ACCRETION FLOW DYNAMICS OF MAXI J1659-152 FROM THE SPECTRAL EVOLUTION STUDY OF ITS 2010 OUTBURST USING THE TCAF SOLUTION

Compact objects, such as black holes (BHs) and neutron stars, are identified by electromagnetic radiations emitted from the accreting disk formed by matter from their companion. This matter is accreted either through Roche-lobe overflow or winds. Some of these objects are transient stellar mass X-ray binaries with a low-mass star acting as a donor star. Study of these objects in X-rays is very interesting as they undergo rapid evolution in their timing and spectral properties, which are strongly correlated to each other. There are a large number of articles by several groups (see, e.g., Belloni et al. 2005; McClintock & Remillard 2006; Nandi et al. 2012; Debnath et al. 2013 etc) that discuss variations of spectral and temporal properties of these transient black hole candidates (BHCs) during their X-ray outbursts. In general, it has been found that these objects show different spectral states (hard, hard-intermediate, soft-intermediate, soft, etc; McClintock & Remillard 2006) and low- and high-frequency quasi-periodic oscillations (QPOs) in power-density spectra (PDSs) in some of these spectral states (Remillard & McClintock 2006). Different branches of X-ray color–color and Hardness–Intensity Diagrams (HIDs; Maccarone & Coppi 2003; Belloni et al. 2005; Debnath et al. 2008, etc.) are related to different spectral states of the outburst phases. It has also been observed by several authors (see Mandal & Chakrabarti 2010; Nandi et al. 2012; Debnath et al. 2013 and references therein) that these observed spectral states show hysteresis loops during their spectral evolutions of an entire epoch of the outburst of these transient BHCs. Simple model fits of accretion rates using the two-component advective flow (TCAF) solution of Chakrabarti & Titarchuk (1995, hereafter CT95) by Mandal & Chakrabarti (2010) indicated that the accretion rates indeed vary differently in the rising and declining states.

In the literature, there are a large number of theoretical or phenomenological models, which describe accretion flow dynamics around a BH. It is well known that emitted radiation contains both thermal and non-thermal components. The thermal component is a multi-color blackbody type emitted in the standard Keplerian disk (Novikov & Thorne 1973; Shakura & Sunyaev 1973) and the other is a power-law (PL) component, originated from the so-called "Compton" cloud (Sunyaev & Titarchuk 1980, 1985). This component is composed of hot electrons and is cooled down by repeated Compton scatterings of the low-energy (soft) photons. There are many speculations about the nature of this Compton cloud, which range from it being a magnetic corona (Galeev et al. 1979) to a hot gas corona over the disk (Haardt & Maraschi, 1993; Zdziarski et al. 2003). CT95, in their TCAF solution, consider that the CENtrifugal pressure supported BOundary Layer (CENBOL) plays the role of the Compton cloud. This CENBOL happens to be the post-shock region of the low angular momentum halo in which a standard Keplerian disk remains immersed while emitting soft photons. The shock in the halo forms due to the piling up of matter behind the centrifugal barrier of the low angular momentum accretion flow component with a sub-critical viscosity parameter (Chakrabarti 1990a, 1990b, hereafter C90ab, 1996). These shocks are found to be stable even under non-axisymmetric perturbations (Okuda et al. 2007). The other component of TCAF is an optically thick standard (SS73) Keplerian (disk) component that is formed in flows with a super-critical viscosity parameter (C90ab). Of course, this disk also has to pass through the inner sonic point to satisfy the boundary conditions on the BH horizon (C90ab; see also Muchotrzeb and Paczyński 1982). Formation of TCAF from a single simulation (see Giri & Chakrabarti 2013; Giri et al. 2015 and references therein) shows that it has a stable configuration. Also, in Mondal et al. (2014a), a self-consistent transonic solution of TCAF in the presence of both cooling and outflows is obtained.

Recently, after the inclusion of this TCAF solution (CT95; Chakrabarti 1997 hereafter C97) in HEASARC's spectral analysis software package XSPEC as an additive table model, Debnath et al. (2014, hereafter DCM14), Debnath et al. (2015, hereafter DMC15), and Mondal et al. (2014b, hereafter MDC14) obtained a clearer picture of the accretion flow dynamics around BHCs as they find evidence of systematically varying accretion rates of the standard disk and the halo and the shock location on a daily basis. From the TCAF fitted spectrum, one can obtain two accretion rates (disk and halo), shock locations, and shock strength. These parameters also give us information about the frequency of QPOs. Transitions of various spectral states that are observed during the outburst phases of a transient BHC can be identified by special behavior of the accretion rate ratio (ARR) and the nature of observed QPOs.

Newly discovered MAXI J1659-152 is an interesting BH binary to study because it is the shortest orbital period BHC observed to date (Kuulkers et al. 2010, 2013). The source was first observed by the MAXI/GSC instrument on 2010 September 25 at the sky location of R.A. $=\;{{16}^{{\rm h}}}{{59}^{{\rm m}}}{{10}^{{\rm s}}}$, decl. $=\;-15{}^\circ 16^{\prime} 05^{\prime\prime}$ (Negoro et al. 2010). The source was simultaneously observed by the SWIFT/BAT instrument at roughly 17° above the Galactic plane (Mangano et al. 2010). Kalamkar et al. (2011) defined the source as a BHC, based on their combined optical and X-ray spectral study, which was initially thought to be a gamma-ray burst and was named GRB100925A. Kuulkers et al. (2013), based on their detailed study of the X-ray intensity variation of observed absorption dips (Kennea et al. 2010), confirmed MAXI J1659-152 to be a short orbital period BH binary of the period $=\;2.414\pm 0.005$ hr.

MAXI J1659-152 showed X-ray flaring activity in 2010, other than low-level activity in 2011, which continued for ∼9 months. During this period, the source was extensively studied in the multi-wave band, such as in various X-ray (Muñoz-Darias et al. 2011; Kalamkar et al. 2011; Yamaoka 2012; Kuulkers et al. 2013), optical/IR (Russel et al. 2010; Kaur et al. 2012), and radio observatories (Miller-Jones et al. 2011; Paragi et al. 2013). van der Horst et al. 2013 made a multi-band campaign to explore multi-wavelength properties of the source during this outburst. Physical parameters, such as distance, disk inclination angle, and masses of the source and the companion, are estimated using various methods. The most acceptable ranges of distance and disk inclination angle are 5.3–8.6 kpc and 60°–80° (Yamaoka 2012; Kuulkers et al. 2013), respectively. Although Shaposhnikov et al. (2011) predicted the mass of the BH (M_BH) as $20\pm 3\;{{M}_{\odot }}$, the preferable range of mass of the source and companion are $3-8\;{{M}_{\odot }}$ (Yamaoka 2012) and $0.15-0.25\;{{M}_{\odot }}$ (Kuulkers et al. 2013), respectively. In this paper, we use $6\;{{M}_{\odot }}$ as the mass of the BH.

We study the spectral and timing properties of the source during its 2010 main outburst phase, which continued for ∼1.5 months, using RXTE PCA archival data. Temporal properties of the BHC along with the evolution of QPO frequency during the declining phase of the outburst are presented in Molla et al. (2015, in preparation, hereafter Paper II).

The paper is organized in the following way: in Section 2, we briefly discuss observation and data analysis procedures using HEASARC's HeaSoft software package. In Section 3, we present results of spectral analysis using TCAF fits file as an additive table model in XSPEC, and a variation of different flow parameters extracted from the model fits. Here, we also compare combined disk blackbody (DBB) and PL model fitted spectral analysis results with that of the TCAF fitted analysis results. Finally, in Section 4, we present a brief discussion and make our concluding remarks.

We analyze the data of 30 observational IDs starting from the first day of RXTE PCA observation, namely, 2010 September 28 (Modified Julian Day, i.e., MJD = 55467) to 2010 November 11 (MJD = 55508). Data reduction and analysis are done using HEASARC's software package HeaSoft version HEADAS 6.15 and XSPEC version 12.8. To analyze archival data of the RXTE PCA instrument, we follow the standard data analysis techniques as done by Debnath et al. (2013, 2015).

For spectral analysis, Standard2 mode Science Data of PCA (FS4a*.gz) are used. Spectra are extracted from all the layers of the PCU2 for 128 channels (without any binning/grouping of the channels). We exclude HEXTE data from our analysis, as we find strong residuals (line features) in the HEXTE spectra at different energies. This could be due to the fact that the "rocking" mechanism for HEXTE stopped. Therefore, we restrict our spectral analysis with the PCA data to the energy range of 2.5–25 keV only. In the entire PCA data analysis, we include the dead-time correction and also the PCA breakdown correction (because of the leakage of propane layers of Proportional Counter Units). The "runpcabackest" task was used to estimate the PCA background using the latest bright-source background model. We also incorporated the $pca\_saa\_history$ file to take care of the SAA data. To generate the response files, we used the "pcarsp" task. Detailed analysis will be discussed in Paper II.

The 2.5–25 keV PCA background-subtracted spectra are fitted with the TCAF based model fits file and with the combined DBB and PL model components in XSPEC. Individual flux contributions for the DBB and PL model components are obtained by using the convolution model "cflux" technique. For the entire outburst, we keep hydrogen column density (N_H) fixed at 3.0 × 10²¹ atoms cm⁻² (Muñoz-Darias et al. 2011) for the absorption model wabs. We also assume a fixed 1.0% systematic instrumental error for the spectral study during the entire phase of the outburst. After achieving the best fit based on the reduced chi-square value ($\chi _{{\rm red}}^{2}\sim 1$), the "err" command is used to find 90% confidence ± error values for the model fit parameters. In Table A1, we mention average values of these two errors in superscript.

For a spectral fit, using the TCAF based model, one needs to supply five model input parameters, other than the normalization constant. These parameters are (i) BH mass (M_BH) in solar mass (${{M}_{\odot }}$) units, (ii) sub-Keplerian rate ($\dot{{{m}_{h}}}$ in ${{\dot{M}}_{{\rm Edd}}}$), (iii) Keplerian rate ($\dot{{{m}_{d}}}$ in Eddington rate ${{\dot{M}}_{{\rm Edd}}}$), (iv) location of the shock (X_s in Schwarzschild radius r_g = $2{\rm G}M/{{c}^{2}}$), and (v) compression ratio (R) of the shock. The model normalization value (norm) is $\frac{R_{z}^{2}}{4\pi {{D}^{2}}}{\rm sin} (i)$, where "R_z²" represents an effective area of the emitting region (purely on dimensional ground), D is the source distance in 10 kpc units, and i is the disk inclination angle. In order to fit a BH spectrum with the TCAF model in XSPEC, we generate the model fits file (TCAF0.1.fits) using theoretical spectra generating software by varying five input parameters in the CT95 code. We then include it in XSPEC as a local additive model. A brief discussion of the TCAF model, its present development, and a detailed description of the range of input parameters and the generation procedure of the current version (v0.1) of the TCAF fits file are given in DCM14 and DMC15. For the spectral analysis with TCAF, the mass of the BH is frozen at $6\;{{M}_{\odot }}$.

Accretion flow dynamics of a transient BHC can be well understood by model analysis of spectral and temporal behaviors of the source during its outburst phase. Here, we present the results of spectral analysis based on TCAF and compared with combined DBB and PL model fitted results. A combined DBB and PL model fitted spectral analysis, though fitted well throughout and in some cases better than TCAF, only gives gross properties of the disk such as fluxes from different components. However, TCAF goes one step further in extracting the detailed flow parameters, such as two disk rates and shock properties. Furthermore, transitions of spectral states are more conspicuous in terms of the fitted parameters. Thus, to study accretion dynamics around BHCs, there appears to be certain definite advantages in fitting with the TCAF solution. A shortcoming of TCAF fit with the current version (v0.1) is that as the spectra become softer, the fit tends to worsen, mainly indicating that the importance of the halo component is reducing. In our next version, this would be taken care of by self-consistently cooling down the second component in order for the flow to automatically tend to have a single component.

All 30 observational IDs spread over the entire period of the 2010 outburst are initially fitted with combined DBB and PL model components in XSPEC. Model fitted disk temperature (T_in in keV), PL photon index (Γ), and flux contributions from the two types of model components are obtained. We then refitted all the spectra with the current version of our TCAF model, and from the fit, accretion flow parameters, such as disk rate ($\dot{{{m}_{d}}}$), halo rate ($\dot{{{m}_{h}}}$), location of the shock (X_s), and compression ratio (R), are extracted.

3.1. Spectral Data Fitted by the TCAF Solution and by the Combined DBB and PL Model

A combined conventional DBB and PL model fit in the 2.5–25 keV energy range RXTE PCA spectra provides us with a rough estimate of flux contributions originated from both thermal (from DBB) and non-thermal (from PL) processes around a BH. From this, we also get an idea about the evolution of the average temperature of the accretion disk and spectral states by monitoring variations of T_in and Γ factors. However, from the variation of the TCAF fit parameters (such as two types accretion rates, $\dot{{{m}_{d}}}$ and $\dot{{{m}_{h}}}$; shock parameters, X_s and R; and derived physical parameters, such as the ARR, shock temperature T_shk, shock height h_shk, and ratio between h_shk to X_s), the accretion flow dynamics, and geometry variation during the outburst phase become very evident. In Table A1, all these fitted/derived parameters are written in a tabular form with estimated errors.

Figures 1–3 show the variation of X-ray intensities, QPO frequencies along with TCAF and combined DBB, PL model fitted and derived (from TCAF) parameters. In Figure 1(a), variation of the background-subtracted RXTE PCA count rate in the $2-25$ keV ($0-58$ channels) energy band with day (MJD) is shown. In Figure 1(c), variation of the TCAF fitted total accretion rates (combined Keplerian disk and sub-Keplerian halo rates) in the $2.5-25$ keV energy band are shown. For comparison, combined DBB and PL model fitted total flux variation with day (MJD) is shown in Figure 1(b). We observe that the variation of the TCAF fitted total flow rate (Figure 1(c)) is different from the flux variations in Figures 1(a)–(b), especially in the early and late stages. In Figure 1 d, the variation of ARR (defined to be the ratio of the sub-Keplerian halo rate $\dot{{{m}_{h}}}$ and the Keplerian disk rate $\dot{{{m}_{d}}}$) is plotted. Observed QPO frequencies (of only dominating primary QPOs) are shown in Figure 1(e). During the entire phase of the current outburst, only three spectral classes, such as hard (HS), hard-intermediate (HIMS), and soft-intermediate (SIMS) are observed. Strangely, the soft state (SS) is not prominent and possibly missing. The sequence is found to be HIMS (rising) $\to$ SIMS $\to$ HIMS (declining) $\to$ HS. We believe that the absence of the HS in the rising phase is due to observational constraints. The detailed behavior of these spectral states and other reports in the literature on them are discussed in the next section.

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In Figure 2, the variations of the TCAF fitted and derived shock parameters, together with combined DBB and PL model fitted results, are shown. In Figures 2(a)–(b), the variations of DBB temperature (T_in in keV) and PL photon index (Γ) with day (MJD) are shown. In Figures 2(c)–(d), the TCAF fitted shock location (X_s in r_g) and compression ratio (R) are plotted with day. In Figures 2(e)–(f), the variations of shock height (h_shk in r_g) and temperature (T_shk in ${{10}^{10}}\;{\rm K}$, which is the initial temperature of CT95 iteration process), derived from X_s and R and using Equations (4) and (5), respectively, of DMC15, are shown. In Figure 2(g), the ratios between shock height and location are plotted. In Figures 3(a)–(b), the variations of DBB flux from DBB and PL model fits and Keplerian disk rate from TCAF fits with day (MJD) are compared. Similarly, in Figures 3(c)–(d), variations of PL flux and sub-Keplerian halo rate from these respective models are compared. Clearly there are "some" similarities in each pair of compared quantities, but not totally, since the PL flux is a function of disk rate as well. In Figures 4(a)–(c), the TCAF fitted 2.5–25 keV background-subtracted PCA spectra of three different spectral states (selected from the approximate middle of each state to gain a better understanding, marked as a, b, and c in column 1 of Table A1) along with residual ${{\chi }^{2}}$ are shown. In Figure 4(d), we show unabsorbed theoretical spectra in the 0.001–3950 keV energy range, which are used to fit observed spectra presented in Figures 4(a)–(c).

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3.2. Evolution of Spectral and Temporal Properties During the Outburst

We study the evolution of spectral properties of Galactic transient BH candidate MAXI J1659-152 during its first (2010) X-ray outburst using the current version v0.1 of the two-component advective flow (TCAF) solution based model after its inclusion as a local additive table model in HEASARC's spectral analysis software package XSPEC (DCM14). This has been done with a model fits file using $\sim 4\times {{10}^{5}}$ theoretical spectra that are generated by varying five model input parameters (two types of accretion, i.e., Keplerian disk $\dot{{{m}_{d}}}$ and sub-Keplerian halo $\dot{{{m}_{h}}}$ rates; two types of shock parameters: location X_s and compression ratio R; and the mass of the BH M_BH) to the modified CT95 code (see DMC15 for details). We re-fitted all these spectra of MAXI J1659-152 with combined DBB and PL model components to get a rough estimate of the variations of the thermal (DBB) and non-thermal (PL) fluxes during the outburst and to compare these with our TCAF fitted results (see Figures 1–3). In Table A1, detailed results of our spectral fit with observed QPO frequencies are presented.

The entire period of the 2010 outburst of MAXI J1659-152 appears to have three spectral classes: hard, hard-intermediate, and soft-intermediate. It did not reach the SS. When we study variations of TCAF parameters in these states, we find that there is a pattern in how the rates, ARR, QPO frequency, etc., behave. These behaviors are similar to what were reported in other sources (see MDC14, DMC15). Specifically, we see a local maximum of the ARR during the transition between hard-intermediate and hard states in all these sources. Clearly, more objects need to be fitted before any firm conclusion can be drawn.

It is interesting that unlike other sources (MDC14, DMC15), this object exhibited no SSs during this outburst according to our model. Only for two days, MJD = 55481.71 and MJD = 55485.16, the fluxes are higher (Table A1), but observation of LFQPOs and the presence of a dip on MJD = 55483.92 in between suggests that the state is not soft, but soft-intermediate. van der Horst et al. (2013), using a disk irradiation model called DISKIR (with a number of free parameters significantly higher than TCAF with irradiation from CENBOL on the Keplerian disk), suggests that the object might have gone to a SS. However, the photon index (see Figure 5 of van der Horst et al. 2013) of those specific days showed significant error bars, and thus it is uncertain if SSs were reached. It is also possible that the inclination angle might also have played a role in hardening the spectra (as discussed in another source by Motta et al. 2010 and by explicit Monte Carlo simulation by Ghosh et al. 2011).

Although low-frequency ($\sim 0.01-30$ Hz) QPOs were observed almost three decades ago, there is a debate on the origin of this temporal behavior in the Fourier-transformed power-density spectrum of the X-ray intensity variation. According to the shock oscillation model (SOM) of Chakrabarti and his collaborators in the mid-1990 s, it can occur when the Compton cooling timescale roughly agrees with the infall timescale (Molteni et al. 1996) or due to the non-satisfaction of Rankine–Hugoniot conditions to form a stable shock (Ryu et al. 1997). Recent numerical simulations of Garain et al. (2014) also demonstrated this in the presence of Comptonization. According to SOM, the QPO frequency is inversely proportional to the infall time (t_infall) in the post-shock region. It also has been observed that these QPO frequencies show monotonically increasing (during the rising phase of the outburst) or decreasing (during the declining phase of the outburst) nature in hard and hard-intermediate spectral states. This evolution of the QPO frequencies can be well fitted with the POS model, which is nothing but the time-varying form of the SOM. Movement of the shock inward could be due to rapid cooling and the consequent collapse of the CENBOL (in the rising phase) and outward due to the lack of cooling in the declining phase (Mondal et al. 2015).

In soft-intermediate spectral states, sporadic QPOs are observed, which may be due to the appearance or disappearance of the oscillating component, namely, CENBOL by intrusion of strong toroidal magnetic fields. Strong sporadic jets are also seen in these states (e.g., Nandi et al. 2001; Radhika & Nandi 2014). Our current TCAF model takes care of the combined effects of CENBOL and the outflow. Separation of the effects of CENBOL and jets is possible from more detailed modeling of timing properties and will be incorporated in a later version of TCAF.

Recently, it has been shown (DMC15, MDC14) using examples of the 2010–2011 outburst of Galactic BHC GX 339-4 and the 2010 outburst of Galactic BHC H 1743-322 how spectral state transitions may be triggered when the relative ratio of the accretion rates, namely, ARR, vary in specific ways. The nature of variation of QPOs (when observed), shock locations, strengths, etc., are also very specific. Exactly the same types of variation of the fitted parameters are also seen for the current source MAXI J1659-152. From the observed variation of Keplerian rates in these objects, we believe that an outburst is triggered due to a sudden rise in viscosity and is turned off due to the reduction in viscosity (CT95; Ebisawa et al. 1996; Chakrabarti et al. 2009). It is possible that this object belongs to a category, with short orbital periods, where the accretion disk around the BH is mostly dominated by the wind accretion compared to disk accretion. The Keplerian disk is always immersed inside a strong sub-Keplerian halo. Therefore, the SS may be difficult to achieve. In this sense, this outburst may be treated as a "failed" outburst. In the future, we will make a detailed spectral and temporal study of other such objects (e.g., XTE J1118+480 of orbital period ∼4.1 hr, González-Hernádez et al. 2013; Swift J1753.5-0127 of orbital period ∼3.2 hr, Zurita et al. 2007) during their X-ray outbursts to check if flow dynamics of these sources also follow a similar trend. Prediction of the QPO frequency from the TCAF solution fitted shock parameters (X_s and R; DCM14) and a comparative study with the POS model solution will be published elsewhere.

A.A.M. acknowledges the support of a DST sponsored Fast-track Young Scientist project fellowship and a MoES sponsored Junior Research Fellowship. S.M. acknowledges the support of a CSIR-NET scholarship. D.D. acknowledges support from project funds of DST sponsored Fast-track Young Scientist and ISRO sponsored RESPOND.

In Table A1, 2.5–25 keV RXTE PCA spectral fitted and derived parameters for 30 observations with two different sets of models: (1) combined disk blackbody (DBB) and power-law (PL), (2) TCAF (v0.1), are mentioned. In Col. 1: Observation IDs, Col. 2: average Modified Julian Day of the observations, Col. 3: DBB model fitted disk temperature (T_in in keV), Col. 4: PL model fitted Photon Index (Γ), Col. 5: DBB model flux in spectral fitted energy range of 2.5–25 keV, Col. 6: PL model flux in the same energy range, Col. 7: combined DBB and PL model fitted values of ${{\chi }^{2}}$ and degrees of freedom (DOF) are mentioned. In Col. 8: TCAF model fitted Keplerian disk rate ($\dot{{{m}_{d}}}$ in Eddington rate $\dot{{{m}_{{\rm Edd}}}}$), Col. 9: TCAF model fitted sub-Keplerian halo rate ($\dot{{{m}_{d}}}$ in $\dot{{{m}_{{\rm Edd}}}}$), Col. 10: accretion rate ratio (ARR) i.e., ratio between halo to disk rates, Col. 11: TCAF model fitted location of the shock (X_s in Schwarzschild radius r_g), Col. 12: TCAF model fitted compression ratio R (ratio between post to pre-shock densities), Col. 13: height of the shock at X_s (in r_g), Col. 14: temperature of the pre-Compton cooled shock at X_s (in 10¹⁰ K), Col. 16: TCAF model fitted values of ${{\chi }^{2}}$ and DOF are mentioned. In Col. 15, we mention frequencies of dominating QPOs (in Hz), observed in the Fourier-transformed power-density spectra of 0.01 sec binned light curves.

Table A1.  The 2.5–25 keV Combined DBB-PL and TCAF Model Fitted Parameters with QPOs

Obs. Id	MJD	Tin	Γ	DBBf d	${\rm PL}f$ d	${{\chi }^{2}}/{\rm DOF}$	$\dot{{{m}_{d}}}$	$\dot{{{m}_{h}}}$	ARR	Xs	R	hshk	Tshk	QPOe	${{\chi }^{2}}/{\rm DOF}$
		(keV)					(${{\dot{M}}_{{\rm Edd}}}$)	(${{\dot{M}}_{{\rm Edd}}}$)		(rg)		(rg)	(${{10}^{10}}\;{\rm K}$)	(Hz)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
X-02-00	55467.19	${{0.184}^{0.014}}$	${{2.008}^{0.009}}$	${{0.041}^{0.075}}$	${{6.265}^{0.005}}$	68.1/46	${{0.197}^{0.022}}$	${{0.642}^{0.030}}$	${{3.259}^{0.513}}$	${{354.4}^{20.4}}$	${{1.214}^{0.017}}$	${{174.4}^{12.5}}$	${{0.222}^{0.010}}$	${{1.607}^{0.009}}$	47.6/35
X-02-01	55468.09	${{0.249}^{0.025}}$	${{2.109}^{0.009}}$	${{0.105}^{0.040}}$	${{6.302}^{0.014}}$	64.3/46	${{0.223}^{0.012}}$	${{0.484}^{0.017}}$	${{2.170}^{0.190}}$	${{258.4}^{12.0}}$	${{1.159}^{0.015}}$	${{114.8}^{6.83}}$	${{0.249}^{0.009}}$	${{2.278}^{0.016}}$	68.4/45
X-02-02	55469.09	${{0.603}^{0.059}}$	${{2.176}^{0.016}}$	${{0.299}^{0.067}}$	${{6.364}^{0.088}}$	41.8/50	${{0.614}^{0.018}}$	${{0.362}^{0.014}}$	${{0.590}^{0.040}}$	${{207.5}^{10.8}}$	${{1.051}^{0.016}}$	${{57.55}^{3.86}}$	${{0.121}^{0.005}}$	${{2.723}^{0.015}}$	57.6/45
X-03-00	55470.26	${{0.504}^{0.080}}$	${{2.198}^{0.011}}$	${{0.312}^{0.025}}$	${{6.406}^{0.013}}$	47.9/50	${{0.850}^{0.055}}$	${{0.242}^{0.036}}$	${{0.285}^{0.061}}$	${{65.20}^{3.29}}$	${{1.085}^{0.017}}$	${{22.62}^{1.49}}$	${{0.609}^{0.025}}$	${{2.749}^{0.014}}$	69.9/45
Y-03-00	55471.51	${{0.622}^{0.046}}$	${{2.199}^{0.016}}$	${{0.367}^{0.039}}$	${{5.782}^{0.192}}$	52.1/50	${{1.091}^{0.032}}$	${{0.188}^{0.032}}$	${{0.172}^{0.034}}$	${{53.46}^{2.89}}$	${{1.071}^{0.011}}$	${{17.17}^{1.11}}$	${{0.639}^{0.024}}$	${{3.028}^{0.019}}$	51.5/45
Y-05-00	55472.07	${{0.632}^{0.041}}$	${{2.226}^{0.029}}$	${{0.500}^{0.038}}$	${{5.682}^{0.019}}$	43.4/50	${{1.321}^{0.015}}$	${{0.175}^{0.022}}$	${{0.132}^{0.018}}$	${{46.60}^{2.71}}$	${{1.063}^{0.013}}$	${{14.21}^{1.00}}$	${{0.662}^{0.027}}$	${{3.329}^{0.023}}$	38.3/45
Y-09-00	55473.47	${{0.763}^{0.028}}$	${{2.306}^{0.019}}$	${{1.091}^{0.040}}$	${{6.021}^{0.058}}$	38.9/50	${{1.238}^{0.018}}$	${{0.241}^{0.017}}$	${{0.195}^{0.017}}$	${{41.17}^{1.79}}$	${{1.057}^{0.011}}$	${{12.01}^{0.65}}$	${{0.688}^{0.022}}$	${{4.709}^{0.024}}$	42.1/45
Y-13-00	55475.43	${{0.835}^{0.023}}$	${{2.343}^{0.024}}$	${{1.430}^{0.053}}$	${{5.519}^{0.044}}$	39.1/50	${{1.278}^{0.035}}$	${{0.291}^{0.016}}$	${{0.228}^{0.019}}$	${{53.73}^{1.85}}$	${{1.051}^{0.011}}$	${{14.91}^{0.67}}$	${{0.474}^{0.013}}$	${{6.108}^{0.050}}$	54.8/45
Y-17-00	55476.67	${{0.878}^{0.021}}$	${{2.368}^{0.028}}$	${{1.768}^{0.045}}$	${{6.020}^{0.029}}$	46.7/50	${{1.296}^{0.019}}$	${{0.346}^{0.019}}$	${{0.267}^{0.018}}$	${{44.53}^{1.16}}$	${{1.052}^{0.011}}$	${{12.46}^{0.46}}$	${{0.584}^{0.014}}$	${{6.981}^{0.087}}$	49.5/45
Y-19-00	55477.72	${{0.881}^{0.022}}$	${{2.365}^{0.030}}$	${{1.903}^{0.120}}$	${{6.128}^{0.028}}$	31.6/50	${{1.328}^{0.025}}$	${{0.364}^{0.030}}$	${{0.274}^{0.028}}$	${{43.73}^{1.83}}$	${{1.051}^{0.012}}$	${{12.13}^{0.65}}$	${{0.585}^{0.019}}$	⋯	45.6/45
Y-23-00	55479.68	${{0.783}^{0.027}}$	${{2.252}^{0.029}}$	${{0.956}^{0.053}}$	${{4.756}^{0.064}}$	40.3/50	${{1.258}^{0.021}}$	${{0.249}^{0.014}}$	${{0.198}^{0.015}}$	${{48.07}^{1.01}}$	${{1.054}^{0.013}}$	${{13.68}^{0.45}}$	${{0.559}^{0.013}}$	${{5.312}^{0.055}}$	45.5/45
Y-27-00	55481.71	${{0.945}^{0.011}}$	${{2.326}^{0.017}}$	${{2.362}^{0.041}}$	${{5.418}^{0.075}}$	42.5/50	${{1.563}^{0.057}}$	${{0.378}^{0.012}}$	${{0.242}^{0.017}}$	${{39.79}^{1.70}}$	${{1.052}^{0.011}}$	${{11.14}^{0.59}}$	${{0.656}^{0.021}}$	${{3.876}^{0.041}}$	81.7/45
Y-30-00	55483.92	${{0.827}^{0.029}}$	${{2.264}^{0.020}}$	${{1.018}^{0.025}}$	${{4.053}^{0.016}}$	45.8/50	${{1.274}^{0.055}}$	${{0.214}^{0.012}}$	${{0.168}^{0.016}}$	${{59.80}^{1.38}}$	${{1.052}^{0.015}}$	${{16.74}^{0.62}}$	${{0.432}^{0.011}}$	${{5.999}^{0.037}}$	52.4/44
Z-02-00	55485.16	${{0.921}^{0.011}}$	${{2.295}^{0.018}}$	${{2.072}^{0.027}}$	${{4.586}^{0.011}}$	44.7/50	${{1.573}^{0.040}}$	${{0.285}^{0.019}}$	${{0.181}^{0.016}}$	${{39.87}^{1.42}}$	${{1.053}^{0.011}}$	${{11.53}^{0.52}}$	${{0.666}^{0.019}}$	${{3.512}^{0.102}}$	73.5/45
Z-03-00	55486.80	${{0.815}^{0.015}}$	${{2.299}^{0.030}}$	${{1.972}^{0.025}}$	${{2.078}^{0.042}}$	44.9/50	${{1.446}^{0.018}}$	${{0.226}^{0.012}}$	${{0.156}^{0.010}}$	${{64.60}^{2.64}}$	${{1.050}^{0.011}}$	${{17.76}^{0.91}}$	${{0.386}^{0.012}}$	⋯	70.1/45
Z-06-01	55489.74	${{0.864}^{0.018}}$	${{2.339}^{0.025}}$	${{1.605}^{0.064}}$	${{3.179}^{0.026}}$	50.9/50	${{1.306}^{0.018}}$	${{0.185}^{0.012}}$	${{0.142}^{0.011}}$	${{50.23}^{2.44}}$	${{1.051}^{0.011}}$	${{13.93}^{0.82}}$	${{0.508}^{0.018}}$	⋯	58.3/45
Z-07-00	55490.72	${{0.869}^{0.019}}$	${{2.259}^{0.024}}$	${{1.481}^{0.055}}$	${{3.513}^{0.020}}$	46.1/50	${{1.312}^{0.016}}$	${{0.211}^{0.011}}$	${{0.161}^{0.010}}$	${{51.64}^{2.41}}$	${{1.052}^{0.011}}$	${{14.45}^{0.83}}$	${{0.502}^{0.017}}$	${{3.283}^{0.030}}$	45.9/45
aZ-09-00	55491.82	${{0.826}^{0.017}}$	${{2.256}^{0.025}}$	${{1.399}^{0.043}}$	${{3.048}^{0.042}}$	44.7/50	${{1.291}^{0.022}}$	${{0.165}^{0.012}}$	${{0.128}^{0.011}}$	${{59.58}^{4.82}}$	${{1.051}^{0.012}}$	${{16.53}^{1.53}}$	${{0.427}^{0.022}}$	⋯	60.9/45
Z-10-00	55493.25	${{0.851}^{0.027}}$	${{2.244}^{0.037}}$	${{1.181}^{0.048}}$	${{3.235}^{0.020}}$	64.6/50	${{1.251}^{0.070}}$	${{0.177}^{0.012}}$	${{0.141}^{0.017}}$	${{53.94}^{2.94}}$	${{1.052}^{0.013}}$	${{15.09}^{1.01}}$	${{0.480}^{0.019}}$	⋯	82.7/45
Z-11-00	55494.23	${{0.797}^{0.027}}$	${{2.333}^{0.044}}$	${{1.235}^{0.081}}$	${{2.669}^{0.017}}$	54.3/50	${{1.308}^{0.021}}$	${{0.160}^{0.013}}$	${{0.122}^{0.012}}$	${{48.60}^{2.02}}$	${{1.052}^{0.011}}$	${{13.60}^{0.71}}$	${{0.534}^{0.017}}$	⋯	46.4/45
Z-13-00	55496.53	${{0.758}^{0.015}}$	${{2.212}^{0.038}}$	${{1.049}^{0.019}}$	${{1.602}^{0.046}}$	45.0/50	${{1.251}^{0.018}}$	${{0.145}^{0.014}}$	${{0.116}^{0.013}}$	${{58.24}^{4.47}}$	${{1.051}^{0.011}}$	${{16.16}^{1.41}}$	${{0.437}^{0.021}}$	⋯	67.1/45
Z-15-00	55498.49	${{0.731}^{0.018}}$	${{2.283}^{0.048}}$	${{1.014}^{0.017}}$	${{1.385}^{0.025}}$	51.5/50	${{1.301}^{0.035}}$	${{0.145}^{0.012}}$	${{0.111}^{0.012}}$	${{53.33}^{3.57}}$	${{1.051}^{0.012}}$	${{14.79}^{1.16}}$	${{0.478}^{0.021}}$	⋯	60.7/45
Z-16-00	55500.31	${{0.719}^{0.023}}$	${{2.307}^{0.041}}$	${{0.725}^{0.056}}$	${{1.564}^{0.014}}$	58.3/50	${{1.321}^{0.025}}$	${{0.155}^{0.017}}$	${{0.117}^{0.015}}$	${{52.80}^{1.74}}$	${{1.051}^{0.012}}$	${{14.65}^{0.65}}$	${{0.483}^{0.013}}$	⋯	57.8/45
Z-16-01	55501.23	${{0.725}^{0.041}}$	${{2.167}^{0.033}}$	${{0.444}^{0.023}}$	${{1.842}^{0.107}}$	52.1/50	${{1.310}^{0.015}}$	${{0.208}^{0.012}}$	${{0.159}^{0.011}}$	${{57.07}^{3.18}}$	${{1.052}^{0.011}}$	${{15.97}^{1.06}}$	${{0.454}^{0.017}}$	${{5.951}^{0.091}}$	41.2/45
bZ-17-00	55502.02	${{0.713}^{0.057}}$	${{2.090}^{0.030}}$	${{0.256}^{0.011}}$	${{1.909}^{0.008}}$	42.5/50	${{1.294}^{0.014}}$	${{0.307}^{0.017}}$	${{0.237}^{0.015}}$	${{61.79}^{3.93}}$	${{1.053}^{0.014}}$	${{17.44}^{1.34}}$	${{0.426}^{0.019}}$	${{4.779}^{0.070}}$	34.7/45
Z-17-01	55503.06	${{0.590}^{0.065}}$	${{1.992}^{0.023}}$	${{0.152}^{0.013}}$	${{1.806}^{0.033}}$	41.4/50	${{1.269}^{0.022}}$	${{0.346}^{0.013}}$	${{0.273}^{0.015}}$	${{63.00}^{5.39}}$	${{1.056}^{0.018}}$	${{18.23}^{1.87}}$	${{0.438}^{0.026}}$	${{3.371}^{0.056}}$	34.3/45
Z-18-00	55504.06	${{0.600}^{0.168}}$	${{1.895}^{0.042}}$	${{0.073}^{0.016}}$	${{1.695}^{0.031}}$	49.6/50	${{1.068}^{0.098}}$	${{0.349}^{0.015}}$	${{0.327}^{0.044}}$	${{102.8}^{12.2}}$	${{1.086}^{0.010}}$	${{35.83}^{4.58}}$	${{0.388}^{0.027}}$	${{2.563}^{0.060}}$	53.6/45
Z-19-00	55505.03	${{0.958}^{0.137}}$	${{1.786}^{0.032}}$	${{0.081}^{0.008}}$	${{1.583}^{0.023}}$	46.5/50	${{1.016}^{0.086}}$	${{0.302}^{0.012}}$	${{0.297}^{0.037}}$	${{179.1}^{17.1}}$	${{1.095}^{0.016}}$	${{65.08}^{7.17}}$	${{0.241}^{0.015}}$	${{2.154}^{0.034}}$	52.8/45
cZ-20-00	55506.20	${{0.962}^{0.146}}$	${{1.724}^{0.044}}$	${{0.107}^{0.011}}$	${{1.456}^{0.018}}$	46.5/50	${{0.948}^{0.068}}$	${{0.272}^{0.021}}$	${{0.287}^{0.042}}$	${{310.0}^{23.2}}$	${{1.104}^{0.023}}$	${{116.9}^{11.2}}$	${{0.149}^{0.009}}$	${{2.028}^{0.033}}$	65.4/45
Z-21-00	55508.09	${{0.692}^{0.126}}$	${{1.755}^{0.036}}$	${{0.031}^{0.009}}$	${{1.381}^{0.011}}$	43.8/50	${{0.939}^{0.027}}$	${{0.261}^{0.025}}$	${{0.278}^{0.035}}$	${{416.2}^{29.7}}$	${{1.131}^{0.028}}$	${{171.9}^{16.5}}$	${{0.134}^{0.008}}$	${{1.638}^{0.056}}$	60.4/45

Notes. Here, X = 95358–01, Y = 95108–01, and Z = 95118–01 mean the initial part of the observation IDs, and (a–c) mark the TCAF model fitted results for three different states, presented in Figure 4. Intermediate void space mark state transitions from HIMS $\to$ SIMS, SIMS $\to$ HIMS, and HIMS $\to$ HS, respectively.

T_in, and Γ values indicate combined DBB and PL model fitted multi-color disk blackbody temperatures in keV and power-law photon indices, respectively.

Average values of 90% confidence ± error values obtained usingthe "err" task in XSPEC are mentioned as a superscript of the spectral fitted/derived parameters.

^dDBBf, PLf represent combined DBB and PL model fitted 2.5–25 keV fluxes for DBB and PL model components, respectively, in units of ${{10}^{-9}}\;{\rm ergs}\;{\rm c}{{{\rm m}}^{-2}}{{{\rm s}}^{-1}}$. $\dot{{{m}_{h}}}$, and $\dot{{{m}_{d}}}$ represent TCAF fitted sub-Keplerian (halo) and Keplerian (disk) rates in the Eddington rate, respectively. X_s (in Schwarzchild radius r_g) and R are the model fitted shock location and compression ratio values, respectively. h_shk (in r_g) and T_shk (in ${{10}^{10}}\;{\rm K}$) are values of shock height and temperature (of the pre-Compton cooled) at X−s derived from Equations (4) and (5) of DMC15, respectively. ^eHere, frequencies of the principal QPO in Hz are presented. DOF means degrees of freedom of the model fit.

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