Inference on Accretion Flow Properties of XTE J1752-223 During Its 2009-10 Outburst

Compact objects, such as, neutron stars and black holes (BHs) are the end products of massive stars. The gravitational pull of BHs is so high that no particle or radiation can escape from them. They both can be detected only by the electromagnetic radiation emitted by the accreted matter falling on them. Most of the black hole candidates (BHCs) in our Galaxy are in close binaries with companion stars which act as donors. Wind material from the companion star or matter accreting via Roche lobe overflow falls towards the black hole due to its intense gravitational pull and starts swirling around it to form accretion disk due to the presence of angular momentum. The observed electromagnetic radiation from a black hole binary is from the accretion flow itself. Some of the black hole candidates in low mass X-ray binaries are transients in nature, which occasionally undergo outbursts. The increased X-ray flux in these transient X-ray binaries shows variability in the temporal and spectral states. Several works have already been done on this and many papers are available in the literature (see, e.g., Tomsick et al. 2000; McClintock & Remillard 2006; Debnath et al. 2008, 2013; Nandi et al. 2012; Rao 2013) to explain the variation of spectral and temporal properties of these objects during their active X-ray outburst phases. It is also reported by some authors that these objects transit through several spectral states (e.g., hard state (HS), hard-intermediate state (HIMS), soft-intermediate state (SIMS), soft state (SS)) during their active outburst phases (see Debnath et al. 2013 and references therein). Depending upon the observed spectral states, Debnath et al. (2017) classified these transient BH binaries into two types: classical or type-I (all four states are observable) and harder or type-II (softer states are missing). Low and high frequency quasi periodic oscillations (QPOs) are generally observable in the power density spectra (PDS) of these sources (see, Remillard & McClintock 2006 for a review). Low frequency QPOs are commonly observed in hard and intermediate spectral states. Generally, it has been observed that during the rising HS and HIMS, frequency of these QPOs monotonically increases with time (day) and during the declining phase, the opposite nature is observed. In SIMS, these QPOs are observed sporadically.

It is well-known that the emitted spectrum, emerging from black hole candidates (BHCs), primarily contains a combination of a multi-color thermal blackbody component and a non-thermal power-law component. The thermal component is the radiation coming from the standard Keplerian disk (Shakura & Sunyaev 1973) and the non-thermal component originates from the hot ‘$Compton$’ cloud (Sunyaev & Titarchuk 1980, 1985). The standard disk contains soft X-ray photons. The ‘$Compton$’ cloud is the repository for hot electrons. The energy of these hot electrons is transferred to those soft X-ray photons in the process of repeated inverse Compton scattering to produce high-energy X-ray photons and this gives the hard power-law tail in the observed spectra of an accreting BH. In TCAF solution (Chakrabarti 1995, 1997; Chakrabarti & Titarchuk 1995, hereafter CT95), the ‘$hot~{}corona$’, which is known as the ‘$Compton~{}cloud$’, is the CENtrifugal pressure supported BOundary Layer (CENBOL) that forms behind the centrifugal barrier due to the piling up of the low viscous and low angular momentum optically thin matter, known as the sub-Keplerian (halo) component. Another component in TCAF solution is the optically thick and geometrically thin Keplerian (disk) component which is submerged inside the sub-Keplerian component. In 2014, this TCAF solution has been implemented into HEASARC’s spectral analysis software package XSPEC as an additive table model after generation of the model fits file to fit energy spectra of black holes (Debnath et al. 2014, 2015a). Now, one can extract information about the physical flow parameters directly from the spectral fits (Debnath et al. 2014, 2015a,b, 2017; Mondal et al. 2014, 2016; Jana et al. 2016, 2019; Chatterjee et al. 2016, 2019). Estimation of the intrinsic source parameters such as the mass of the black hole (Molla et al. 2016, 2017; Debnath et al. 2017 and references therein; Nandi & Chakrabarti 2019) and X-ray flux contributions from jets/outflows are also possible (Jana et al. 2017, 2019; Chatterjee et al. 2019) from spectral analysis with the TCAF model.

The stellar-mass black hole (SBH) candidate XTE J1752-223 was monitored and discovered by Rossi X-ray Timing Explorer (RXTE) on October 21, 2009 (Shaposhnikov et al. 2010) at the position R.A.=$268.05\pm 0.08$, Dec=$-22.31\pm 0.02$ (J2000 coordinate system). Markwardt et al. (2009a) proposed the source as a BHC based on their analysis. Ratti et al. (2012) suggested the location of the source to be in the Galactic bulge. During the outburst, the source was active for almost 8 months. RXTE monitored the source roughly on a daily basis except from Nov. 20, 2009 to Jan. 19, 2010 as during this phase RXTE pointed observations were not possible due to the Sun constraint. After the discovery the source was also monitored by MAXI, Swift and other satellites. The X-ray behavior of the source during the outburst was matched with typical phenomenological picture of the black hole transients, confirming XTE J1752-223 as a strong accreting black hole candidate (Nakahira et al. 2010; Shaposhnikov et al. 2010; Curran et al. 2011). Strong, relativistic iron emission lines were detected by $Suzaku$ and $XMM-Newton$ (Reis et al. 2011). Reis et al. (2011) estimated spin of the source as $a=0.52\pm 0.11$. Miller-Jones et al. (2011) estimated the disk inclination angle of the source to the line of sight as $i<49^{\circ}$. Torres et al. (2009a,b) reported a bright optical and a near-infrared counterpart just after the X-ray discovery. Brocksopp et al. (2009) reported a radio counterpart with a flux density of 2 mJy at both 5.5 and 9 GHz using Australia Telescope Compact Array (ATCA) with a spectrum consistent with that of a compact jet in hard state. Brocksopp et al. (2010b,c) showed the presence of resolved jet components by additional radio observations using the European VLBI Network (EVN). In the intermediate state the radio emission still produced compact jets and the radio flux became more variable (Brocksopp et al. 2013). Russell et al. (2012) discussed a late jet re-brightening in the decaying hard state from multi-wavelength observations. Shaposhnikov et al. (2010) found that the source exhibited all the canonical spectral states of a classical black hole candidate. They also reported a mass estimate for the black hole $M_{BH}=9.8\pm 0.9~{}M_{\odot}$ and a distance of $d\sim 3.5\pm 0.4$ kpc. According to Brocksopp et al. (2013), this object was jet active during the entire duration of the outburst. According to their report, the jet was compact till 2010 Jan. 21 (MJD 55217.87) on which the 1st peak in the radio light curve (both 5.5 and 9 GHz) occurred. Again, the jet became compact after 2010 March 24 (MJD 55279.63) where the last radio peak occurred. In the intermediate region, optically thin radio flares were present which gradually decreased in flux density. Shaposhnikov et al. (2010) reported the existence of high soft state during this outburst from MJD $\sim 55220.68$ to MJD $\sim 55279.63$ when high radio flares were active (Brocksopp et al. 2013). It is reported in the literature that compact jets are generally seen in hard states, while discrete or blobby jets are observed in intermediate (HIMS and SIMS) states (see, Jana et al. 2017 and references therein). In soft states, jet bases are cooled down and no jet is observed. In the present case, the source has a short orbital-period ($P_{orb}\leq 6.8$ hr) with an M type mass donor as the companion star (Ratti et al. 2012). Recent study of this types of objects (MAXI J1659-152, MAXI J1836-194, Swift J1753.5-0127, XTE J1118+480) by our group suggests that these type-II or harder type of outbursting sources do not show soft spectral state (Debnath et al. 2015b, 2017; Jana et al. 2016; Chatterjee et al. 2019). In this paper, we intend to study the accretion flow properties during this outburst through careful analysis of the evolution of the spectral and the temporal properties with two types of models: phenomenological disk blackbody plus power-law (DBB+PL) models and physical TCAF model. Through these analysis we wish to verify if this short period source indeed has a soft state during this outburst as reported by previous authors. If the answer is ‘yes’ then our goal would be to find physical mechanisms for the production of jets in the soft state.

This paper is organized in the following way. In §2, we briefly discuss about the data analysis technique using HEASARC’s HEASoft package. In §3, we present spectral and temporal analysis results of the source. Finally, in §4, a brief discussion on the results of the accretion flow dynamics of this BHC and concluding remarks are presented.

RXTE PCA monitored XTE J1752-223 roughly on a daily basis (except operational shutdown during 2009 Nov. 16 to 2010 Jan. 18) till 2010 Aug 6 after its discovery on October 2009. Here we analyzed $32$ observations of RXTE PCA from October 26, 2009 (MJD 55130.96) to June 21, 2010 (MJD 55368.94) to study the spectral and timing properties of this source during this outburst. We have used HEASARC’s software package HEASoft version HEADAS 6.19 and XSPEC version 12.9 for the analysis of the archival data of RXTE PCA instrument. We extract data from the best calibrated proportional counter unit 2 (PCU2). We generally follow the methods mentioned in Debnath et al. (2013, 2015a) for data reduction and analysis.

For timing analysis, we also create the power density spectra (PDS) which are generated using XRONOS task ‘powspec’ on $0.01$ sec time binned RXTE PCA light curves in the energy range $2-15$ keV to find any signature of low frequency quasi periodic oscillation (QPOs). The normalization factor in ‘powspec’ is taken to be ‘-2’ to have expected ‘white’ noise subtracted rms fractional variability. The centroid frequency of the QPOs is found by fitting the PDS with Lorentzian profiles. The coherence parameter $Q~{}(=\nu/\bigtriangledown\nu)$ and amplitudes (= $\%$ rms) make the selection of QPOs in PDS where, $\nu$, $\bigtriangleup\nu$ are the centroid QPO frequency and the full-width at half-maximum respectively as discussed in Debnath et al. (2008). We also used RXTE ASM light curve data to study the evolution of dynamic photon index ($\Theta$) and variation of intensity (1.5-12 keV) with it to study the temporal properties. The dynamic photon index ($\Theta$) is the slope of the hard region of a spectrum (Ghosh & Chakrabarti (2019). We have discussed about $\Theta$ in more detail in the result section (3.1.2). We also studied MAXI GSC (in 2-10 keV) and Swift BAT (in 15-50 keV) daily average light curves and their count ratios for our temporal study.

For spectral analysis, the standard data reduction procedure for extracting the RXTE PCA (PCU2) spectral data are used. The background subtracted spectra are first fitted with the phenomenological disk black body ($DBB$) + power-law ($PL$) model. We have fitted $32$ PCA observations with the $DBB+PL$ model in the energy range of $2.5-25$ keV. A fixed value of 1$\%$ systematic error and hydrogen column density ($N_{H}$) of $0.46\times 10^{22}~{}atoms~{}cm^{-2}$ (Shaposhnikov et al. 2010) for photoelectric absorption model $phabs$ are used to fit the spectra. Additional Gaussian iron line of peak around $6.4$ keV for $Fe$ emission line is used to achieve the best fit. The fluxes of different model components of the fitted spectra are calculated using the $cflux$ calculation method.

We refit all the spectra with the current version (v0.3.1) of TCAF model $fits$ file as an additive table model into HEASARC’s spectral analysis software package XSPEC. Here a fixed value of 1$\%$ systematic error also has been used. For fitting the spectra of a black hole (BH) with TCAF model fits file, one requires to supply six parameters including the mass of the BH and normalization. The normalization is expected to remain constant or vary in a very narrow range throughout the entire outburst unless there is an occurrence of phenomenon like jets (for more details see, Molla et al. 2016; Jana et al. 2017). The model input parameters are: $i)$ Keplerian disk rate ($\dot{m}_{d}$ in Eddington rate ${\dot{M}}_{Edd}$), $ii)$ sub-Keplerian halo rate ($\dot{m}_{h}$ in ${\dot{M}}_{Edd}$), $iii)$ location of shock ($X_{s}$ in Schwarzschild radius $r_{s}=2GM_{BH}/c^{2}$), $iv)$ compression ratio ($R=~{}{\rho}_{+}/{\rho}_{-}$, where ${\rho}_{+}$ and ${\rho}_{-}$ represent the densities in the post-shock and pre-shock flows), $v)$ mass of the BH ($M_{BH}$) in solar mass ($M_{\odot}$) unit. The normalization is a function of the distance and inclination angle. Unless there is any separate dominating physical processes whose effects are not considered in the present version of the TCAF model fits file, or disk is not precessing, the normalization should not vary from observations to observations. Our procedure is to keep it as a free parameter while fitting the spectra, and it generally comes into a narrow range throughout the outburst(s) of a particular BHC observed with same satellite instrument (see, Molla et al. 2016, 2017). This would determine the normalization once and for all even without knowing the distance and inclination angle. In case the mass of the source is also not known, one may also keep it as a free parameter to find probable value of it (see, Molla et al. 2016; Debnath et al. 2017 and references therein) from each observation using this normalization constant. To obtain the best model fit (${{\chi}^{2}}_{red}\simeq 1$), a Gaussian iron line of peak around $6.4$ keV is used. In some of the observations another additional Gaussian line of peak around $4.2$ keV is used, which may be due to red-shifted $FeK_{\alpha}$ line.

Studying X-ray properties in both temporal and spectral domains of transient black hole candidates helps understanding the accretion flow properties of these sources during various outbursting phases. Here, we report both these properties of the Galactic BHC $XTE~{}J1752-223$ during its 2009-10 outburst.

The detailed analysis results are given in Table 1, 2. In Table 1, primary (dominating) observed QPO parameters obtained from Lorentzian model fitted are mentioned. In Table 2, we mentioned spectral parameters obtained from fits using two types of models: i) combined DBB and PL models, ii) TCAF model based fits file in XSPEC.

In Fig. 1 (a-b), variation of MAXI GSC (in 2-10 keV; online red), Swift BAT (in 15-50 keV; online blue) light curves and hardness ratios (BAT/GSC counts; online green) are shown. In Fig. 1 (c) the variation of radio light curves at both 5.5 and 9 GHz frequencies are shown. These radio light curve data are collected from Brocksopp et al. (2013). In Fig. 2, we show the hardness intensity diagram (HID). In Fig. 3 (a-b), we show the variation of dynamic photon index ($\Theta$) and variation of intensity with $\Theta$. In Fig. 4 (a-c), we show the variations of PCA count rate, total flux (DBB+PL) and total rate (${\dot{m}}_{d}+{\dot{m}}_{h}$) with day in MJD. In Fig. 5 (a-d), the variations of $DBB+PL$ fitted power-law flux, disk black body flux, power-law photon index ($\Gamma$) and disk temperature ($T_{in}$) with MJD are shown, which are obtained by fitting PCA spectra in $2.5-25$ keV energy range. Similarly in Fig. 6, we show the variations of TCAF model fitted parameters: disk rate (${\dot{m}}_{d}$), halo rate (${\dot{m}}_{h}$), shock location ($X_{s}$), compression ratio ($R$) and mass of the source ($M_{BH}$). In Fig. 7, accretion rate ratio intensity diagram (ARRID) is shown.

Galactic transient BHC XTE J1752-223 was monitored in multi-waveband during its 2009-10 outburst immediately after discovery by RXTE all sky monitor (ASM) on 2009 Oct. 21 (MJD=55125). RXTE PCA monitored this source starting from 2009 Oct. 26 (MJD=55130.93) roughly on a daily basis except from 2009 Nov. 16 to 2010 Jan. 18 (operational shutdown period due to Sun constraint). We found that non-operational period of MAXI and Swift satellites were less as compared to RXTE. So, to study outburst profiles (daily average count rates) and hardness-ratio (HR) we use MAXI GSC (in $2-10$ keV) and Swift BAT (in $15-50$ keV) data from 2009 Oct. 23 (MJD=55127) to 2010 Jun. 22 (MJD=55369). We also made use of the RXTE ASM data (daily average light curve) to make dynamic photon index ($\Theta$), to check the existence of soft state during the outburst. Spectral analysis is made using RXTE PCU2 data (in $2.5-25$ keV). Here we analyzed $32$ observations spreaded over the outburst period. Two types of models such as $i)$ commonly used combined DBB plus PL model, and $ii)$ physical accretion flow model namely TCAF model, are used for our spectral analysis.

Although low frequency QPOs are very common in this type of stellar mass BHCs, we observed them only in six observations out of the $32$ observations under consideration. Evolving type-C QPOs of frequencies from $2.20$ to $6.15$ Hz are observed during 2010 Jan. 19-21. Later we observed sporadic type-B QPOs. All these QPOs are observed during the rising phase of the outburst. Depending upon the nature of evolution of spectral (model fitted parameters) and temporal ($\Theta$, HR, QPO) properties, we make an effort to understand spectral nature of the source during the outburst. We find the presence of these major spectral states: HS, HIMS and SIMS or SS. The outburst started and ended with HS via intermediate states to form a hysteresis loop in the following sequence : HS (rising) $\rightarrow$ HIMS (rising) $\rightarrow$ SIMS or SS $\rightarrow$ HIMS (declining) $\rightarrow$ HS (declining).

We classified the spectral state during 2009 Oct. 23 (MJD=55127) to 2010 Jan. 12 (MJD=55208.64) as the rising HS. During this phase of the outburst, high values of HR ($\sim 3-4$) as well as PL flux or halo rate are observed. From our spectral study of initial four spectra, we see highly dominating halo rate in presence of strong shock located far away from the BH. High DBB temperature ($T_{in}\sim 1.25-1.44$ keV) and low PL index ($\Gamma\sim 1.35-1.39$) values are also observed. Although, we have not been able to make spectral analysis on MJD=55208.64, based on variation of HR, we identify this as HS (rising) to HIMS (rising) transition day. After this observation, HR decreases rapidly due to rapid fall in BAT count and rise in GSC count. This phase (rising HIMS) is continued for the next $\sim 10$ days till 2010 Jan. 22 (MJD-55218.80), when we observe HR as $0.1$. Our spectral and temporal analysis also support this. Dominating halo was found to form a strong shock. During this phase of our outburst, we also see monotonically evolving low frequency QPOs ($2.20-6.15$ Hz). These evolving QPOs are characteristic feature of HS and HIMS (see, Debnath et al. 2013 and references therein). We define MJD=55218.80 as HIMS (rising) to softer state transition day as on this day, we see that GSC flux reaches at its maximum. On this day, there are two PCA observations: In the first one (MJD=55218.16), we see a maximum frequency ($6.15$ Hz) of the evolving type-C QPO and on the second one (MJD=55218.82), we see a much lower ($3.51$ Hz) type-B QPO. On the next day, QPOs are absent and re-appeared two days later (on MJD=55220.71 at $2.19$ Hz). This sporadic nature of the QPO is the characteristic feature of SIMS. From spectral analysis, we also see cooler disk (DBB $T_{in}\sim 0.37-0.92$ keV) with higher $\Gamma$ ($\sim 1.84-2.22$). Decreasing PL flux or halo rate with higher DBB flux or disk rate are observed during this phase of the outburst.

We identify 2010 Mar. 24 (MJD=55279.63) as SIMS or SS to HIMS (declining) phase. This is because, after this phase, we see rise in HR due to faster increase in BAT count. This increase in HR is continued for the next $\sim 10$ days till 2010 Apr. 03 (MJD=55289.36). Our spectral analysis also shows that during this phase of the outburst, increasing trend of $T_{in}$ with fall in DBB flux and rise in PL flux. PL index $\Gamma$ also shows a decreasing nature. Decreasing disk rate in presence of receding shock is observed during this phase. MJD=55289.36 is identified as the transition day between HIMS (declining) to HS (declining) as on this day, we see higher HR due to local maximum of BAT count. After that both BAT and GSC counts, DBB and PL fluxes and disk and halo rates decrease. Noticeably, on the transition day we see much lower disk rate as compared to highly dominating halo rate in presence of a receding strong shock. Interestingly, we have not seen any signature of evolving QPOs during declining HS, HIMS as well as rising HS. Since these QPOs (generally type-C) form due to resonance between compressional heating and Compton cooling time scales inside CENBOL (Molteni et al. 1996; Chakrabarti et al. 2015), it is possible that the timescales did not match as the halo rate was too large.

It is well known that the spectral and the temporal properties are strongly correlated. HID or so-called ‘q’-diagram (see, Fig. 2) gives a quick-look of it, where different spectral states are linked with the different branches of the diagram. In Fig. 2, A-B, E-F mark HS of the rising and the declining phases respectively, where as B-C, D-E indicate HIMS of the rising and the declining phases respectively. Here, C-D marks SIMS or SS. In 2016, Jana et al. reported that ARRID (see, Fig. 7) provides more physical picture than HID. In Fig. 7, one could find more clear indication or turn-over in the plot nature when a spectral state transition occurs (see for example, points C, D, E).

This source was extensively studied during its only outburst (2009-10) till date by many researchers to explore its properties in multi-waveband. Shaposhnikov et al. (2010) studied both spectral and timing properties of the source using RXTE PCA data and classified entire outburst into low-hard (LHS), intermediate (IS) and high soft (HSS) spectral states. Nakahira et al. (2010) and Curran et al. (2011) also studied independently with data of MAXI and Swift satellites and found similar spectral states including HSS. These reports of presence of SS or HSS, during 2009-10 outburst of XTE J1752-223 is quite unusual for the object as the source belongs to a class of objects of short orbital period which generally do not show SS during an outburst. We therefore were motivated to verify these reported states using the physical TCAF fits. Fig. 1(c), suggests that the source was highly active in radio during entire phase of the outburst (also see, Brocksopp et al. 2013). It is quite unusual to see jets during SS, if we consider radio has been emitted from jets. So, to confirm if the source actually went in SS or not, we calculated dynamic photon index ($\Theta$) using RXTE ASM data as method described in Ghosh & Chakrabarti (2019). $\Theta$ is found to be $<-1$ during MJD=55219 to 55233, which indicates the presence of a softer state, although during the entire outburst, the power-law photon index ($\Gamma$) never crossed a value $>2.3$. So, we term this whole period (from MJD 55218.80 to MJD 55279.63) as SIMS or SS.

We have also estimated the disk (soft) flux percentage in $2.5-20$ keV energy band from DBB+PL model fitted spectra and power continuum (r), integrated over $0.1-10$ Hz in PDS. These analysis were done using methods defined in Remillard (2004). The disk i.e., DBB flux percentage was found more than $75\%$ during the period from MJD=55221.3 to MJD=55279.6 (see, Table 3). Now, according to Remillard (2004), this period of observation should be defined as SS. However, this paper also suggests that if $r$ is $<0.06$, that could also be the indication of the presence of SS. Here, $r$ was less than $0.06$ from the day when RXTE rediscovered the source (on MJD 55215.9) after Sun constraints till the end of our studied period. So according to him, this day should be the beginning of the SS as there was no prior PCA observation. However, there were presence of type-C QPOs on four days (MJD 55215.9, 55216.9, 55217.8 and 55218.1) and type-B sporadic QPOs on two days (MJD 55218.8 and 55220.6) on which $r$ was $<0.06$. The QPO information and spectral fitted parameters tell us that the source was still in intermediate state (HIMS and SIMS) at-least until MJD=55220.6. The dynamic photon index ($\Theta$ as defined earlier) was also found to be less than $-1$ from MJD=55218.8 to 55233.0, which again tells us that the softer states (SIMS or SS) could be started on MJD=55218.8. For the above contradictions, we found difficulty to define exact transition day between SIMS and SS and vise-verse and designated whole middle phase (from MJD 55218.8 to MJD 55279.6) of the outburst as mixture of two softer spectral states i.e., as ‘SIMS or SS’.

Optically thin radio flares were also present during this time period of the outburst (see Fig. 1(c)). During accretion, matter can bring in a large amount of stochastic magnetic flux tubes which due to azimuthal velocity, form a very strong toroidal flux tubes (Nandi & Chakrabarti 2001). The magnetic tension acting on these flux tubes could be very strong collapsing toroidal flux tubes and forming sporadic outflows. We believe that the disk could be magnetically dominated in order to see these jets. We calculated equipartition magnetic field strengths during the flaring as well as intermediate phases and found presence of strong magnetic field in the region from MJD=55215 to 55285. We believe that this high magnetic field acts as a driving force for the optically thin radio flares in the SIMS or SS. The details calculation of magnetic field and its effect and correlation with radio flares are beyond the scope of this paper and will be published elsewhere.

Recent studies using TCAF confirmed masses of many BHCs from the spectral analysis (Molla et al. 2016, 2017; Jana et al. 2016, 2019; Chatterjee et al. 2016, 2019; Debnath et al. 2017). In TCAF, mass of the BH is an important model input parameter. So, by fitting (keeping it as free while fitting) one gets the best fitted masses. Here we see the variation of the model fitted masses between $8.1-11.9$ $M_{\odot}$. The average observed mass is $10$ $M_{\odot}$. So, we believe that the probable mass range of the source is $8.1-11.9$ $M_{\odot}$, or $10\pm{1.9}~{}M_{\odot}$. This estimated mass of the source falls roughly in the same range as predicted by Shaposhnikov et al. (2010). They estimated mass of source as $8-11$ $M_{\odot}$ or $9.8{\pm 0.9}~{}M_{\odot}$ from their QPO frequency vs. spectral slope correlation method.

This work made use of ASM and PCA data of NASA’s RXTE satellite; Swift BAT data provided by UK Swift Science Data Centre at the University of Leicester; and MAXI GSC data provided by RIKEN, JAXA and the MAXI team. K.C. acknowledges support from DST/INSPIRE fellowship (IF170233). D.D. and S.K.C. acknowledge support from Govt. of West Bengal, India and 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. A.J. and D.D. acknowledge support from DST/GITA sponsored India-Taiwan collaborative project (GITA/DST/TWN/P-76/2017) fund. A.J. also acknowledges CSIR SRF fellowship (09/904(0012)2K18 EMR-1).