Detecting Wandering Intermediate-Mass Black Holes with AXIS in the Milky Way and Local Massive Galaxies

Abstract

This white paper explores the detectability of intermediate-mass black holes (IMBHs) wandering in the Milky Way (MW) and massive local galaxies, with a particular emphasis on the role of AXIS. IMBHs, ranging within ${10}^{3-6}{\mathrm{M}}_{\odot }$, are commonly found at the centers of dwarf galaxies and may exist, yet undiscovered, in the MW. By using model spectra for advection-dominated accretion flows (ADAFs), we calculated the expected fluxes emitted by a population of wandering IMBHs with masses of ${10}^5{\mathrm{M}}_{\odot }$ in various MW environments and extrapolated our results to massive local galaxies. Around $40\%$ of the potential population of wandering IMBHs in the MW can be detected in an AXIS deep field. We proposed criteria to aid with selecting IMBH candidates using already available optical surveys. We also showed that IMBHs wandering in >200 galaxies within 10 Mpc can be easily detected with AXIS when passing within dense galactic environments (e.g., molecular clouds and cold neutral medium). In summary, we highlighted the potential X-ray detectability of wandering IMBHs in local galaxies and provided insights for guiding future surveys. Detecting wandering IMBHs is crucial for understanding their demographics and evolution and the merging history of galaxies. This white paper is part of a series commissioned for the AXIS Probe Concept Mission; additional AXIS white papers can be found at the AXIS website.

1. Introduction

Many of the black holes (BHs) observed thus far are accreting at or near the Eddington rate ${\dot{M}}_{\mathrm{Edd}}\approx 1.4\times {10}^{18}{M}_{•}\mathrm{g}{\mathrm{s}}^{-1}$, where $M_{•}$ is the mass of the compact object in solar masses. In this limiting case, the outward acceleration on a test particle resulting from radiation pressure is balanced by the inward gravitational acceleration. Notably, this is the case for high-luminosity quasars, which are characterized by super-massive BHs with masses $M_{•}>{10}^6{\mathrm{M}}_{\odot }$. In the conventional $\alpha$-disk model [1,2], ∼10% of the rest-mass energy ($M{c}^2$) of the infalling material is radiated away [3].

This standard picture of accretion has been widely tested, especially in the high-z Universe [4], where the large availability of gas makes accretion at the Eddington rate feasible [5]. However, the radiative efficiency, $ϵ$, can significantly deviate from the typical $10\%$ value, both for strongly super-Eddington ($\dot{M}\gg {\dot{M}}_{\mathrm{Edd}}$) and sub-Eddington ($\dot{M}\ll {\dot{M}}_{\mathrm{Edd}}$) accretion rates [6,7,8,9,10]. For accretion rates in the range $0.01{\dot{M}}_{\mathrm{Edd}}<\dot{M}<{\dot{M}}_{\mathrm{Edd}}$, the accreting material creates a radiatively efficient, geometrically thin and optically thick accretion disk [1]. The radiative efficiency in this particular case depends on the spin of the black hole and varies from ∼6% for non-rotating black holes to ∼32% for maximally rotating ones [11]; hence, it is ∼10% on average.

Below $1\%$ of the Eddington rate, theoretical calculations suggest that the flow enters the regime of advection-dominated accretion flow (ADAF) [12,13,14,15,16]. BHs accreting in ADAF mode exhibit radiative efficiencies several orders of magnitude lower than the typical ∼10% value. Given the rarity of conditions supporting large accretion rates in the local Universe, it is likely that a substantial fraction of BHs accretes in the ADAF mode, e.g., the super-massive BH at the center of the MW [17]. Similarly, a putative population of intermediate-mass BHs (IMBHs) wandering in galaxies would also accrete in ADAF mode. It is important to note that, while accretion processes characterized by rates lower than $1\%$ of the Eddington rate are typically denominated ADAF, the specifics of the accretion flow and its effects on the environment (e.g., the possibility of forming a jet, see Tchekhovskoy et al. [18]) depend on environmental properties (e.g., its density) and on the evolutionary history of the system.

IMBHs are a bridge between stellar mass and super-massive objects and have masses in the range ${10}^3{\mathrm{M}}_{\odot }<M_{•}<{10}^6{\mathrm{M}}_{\odot }$, although the definition greatly varies depending on the sub-field of interest. Central IMBHs have been extensively detected in dwarf galaxies; their mass generally follows the scaling relations between black hole mass and stellar mass [19]. Additionally, dwarf galaxies have active fractions ranging from ∼5% to $22\%$ [20,21]. Some of these central black holes in dwarf galaxies, and up to $z\sim 3$, are found to be significantly overmassive with respect to the stellar content of their hosts, in violation of scaling relations [22,23]. Exceptionally overmassive black holes are now systematically found in the high-z Universe [24,25] by JWST. The redshift evolution of these populations of black holes and the role that wandering black holes played in their formation (see, e.g., [26]) is still unclear. For these reasons, recent studies are focusing on investigating the existence of wandering IMBHs in the MW and massive galaxies and their orbital and radiative properties [26,27,28,29].

IMBHs potentially wandering in the MW could have formed (i) in situ and (ii) ex situ. In situ (i.e., within the galaxy) formation channels include direct collapse of high-mass quasi-stars [30,31], super-Eddington accretion onto stellar-mass BHs [32], runaway mergers in dense globular stellar clusters [33,34,35,36,37], and supra-exponential accretion on seed black holes in the early Universe [38,39]. The ex situ channel forms wandering black holes through tidal disruption of satellite/dwarf galaxies when merged into larger halos [40,41,42,43].

These wandering IMBHs accrete from the interstellar medium (ISM) at low rates $\dot{M}\ll {\dot{M}}_{\mathrm{Edd}}$, resulting in electromagnetic signatures typical of the ADAF accretion mode. A recent study [44] modeled the accretion and radiation properties of putative IMBHs with masses of ${10}^5{\mathrm{M}}_{\odot }$ wandering in the MW using five realistic ISM environments [45]: molecular clouds (MCs), cold neutral medium (CNM), hot neutral medium (HNM), warm ionized medium (WIM), and hot ionized medium (HIM). MC is the densest environment, with typical gas number densities of ${10}^2$–${10}^4{\mathrm{cm}}^{-3}$, while HIM is the most rarified environment, with typical gas number densities of ${10}^{-3}{\mathrm{cm}}^{-3}$. All results presented here consider the volume fractions of the different environments considered. MC is the most uncommon environment, occupying only ∼0.05% of the volume of the MW, while HIM is the most common, with a volume occupation fraction of ∼47%: almost half of the entire volume [44]. The mass of a perturbing black hole was chosen as the typical mass of IMBHs detected in the nuclei of dwarfs [20]. The accretion rate onto the IMBH was estimated using a Bondi rate, which was adequately adjusted to account for outflows and convection [44,46,47,48].

This white paper first summarizes the result presented in [44], which focused on the X-ray properties of wandering IMBHs in the MW. Then, it expands on the contribution that AXIS [49] could provide to detect these sources. Lastly, it predicts the observability of IMBHs wandering in local galaxies.

2. Detecting Wandering IMBHs Using X-rays with AXIS

2.1. Accretion Rates and Spectral Energy Distributions

The left panel of Figure 1 shows the distribution of accretion rates predicted for a ${10}^5{\mathrm{M}}_{\odot }$ IMBH wandering in typical ISM environments of the MW. The accretion rates range between ${10}^{-14}$ and ${10}^{-4}{\mathrm{M}}_{\odot }{\mathrm{yr}}^{-1}$; hence, they span ∼10 orders of magnitude. MC and CNM environments show the highest accretion rates because they are the densest; as such, they offer the best chance for X-ray detection of IMBHs in the MW.

As a reference, the Eddington rate for a ${10}^5{\mathrm{M}}_{\odot }$ IMBH is ${\dot{M}}_{\mathrm{Edd}}\approx 2\times {10}^{-3}{\mathrm{M}}_{\odot }{\mathrm{yr}}^{-1}$: all accretion rates predicted are strongly sub-Eddington. The resulting spectral energy distributions (SEDs) typical for the five ISM environments are shown in the right panel of Figure 1, with Eddington ratios (i.e., the actual accretion rate normalized to the Eddington rate) ranging from ${10}^{-11}$ to ${10}^{-3}$. The SEDs were calculated using a code designed specifically for ADAF mode accretion [50]. The SED peak shifts to higher frequencies with increasing accretion rates.

2.2. X-ray Observability and Selection Criteria: The Role of AXIS

The left panel of Figure 2 shows the resulting (volume-weighted) X-ray flux distribution. These results suggest that AXIS, in its proposed deep survey [51,52] with a flux limit ∼3 × ${10}^{-18}\mathrm{erg}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}$ and an area of $0.1{\mathrm{deg}}^{-2}$, will detect a fraction, in number, of ∼38% of wandering IMBHs in the MW, assuming a uniform sampling of the region occupied by the galaxy [49].

To aid in the task of selecting IMBH candidates, [44] proposed essential selection criteria to be used in photometric surveys. The right panel of Figure 2 shows two luminosity ratios calculated as a function of the Eddington ratio of the IMBH: (i) the X-ray-to-optical/UV ratio represented by the standard ${\alpha }_{\mathrm{ox}}$ parameter [53] and (ii) the optical/UV to sub-mm ratio (see [44] for their definition). A combination of X-ray, optical, and sub-mm observations can sift out potential candidates and uniquely determine the accretion rate onto wandering IMBHs.

Predicting the number of IMBHs detectable by AXIS in a deep galactic survey is challenging because the total number of such sources is unknown. The MW has encountered ∼$15\pm 3$ galaxies with stellar mass $>{10}^7{\mathrm{M}}_{\odot }$ during its cosmic evolution [54]. Such galaxies could have hosted IMBHs that are massive enough to be detected in AXIS searches. Therefore, assuming an expected number of ∼10 IMBHs, ref. [28] showed that these objects are more likely to wander in the innermost ∼1 kpc of the MW. However, it is informative to compare the capabilities of AXIS with those of other facilities that are currently operational.

Table 1. Volume-weighted detectability of wandering IMBHs of ${10}^5{\mathrm{M}}_{\odot }$ in the MW by AXIS, Chandra, and eROSITA. The detectability indicates the percent of the total number of objects that are detectable by a given instrument.

X-ray Telescope	Flux Limit $\left[\mathbf{erg}{\mathbf{s}}^{-1}{\mathbf{cm}}^{-2}\right]$	Detectability
AXIS	$3.0\times {10}^{-18}$	$38\%$
Chandra	$2.0\times {10}^{-16}$	$27\%$
eRosita	$2.0\times {10}^{-14}$	$13\%$

shows that AXIS would allow for a significant improvement of at least $40\%$ over current facilities, thanks not only to its extraordinary sensitivity but also to its wide field of view.

2.3. Extending the Search to Local Galaxies

The left panel of Figure 2 shows that the passage of a ${10}^5{\mathrm{M}}_{\odot }$ IMBH generates the highest X-ray fluxes within MC and CNM environments. Galaxies in the same mass category of the MW share a similar environmental composition. Hence, we investigate the fluxes that the passage of equally massive IMBHs would produce in nearby galaxies.

In Figure 3, we show the X-ray fluxes (0.2–10 keV) generated by the passage of a ${10}^5{\mathrm{M}}_{\odot }$ IMBH in the five ISM environments for a range of distances between 1 kpc and 10 Mpc. We indicate the distance to a few example locations, from the galactic center to the Andromeda galaxy, noting that within a radius of 4 Mpc, there are more than 200 galaxies, although many of them are dwarfs [55]. We calculated the flux reported in Figure 3 for the five ISM environments from their median luminosities. As some environments exhibit a range of luminosities spanning ∼13 orders of magnitudes (see Figure 2), the typical values of fluxes in Figure 3 are indicative.

From Figure 3, we see that the median luminosities generated in the WNM, WIM, and HIM are invisible to AXIS or are detectable only within the MW. On the contrary, fluxes generated in the CNM and MCs are detectable by an AXIS deep field well outside the MW. AXIS imaging reaching a depth of ∼$3\times {10}^{-18}\mathrm{erg}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}$ could detect the electromagnetic signature of the passage of an IMBH of ${10}^5{\mathrm{M}}_{\odot }$ in hundreds of galaxies within 10 Mpc distance. Although MC and CNM environments occupy only a small volume fraction of a typical MW-like galaxy ($0.05\%$ and $1\%$, respectively; see [45]), the availability of a large number of external galaxies within reach dramatically expands the chances of detecting such signatures.

As most of the X-ray luminosities of the sources considered here are <${10}^{40}\mathrm{erg}{\mathrm{s}}^{-1}$, contamination from X-ray binaries (XRBs) is of concern. To disentangle their emissions, synergies with observatories that use other wavelengths (e.g., JWST, Roman, and Rubin) will be fundamental.

3. Concluding Remarks

To conclude, AXIS represents a significant improvement over current X-ray facilities and opens the way to detect a completely unknown population of black holes. In the MW and, even more crucially, in >200 local galaxies, AXIS can detect the X-rays emitted by the passage of IMBHs within dense ISM environments. Such detections are crucial for understanding the demographics and evolution of IMBHs and the merging history of galaxies.