A Comprehensive Study of Soft X-ray Absorption Features in GX 13+1 Using XMM-Newton Observations

Abstract

In this study, a comprehensive analysis of the reflection grating spectrometer (RGS) data (energy range 0.33 keV to 2.5 keV) of GX 13+1 from the XMM-Newton space observatory was conducted. Numerous absorption lines have been described in earlier publications, although the majority of these investigations focused on the energy range between 3 keV and 10 keV. We considered all ten on-axis observations for spectral analysis, but during timing analysis, off-axis observations were also analysed. A fresh dip in off-axis observation 0122340701(B) was observed together with the previously reported dip in on-axis observation 0505480501(F). No burst or eclipsing was observed in any of the observations. The spectral analysis revealed the presence of the highly ionized elements, Si XIII 1s²–1s2p and 1s²–1s3p transitions with energies of 2.02 keV and 2.24 keV, respectively, as well as Mg XII 1s–6p transitions with energies of 1.91 keV and Al XIII 1s–4p transitions with energies of 2.15 keV. Before this study, no analyses of XMM-Newton data reported Mg XII and Al XIII elements. Moreover, the 1s–6p transitions of Mg XII and 1s–4p transitions of Al XIII were not even reported in any Chandra data analysis. The equivalent hydrogen column densities obtained (2.35 × 10²² cm⁻² to 4.18 × 10²² cm⁻²) are consistent with previously reported values. The equivalent widths of neighbouring observations are found to be nearly the same. This supports us in suggesting that the absorptions may be due to the presence of an interstellar medium (ISM) in the line of sight (LOS) of the source.

1. Introduction

The spectral analysis of background sources using high-resolution telescopes commissioned in observatories such as Chandra and XMM-Newton not only opens up a new avenue to detect and analyse both emission and absorption lines but also facilitates understanding of the source and the intervening medium. It is comparatively easy to configure the origin of the emission lines, but in the case of the absorption lines, it takes time because of their multiple points of origin, such as the source [1,2,3,4,5,6], dipping in X-rays [1,2,5,7,8], the instrument [9], and the interstellar medium (ISM) [10,11,12]. If the lines are less clear and weaker and there is no evidence of a significant blue shift, then we may assume that the lines may be caused by the ISM [10,11,12].

The study of the ISM is very interesting and crucial as it provides a wealth of information about the physical and chemical changes undergone in the formation and progression of galaxies. The ISM is a dynamic multiphase structure with a wide variation of temperature (0 K to 10⁶ K) and density (n_H~10⁻³ to 10² cm⁻³). Yao and Wang (2005) are credited as the first to introduce the multiphase structure of ISM [12]. Although it makes up less than 10% of the total mass of the galaxy, it still produces a conducive environment for star formation. The cosmic rays and magnetic fields present in it plays an important role during star formation. Gas, dust, cosmic radiation, and magnetic fields make up the majority of the ISM [13,14]. Juett et al. (2004 and 2006) conducted a pioneering study of the ISM, starting with the measurement of the column density of oxygen. They further constrained the abundance ratio of O/Ne and Fe/Ne [11]. Wilms et al. (2000), in 2000, produced a detailed measurement of ISM abundance, which is currently considered to be the standard ISM abundance. The study of absorption lines and absorption edges observed in the spectra of background sources helps us to determine the temperature, ionisation state, density, and different phases of the ISM. Additionally, it is of great importance to understand the chemical compositions of dust grains and to estimate the dust-to-gas ratio in the ISM. The ratio of the mass of dust and gas in ISM is estimated to be 0.005–0.01 [14]. Although ample work has been carried out on absorption spectroscopy, research on the ISM within the soft X-ray energy range is sparse. The chances of the complete absorption of the continua by the intervening medium in the line of sight remain high. Thus, the choice of a suitable source is very crucial. X-ray binaries are bright continuum sources located behind sizeable column densities of interstellar gas and are thus ideal targets for absorption spectroscopy of the ISM. These are categorized into various groups and subgroups, with the low-mass X-ray binary (LMXB) among them [15].

In the present study, we aim to investigate the chemical composition of the ISM in the soft X-ray energy range and evaluate the cause of the origin of the absorption features in the spectra of GX 13+1. For this purpose, we have processed all the on-axis observations recorded in the reflection grating spectrometer (RGS) of the XMM-Newton space observatory. The better photon accumulating capacity, larger effective area in the energy range of 0.33–2.5 keV, and modest spectral resolution with a larger throughput of XMM-Newton make it suitable for our study. The off-axis observations were ignored in the spectral analysis because the effective area of observation in these cases decreases significantly. The latest calibration of the XMM-Newton instruments increases the chances of observation of fine structures by limiting errors caused by instrument Au-M edges. The thorough pile-up checking, fine binning, and use of C-stat might improve the quality of evaluation and help us to constrain the origin of absorption lines.

2. The Source GX 13+1 and Its Spectral Characteristics

We have chosen GX 13+1, a neutron star soft X-ray transient (NSSXT) as the background source for the study. The source, GX 13+1, is an LMXB [16,17] composed of a neutron star paired with an evolved late-type K5III star as its companion [18,19]. It is a hybrid source with a resemblance to both Atoll and Z-type LMXB sources. Initially, it was classified as the most luminous Atoll source with an intermediate luminosity of 0.1 Eddington luminosity [20], but later, its properties were found to be similar to those of the Z sources as well [19,21,22,23]. Its brightness, ∼6 × 10⁻⁹ erg cm⁻² s⁻¹ , makes it suitable for the study of absorption lines originating from the ISM. In 1997, Chirstian et al. (1997) estimated the distance of GX 13+1 to range from 4.7 to 7.0 kpc [24], but two years later, Bandyopadhyay et al. (1999) produced a more coherent measurement of its distance utilising infrared spectroscopy and suggested the distance to be 7 ± 1 kpc [19]. Furthermore, the most accurate orbital period obtained so far is 24.5274 days [25].

The table below (

Table 1. Absorption lines detected (Column 3) in the spectral analysis of GX 13+1 using XMM-Newton data.

XMM-Newton Observations
Sl No	Data Used (XMM-Newton) Observation ID	Absorption Line	Energy (keV)	Camera	Location of Absorption Lines/Edge	Reference
1	0122340101	H-like Ca XX Kα lines H and He-like Fe XXV Kα and Fe XXV Kβ lines, Fe XXVI Kα and Fe XXVI Kβ lines	4.15, 6.73, 7.00, 7.85, and 8.26	European Photon Imaging Camera-PN (EPIC-PN)	Absorbing plasma near the central source	Sidoli et al. (2002) [26]
	0122340901
	0122341001
2	0122340101	H and He-like Fe XXV Kα and Fe XXV Kβ lines, Fe XXVI Kα and Fe XXVI Kβ lines	6.7, 7.00, and 8.83	EPIC-PN	Absorbing material close to the primary source.	Sidoli et al. (2003) [27]
	0122340901
	0122341001
3	0122340101	Kα and Kβ lines of Fe XXV and Fe XXVI Weak absorption lines of Si XIII, Si XIV, S XV and S XVI Ca XX	6.53 to 8.34 and 1.8, 2.0, 2.5, 2.62, and 4.2	EPIC-PN and RGS	Accretion disk	Trigo et al. (2012) [20]
	0122340901
	0122341001
	0505480101
	0505480701
	0505480201
	0505480501
	0505480301
	0505480401
4	0505480101	Kα and Kβ He-like Fe XXV line Kα and Kβ H-like Fe XXVI line	6.7, 7.0, and 7.8	EPIC-PN	Accretion disk	Maiolino et al. (2019) [28]
	0505480201	Kα He-like line Fe XXV

) is a summary of all the absorption lines reported by various authors in the spectra of GX 13+1 while analysing data recorded by the XMM-Newton observatory.

In most of the above work, data recorded by the European Photo Imaging Camera (EPIC-PN) were emphasized due to its wide range of energy and availability of sufficient data. The H and He-like Kα and Kβ lines of Fe XXV and Fe XXVI were commonly detected in all of the above work, Sidoli et al. (2002) [26] additionally found H-like Ca XX Kα lines in the spectra. As shown in Row 3 (Table 1), weak absorption lines from Si XIII, Si XIV, S XVI, and S XV were detected by Trigo et al. (2012) [20] while analysing RGS data.

Subsequent Chandra observations revealed more ionised materials. The high and medium energy grating cameras (HEG, MEG) and high energy transmission grating spectrometer (HETGS) of Chandra observations revealed many absorption lines such as Kα lines from H-like Fe, Si, S, Mg, Al, Ca, and Ar, as well as He-like Fe (

Table 2. Absorption lines detected in spectral analysis of GX 13+1 using Chandra data.

Chandra Observations
Sl. No	Data Used (Chandra) Observation ID	Lines Detected	Energy (Kev)	Camera Used	Location/Cause of Absorption Lines	Reference
1	2708	Si K edge XAFS	1.846 and 1.865	High and Medium Grating arms (HEG and MEG)	ISM	Veda et al. (2005) [29]
		S K edge XAFS	2.474 and 2.490
		Mg K edge	1.307
		Fe	-
2	11814	Mg XII 1S-2P	1.474	HEG and MEG	XAFS and ISM	D‘Ai et al. (2014) [30]
		Al XIII 1S-2P	1.727
		Mg XII 1S-3P	1.745
		Si XIV 1S-2P	2.007
		S XVI 1S-2P	2.623
		Ca XX 1S-2P	4.118
		Fe XXV 1S2-1S2P	6.706
		Fe XXVI 1S-2P	6.978
		Fe XXVI 1S-3P	8.273
3	2708	Kα lines from	----	HEG and MEG	Disk Wind	Allen et al. (2018) [31]
	11814 11815	Fe XXVI,
	11816	Fe XXV,
	11817	Ca XX, S XVI,
	11818	Si XIV, Mg XII and
	13197	Ar XVIII
4	---	Si I, Si II, Si III,	---	High energy transmission grating spectrometer (HETGS)	ISM	Gatuzz et al. (2020) [13]
		Si XII and Si XIII

). This also indicates the possibility of tracing the same ionised elements through analysing data recorded by XMM-Newton Observatory. Table 2 is a summary of absorption lines and edges reported by various authors who analysed data recorded by the Chandra Observatory.

As summarised in Column 6 (six) of Table 1 and Table 2 various causes were attributed to the origin of these absorption lines. In most of the cases, the origin was suggested to be a result of the accretion disk or to be local to the source (Table 1). Few studies provide information that disk wind is also responsible for causing absorption lines in the spectra [13,30]. Around the same time, Veda et al. (2005) [29], D’Ai. et al. (2014) [30], and Gatuzz et al. (2020) [13] claimed that the absorption lines seen in the spectra of GX 13+1 were caused by ISM.

3. Materials and Methods

GX 13+1 is one of the brightest NSSXTs located at 5⁰ < l < 20⁰ and within b < 1⁰ towards the Galactic center region. The XMM-Newton observatory captured this object 15 times (fifteen) and all of the instruments on board collected data during these occasions. In the present work, we are primarily interested in the data acquired by the high-resolution reflection grating spectrometer (RGS). The techniques for data extraction, data reduction, and data filtering are described in depth in the sections that follow. Additionally, as our goal is to establish whether the absorption seen in the spectra is caused by ISM or not, several techniques may be used to validate the absorption such as:

(1)

comparing derived N_H (hydrogen column density) with galactic N_H obtained via H1 observation [32],

(2)

comparing values of the equivalent width of the nearby observations [33],

(3)

comparing the derived temperature with the previously established temperature of ISM [33],

(4)

examining the consistency of elemental abundance with solar abundance [29,33],

(5)

measuring the blue shift and the dispersion velocity [6,12,33],

(6)

measuring the distance at which the absorption has taken place [34].

Out of all of these possible methods, in the present work, methods expressed in serial numbers (1) and (2) are used to justify the possible role of ISM in causing the absorption lines. The other approaches could not be used since the relevant data, such as dispersion velocity, elemental abundance, blue shift (if any), the distances at which the absorptions occurred, etc., were not available.

3.1. Observation

We examined the 10 (ten) better-calibrated on-axis observations out of the 15 (fifteen) observations that were captured by the XMM-Newton cameras up to 2017. The details of these observations are listed in

Table 3. Observation log of GX 13+1 using XMM-Newton (instrument: RGS 1).

Obs.No.	Obs. ID *	On-axis/ Off-axis	Exposure Date	Exposure Duration RGS1 (Sec)	Effective Exposure RGS1 (Sec)	Net Count Rate (Counts/Sec)
1	122340101(C)	ON-AXIS	30 March 2000	10,005	9694	1.810 ± 0.015
2	122340501(J)	OFF-AXIS	30 March 2000	20,603	20,130	2.172 ± 0.014
3	122340601(O)	OFF-AXIS	1 April 2000	43,707	42,710	0.932 ± 0.004
4	122340901(G)	ON-AXIS	8 April 2000	12,209	11,850	2.221 ± 0.015
5	122341001(E)	ON-AXIS	1 April 2000	8607	8368	1.924 ± 0.017
6	122340701(B)	OFF-AXIS	3 April 2000	40,612	39,710	1.312 ± 0.007
7	122340201(D)	OFF-AXIS	9 April 2000	23,619	22,970	2.824 ± 0.011
8	122340401(Q)	OFF-AXIS	11 April 2000	23,620	23,060	2.497 ± 0.010
9	505480101(A)	ON-AXIS	9 March 2008	18,581	18,470	2.250 ± 0.012
10	505480201(H)	ON-AXIS	11 March 2008	13,689	13,600	2.276 ± 0.014
11	505480701(P)	ON-AXIS	11 March 2008	13,918	13,800	2.267 ± 0.014
12	505480301(N)	ON-AXIS	22 March 2008	16,615	16,520	2.013 ± 0.012
13	505480501(F)	ON-AXIS	25 March 2008	13,143	13,060	1.666 ± 0.012
14	505480401(M)	ON-AXIS	5 September 2008	16,813	16,720	1.836 ± 0.115
15	802820201(L)	ON-AXIS	8 April 2017	62,838	62,650	1.935 ± 0.061

Note: * hereafter, the observations may be reflected by the letter assigned to them (Column 2 of Table 3).

. In all of the observations, data were recorded by all the onboard instruments simultaneously, and in all of these data-acquiring periods, the RGS was operated in standard science mode (spectroscopy mode). The RGS covers an energy range of ~0.35 to 2.5 keV with a resolving power of ~300 at 15 Å [35,36]. These observations were previously considered for analysis by Sidoli et al., (2001) and (2002) [8,26]; Trigo et al., (2006) and (2012) [23,37]; Maiolino et al. (2019) [28]; Cacket et al. (2008) [33]; D’Ai et al. (2014) [30]; and Iaria et al. (2014) [25], but mostly the EPIC-PN [38] data were analysed in detail. The data considered for analysis were collected over a period of sixteen years (Table 3), covering a total exposure of 1.87 × 10⁵ s, i.e., nearly 8.8% of the total orbital period, 2.12 × 10⁸ s [25].

3.2. Data Reduction

The raw RGS data products were analysed and reprocessed using the standard XMM-Newton Science Analysis System (SAS), version 19.0.1. The SAS task ‘rgsproc’ was used to produce calibrated RGS event lists, spectra, and response matrices. The event list thus obtained was free from bad pixels of various types signalled by ‘refflags’, as the filtering option of bad pixels remains on by default. To contain the hot pixels and the single columns, we chose the option keep cool = no to discarding the single columns [20].

3.3. Pile-Up

As the source GX 13+1 is a bright (nearly equal to 0.2 Crab) [31] source, the spectra may suffer from a significant pile-up. It may reduce the observed flux of the source and make the spectrum artificially harder than actually it is [39]. There is a possibility that it may reduce the equivalent width of the absorption lines [31]. It might also reject complicated events via onboard processing and may also trigger the migration of photons to a higher order from the first order.

Data piling can be estimated either using the method described in SAS threads or via the method used by de Vries (2006) [32] and Cacket et al. (2008) [33]. We opted for the second method here, since in the first method, the estimation of pile-up is carried out by visually comparing the spectra obtained from fluxed files derived from ‘rgsproc’, and thus the method is subjective. Additionally, since the RGS2 CCDs are read via a single node while RGS1 is found in a double node, the chances of piling in RGS2 are always high (XMM-user manual). Therefore, in our analysis, we have not used data of RGS2 to avoid the possibility of adding pile-ups in the process (RGS-SRON-CAL-ME-06/001, Issue dt. 2 November 2006). Using the ‘rgsfluxer’ command, we created separate first-order and second-order fluxed files of RGS1, and then we created a comparison plot to observe how the strength of the first and second-order flux varied with respect to each other at different wavelengths (Figure 1a,c). Further, the ratio of first-order and second-order flux of each RGS is obtained. The flux ratio thus obtained is then plotted against the corresponding wavelength (Figure 1b,d). If the value of the flux ratio lies close to 1 it indicates that piling is at the lowest level or that the data is free from X-ray loading.

The observations 122340501(J), 122340401(Q), and 505480301(N) are found to be piled up across the entire wavelength distribution, as shown below in case one of the observations 122340401(Q). The observations 122340501(J) and 122340401(Q), being off-axis observations are not part of this analysis, and observation 505480301(N) is avoided for further analysis as it is piled up. Additionally, in almost all of the observations at very low wavelengths, around 4–5 Å, data piling is observed, and therefore, while performing spectrum analysis, we avoided this region (i.e., analysis is restricted up to 2.3 keV wherever necessary). Figure 1a,b represent the non-piled data of the observation 0122341001(E). Thus, out of the 10(ten) on-axis observations, 9(nine) observations were found to be suitable for further analysis (excluding 505480301(N)).

3.4. Timing Analysis

To look for any dipping and/or eclipsing activity that could be observed due to the use of the newer version of SAS, we generated background-subtracted light curves for energy ranges of 0.3 to 1.5 keV and 1.5 to 2.5 keV [22] using SAS task ‘rgslccorr’, with the eventlist and srclist, produced by SAS task ‘rgsproc’. The bin size was chosen to be 60 s. All observations show high variability, and the average count rate changes significantly from one observation to the next. We then examined the hardness ratio between the said energy ranges for each observation to confirm whether any dipping activity was noticed. The off-axis observations were ignored in the case of spectral analysis because the effective area of observation in these cases decreases significantly. Since the decrease in the effective area does not affect timing analysis, light curves were drawn for all the fifteen observations acquired by RGS.

3.5. Model Fitting

We only used the reflection grating spectrometer (RGS) data of XMM-Newton as the RGS data are sensitive in the soft X-ray energy band and thus are suitable for ISM absorption. Additionally, we were not interested in constraining the source continuum at energies higher than the RGS band. The high spectral resolution (the spectral resolution of the first-order RGS is 0.06–0.07 Å) of RGS over EPIC makes it further suitable for studying narrow absorptions. Throughout the analysis, care has been taken to preserve narrow absorption lines for which each RGS spectra was rebinned by a factor of 2 (two) using GRPPHA (i.e., 1/3FWHM). This makes the bin size 0.02 Å [14]. We used the C-statistics [40] throughout the work instead of ꭓ² so that a small bin size could be considered. A 90% confidence level was adopted for all spectral uncertainties. We used the latest version 12.11.1 of XSPEC, an X-ray spectral fitting package (https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual accessed on 16 July 2019), for spectrum generation and processing [41]. To avoid the effect of data loading, we ignored energy below 1.1 and above 2.3 keV in all our analyses. The soft X-rays in the case of LMXB originate mostly either from the compact star itself or from the interiors of the accretion disc. Whereas the intermediate and hard X-rays originate from the collision of photons emitted from the innermost part with electrons present in the ionised corona. Thus to obtain the best fit of the continuum, all suitable models available in XSPEC and their various combinations were tried. The best fit was obtained with a combination of the Tuebingen–Boulder ISM absorption model (Tbabs model) and the Blackbody radiation and Powerlaw models. The associated parameters of the models used, along with their units, are shown in

Table 4. List of models used and the parameters measured.

Model	Abbreviation	Free Parameter	Unit
Tuebingen–Boulder ISM Absorption Model	Tbabs	NH	×1022 cm−2
Blackbody Spectrum, area normalised	bbodyrad	kT	keV
		norm(K)	Normalization K = $\frac{R_{km}^2}{D_{10}^2}$, where Rkm is the source radius in km and D10 is the distance to the source in units of 10 kpc.
Powerlaw	powerlaw (pow)	PhoIndex (α)	photon index of power law (dimensionless)
		norm (K)	photons/keV/cm2/s at 1 keV
Gaussian	gauss	LineE	E, line energy in keV
		Sigma	σ, line width in keV
		norm	K, total photons/cm2/s in the line

.

4. Results and Discussion

We analysed high-resolution RGS data of 10 (ten) on-axis observations of GX 13+1 LMXB acquired between March 2000 to April 2017, to identify the absorption features seen in the spectra and thereby to evaluate the chemical composition of ISM in the soft X-ray energy range. As summarised in Table 1 and Table 2, absorption lines may have local [20,27,28,42] or astrophysical origin [13,29,30]. The absorption may be because of phenomena such as disk wind [31] and dipping or it may be due to the instrument as well. Therefore a systematic approach has been made to study the probable cause of absorption lines. Out of all the available approaches to prove that the absorption lines or edges visible in the spectra are created by ISM in the current study, methods expressed in Serial Numbers (1) and (2) (see Section 3) are utilized.

4.1. Light Curve, Hardness Ratio, and Dip

The timing analysis may help us ascertain whether the origin is either dipping or the background. So far, 20 LMXBs have shown clear dips and a majority of them hoistneutron star as compact object and the source GX 13+1 is one of these. In GX 13+1, dipping was suspected in many analyses [37]. In the year 2014, Iaria et al. (2014) [25] published an analysis of observations recorded by RXTE/ASM and MAXI. They reported periodic dipping in the light curve of GX 13+1 with a periodicity of ~24.5274 days. Almost at the same time, D’Ai et al. (2014) [30] also reported a clear dip in GX 13+1, using observations recorded in the Chandra observatory. It was Trigo et al. (2012) [20], who searched for the signature of a dip in light curve with data recorded in the XMM-Newton observatory. They analysed all the observations except the observation recorded in the year 2017 and observation 0505480701(P), due to the non-availability of PN data. In their analysis, partial dipping activity was reported in observation 0505480501(F) (25 March 2008) in both the RGS as well as the EPIC-PN light curves.

We plotted the light curve of all the ten on-axis and five off-axis observations recorded in the reflection grating spectrometer from the years 2000 to 2017 to re-verify the dipping behaviour so far reported, as the dipping phenomenon significantly modifies the X-ray spectrum below 2–4 keV [37]. In this work, we only displayed the light curves from the two observations where the dipping phenomena were noted. The remaining observations’ light curves do not exhibit any appreciable dipping, eclipsing, or burst activity.

As shown in Figure 2a, a clear dip can be noticed at the beginning of the observation 0505480501(F). This is the same dipping that was reported by Trigo et al. (2012) [20]. It is clear from the curves that the shape of the hard and soft light curves plotted by Trigo et al. (2012) [20] using EPIC-PN data or as carried out by us using RGS data looks almost similar except for the counts/s. Apart from this, we noticed new dipping activity towards the end of the off-axis observation 0122340701(B), where counts s⁻¹ seem to drop by ~2. The time unit is expressed in hours since the observation began. The bin time is considered to be 60 s in each case. The newly observed dip can be seen in Figure 2b at around 23:36 h on 3 April 2000. However, no eclipse or burst was detected in any of the observations and thus the source may be inclined at an angle i, 60⁰ < i < 80⁰ [43]. As seen in Table 5, there was a shift in both the neutral and ionized material’s column densities. This is a common feature of dipping sources, and a similar observation is also reported by D’Aì et al. (2014) [30].

Table 5. Obtained ionic column density using the Spitzer Jr. L. (1998) [44] formula of connecting equivalent width, oscillator strength, and wavelength of the ionised element detected.

Obs. ID	Element/Ion	Transition	Eqwidth ×10−14 (cm)	WL ×10−8 (cm)	Oscillator Strength (Verner et al. 1996 [45])	Ni ×1016 (cm−2)	NH ×1022 (cm−2)	KBT (keV)	KBT (106K)
122340101(C)	Si XIII	1s2-1s2p	8.45	6.6480	7.57× 10−1	0.003	4.18	0.606742	7.04
505480501(F)	Si XIII	1s2-1s3p	26.9	5.6807	1.52 × 10−1	0.06	3.46	10.6483	123.52
505480101(A)	Mg XII	1s-6p	25.1	6.4975	2.60 × 10−3	2.6	4.05	0.557765	6.47
802820201(L)	Al XIII	1s-4p	8.18	5.7396	9.67 × 10−3	0.29	4.18	0.528863	6.13

Table 5. Obtained ionic column density using the Spitzer Jr. L. (1998) [44] formula of connecting equivalent width, oscillator strength, and wavelength of the ionised element detected.

Obs. ID	Element/Ion	Transition	Eqwidth ×10−14 (cm)	WL ×10−8 (cm)	Oscillator Strength (Verner et al. 1996 [45])	Ni ×1016 (cm−2)	NH ×1022 (cm−2)	KBT (keV)	KBT (106K)
122340101(C)	Si XIII	1s2-1s2p	8.45	6.6480	7.57× 10−1	0.003	4.18	0.606742	7.04
505480501(F)	Si XIII	1s2-1s3p	26.9	5.6807	1.52 × 10−1	0.06	3.46	10.6483	123.52
505480101(A)	Mg XII	1s-6p	25.1	6.4975	2.60 × 10−3	2.6	4.05	0.557765	6.47
802820201(L)	Al XIII	1s-4p	8.18	5.7396	9.67 × 10−3	0.29	4.18	0.528863	6.13

Figure 2. Left panel, top to bottom (a): light curve (0.3–1.5) keV, light curve (1.5–2.5) keV, and hardness ratio [46]. Time is in hours since the start of the observation on 25 March 2008 at 23:19:15 UTC, Obs. ID: 0505480501(F). Right panel, top to bottom (b): light curve (0.3–1.5) keV, light curve (1.5–2.5) keV, and hardness ratio [46]. Time is in hours since the start of the observation on 3 April 2000 at 12:32:36 UTC, Obs. ID: 0122340701(B). Bin time in each case is 60 s.

Figure 2. Left panel, top to bottom (a): light curve (0.3–1.5) keV, light curve (1.5–2.5) keV, and hardness ratio [46]. Time is in hours since the start of the observation on 25 March 2008 at 23:19:15 UTC, Obs. ID: 0505480501(F). Right panel, top to bottom (b): light curve (0.3–1.5) keV, light curve (1.5–2.5) keV, and hardness ratio [46]. Time is in hours since the start of the observation on 3 April 2000 at 12:32:36 UTC, Obs. ID: 0122340701(B). Bin time in each case is 60 s.

4.2. Spectral Analysis

The observatories such as XMM-Newton and Chandra are significantly aiding us in developing our understanding of the LMXB system, the emission processes, the accretion mechanism, and the physical and chemical conditions of the intervening material through which the X-rays travel. Munoz-Darias et al. (2014) [47] have shown that the hysteresis pattern of Neutron Star Low Mass X-ray Binary (NSLMXB) can be divided into soft (0.5 to 2 keV), hard (3 to 10 keV), and intermediate states (2 to 3 keV). The soft state X-ray emissions mostly originate from NS or the innermost part of the accretion disk associated with a blackbody or disc-blackbody component while the intermediate and hard states originate from the interaction of the soft photons emitted from the innermost region with the electrons in the thermal corona surrounding the NS and is associated with inverse Compton emission, which can be described by compTT, absorbed powerlaw, cut-off powerlaw, etc.

We tried to fit the continuum with various simple additive models in XSPEC, such as bbody, compTT, absorbed powerlaw, cut-off powerlaw, powerlaw, etc., in combination with the multiplicative model Tbabs. The Tbabs model in XSPEC is used to calculate the sum of X-ray absorption cross-sections caused by ISM in the gas phase, the grain phase, and also the molecules in the ISM (https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual, accessed on 16 July 2019). For absorption cross-sections and abundances, Verner et al. (1996) [45] and Wilms et al. (2000) [48] are adopted, respectively. The parameter N_H was left free in all of the fits so that the Tbabs model could indicate both the variable absorbing material close to the source and galactic absorption caused by neutral hydrogen [28]. A single power law continuum or a single blackbody model converges the fit well, but the best fit is obtained with the combination of model Tbabs (bbodyrad + powerlaw) along with Gaussians to accommodate the negative residuals observed between 1.7 to 2.3 keV. The ratio C-stat/dof with this combination of models always lies well below 1.5 and offers a better fit than any other combinations in all of the observations. The (bbody + powerlaw) combination in fitting RGS data was also tested by Pinto et al. (2012) [49], and they found that the best-fit values of N_H were consistent within error limits when compared with a best-fit using a single power law model. Iaria et al. (2014) [25] also used powerlaw to fit RGS data in the energy range 0.5 to 1.1 keV. Similarly, the (bbodyrad + powerlaw) combination was found to be very effective in many Neutron Star LMXB (NSLMXB) in previous studies as well [31] when both EPIC-PN and RGS data were analysed. The blackbody radiation model focuses on the nature of the continuum intrinsic to the source while the powerlaw is used to accommodate energy components originating from the corona. We left the photon index to vary independently during fit, as was done by D’Ai et al. (2014) [30], because if the index of the power law is associated with a comptonised spectrum, the low index value becomes difficult to interpret.

A close examination of the plot suggests the presence of broad negative residuals around 1.7 to 2.3 keV, which reflects the presence of absorption lines in the spectra. We tried to fit the continuum with the Gaussian model, keeping the normalisation negative and all of the other parameters free. This improved the distribution of the residual in the spectra and resulted in the ratio of Cstat/dof results being nearly equal to 1.5. The equivalent widths of the lines were determined via the fitted Gaussian lines. We looked for the presence of any instrumental features around observed absorption lines (in each case the effective area of the instrument was confirmed using the command: plot ‘eff’ in XSPEC). We also verified that the absorptions were not caused by bad pixels (the method described in Cabot et al. (2013) [50] was used) or even by the background (we confirmed whether the same absorption was seen in the background or not, using the background templates available through the SAS task rgsbackmodel). Since the latest calibration and latest version of the SAS software were used for analysis [28], the absorption lines could also not have been caused by calibration uncertainties. Therefore the origin of these absorption lines could be astrophysical. During timing analysis, no significant burst was seen; therefore, the burst removal procedure was not executed.

The absorption lines detected in various spectra and corresponding residuals are shown in Figure 3a–d, and the best parameters are shown in

Table 6. The results of the RGS best spectra fit in the range 1.3–2.3 keV of GX 13+1.

Component	Parameter	Unit	Obs. Id 122340101 (C)	Obs. Id 122340901 (G)	Obs. Id 122341001 (E)	Obs. Id 505480101 (A)	Obs. Id 505480201 (H)	Obs. Id 505480501 (F)	Obs. Id 802820201 (L)
Tbabs	NH	×1022 atoms cm−2	${4.18}_{-1.27}^{+1.09}$	${3.68}_{-0.60}^{+1.07}$	2.48 ± 0.62	${4.05}_{-0.47}^{+0.05}$	${3.95}_{-0.31}^{+1.25}$	${3.46}_{-0.12}^{+0.05}$	${4.18}_{-0.62}^{+0.69}$
bbodyrad	kTbb	keV	${0.61}_{-0.15}^{+0.43}$	${0.11}_{-0.11}^{+0.03}$	$\mathrm{X}$	${0.56}_{-0.44}^{+4.97}$	${1.73}_{-1.73}^{+66.37}$	${0.59}_{-0.59}^{+0.82}$	${0.53}_{-0.06}^{+0.21}$
	norm		${6376}_{-4263}^{+5907}$	${3.8\times {10}^7}_{-1.63\times {10}^7}^{+2.85\times {10}^8}$	X	${25.68}_{-18.46}^{+38.12}$	${2.92}_{-2.67}^{+38.99}$	${653.15}_{-4138}^{+5343}$	${7995}_{-5773}^{+5762}$
powerlaw	Γ		7.53 #	${1.97}_{-0.47}^{+0.84}$	${0.008}_{-1.22}^{+0.88}$	${2.89}_{-0.43}^{+0.69}$	${2.81}_{-1.27}^{+0.87}$	${2.09}_{-0.13}^{+3.34}$	${7.04}_{-0.97}^{+0.85}$
	norm	ph/keV/cm2/s at 1 keV	${21.94}_{-19.12}^{+113}$	${3.24}_{-2.22}^{+4.44}$	${0.44}_{-0.14}^{+0.35}$	${7.02}_{-2.66}^{+5.15}$	${6.21}_{-2.69}^{+7.46}$	${1.92}_{-0.89}^{+0.41}$	${18.73}_{-13.86}^{+35.29}$
Gaussian1	LineE	keV	${2.02}_{-0.012}^{+0.011}$	${2.24}_{-0.05}^{+0.04}$	1.88 ± 0.01	1.91 ± 0.01	2.04 ± 0.01	${2.20}_{-0.007}^{+0.005}$	${2.27}_{-0.03}^{+0.05}$
	Element		Si XIII	Si XIII	Mg XII	Mg XII	Al XIII	Si XIII	Outside the spectra range
	Sigma (σ)	keV	${0.006}_{-0.006}^{+0.017}$	${0.004}_{-0.03}^{+0.03}$	**	0.011 ± 0.01	${0.004}_{-0.005}^{+0.019}$	**	${0.0009}_{-0.01}^{+0.02}$
	EW	eV	${-10.5}_{-5.18}^{+5.29}$	−72.7 ± 0.03	${-7.20}_{-3.98}^{+4.00}$	${-3.12}_{-2.2}^{+2.3}$	${-19.63}_{-28.62}^{+13.91}$	${-33.48}_{-11.2}^{+11.4}$	${-211.17}_{-89.66}^{+51.24}$
Gaussian2	LineE	keV	X	X	${2.41}_{-0.24}^{+1.64}$	X	${2.07}_{-0.01}^{+0.03}$	X	${2.15}_{-0.006}^{+0.004}$
	Element		X	X	X	X		X	Al XIII
	Sigma (σ)	keV	X	X	${0.17}_{-0.21}^{+0.13}$	X	${0.03}_{-0.02}^{+0.01}$	X	${0.003}_{-0.001}^{+0.010}$
	EW	keV	X	X	X	X	$-{30.73}_{-19.13}^{+19.78}$	X	−10.17 ± 0.004
Luminosity		erg per sec	3.3 × 1037	3.2 × 1037	3.2 × 1037	2.99 × 1037	2.57 × 1037	2.73 × 1037	2.88 × 1037
c-stat/d.o.f			437/429	642/534	562/536	538/475	589/510	541/518	714/489

Note: The symbols used in the table indicate the following: X = no value obtained; ** = parameter measured at the hard limit; # = error calculation not achieved.

.

As can be seen from Table 6 (summary of best-fit results of the seven observations in which the absorption line was detected), out of nine on-axis observations in seven observations, we detected absorption lines caused by highly ionised elements present in the ISM. The absorption lines are caused by highly ionised species of Si XII, Mg XII, and Al XIII (

Table 7. Best-fit parameters of absorption lines seen in various observations.

Obs. ID.	LineE (keV)	EqWidth	Observed WL(Å)	Theoretical WL(Å)	Element/ Ion	Transition	Reference
122340101(C)	${2.02}_{-0.012}^{+0.011}$	${-10.5}_{-5.18}^{+5.29}$	6.153	6.6480	Si XIII	1s2-1s2p	Trigo et al. (2012) [20]
505480501(F)	${2.20}_{-0.007}^{+0.005}$	−33.48 ± 11.3	5.650	5.6807	Si XIII	1s2-1s3p	Trigo et al. (2012) [20]
505480101(A)	1.91 ± 0.01	−3.12 ± 2.2	6.507	6.4974	Mg XII	1s-6p	Reported in this study
802820201(L)	${2.15}_{-0.006}^{+0.004}$	−10.17 ± 0.004	5.781	5.7396	Al XIII	1s-4p	Reported in this study

). The addition of Gaussian visibly improves the value of C-stat per dof. The C-stat/dof values obtained for observations 122340101(C), 505480501(F), 505480101(A), and 802820201(L) are 1.01, 1.04, 1.13, and 1.46, respectively, and are well below 1.5. The best-fit energy of the absorption lines were observed, and their equivalent widths (EWs) are (1) ${2.02}_{-0.012}^{+0.011}$,${-10.5}_{-5.18}^{+5.29}$; (2) ${2.20}_{-0.007}^{+0.005}$ and −33.48 ± 11.3; (3) 1.91 ± 0.01 and −3.12 ± 2.2; and (4) ${2.15}_{-0.006}^{+0.004}$ and −10.17 ± 0.004, respectively. The Silicon absorption lines detected were similar to the lines detected by Trigo et al. (2012) [20] (Table 1). The Magnesium and Aluminium lines were not detected previously in any XMM-Newton data analysis. Although these highly ionised elements had been reported in Chandra observations previously, the transition levels were not similar to what we obtained. Another reason for the non-detection of the Al XIII absorption line could be the recording of this observation in the year 2017, which was long after the work mentioned in Table 2. We allowed the photon index of the powerlaw to be a free parameter throughout the entire analysis, since a low index value is very difficult to interpret if the index of the power law is associated with a comptonised spectrum [30]. Except for observations C, M, and L, we obtained a photon index value of below 3, suggesting the compotonised origin of seed photons from the corona; this is consistent with the value obtained by Halparn and Wang (1997) [51] and Allen et al. (2018) [31]. At the same time, the values of gamma for this source are similar to the previous results obtained by Trigo et al. (2012) [20]. From Table 7, we can see that the blackbody temperature obtained was of the order of 10⁶ K, and this is the temperature of the plasma near the source.

We attempted to infer some of the properties of the absorber with the help of the EWs of the absorption features. Assuming that the lines are not saturated and are on the linear part of the curve of growth, we determined the ionic column density of the detected ions using the relationship between equivalent width, the wavelength of the absorption line, and the oscillator strength, as proposed by Spitzer Jr. L. (1998) [44] in the year 1978, and the obtained results are nearly the same as those reported in a previous work (Table 5) [33]. We know that during dips, the column density of neutral hydrogen is highly variable [37], and this is evident in the case of observation 505480501(F) (Table 5). Furthermore, the dipping indicates the high inclination of the source and line of sight pass through the high impact point of the accretion disk and inflowing matter, i.e., at the bulge, and this may be the cause of the high rise in temperature, as reported in Table 5. The best-fit results of those observations in which no absorption line or absorption edge was detected are summarized in

Table 8. The results of the RGS best spectra fit in the range 1.3–2.3 keV of GX13+1 for those observations in which no absorption line was detected.

Component	Parameter	Unit	Obs. ID. 505480701(P)	Obs. ID. 505480401(M)
Tbabs	NH	×1022 atoms cm−2	${3.95}_{-0.52}^{+0.79}$	${4.12}_{-0.60}^{+1.07}$
bbodyrad	kTbb	keV	${0.17}_{-0.12}^{+0.19}$	${0.72}_{-0.36}^{+0.15}$
	norm		${2732}_{-2461}^{+1017}$	${2235.02}_{-1945}^{+1251}$
powerlaw	Γ		${2.82}_{-0.41}^{+0.79}$	${6.04}_{-1.21}^{+1.15}$
	norm	ph/keV/cm2/s at 1 keV	${6.56}_{-2.57}^{+9.78}$	${13.56}_{-1.97}^{+2.59}$
Gaussian1	LineE	keV	X	${1.76}_{-0.05}^{+0.06}$
	Element		X	X
	Sigma (σ)	keV	X	${8.34}_{-0.04}^{+0.07}$
	EW	eV	$\mathrm{X}$	$\mathrm{X}$
Gaussian2	LineE	keV	X	2.07 ± 0.02
	Element		X	X
	Sigma (σ)	keV	X	${0.002}_{-0.02}^{+0.03}$
	EW	keV	X	X
Luminosity		erg per sec	2.46 × 1037	2.62 × 1037
C-stat/d.o.f			485/481	574/514

Note: The symbol X in the table is used to indicate no value obtained.

.

The choice of components in a continuum influences the estimation of N_H caused by the limited energy band of RGS and its low statistics. Even the combination of data from RGS1 and RGS2 cannot improve these scenarios, so the use of RGS1 data alone will yield the same result. In most cases, our best-fit values of N_H agree with those reported earlier, e.g., the N_H of 2.9 × 10²² cm⁻² reported by D’Ai et al. (2014) [30] or that reported by Trigo et al. (2012) of 2.72–2.92 × 10²² cm⁻² [20], are quite similar to the values obtained in our observation 0505480101(A); similarly, the values 3.1–3.9 × 10²² cm⁻² obtained in observations F, G, H, and P (Table 6) are nearly equal to what has been reported by Sidoli et al. (2002) [26], Veda et al. (2005) [29] and/or Schulz et al. (1989) [23]. This is analogous with observations A, C, L, and M (Table 6). The reported N_H values in our analysis are ~2 to 3 factors higher than the galactic N_H (H1 column density for a sky position calculator of N_H: 1.64 × 10²² cm⁻²) for this source. Since equivalent widths between observations are nearly similar (Table 6), the derived values of N_H are close to the value of HI for this source [32,33], and the ionic densities calculated are also close to the values previously reported, so we can conclude that the absorption lines may be caused by ISM [33], and this is consistent with the proposal made by Veda et al. (2005) [12]. As reported by Pinto et al. (2010) [14], only ~1–2% of the total column density of ISM is the hot gas; thus, we can further conclude that the major constituents of this hot gas are the highly ionised elements with transitional energy of below 3 keV. The high value of Mg XII, 2.6 × 10⁻¹⁶ cm⁻² primarily indicates that the presence of Mg XII is highest in the LOS. Furthermore, since the values of line widths (σ) of absorption lines are too small, this indicates there is no material outflow in the path. We know ISM is stable on short time scales [14], which further satisfies the necessary condition of absorption lines to be produced by ISM. The measurement of outflow velocity and or dispersion velocity would help us to ascertain our claim, and this needs further analysis. We defer the measurement of velocity dispersion for hot ionised gas to a future publication.

5. Conclusions

In this study, we systematically analysed all the on-axis observations of GX13+1 recorded using the high-resolution reflection grating spectrometers of the XMM-Newton observatory. We have taken into account the possibility of X-ray loading and checked the data thoroughly to avoid errors caused by piling. All other probable causes of errors were also addressed. The main conclusions can be summarised as follows:

• The luminosity of the source is found to be in a range of (2.462–3.3) × 10³⁷ erg s⁻¹ (Table 6), which is consistent with the previous results [31].
• The occurrence of a dip in LMXB is not a regular phenomenon. For this source, a dip was reported for the first time by Trigo et al. (2012) in the year 2012 [20]. We detected one further dip in the light curve of the off-axis observation 0122340701(B), which further proves that the source inclination is moderately high.
• No burst or eclipse was observed in any of the light curves.
• In most of the cases, our best-fit values of N_H agree with those reported previously [20,23,30,33]. On average, the N_H values obtained in this study are slightly higher than those of the 21 cm HI estimates, probably because the X-ray above 25 Å take into account the contribution from HI and HII [14]. The higher value of N_H also suggests the presence of additional absorption [26].
• Since the equivalent widths in some of the cases are very similar, the derived values of N_H are close to the value of HI for this source [32,33], and the ionic density calculated is also close to the values previously reported, which implies that the absorptions may be caused by ISM [33], as proposed by Veda et al. (2005) [12] in their work.
• We significantly detected the 1s²-1s2p (2.02 keV) and 1s²-1s3p (2.24 keV) transitions of Si XIII, the 1s-6p (1.91 keV) transitions of Mg XII, and the 1s-4p (2.15 keV) transitions of Al XIII, of which the 1s-6p (1.91 keV) transitions of Mg XII and the 1s-4p (2.15 keV) transitions of Al XIII were not reported either in any analysis of the XMM-Newton data nor in the Chandra observations.