NET qualified UGC fellowship (June-2018, 527223). S.K.N., D.D. and S.K.C. acknowledge support ISRO sponsored RESPOND project (ISRO/RES/2/418/17-18) fund. D.D. and S.K.C. also acknowledge support from Govt. of West Bengal, India and DST/GITA sponsored India-Taiwan collaborative project (GITA/DST/TWN/P-76/2017) fund.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


### *Article* **Changing Accretion Geometry of Seyfert 1 Mrk 335 with** *NuSTAR***: A Comparative Study**

**Santanu Mondal \* and C. S. Stalin**

Indian Institute of Astrophysics, II Block, Koramangala, Bangalore 560034, India; stalin@iiap.res.in **\*** Correspondence: santanu.mondal@iiap.res.in

**Abstract:** We present a detailed spectral study of the narrow-line Seyfert 1 galaxy, Markarian 335, using eight epoch observations made between 2013 and 2020 with the *Nuclear Spectroscopic Telescope Array*. The source was variable during this period both in spectral flux and flow geometry. We estimated the height of the Compton cloud from the model fitted parameters for the whole observation period. This allowed us to investigate the underlying physical processes that drive the variability in X-rays. Our model fitted mass varies in a narrow range, between (2.44 <sup>±</sup> 0.45 <sup>−</sup> 3.04 <sup>±</sup> 0.56) <sup>×</sup> <sup>10</sup>7*<sup>M</sup>*, however, given the large error bars, it is consistent with being constant and is in agreement with that known from optical reverberation mapping observations. The disk mass accretion rate reached a maximum of 10% of the Eddington rate during June 2013. Our study sheds light on mass outflows from the system and also compares different aspects of accretion with X-ray binaries.

**Keywords:** galaxies: active; galaxies: jets; galaxies: nuclei; radiative transfer; Seyfert 1 objects: individual: Mrk 335

### **1. Introduction**

Active galactic nuclei (AGN) host an accretion disk with an energetic X-ray-producing Compton cloud (so-called corona) around a supermassive black hole at the center. The emitted X-ray radiation also acts as one of the most direct probes of accretion onto AGN. AGN show rapid flux and polarization variations, which indicate that the observed high energy radiation mainly originates from the inner few to tens of Schwarzschild radii (*r<sup>s</sup>* = 2*GM*BH/*c* 2 ; *M*BH, G, and c are the mass of the black hole, gravitational constant, and the speed of light, respectively) from the event horizon of the black hole [1]. The power-law (PL) component is widely accepted as the effect of inverse Compton scattering (ICS) of thermally produced soft photons from the accretion disk by a corona of hot electrons at the inner edge of the disk [2,3]. However, the geometry and size of the corona, as well as the physical mechanisms governing the energy transfer between the disk and the corona, are not well understood, which necessitates a physical model to better understand the observed signatures in them.

There are proposed models in the literature [4] that consider the corona to be the region between the truncation radius and the innermost stable circular orbit. However, it is not clear why the disk truncates at a certain radius from the central black hole and how the truncation radius is connected with the corona. Furthermore, most of the models in the literature [5,6] use optical depth, the coronal temperature, or the spectral index as a parameter to compute the spectrum from the corona. None of these are the basic physical quantities of accretion. According to the two-component advective flow (TCAF) model [7,8], at a certain distance from the black hole (BH) where the gravitational force balances with the centrifugal force, shock forms by the low angular momentum, hot, sub-Keplerian halo, and satisfies Rankine–Hugoniot conditions, which is the region of the truncation of the disk. Apart from that, as the two forces balance each other, accretion of matter virtually stops and its velocity decreases, which also increases the optical depth of the corona region. As the gravitational force dominates closer to the BH, velocity again

**Citation:** Mondal, S.; Stalin, C.S. Changing Accretion Geometry of Seyfert 1 Mrk 335 with *NuSTAR*: A Comparative Study. *Galaxies* **2021**, *9*, 21. https://doi.org/10.3390/ galaxies9020021

Received: 19 February 2021 Accepted: 23 March 2021 Published: 25 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

increases and the flow passes through the inner sonic point and falls onto the BH, therefore the flow is transonic [7]. Beyond this shocked region, both the disk and halo matter pile up to decide the optical depth and temperature of the corona region. The same region also upscatters the incoming soft radiation from the disk via ICS. A typical X-ray spectrum of AGN in the 2–10 keV region shows primarily the signature of a PL. Due to ICS, the corona cools down and its area decreases, leading to a low brightness level and a softer spectrum [9]. These physical properties and the dynamics of the flow make TCAF more favorable as a physical model than other existing models in the literature. In addition to the above, TCAF uses mass accretion rates and the mass of the BH as model parameters, which are the basic physical quantities of a flow. Furthermore, the same shock location, which can explain the spectral features, may also be able to explain the temporal features from its oscillation [10,11]. Therefore, among the various models available in the literature to understand the observed X-ray emission in AGN, we preferred to consider the TCAF model for our study.

The TCAF model has five parameters: (i) mass of the black hole (*M*BH), (ii) disk accretion rate (*m*˙ *<sup>d</sup>* ), (iii) halo accretion rate (*m*˙ *<sup>h</sup>* ), (iv) location of the shock (*Xs*), and (v) shock compression ratio (R). Increasing *m*˙ *<sup>d</sup>* and keeping the other parameters fixed increases the number of soft photons from the Keplerian disk [12], making the spectrum softer. Higher *m*˙ *<sup>h</sup>* increases the corona temperature and hardens the spectrum. Similarly, increase of either *X<sup>s</sup>* or R leads to hardening of the spectrum. However, in reality all parameters change in multidimensional space. Therefore, such variations may not sustain due to non-linear changes in optical depth and coronal temperature in different epochs. A detailed parameter study has been made in [13]. In recent years, the TCAF model has been implemented in XSPEC and has been used widely to study both X-ray binaries (XRBs) [14–16] and AGN [17–19]. However, there are physical processes that are not yet incorporated in the current TCAF model, e.g., jets, bulk motion Comptonization, and the spin effect of the BH.

Apart from the above components, many AGN exhibit extra features in their X-ray spectra that likely originate from the accretion disk [20]. The so-called X-ray reflection features produced by an accretion disk might be because of its illumination from the central compact object, such as a magnetically dominated corona residing above the surface of the disk (e.g., [2,21,22]). A prominent feature in the X-ray spectrum is the Fe K*α* emission line at around 6.4 keV, which is due to fluorescence in a dense and relatively cold medium [23–25]. The shape of the Fe K*α* line is a powerful probe of the general relativistic effects close to the BH [26,27], leading to estimates of the spin of the BH [28–30]. Indeed, observations over the last decades by X-ray satellites have uncovered relativistically broadened Fe K*α* lines in the spectra of several AGN [31–33] and black hole XRBs (e.g., [34]). Models of X-ray reflection spectra [5,35] show additional features that can collectively constrain the ionization state, heating, and cooling of the illuminated surface [36].

Mrk 335 is a bright, narrow-line Seyfert 1 (NLS1) galaxy at a redshift of z = 0.026 [37], with a black hole mass *<sup>M</sup>*BH <sup>=</sup> 2.6 <sup>×</sup> <sup>10</sup>7*<sup>M</sup>* [38], and shows ionized absorption in the X-ray and ultra-violet (UV) bands [39]. It has been observed to go into extremely low-flux states [40] where the soft X-ray flux dropped by a factor of up to ∼30, while the hard flux dropped only by a factor of ∼2 in 7 years. Using observations from XMM-Newton, Ref. [41] found signatures of absorption and high reflection fractions in the spectrum of Mrk 335 in its lowest flux state, whereas at the intermediate flux state the observed X-ray spectrum is explained well by a blurred reflection model without the requirement of variable absorption [42]. Ref. [43] estimated a high-frequency lag of ∼150 s between the continuum-dominated energy bands and the iron line and soft excess components for this source. This time lag suggests that the continuum source is located very close to the central black hole and that relativistic effects are worth considering. Using combined *Swift* and *NuSTAR* observations, Ref. [44] interpreted the X-ray flare during 2014 as arising from the vertical collimation and ejection of the X-ray-emitting corona at a mildly relativistic velocity, which causes the continuum emission to be relativistically beamed away from the disk. Ref. [45] discussed the effect of the geometry of the corona on the relativistically blurred X-

ray reflection arising from the accretion disk, which can also explain the variability between low- and high-flux states. Ref. [46] performed structure function analysis using long-term *Swift* optical/UV and X-ray data for Mrk 335 and showed that the X-ray low-flux state could be due to the physical changes in the corona or absorption, whereas the variability in the optical/UV band is more consistent with the thermal and dynamic timescales associated with the accretion disk. Ref. [47], studied the low-flux state data using *XMM-Newton* and observed absorption lines from a highly ionized outflowing wind.

Several studies on Mrk 335 clearly show that the system is highly variable, leaving a range of possibilities for its dynamical behavior and emission features. Mrk 335 is known to show changes in geometry [45], and these can be found from a disk-based model fit such as TCAF to data. It is not clear to date if there is any change in the mass accretion of the source, and if so, what effects it can have on the geometry of the corona in the source. To investigate the above, in this work we chose this object and carried out an analysis of the X-ray data on the source acquired by *NuSTAR* during the period 2013–2020. This paper is organized as follows: in the next section, we describe the observation details and the analysis procedures. In §3, we explain our results obtained from model fits to the data. We summarize our conclusions in the final section.

### **2. Observation and Data Analysis**

In the present manuscript, we analyzed archival data (https://heasarc.gsfc.nasa.gov/ docs/cgro/db-perl/W3Browse/w3browse.pl (accessed on 10 June 2020)) from *NuSTAR* observations of Mrk 335 made during 2013–2020. During this time interval Mrk 335 was observed nine times; for one observation data quality was not good, so we considered the remaining eight observations. The details of the observations are listed in Table 1. The *NuSTAR* data in the energy range of 3.0–30 keV (as the data are noisy above 30 keV), were extracted using the standard NUSTARDAS V1.3.1 (https://heasarc.gsfc.nasa.gov/ docs/nustar/analysis/ (accessed on 10 June 2020)) software. We ran the NUPIPELINE task to produce cleaned event lists and NUPRODUCTS for generation of the spectra. We used a region of 8000 for the source and 10000 for the background using ds9. The data were grouped by the *grppha* command, with a minimum of 30 counts per energy bin. The same binning was used for all the observations. For spectral analysis of the data we used XSPEC (https://heasarc.gsfc.nasa.gov/xanadu/xspec/ (accessed on 10 June 2020)) [48] version 12.8.1. We used the absorption model TBABS [49] with the Galactic hydrogen column density fixed at 3.6<sup>×</sup> <sup>10</sup><sup>20</sup> atoms cm−<sup>2</sup> [50] throughout the analysis.

**Table 1.** Log of observations.


### **3. Results and Discussion**

We fit the *NuSTAR* observations of Mrk 335 taken between 2013 to 2020. During this observation period the source showed significant variability in spectral flux (see Figure 1). We performed spectral analyses using different models. First, we performed spectral fitting using a simple power-law (PL) model as TBABS(GAUSS+PL), where the PL index (Γ) varied from 0.72–1.84, a change by a factor greater than two, which is clearly an indication of significant changes in the flow behavior and corona properties. The model fitted parameters are provided in Table 2. Our model fits show that the line energy and width vary in a broad

range, which point to complex geometry changes and gravity effects (more especially line broadening) in the source.

**Figure 1.** Spectra of all eight observations in the 3–30 keV energy range. Variability of the source is evident.


**Table 2.** Best-fitting parameters with the TBABS(GAUSS+PL) model.

ΓPL and *N*PL are the PL index and normalization. *E<sup>g</sup>* and *σ<sup>g</sup>* are the Gaussian line energy and width, respectively.

In addition to the simple PL model, we also modeled the observed spectra using the complex phenomenological model PEXRAV [51] and the physical model TCAF [8]. The results of PEXRAV model fits are given in Table 3. Our PL model fits indicate that the source passed through hard and soft spectral states similar to XRBs, where the timescale for changing from one state to other is in the order of a few days to weeks, which is the viscous timescale ([52] and references therein). We found a similar timescale when the corona changed from its maximum size to its minimum, which is around 12 days. However, as the viscous timescale for AGN is in the order of a few hundred to a few Myr (scaled by the mass of the BH), it may not be possible to observe a similar timescale for other AGN. In future we aim to explore this aspect of accretion to estimate the viscosity of the flow.

From PEXRAV model fits, we found the reflection fraction to be high with *R*ref > 0.9 for all the epochs. When the Fe abundance (*A*Fe) was made a free parameter, *A*Fe was found to vary from sub-solar to super-solar values during the epochs analyzed here, which is quite unphysical. It has been pointed out by [53] that reflection model fits to observed X-ray spectra are generally found to yield high *A*Fe values. In addition, according to [54], the high *A*Fe obtained from model fits to data could be due to some unknown physical effects being overlooked in current models. Therefore, for PEXRAV model fits, we froze *A*Fe to solar value. For the observation day MJD = 56,468, we required one extra Gaussian

line component at low energy ∼5 keV. From the line component and its width, it can be seen that both narrow and broad lines are present in this epoch. We kept the disk inclination (*i*inc) fixed to 45◦ throughout [55]. Next we applied the physical model TCAF, having the form TBABS(TCAF+GAUSS), to extract the accretion flow parameters. For all observations, goodness of fit is more or less similar to the PEXRAV model. The TCAF model fitted parameters are provided in Table 4. For some observations, better fits were achieved after adding some additive model components, which are detailed in the table. For the majority of the epochs, the *χ* <sup>2</sup>/*do f* obtained from PEXRAV and TCAF model fits are in agreement, whereas for three epochs, the *χ* <sup>2</sup>/*do f* from TCAF fits are marginally larger than those obtained from PEXRAV model fits. This might be due to differences in the spectral components between models, e.g., TCAF does not include line features, which may give relatively higher *χ* <sup>2</sup>/*do f* . In Figure 2, we show different model fitted spectra for the OBSID 60001041002/3 in the left/right panels of the figure. Figure 3 shows the same spectral fitting but for the OBSID 60001041005 (left panel) and 80001020002 (right panel). The rest of the observational fits are shown in Appendix A.

**Table 3.** Best-fitting parameters with the TBABS(PEXRAV+GAUSS) model.


Γ, *E*cut, and *R*ref are model PL photon index, cutoff energy, and reflection scaling factor, respectively. *E<sup>g</sup>* and *σ<sup>g</sup>* are the Gaussian line energy and width. We kept the disk inclination fixed at 45◦ [55] and *A*Fe at Solar abundance value. *a* : Gaussian component was added at 5.02 ± 0.18 keV with line width 0.64 ± 0.20 keV. The origin of this line is not clear yet, however, a similar line was observed for Mrk 335 earlier [56].



*m*˙*<sup>h</sup>* and *m*˙*<sup>d</sup>* represent TBABS(TCAF+GAUSS) model fitted sub-Keplerian (halo) and Keplerian (disk) rates, respectively. *X<sup>s</sup>* and *R* are the model fitted shock location and shock compression ratio values, respectively. *E<sup>g</sup>* and *σ<sup>g</sup>* are the Gaussian line energy and width. *<sup>a</sup>* : Gaussian component was added at 3.44 <sup>±</sup> 0.07 keV with line width 1.55 <sup>±</sup> 0.21 keV. *<sup>b</sup>* : DISKLINE [26] component was added with line energy at 6.12 ± 0.10 keV, powerlaw of emissivity (*β*) = −2.98 ± 0.70, inner radius (*R*in) = 34.6 ± 24.4 *rg*(*GM*/*c* 2 ), and disk inclination was frozen at 45◦ . *c* : ZXIPCF [57] multiplicative model component was used for parameters: column density (*NH*) = <sup>68</sup> <sup>±</sup> 10.91 <sup>×</sup> <sup>10</sup><sup>22</sup> cm−<sup>2</sup> , covering fraction (*f<sup>c</sup>* ) = 0.45 <sup>±</sup> 0.05, *log<sup>ξ</sup>* <sup>=</sup> 1.2 <sup>±</sup> 0.3. *<sup>d</sup>* : Gaussian component was added at 4.16 ± 0.11 keV with line width 0.29 ± 0.14 keV.

**Figure 2.** Sample fit of 3–30 keV spectra with PL, PEXRAV, and TCAF models for OBSIDs 60001041002 (**left panel**) and 60001041003 (**right panel**) along with the residuals.

**Figure 3.** Same as Figure 2 but for the OBSIDs 60001041005 (**left panel**) and 80001020002 (**right panel**) along with the residuals.

We used TCAF model fitted parameters to estimate the geometrical height of the shock (*H*shk). The height of the corona is basically the height of the shock, as the shock is the boundary layer of the corona. We estimated (*H*shk) using the equation below (see also [14]):

$$H\_{\rm shk} = \left[\frac{\gamma(R-1)X\_s^2}{R^2}\right]^{1/2} \,\mathrm{}^\prime\,\tag{1}$$

where *γ* is the adiabatic index, *X<sup>s</sup>* is the location of the shock or the boundary of the corona, and R is the shock compression ratio (= *ρ*+/*ρ*−), a ratio of the density of the downstream to the density of the upstream of the flow.

In Figure 4, we show the variation of various model parameters obtained from TCAF model fits as well as the variation of the hardness ratio (HR) with time. The halo rate was always higher than the disk rate by an order of magnitude or more, which implies that the flow was dominated by low angular momentum matter, which might be accreted from the wind or host galaxies. The *m*˙ *<sup>d</sup>* was found to vary by a factor of ∼40 from 0.24 to 10% of the Eddington rate and the *m*˙ *<sup>h</sup>* varied between 1.2–3.1 times the Eddington rate. The size of the shock location (*Xs*) or corona changed significantly and reached up to 6 *r<sup>s</sup>* during 25 June 2013 (60001041005) and 8*r<sup>s</sup>* during 2014 (80001020002). For OBSID 60001041005, we required an extra-broad (1.55 keV) Gaussian component at a low energy of 3.44 keV, which was also found to be broadened by strong gravitational effects [27]. For OBSID 80001020002, we required an additive DISKLINE [26] component at a line energy of 6.12 keV, with emissivity power-law index (*β*) ∼ −3.0 and *R*in = 24.4*rg*(*GM*/*c* 2 ), as the current TCAF model does not include line emission due to gravitational effects in the fit. It is worth noting that the *X<sup>s</sup>* is achieved for the highest *m*˙ *<sup>d</sup>* , which might be due to the cooling effect inside the corona. As the accretion rate increased, more disk photons got intercepted by the corona. This cooled the corona, causing the shock to move inwards and thus causing a significant change in the size of the corona. Such change in the corona could also be due to the activity of the jet, which extracted a significant amount of thermal energy and contracted the corona [58]. Therefore, it is also possible to establish a jet–disk connection using TCAF model fits to AGN spectra similar to XRBs ([59–61] and references therein).

**Figure 4.** Two-component advective flow (TCAF) model fitted parameter evolutions with observation days are shown along with hardness ratio (HR) estimated from the power-law (PL) model fitted fluxes.

Such movement of the shock can give rise to the observed variability in spectral and temporal properties [62]. During 2014, *m*˙ *<sup>h</sup>* further increased and made the corona hotter and the shock receded slightly. During 2018 the shock moved further away and the corona became bigger, therefore intercepting more soft photons and generating highenergy photons, which can also ionize the disk atmosphere. For this particular observation, we required the partial covering fraction model (ZXIPCF), with a covering factor (*f<sup>c</sup>* = 0.45) and low ionization parameter (*logξ* = 1.2). For OBSID 90602619004, during 2020, we required another narrow line (0.29 keV) component, when the shock again moved inward. The model-fitted shock compression ratio also varied in a broad range, which also dictates the strength of the shock and the optical depth of the corona. The 5th panel of

Figure 4 (from the top) shows the variation of this parameter. The bottom panel of Figure 4 shows the estimated height of the corona, which changes significantly for the whole observation period.

The mass of the BH is one of the parameters in TCAF. Therefore, keeping it as a free parameter in the TCAF model fits to the observed spectra will yield an *M*BH value for Mrk 335. We kept *M*BH as a free parameter during our fitting and we found *M*BH to vary in a range between (2.44 <sup>±</sup> 0.45 to 3.04 <sup>±</sup> 0.56) <sup>×</sup>107*<sup>M</sup>*. Considering the large error bars, the derived BH mass is consistent with being constant. Our derived *M*BH is consistent with that estimated by [38] using optical reverberation mapping observations, however, it is an order of magnitude larger than that obtained by [53]. Such a low mass found by [53] could be due to them not considering an expanded corona in their model fit to the data. Our results on *M*BH also show that by fitting accretion-disk-based models such as TCAF to observed X-ray spectra, one can estimate the mass of BHs in AGN. We also found that freezing *M*BH to some fixed value from the above range and redoing the fit has a negligible effect on other derived parameters, such as *m*˙ *<sup>d</sup>* , *m*˙ *<sup>h</sup>* , *X<sup>s</sup>* , and R.

The viscous timescale in AGN is much longer compared to that of XRBs. At small timescales (in the order of a few days or months), significant changes in the accretion rate are not expected, similar to the case for heating and cooling rates. Thus, at such timescales, variability is expected to be less. This is in fact observed in the radio-quiet category of AGN and accretion-disk-based models can explain the observed flux variations in them. However, this might not be the case in the radio-loud category of AGN, as relativistic jets play a dominant role in the flux variations observed in them. Even in those sources where the ejection of jets extracts thermal energy from the corona, the change in the shock location can be drastic in them even though the cooling is less. Results on this will be reported elsewhere.

### **4. Conclusions**

In the present paper, we analyzed *NuSTAR* data for Mrk 335, observed between 2013 and 2020, to understand the dynamics of the flow and the accretion behavior of the source. We found that the source was significantly variable both in spectral flux, accretion geometry, and reflection fraction. We also found the geometry of the corona to change between epochs. Such a change can affect the reflection fraction and the spectral energy distribution of the illuminating radiation, and consequently the ionization rate. From the TCAF model fits we obtained the dynamics of the flow along with the geometry change of the corona and accretion rates. In our TCAF model fits, the line profiles due to relativistic effects were taken into account using an additive DISKLINE model wherever needed rather than using it throughout for all observations. Among other models, even though the XILLVER model has relativistic and reflection effects incorporated, the accretion dynamics and the origin of corona are still lacking in the model. Therefore we did not take into account such models in our current study. Below we provide the key findings on the variable nature of the source.


**Author Contributions:** Conceptualization, methodology, formal analysis, writing—original draft preparation, S.M.; conceptualization, supervision, writing—review and editing, C.S.S. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** We used archival data for our analysis in this manuscript. Appropriate links are given in the manuscript. For the details of the data fitting, one can directly contact the first author.

**Acknowledgments:** We thank both referees for their constructive and insightful suggestions that improved the quality of the manuscript. SM acknowledges the Ramanujan Fellowship (# RJF/2020/000113) by SERB, Govt. of India. This research made use of the *NuSTAR* Data Analysis Software (NUSTARDAS) jointly developed by the ASI Science Data Center (ASDC), Italy, and the California Institute of Technology (Caltech), USA. This research also made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by NASA/Goddard Space Flight Center.

**Conflicts of Interest:** The authors declare no conflicts of interest.

### **Appendix A**

Here we show the spectral fitting plots for the rest of the observations using all three models.

**Figure A1.** Same as Figure 2 but for the OBSIDs 80201001002 (**left panel**) and 90602619004 (**right panel**) along with the residuals.

**Figure A2.** Same as Figure 2 but for the OBSIDs 90602619006 (**left panel**) and 90602619008 (**right panel**) along with the residuals.

### **References**


**Chandra B. Singh 1,\* ,†, David Garofalo 2,† and Benjamin Lang <sup>3</sup>**

	- benjamin.lang.447@my.csun.edu

**Abstract:** The discovery of 3C 273 in 1963, and the emergence of the Kerr solution shortly thereafter, precipitated the current era in astrophysics focused on using black holes to explain active galactic nuclei (AGN). But while partial success was achieved in separately explaining the bright nuclei of some AGN via thin disks, as well as powerful jets with thick disks, the combination of both powerful jets in an AGN with a bright nucleus, such as in 3C 273, remained elusive. Although numerical simulations have taken center stage in the last 25 years, they have struggled to produce the conditions that explain them. This is because radiatively efficient disks have proved a challenge to simulate. Radio quasars have thus been the least understood objects in high energy astrophysics. But recent simulations have begun to change this. We explore this milestone in light of scale-invariance and show that transitory jets, possibly related to the jets seen in these recent simulations, as some have proposed, cannot explain radio quasars. We then provide a road map for a resolution.

**Keywords:** black hole physics; rotating black holes; relativistic jets; active galactic nuclei; supermassive black holes; radio galaxies

### **1. Introduction**

Radio quasars are active galaxies that harbor strong, collimated jets, mostly of FRII radio morphology [1] , but that also shines brightly in the optical, suggesting they are accreting black holes in radiatively efficient mode [2]. They are not distributed randomly in space and time, with a greater probability of being found in isolated environments and at higher redshifts, at least compared to FRI radio galaxies, which are found in richer environments and comparably lower redshifts [3,4]. FRI radio galaxies differ from radio quasars not only in their jet morphology but also in their 'radio mode' accretion, as opposed to 'quasar mode', indicating the disk is radiatively inefficient.

Many X-ray binaries cycle through states with radio-emitting jets present during so-called 'hard' states, but absent during so-called 'soft' states [5,6]. The consensus is that the former is related to radiatively inefficient accretion, similar to jet mode accretion in FRI radio galaxies, while the latter is associated with radiatively efficient accretion, similar to quasar mode ([7–10] and references therein). It is often found that as X-ray binaries transition from the hard state to the soft one, a transitory, ballistic, or more powerful and collimated jet, is generated [11,12]. It has been claimed that such a jet taps into black hole rotational energy [13] unlike the hard state jet [9]. Despite these general properties, a subclass of X-ray binaries does not suppress jets in soft states [14]. And when these neutron star X-ray binaries do suppress jets, their transitory jets tend to be weaker [15].

The observational evidence described above points to a picture in which accreting supermassive black holes combine radiatively efficient accretion with jets while stellar-mass

**Citation:** Singh, C.B.; Garofalo, D.; Lang, B. Powerful Jets from Radiatively Efficient Disks, a Decades-Old Unresolved Problem in High Energy Astrophysics. *Galaxies* **2021**, *9*, 10. http://doi.org/10.3390/galaxies9010010

Received: 6 January 2021 Accepted: 23 January 2021 Published: 26 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

black holes do not. In the past, and again recently via general relativistic magnetohydrodynamic (GRMHD) simulations, resolving this issue hinges on the assumption that radio quasars are the large scale analog of transitory burst states in black hole X-ray binaries, during which X-ray binaries are approaching the soft state, so a stable radiatively efficient disk is in the process of formation, although it has not yet formed. The goal of this work is to highlight the incompatibility between well-accepted theory and the observations. We then produce a roadmap for GRMHD simulations designed for getting at a better solution, one that appeals to ideas that have been available for a decade.

In Section 2, we analyze the history of GRMHD simulations in their struggle to generate thin disks in an attempt to understand the disk radiative efficiency. The point here is to understand the conditions that produce jet suppression. Within the context of that history, we single out recent simulations by [16,17] that promise to take our understanding of jet formation in thin disks to a new level. This leads to an exploration of the jet-disk connection in light of scale invariance and the roadmap alluded above. We then conclude.

### **2. Disks and Jets in GRMHD**

Within the last half-decade, GRMHD simulations have pushed the boundary of disk thickness to extremes, with values about an order of magnitude smaller than two decades ago. The height to radius ratio, or scaleheight, *H*/*R*, is found to be on average equal to 0.20–0.26 in the simulations dating back a decade and a half ago [18–24], while, a decade later, we see *H*/*R* decrease to 0.13 [25]. In-between we see a disk scaleheight of *H*/*R* ∼ 0.1 associated with disk radiative efficiency of 6% that of the relativistic Novikov-Thorne model [26], followed up with disks as thin as *H*/*R* ∼ 0.06 but up to 10% difference in efficiency with respect to the Novikov & Thorne disk [27,28]. Similar results were found in [29], with *H*/*R* ∼ 0.1 and deviation from Novikov & Thorne disks of 5%. By 2019 we see *H*/*R* ∼ 0.03 [16,17]. To model radio quasars, simulations need to produce disks with high radiative efficiency, as well as high jet efficiency. The quasar-like radiation from the nucleus appears to require a scaleheight of 0.01 from analytic models. Achieving this has been a challenge. The decrease in disk efficiency associated with an increase in jet efficiency was thought to be a good description of hard state jets in X-ray binaries and of radio galaxies, both observed to produce X-ray and radio jet signatures but weak emission lines. But radio quasars appear to upend this inverse trend between jet and disk efficiency. Ref. [30] have explored the blazar subclass of radio quasars (flat spectrum radio quasars (FSRQs), attempting to fit observations with simulations of disks in the context of moderately thin disks (those of [25]). We will explore this in the next section but the basic conclusion is the need for some missing ingredient that allows for both large jet and disk efficiency. Finally, Ref. [16] have produced the thinnest disks in GRMHD, with *H*/*R* ∼ 0.03, with the absence of jet suppression. This is an important milestone for simulations. Ref. [16,17] also attempt to explain radio quasars, which they explore in the context of scale invariance, anchoring their arguments to transitory ballistic jets observed in X-ray binaries. We explore their analysis in that context, as well.

### *2.1. FSRQ Jets from Moderately Thin Disks*

Flat-spectrum radio quasars (FSRQs) are the blazar subclass of active galactic nuclei (AGN) emitting the most relativistic jets along our line of sight with relatively high accretion rates. Using gamma-ray luminosity from the Fermi Large Area Telescope as a proxy for jet powers, and independent measurements of black hole mass, Ref. [30] produce the best fit correlation between jet power and black hole mass from observations of 154 FSRQs. The ideas are built on the work of [31] who uncovered a correlation between gamma-ray luminosity *L<sup>γ</sup>* and total blazar jet power *Pjet* given by

$$
\log\_{10} P\_{\text{jet}} = 0.51 \log\_{10} L\_{\gamma} + 21.2 \,\text{.}\tag{1}
$$

in units of erg/s. Soares & Nemmen (2020) compiled observational data for 154 FSRQs and fitted a relation between *L<sup>γ</sup>* and black hole mass M, obtaining

$$
\log\_{10} M = 0.37 \log\_{10} L\_{\gamma} - 8.95 \,\text{.}\tag{2}
$$

with *M* in terms of solar masses and *L<sup>γ</sup>* in erg/s. Combining Equations (1) and (2), we obtain

$$
\log\_{10} P\_{\text{jet}} = 1.38 \log\_{10} M + \text{33.53},\tag{3}
$$

which produces constraints on models that connect jet power to black hole mass. Ref. [30] show that 97% of their FSRQ sample satisfies jet energetics as a function of black hole mass (Equation (3)) for moderately thin disks (*H*/*R* = 0.13). If the radiative efficiency in such moderately thin disks is insufficient to explain the quasar-like spectrum, the success of equation (3) to the sample becomes moot. In that case, it means the scaleheight must satisfy *H*/*R* < 0.1, which means the GRMHD simulations adopted by [30] fail to explain the sample. If, as mentioned, radiatively efficient disks satisfy *H*/*R* = 0.01, the mismatch is of course much worse. Ref. [30] report that it drops from 0.098 to <sup>6</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> , which is 163 times smaller. The basic question here is whether or not the disk thickness that is compatible with jet energetics, is also compatible with the required radiative efficiency. What has been a constant staple in GRMHD simulations is the trend noted above. The thickness that seems to be needed to explain the high enough jet efficiency works against the thinness that is needed to explain the radiative output. A common way out of the above conundrum has been to assume that radio quasars do not have radiatively efficient disks into the inner regions and that while further out the radiation escapes, the energy is retained in the inner regions and the disk scaleheight puffs up there as a result. And this thick disk would be needed to explain the formation of a jet. This, it was thought for decades, would explain a quasar-like spectrum due to the outer cool, radiatively efficient disk, coupled to a powerful jet produced by a thick inner disk. Soares & Nemmen (2019) also mention this possibility. Several recent observations show that this idea fails ([32–35] and references therein).

While magnetically arrested GRMHD disk simulations struggle from a numerical perspective to accurately evolve strongly magnetized regions, radiation is arguably a more difficult problem. As a result, it is treated with a variety of prescriptions from ad hoc cooling functions to keep the disk as thin as possible (e.g., [25]) to more realistic ones that include radiative transport [36]. Given the differences in how the disk is cooled, the radiative nature of the disk can vary greatly among simulations, giving little confidence that GRMHD is providing insights into radiatively efficient disk physics. In [25], for example, the efficiency is twice that of Novikov & Thorne, but it is all emitted within the very central region. This appears difficult to square with typical quasar spectra.

A promising result is obtained in the GRMHD simulations of [16], with the GPUaccelerated code H-AMR [37], which simulates the thinnest possible tilted disk with good enough resolution to resolve the magnetorotational instability with *H*/*R* = 0.03 around a black hole of spin 0.9375. This simulation also provided a demonstration within a turbulent MHD accretion disk of the Bardeen-Petterson alignment of the disk and black hole. The total efficiency of the disk was found to be higher than that of the Novikov & Thorne prediction by a factor of 3. Perhaps most importantly, a powerful jet was present.

### *2.2. Jet and Disk Efficiency in GRMHD*

Attempts at understanding the compatibility and/or difference between GRMHD and their ability to model thin disks and their compatibility with jets to model radio quasars are obscured in that some GRMHD simulations incorporate or produce physics that is completely different from others. For example, some simulations argue that the Novikov & Thorne solution is not too different from what the disk produces in GRMHD (e.g., [29,38] while other more recent simulations with magnetic fields flooding the system (e.g., [25,39–41] conclude that almost all the radiation is emitted near or inside of the innermost stable circular orbit (ISCO). Other GRMHD simulations suggest that strong magnetic fields might

be generated in situ via dynamo action [42]. What is the origin of such vastly different physical pictures? One clear candidate is the variety of different mechanisms incorporated in simulations to treat radiation, with some ad-hoc while others are more faithful to the physics. For example, Ref. [36] performed 3D GRMHD simulations taking into account the time-dependent radiative transfer equations of accretion disks with *H*/*R* ∼ 0.1 around a black hole with a spin of 0.5 using the HARMRAD code [43]. The radiative efficiency of the disk was found to be slightly lower than that of the Novikov & Thorne prediction while in the case of [25], the efficiency was twice the efficiency of Novikov & Thorne when the effects of scattering and absorption of radiation were not taken into account. These different processes change the efficiency but also the location where the radiation is emitted, as already discussed. Ref. [44] performed a radiative GRMHD simulation of a geometrically thin, sub-Eddington accreting disk (*H*/*R* ∼ 0.15) around a zero spin black hole using the KORAL code [45,46]. Although a significant amount of dissipation was found inside the marginally stable orbit as in [25] simulations, the efficiency of the disk was found to be very close to that of Novikov & Thorne. All the results from available GRMHD simulations have been summarized in Table 1.

Uncertainty very much still dominates our understanding of numerical simulations of accretion onto black holes, but a bottom line is beginning to emerge: Strong disk magnetic fields seem to be a by-product of strong black hole threading magnetic fields but strong disk magnetic fields do not allow disks to remain thin [47–49]. And disks that are not thin might not be able to radiate efficiently. It seems there is possibly another factor that can allow the compatibility between the thinness of the disk and the condition of jet formation.

### *2.3. Scale Invariance and the Jet-Disk Connection*

Let us assume that jet efficiency is sufficient in GRMHD to explain radio quasars. We will now show that arguments explaining radio quasars using these simulations nonetheless run into problems. As discussed by [16], radiatively efficient disks appear not to produce relativistic jets, which suggests to them that they are uncovering a transitional process that manifests itself in black hole X-ray binaries as the disk evolves from the hard state to the soft state [7]. The first issue here is the need to show in GRMHD that as the disk collapses from the hard state and transitions toward the soft state, the jet power depends on black hole spin, whereas in the state that precedes it (the hard state), the jet power is less dependent on black hole spin. In other words, it is crucial that this time-dependent scenario must be simulated. These conclusions are based on the observation that jet power does not correlate with a spin in the hard state [9], while it may correlate with it in the transitory state [13,50]. Second, and more fundamentally, the time evolution implicit in the above scenario does not lend itself to scaling up this transitory jet and applying it to radioquasars [51,52]. This crucial point has by and large gone unnoticed. The problem is that radio quasars distribute themselves on average at higher redshift compared to FRI radio galaxies and such a distribution cannot emerge from transitions that take hard state jets into transitory ballistic jets, which reverse the time sequence. The scale-invariant approach, thus, predicts radio quasars occupying lower redshifts compared to FRI radio galaxies. If we incorporate the full cyclical behavior of X-ray binaries in a scale-invariant application to radio quasars, then we would conclude that radio quasars and FRI radio galaxies do not show any redshift dependent difference, but that best-case scenario is not observed. In short, using the time evolution of X-ray binaries in trying to understand radio quasars predicts either that radio quasars are distributed at relatively lower redshifts or that they are not distributed differently in redshift compared to FRI radio galaxies. But the observations are not compatible with these scenarios.


**Table 1.** Results from some representative general relativistic magnetohydrodynamic (GRMHD) simulation works showing black hole spin (a/M), scale height (*H*/*R*), disk radiative efficiency (*ηr*), jet efficiency (*ηj* ), total efficiency (*ηT*), and cooling method implemented. Here, *ηNT* means efficiency predicted by the Novikov Thorne (1973) model, and NA means not available information.


These issues—and many others—have been resolved in semi-analytic models [4] via the introduction of a key feature for accreting black holes, namely counterrotation between the disk and the black hole, a window on accretion than many have found fruitful (a subset of these are [53–68]. In counter-rotating disk configurations, the process that suppresses the jet weakens as the black hole spin increases, thereby allowing the conditions that lead to strong, collimated jets, to couple to bright disk states. The radio-loud/radioquiet dichotomy in this picture is based on a high black hole spin for both families of accreting black holes. Whereas radio quasars are high spinning counter-rotating accretion configurations, jetless quasars are high spinning, prograde accreting black holes. This is due to the small value of the inner disk boundary for high prograde configurations. Because the disk reaches deep into the gravitational potential of the black hole for high prograde spins, a greater amount of energy is generated from the disk at all disk locations, and the disk is radiatively dominated or quasar-like. Recently, we have been able to explain the lack of symmetry in the radio loud/radio quiet dichotomy with jetless (or radio quiet) AGN dominating the distribution at about 80% [33]. These ideas have allowed for theory to be compatible with scale invariance and with the observed distribution of radioloud and radio-quiet quasars across cosmic time. Our roadmap for GRMHD simulations involves, therefore, exploring the nature of the jet-disk connection for corotating, as well as counterrotating accreting black holes. Whereas the jet efficiency was found to be slightly higher in the former, we suspect that, with better treatment of the radiation processes, the results will start to shift, and counterrotation will emerge as a key ingredient.

### **3. Conclusions**

The existence of a subset of active galaxies with high observed radiative efficiency and powerful jets—radio quasars—has remained a major unsolved problem in high energy astrophysics for decades. In this work, we have explored the state of the art in numerical simulations of accretion onto black holes and find that where the comparison to observation is possible, tensions arise. We find a variety of very different physical scenarios that fail to produce a coherent picture for radio quasars and their FSRQ subclass from GRMHD. And we have singled out what appears to be the problem: the strong disk magnetic fields that accompany the strong black hole-threading field work to support greater disk thickness, which in turn decreases the radiative efficiency of the disk. How can we simulate accreting black holes capable of sustaining strong black hole horizon magnetic fields despite weak magnetic fields in their disk? The simulations of [16,17] constitute a milestone in this respect since they produce strong jets despite unprecedented small *H*/*R* values. Much work is required to single out the physical processes that would allow such disks to still drag the sufficiently strong magnetic field onto the black hole despite the disk thinness. And, this would need to be understood and juxtaposed to simulations where increased disk thinness has the opposite effect on the magnetic field threading the black hole, or on some other quantity associated with jet suppression. Whatever scale-invariant processes will be identified, it is clear that they cannot be associated with transitory ballistic jets in X-ray binaries. We have then made contact with the idea that counterrotating black holes may resolve such issues and have thus encouraged the GRMHD community to go back and explore the jet-disk connection in that context with these new simulations.

**Author Contributions:** Conceptualization, D.G. and C.B.S.; methodology, D.G.; validation, D.G., C.B.S., and B.L.; investigation, D.G., C.B.S., and B.L.; writing—original draft preparation, D.G. and C.B.S.; writing—review and editing, D.G. and C.B.S.; supervision, D.G.; project administration, D.G.; funding acquisition, D.G.and C.B.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China grant number 12073021.

**Data Availability Statement:** No data was generated during this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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