Accretion Flow Evolution of a New Black Hole Candidate MAXI J1348–630 during the 2019 Outburst

Black hole X-ray binaries (BHXRBs) consist of a black hole (BH) and a companion main-sequence star. Transient BHXRBs spend most of the time in the quiescent state. They occasionally go into outbursts, which often last from weeks to months. During an outburst, the X-ray intensity of the source could rise by several orders of magnitude in comparison to that in the quiescence phase. In a BHXRB, matter from the companion star is accreted onto the central BH and forms an accretion disk. In the accretion process, the gravitational potential energy of the accreted matter is converted to heat that is radiated in the entire electromagnetic wave bands, e.g., from radio to γ-ray range. An outbursting BHXRB shows rapid changes in both spectral and temporal properties. The hardness–intensity diagram (Belloni et al. 2005) or accretion rate–intensity diagram (Jana et al. 2016) shows the correlation between spectral and temporal parameters in different spectral states. In general, a BHXRB exhibits four different spectral states, namely, hard state (HS), hard-intermediate state (HIMS), soft-intermediate state (SIMS), and soft state (SS). When a BHXRB evolves through these states in the sequence HS → HIMS → SIMS → SS → SIMS → HIMS → HS, it produces a so-called hysteresis loop (for more details, see Remillard & McClintock 2006; Debnath et al. 2013, and references therein). The BHXRBs also exhibit quasi-periodic oscillations (QPOs) in some spectral states (see Remillard & McClintock 2006, for a review). Unlike the high-frequency QPOs (HFQPOs; QPO frequency ≥40 Hz), which are rare, low-frequency QPOs (LFQPOs) are common in BHXRBs and are classified into three types—A, B, and C (Casella et al. 2005), depending on their nature (Q-value, rms amplitude, noise, etc.). Different spectral and temporal properties characterize each spectral state. In the HS and HIMS, the hard X-ray flux dominates with evolving Type C QPOs. In the SIMS and SS, the soft X-ray flux dominates over the hard X-ray flux. Type A or Type B QPOs may be observed sporadically in the SIMS. QPOs are not seen in the SS.

In general, an X-ray spectrum of BHXRBs consists of two components: a soft multicolor disk blackbody (diskbb) and a hard power-law component. The multicolor blackbody component originates from a standard thin disk (Novikov & Thorne 1973; Shakura & Sunyaev 1973), while the power law originates from a hot Compton cloud consisting of hot electrons (Sunyaev & Titarchuk 1980, 1985). There exist various models in the literature to explain the nature of the Compton cloud, e.g., magnetic corona (Galeev et al. 1979), evaporated disk (Esin et al. 1997), disk-corona model (Zdziarski et al. 1993), two-component advective flow (TCAF) solution (Chakrabarti & Titarchuk 1995, hereafter CT95; Chakrabarti 1997), etc. Except for TCAF, which is based on viscous and radiative transonic flow solutions, other models are phenomenological.

In TCAF, the accretion disk has two components: an optically thick, geometrically thin high viscous Keplerian flow on the equatorial plane submerged inside an optically thin, low viscous sub-Keplerian flow (for a review on TCAF, see Chakrabarti 2016). The sub-Keplerian flow moves faster and temporarily slows down at the centrifugal barrier and forms an axisymmetric shock (Chakrabarti 1990) when the inflowing matter piles up at the barrier. The post-shock region being hot and puffed up acts as the Compton cloud and is known as the CENtrifugal pressure supported BOundary Layer (CENBOL). The soft photons that originate from the Keplerian disk contribute to the multicolor blackbody spectrum. A fraction of these photons are intercepted by the CENBOL and undergo inverse-Compton scattering with the hot electrons of the CENBOL and become hard photons. These hard photons produce the hard power-law tail observed in the spectra. Physical oscillation of the CENBOL causes the fraction of intercepted photons to oscillate, resulting in LFQPOs often observed in the power density spectra (PDS). CENBOL oscillation is triggered when the compressional heating timescale of the flow roughly matches the radiative cooling timescale and a resonance condition is satisfied (Molteni et al. 1996). It may also be triggered if Rankine–Hugoniot conditions are not satisfied in a time-dependent transonic flow even though there are two physical sonic points (Ryu et al. 1997). A bipolar jet is launched from the hot CENBOL region in the harder states (Chakrabarti 1999). The jet is absent when the CENBOL itself is collapsed in the softer states.

In general, an outburst is believed to be triggered by the sudden rise of viscosity at the outer edge of the disk (Ebisawa et al. 1996). When an outburst starts, the sub-Keplerian flow rushes toward the BH and forms an axisymmetric shock at the centrifugal boundary. A strong shock is formed with a large and hot CENBOL. In the initial phase, the Keplerian disk accretion rate is low (as it moves in a viscous timescale), and therefore it cannot cool the CENBOL efficiently, and HS is observed. In this state, the accretion rate ratio (ARR) is found to decrease with the progress of the outburst as we see a monotonic rise in the disk accretion rate. The shock becomes weak as it moves toward the BH. A strong, compact jet could be observed in this state of the outburst. The HS is associated with the evolving Type C QPOs. The QPO frequency monotonically increases with the progress of the outburst as the shock location decreases. This is because the QPO frequency (ν) varies with the shock location as $\nu \sim {X}_{s}^{-3/2}$ (Chakrabarti & Manickam 2000; Chakrabarti et al. 2008). QPOs exist as long as the resonance condition due to rough agreement between the heating and cooling of the CENBOL is satisfied.

As the outburst progresses, the source enters into the HIMS. In this state, the Keplerian disk accretion rate becomes comparable with the sub-Keplerian halo accretion rate. As a result, ARR further decreases. The shock continues to move inward. Evolving Type C QPO is observed in this state as well. With the further rise in the Keplerian disk accretion rate, the BH exhibits SIMS. Here, the disk accretion rate is comparatively higher than the sub-Keplerian halo accretion rate. A discrete ejection or blobby jet could be observed in this state. Sporadic Type B or Type A QPOs could be found in this state. The shock becomes weak and moves inward. With the progress in the outburst, the source enters into the SS. In this state, the Keplerian disk accretion rate efficiently cools down the CENBOL. No QPO is observed in this state. Generally, we do not see any jet in this spectral state.

The source enters the declining phase when the viscosity is turned off or reduced (Ebisawa et al. 1996; Roy & Chakrabarti 2017). As the Keplerian disk is already formed, it is difficult to drain the matter as the viscosity is reduced. Thus, the source remains in the SS and the SIMS in the declining phase for a relatively long time. As the outburst progresses further, the accretion rate decreases and the source goes through the HIMS and the HS before going to the quiescence state. In the declining phase, evolving decreasing QPO frequency is observed in the HIMS and HS. One could also observe outflows in these two harder spectral states.

To fit a spectrum, TCAF uses only four flow parameters, namely, accretion rates of the Keplerian and the sub-Keplerian components, the size of the CENBOL (i.e., the shock location), and density variation inside CENBOL required to obtain the optical depth (obtained from the shock strength). Apart from these, one instrument parameter, namely, the normalization factor (which gives the ratio of emitted to observed photon spectrum), and one system parameter, namely, the mass of the BH, are required. In 2014, the TCAF solution was implemented in XSPEC (Arnaud 1996) as a local additive model to carry out spectral analysis of BHXRBs (Debnath et al. 2014, 2015b for more details). The accretion dynamics of several BH candidates (BHCs) are studied successfully with this model (Mondal et al. 2014, 2016; Debnath et al. 2015a, 2017, 2020; Molla et al. 2017; Chatterjee et al. 2019, 2020; Shang et al. 2019; Jana et al. 2020b). In each case, we have obtained the evolution of the actual physical parameters of the flow and the mass of the BH very successfully. This motivated us to study the properties of the newly discovered BHC MAXI J1348–630 during the 2019 outburst with the TCAF model.

MAXI J1348–630 is a Galactic BHXRB that was discovered very recently on 2019 January 26 by MAXI/GSC (Yatabe et al. 2019) at R.A. = 13^h48'12'', decl. = −63°4'4''. Later, the Swift/XRT localized the position of the source at R.A. = 13^h48'1273, decl. = −63°16'268 (Kennea et al. 2019). The source was also observed by the International Gamma-Ray Astrophysics Laboratory, NICER, and HXMT (Chen et al. 2019; Lepingwell et al. 2019; Sanna et al. 2019). Optical (Denisenko et al. 2019; Russell et al. 2019a) and radio (Russell et al. 2019b) observations of the source were also carried out during the outburst. The outburst lasted for about 4 months. MAXI J1348–630 was observed to rebrighten a few times after this main outburst (Negoro et al. 2019). Observation of the QPO on 2019 January 30 was reported with the Swift/XRT and HXMT (Chen et al. 2019; Jana et al. 2019). A preliminary data analysis with the TCAF model leads us to estimate the mass of the BH to be in the range of 8.5–11 M_⊙ (Jana et al. 2019). However, Tominaga et al. (2020) estimated the mass of the BH as 16 M_⊙ from the spectral analysis with the MAXI data. They have also estimated the distance of the source as 4–8 kpc.

In this paper, we study the accretion flow dynamics of MAXI J1348–630 with the TCAF model. The paper is organized in the following way. In Section 2, we discuss observation and data analysis. The results obtained from this work are presented in Section 3. In Section 4, we present a discussion and concluding remarks.

We studied the newly discovered MAXI J1348–630 during its 2019 outburst using Swift and MAXI data in the 1–150 keV energy range. In our analysis, we used a total of 27 observations of the source with the Swift/XRT (1–10 keV range), Swift/BAT (15–150 keV range), and MAXI/GSC (7–20 keV range) between 2019 January 26 and May 15. Among 27 observations, there were 4 epochs of observations during which all three instruments, 11 epochs of observations during which Swift/XRT and MAXI/GSC, and 1 epoch of observation during which Swift/XRT and Swift/BAT were used simultaneously. There were 1 and 10 epochs of observations during which only Swift/BAT and Swift/XRT were used, respectively. The details of the log of observations of the source used in the present work are given in Table 1.

Table 1.  TCAF Model Fitted Results

ObsID	UT Date	Day	XRT expa	+BAT expa	NH b	$\dot{{m}_{d}}$ c	$\dot{{m}_{h}}$ c	ARR	XSd	R	N	LEe	LWe	LN	${\chi }^{2}/\mathrm{dof}$
	(mm-dd)	(MJD)	(s)	(s)	(1022 cm−2)	(${\dot{M}}_{\mathrm{Edd}}$)	(${\dot{M}}_{\mathrm{Edd}}$)		(rs)			(keV)	(keV)	(photons cm−2 s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
00885807000	Jan 26	58,509.45	1223f	3794	${1.09}_{-0.17}^{+0.14}$	${0.36}_{-0.02}^{+0.02}$	${0.41}_{-0.02}^{+0.03}$	1.15 ±0.12	${274}_{-3}^{+7}$	${3.07}_{-0.13}^{+0.12}$	${268}_{-25}^{+23}$	⋯	⋯	⋯	312/287
00885845000	Jan 26	58,509.51	⋯	2945	${0.88}_{-0.22}^{+0.31}$	${0.45}_{-0.03}^{+0.01}$	${0.52}_{-0.02}^{+0.02}$	${1.17}^{\pm 0.08}$	${245}_{-9}^{+5}$	${2.46}_{-0.12}^{+0.11}$	${401}_{-23}^{+28}$	⋯	⋯	⋯	57 /51
00885960000	Jan 27	58,510.05	1455f	4907	${0.66}_{-0.9}^{+0.11}$	${0.54}_{-0.05}^{+0.04}$	${0.55}_{-0.01}^{+0.03}$	1.02 ±0.12	${225}_{-8}^{+4}$	${1.82}_{-0.10}^{+0.14}$	${295}_{-22}^{+15}$	⋯	⋯	⋯	314/265
00886266000	Jan 28	58,511.58	1838f	3838	${0.63}_{-0.21}^{+0.24}$	${0.55}_{-0.05}^{+0.05}$	${0.56}_{-0.02}^{+0.04}$	1.02 ±0.11	${217}_{-5}^{+5}$	${1.50}_{-0.03}^{+0.04}$	${202}_{-20}^{+22}$	${6.16}_{-0.05}^{+0.14}$	${1.93}_{-0.06}^{+0.05}$	${0.31}_{-0.03}^{+0.04}$	302/262
00886496000	Jan 29	58,512.43	317f	2781	${0.97}_{-0.14}^{+0.13}$	${0.62}_{-0.07}^{+0.05}$	${0.58}_{-0.01}^{+0.03}$	0.96 ±0.13	${209}_{-7}^{+6}$	${1.48}_{-0.16}^{+0.13}$	${341}_{-39}^{+35}$	⋯	⋯	⋯	328/266
00011107001	Jan 30	58,513.11	834f	⋯	${1.05}_{-0.10}^{+0.12}$	${0.66}_{-0.04}^{+0.03}$	${0.59}_{-0.02}^{+0.04}$	0.90 ±0.08	${202}_{-6}^{+5}$	${1.39}_{-0.15}^{+0.10}$	${159}_{-21}^{+15}$	${6.59}_{-0.11}^{+0.13}$	${1.00}_{-0.04}^{+0.08}$	${0.29}_{-0.05}^{+0.04}$	728/583
00088843001	Feb 1	58,515.75	2033f	⋯	${1.16}_{-0.21}^{+0.24}$	${0.71}_{-0.07}^{+0.06}$	${0.59}_{-0.03}^{+0.02}$	0.83±0.09	${191}_{-7}^{+4}$	${1.24}_{-0.04}^{+0.10}$	${870}_{-37}^{+53}$	${6.74}_{-0.10}^{+0.14}$	${1.93}_{-0.07}^{+0.10}$	${0.28}_{-0.04}^{+0.03}$	357/297
00011107002	Feb 3	58,517.67	870f	⋯	${0.58}_{-0.10}^{+0.11}$	${0.76}_{-0.06}^{+0.09}$	${0.62}_{-0.04}^{+0.03}$	${0.82}^{\pm 0.09}$	${172}_{-3}^{+5}$	${1.15}_{-0.05}^{+0.10}$	${288}_{-44}^{+33}$	${6.16}_{-0.07}^{+0.15}$	${1.00}_{-0.09}^{+0.12}$	${0.15}_{-0.02}^{+0.03}$	229/181
00011107004	Feb 7	58,521.07	$1749$ f	⋯	${1.49}_{-0.25}^{+0.22}$	${0.95}_{-0.09}^{+0.08}$	${0.73}_{-0.02}^{+0.04}$	${0.77}^{\pm 0.08}$	${86}_{-2}^{+2}$	${1.10}_{-0.05}^{+0.08}$	${134}_{-25}^{+22}$	${6.90}_{-0.13}^{+0.07}$	${1.00}_{-0.07}^{+0.10}$	${0.10}_{-0.01}^{+0.02}$	142/128
00011107005	Feb 9	58,523.00	$1414$ f	⋯	${1.33}_{-0.18}^{+0.23}$	${1.34}_{-0.08}^{+0.08}$	${0.71}_{-0.03}^{+0.05}$	${0.53}^{\pm 0.05}$	${61}_{-5}^{+3}$	${1.10}_{-0.03}^{+0.07}$	${164}_{-24}^{+16}$	${6.93}_{-0.15}^{+0.10}$	${0.83}_{-0.07}^{+0.07}$	${0.12}_{-0.01}^{+0.02}$	129/130
00011107007	Feb 10	58,524.53	$809$ f	⋯	${1.88}_{-0.47}^{+0.34}$	${1.64}_{-0.09}^{+0.10}$	${0.62}_{-0.03}^{+0.04}$	${0.38}^{\pm 0.04}$	${56}_{-4}^{+2}$	${1.09}_{-0.04}^{+0.07}$	${323}_{-54}^{+40}$	${6.75}_{-0.25}^{+0.22}$	${0.71}_{-0.05}^{+0.03}$	${0.11}_{-0.03}^{+0.01}$	238/209
00011107010	Feb 13	58,527.44	$1465$ f	⋯	${2.43}_{-0.37}^{+0.27}$	${1.55}_{-0.12}^{+0.11}$	${0.50}_{-0.03}^{+0.03}$	${0.32}^{\pm 0.03}$	${66}_{-3}^{+4}$	${1.13}_{-0.34}^{+0.10}$	${55}_{-12}^{+18}$	${6.93}_{-0.19}^{+0.17}$	${0.88}_{-0.09}^{+0.10}$	${0.15}_{-0.03}^{+0.02}$	122/133
00011107011	Feb 16	58,530.29	$1464$ f	⋯	${1.20}_{-0.27}^{+0.23}$	${1.44}_{-0.11}^{+0.08}$	${0.44}_{-0.01}^{+0.04}$	${0.31}^{\pm 0.02}$	${77}_{-3}^{+2}$	${1.19}_{-0.24}^{+0.08}$	${85}_{-11}^{+12}$	${6.67}_{-0.21}^{+0.18}$	${0.64}_{-0.05}^{+0.05}$	${0.19}_{-0.03}^{+0.02}$	141/136
00011107012	Feb 17	58,531.35	$1460$ f	⋯	${0.89}_{-0.17}^{+0.19}$	${1.29}_{-0.11}^{+0.12}$	${0.45}_{-0.04}^{+0.02}$	${0.34}^{\pm 0.04}$	${82}_{-5}^{+4}$	${1.24}_{-0.15}^{+0.09}$	${41}_{-13}^{+15}$	${6.42}_{-0.17}^{+0.13}$	${0.71}_{-0.06}^{+0.05}$	${0.18}_{-0.01}^{+0.02}$	130/136
00011107013	Feb 19	58,533.54	$1024$ f	⋯	${3.24}_{-0.41}^{+0.30}$	${1.13}_{-0.07}^{+0.08}$	${0.47}_{-0.04}^{+0.03}$	${0.41}^{\pm 0.04}$	${91}_{-5}^{+4}$	${1.36}_{-0.13}^{+0.12}$	${59}_{-12}^{+15}$	⋯	⋯	⋯	255/224
00011107014	Feb 21	58,535.80	$1129$ f	⋯	${1.26}_{-0.25}^{+0.21}$	${1.09}_{-0.12}^{+0.10}$	${0.41}_{-0.02}^{+0.02}$	${0.37}^{\pm 0.04}$	${94}_{-3}^{+3}$	${1.41}_{-0.14}^{+0.11}$	${117}_{-11}^{+15}$	⋯	⋯	⋯	269/224
00088843002	Mar 8	58,550.49	2079	⋯	${1.79}_{-0.36}^{+0.39}$	${0.77}_{-0.08}^{+0.07}$	${0.33}_{-0.02}^{+0.03}$	${0.43}^{\pm 0.04}$	${131}_{-4}^{+3}$	${1.35}_{-0.09}^{+0.09}$	${301}_{-50}^{+37}$	⋯	⋯	⋯	271/212
00011107017	Mar 11	58,553.87	955	⋯	${2.77}_{-0.46}^{+0.41}$	${0.64}_{-0.06}^{+0.03}$	${0.32}_{-0.01}^{+0.02}$	${0.50}^{\pm 0.06}$	${137}_{-6}^{+2}$	${1.44}_{-0.10}^{+0.09}$	${476}_{-43}^{+40}$	⋯	⋯	⋯	252/218
00011107019	Mar 17	58,559.13	1188	⋯	${2.07}_{-0.40}^{+0.32}$	${0.52}_{-0.03}^{+0.03}$	${0.27}_{-0.03}^{+0.02}$	${0.52}^{\pm 0.06}$	${153}_{-6}^{+4}$	${1.53}_{-0.11}^{+0.11}$	${801}_{-58}^{+44}$	⋯	⋯	⋯	961/891
00011107020	Mar 20	58,562.04	1001	⋯	${1.61}_{-0.29}^{+0.22}$	${0.39}_{-0.03}^{+0.04}$	${0.21}_{-0.02}^{+0.02}$	${0.54}^{\pm 0.07}$	${147}_{-4}^{+6}$	${1.47}_{-0.08}^{+0.12}$	${312}_{-27}^{+39}$	${6.06}_{-0.10}^{+0.13}$	${0.49}_{-0.04}^{+0.04}$	${0.08}_{-0.01}^{+0.02}$	1021/880
00011107024	Apr 1	58,574.38	1025	⋯	${2.66}_{-0.30}^{+0.39}$	${0.30}_{-0.03}^{+0.02}$	${0.17}_{-0.01}^{+0.01}$	${0.57}^{\pm 0.07}$	${159}_{-5}^{+7}$	${1.53}_{-0.10}^{+0.13}$	${96}_{-13}^{+16}$	⋯	⋯	⋯	904/885
00896552000	Apr 4	58,577.25	1575	3893	${1.82}_{-0.27}^{+0.22}$	${0.26}_{-0.01}^{+0.01}$	${0.17}_{-0.02}^{+0.01}$	${0.66}^{\pm 0.07}$	${163}_{-8}^{+6}$	${1.79}_{-0.15}^{+0.11}$	${294}_{-27}^{+35}$	⋯	⋯		285/267
00011107027	Apr 12	58,585.20	980	⋯	${2.32}_{-0.31}^{+0.26}$	${0.15}_{-0.02}^{+0.01}$	${0.12}_{-0.01}^{+0.01}$	${0.81}^{\pm 0.10}$	${164}_{-2}^{+5}$	${2.02}_{-0.14}^{+0.12}$	${401}_{-31}^{+38}$	⋯	⋯	⋯	1174/892
00011107028	Apr 15	58,588.72	1020	⋯	${1.47}_{-0.18}^{+0.15}$	${0.14}_{-0.01}^{+0.01}$	${0.11}_{-0.01}^{+0.01}$	${0.83}^{\pm 0.11}$	${166}_{-7}^{+6}$	${2.25}_{-0.13}^{+0.10}$	${213}_{-18}^{+16}$	⋯	⋯	⋯	995/892
00011107029	Apr 24	58,597.04	1015	⋯	${1.63}_{-0.18}^{+0.24}$	${0.13}_{-0.01}^{+0.01}$	${0.11}_{-0.01}^{+0.00}$	${0.85}^{\pm 0.10}$	${185}_{-6}^{+8}$	${2.28}_{-0.11}^{+0.13}$	${287}_{-35}^{+42}$	⋯	⋯	⋯	969/899
00011107035	May 12	58,615.97	604	⋯	${1.09}_{-0.17}^{+0.14}$	${0.08}_{-0.01}^{+0.01}$	${0.09}_{-0.01}^{+0.01}$	${1.01}^{\pm 0.14}$	${192}_{-7}^{+5}$	${2.55}_{-0.10}^{+0.14}$	${116}_{-16}^{+13}$	⋯	⋯	⋯	682/917
00011107036	May 15	58,618.74	1079	⋯	${1.37}_{-0.22}^{+0.20}$	${0.07}_{-0.01}^{+0.01}$	${0.08}_{-0.01}^{+0.01}$	${1.10}^{\pm 0.19}$	${179}_{-6}^{+7}$	${2.95}_{-0.17}^{+0.15}$	${277}_{-37}^{+31}$	⋯	⋯	⋯	698/892

Notes.

^aExposures time are given in s. ^bLine-of-sight hydrogen column density is in 10²² cm⁻² and is given in Column (6). TCAF model fitted/derived parameters are mentioned in Columns (7)–(12). Mass of the BH is frozen at 9.1 M_⊙. ^cAccretion rates ($\dot{{m}_{d}}$ and $\dot{{m}_{h}}$) are in Eddington accretion rate (${\dot{M}}_{\mathrm{Edd}}$). ^dShock location is in Schwarzschild radius (r_s). Gaussian model fitted parameters are mentioned in Columns (13)–(15). ^eIron line energy (LE) and line width (LW) are given in keV. Best-fitted values of ${\chi }^{2}$ and degrees of freedom are mentioned in Column (16) as ${\chi }^{2}/\mathrm{dof}$. Errors are obtained using the "err" task in XSPEC with 90% confidence. The horizontal lines separate different spectral states. ^findicates MAXI/GSC observation.

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We used WT mode data for the XRT observations. We used grade-0 data to reduce pileup effects. Using the xrtpipeline command, cleaned event files were generated. A circular region of a radius of 30 pixels was chosen for the source. Using the XSELECTv2.4, source and background light curves (0.01 s time resolution) and spectra were generated. We rebinned the spectra with 10 counts bin⁻¹ using the grppha task. To generate Swift/BAT spectra, standard procedures were followed, as suggested by the instrument team. Using the batbinevt task, detector plane images were generated. We used batdetmask for appropriate detector quality. We ran bathotpix to find noisy detector pixels and quality mapping. The batmaskwtevt task was used to apply mask weighting to the event mode data. With batphasyserr, a systematic error was applied to the BAT spectra. Using the batupdatephakw task, ray-tracing was corrected. The response matrices for the BAT spectra were generated with the batdetmask task. The 7–20 keV MAXI/GSC spectra were generated by the MAXI on-demand process web tool (Matsuoka et al. 2009).

For spectral analysis, we use the TCAF model-based fits file as the additive table model. As mentioned in the Introduction, to fit using TCAF, four input flow parameters, such as the Keplerian disk accretion rate (${\dot{m}}_{d}$ in ${\dot{M}}_{\mathrm{Edd}}$), the sub-Keplerian halo accretion rate (${\dot{m}}_{h}$ in ${\dot{M}}_{\mathrm{Edd}}$), the shock location (X_s in Schwarzschild radius r_s = $2{{GM}}_{\mathrm{BH}}/{c}^{2}$), and the dimensionless shock compression ratio ($R={\rho }_{+}/{\rho }_{-}$, ratio of post-shock matter density to the pre-shock matter density), are essential. Also, one system parameter, i.e., the mass of the BH (M_BH in M_⊙), and one instrument parameter, namely, the normalization constant (N), are required. In case M_BH is not known, we can extract it as well. Each observation yields a best-fitted value of mass along with other parameters (see the Appendix). The average of these masses comes out to be 9.1 M_⊙. Freezing the mass at this value, we reanalyze all the data to obtain the final value of each parameter.

We ran the powspec task to generate the PDS from the 0.01 s time binned XRT light curves in the energy range of 1–10 keV. We searched for the presence of LFQPOs in the PDS. We studied the PDS with a different number of bins (i.e., 1024, 2048, 4096, and 8192) and subintervals. To obtain frequency (ν), width (Δν), Q-value (ν/Δν), rms amplitude, etc., we fitted observed QPOs with the Lorentzian model. To fit the continuum of the PDS, we used power-law and linear models with the Lorentzian model.

3.1. Outburst Profile

MAXI J1348–630 was in the outbursting phase for almost 4 months. The light curves in different energy ranges and the hardness ratios (HRs) during the entire outburst are shown in several panels of Figure 1. From the MAXI and Swift/XRT light curves (panels (a) and (b) of Figure 1), the outburst can be characterized as "slow-rise-slow-decay" (SRSD; Debnath et al. 2010). In Figure 1(a), we show the variation of MAXI/GSC flux in three different energy bands (e.g., 2–10 keV, 2–4 keV, and 4–10 keV) during the outburst. The variations of 1–10 keV Swift/XRT flux and 15–50 keV Swift/BAT flux covering the entire duration of X-ray outburst are shown in panel (b). HR1 (ratio between fluxes in 4–10 keV and 2–4 keV ranges (obtained from MAXI/GSC)) and HR2 (ratio between fluxes in 15–50 keV (obtained from Swift/BAT) and 2–10 keV flux (obtained from MAXI/GSC)) ranges are shown in panels (c) and (d) of Figure 1, respectively.

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From Figure 1(a), we see that the total flux (2–10 keV MAXI/GSC flux) and the soft X-ray flux (2–4 keV MAXI/GSC flux) increased slowly from 2019 January 25 (MJD 58,508) and reached the maximum value on 2019 February 9 (MJD 58,523). After that, the flux in both the energy ranges decreased gradually. The 4–10 keV MAXI/GSC flux also increased slowly and attained maximum on 2019 February 6 (MJD 58,520), which was 3 days before the peak of the soft X-ray (2–4 keV) flux. After that, it decreased slowly until the end of the outburst. High-energy (15–50 keV range) Swift/BAT flux increased rapidly compared to the MAXI/GSC flux. It attained its peak on MJD 58,516, after which it declined sharply until 2019 February 8 (MJD 58,522). After the sharp decline, the BAT flux decreased very slowly. The BAT flux again increased briefly since 2019 April 27 (MJD 58,600), though soon after it declined again from MJD 58,605. The 1–10 keV Swift/XRT fluxes were estimated from the spectral fitting by using the TCAF model. From panel (b) of Figure 1, it can be seen that the XRT flux increased slowly at the rising phase and was maximum on 2019 February 10 (MJD 58,524.53). It is possible that if the XRT observation were available, the XRT flux would have attained a maximum value on 2019 February 9 (MJD 58,523), when the 2–10 keV flux from MAXI/GSC was maximum. The Swift/XRT flux decreased slowly after reaching the maximum value.

3.2. Hardness Ratio

3.3. PDS

We studied the PDS generated from the light curves in the 1–10 keV range with a time resolution of 0.01 s, obtained from the Swift/XRT data. During our investigation of the presence of QPOs in the XRT light curves, we observed QPOs only in two observations in the rising phase of the outburst, e.g., on 2019 January 29 and 30. The PDS are fitted with combined Lorentzian, linear, and power-law models. The model fitted χ²/dof obtained are 143/113 and 136/112 for the two QPO observations on 2019 January 29 and 30, respectively. In Figure 2, we show a PDS observed on 2019 January 29 (MJD 58,512.43), where a 0.57 ± 0.04 Hz QPO with a Q-value of 4.5 ± 0.4 and 8 ± 0.8% rms was seen. The second QPO was detected at 0.66 ± 0.04 Hz with a Q-value of 2.8 ± 0.3 and 5 ± 0.6% rms on 2019 January 30 (MJD 58,513.11). We did not detect any QPO in the declining phase of the outburst. The rapid change in Q-values indicates a rapid falling out of the resonance condition, which is believed to be the origin of these QPOs.

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3.4. Spectral Properties

We used 1–150 keV combined data from Swift/XRT, Swift/BAT, and MAXI/GSC for the spectral analysis of the BHC MAXI J1348–630 during its 2019 outburst. We used the TCAF model-based fits file for the spectral study. Along with the TCAF model, we used TBabs for absorption (Wilms et al. 2000) and Gaussian for the line emission. A Gaussian function at ∼6.4 keV was used to incorporate the Fe–Kα emission line. In general, we used a TBabs(TCAF + Gauss) model for the spectral analysis. We kept the hydrogen column density (N_H) free during our analysis. We found it to vary between 0.58 × 10²² cm⁻² and 3.24 × 10²² cm⁻² during the observation period. In Figure 3, we show the TCAF model fitted spectra in the 1–150 keV energy range for four different spectral states. Spectra in the HS in the rising phase (2019 January 27, ObsID 00885960000), HIMS in the rising phase (2019 February 3, ObsID 00011107002), SS (2019 February 10, ObsID 00011107007), and SIMS in the declining phase (2019 April 4, ObsID 00896552000) are shown in panels (a), (b), (c), and (d), respectively. The residuals obtained from the TCAF model fit are shown in the bottom panels of each spectrum. As quoted in the previous section, the TCAF model fit yields several parameters such as the Keplerian disk accretion rate (${\dot{m}}_{d}$), the sub-Keplerian halo accretion rate (${\dot{m}}_{h}$), the shock location (X_s), the shock compression ratio (R), etc., for each observation in the present work. The evolution of (a) the total accretion rate (${\dot{m}}_{d}$+${\dot{m}}_{h}$), (b) the Keplerian disk accretion rate (${\dot{m}}_{d}$), (c) the sub-Keplerian halo accretion rate (${\dot{m}}_{h}$), and (d) the accretion rate ratio (ARR = ${\dot{m}}_{h}$/${\dot{m}}_{d}$) during the outburst is shown in Figures 4(a)–(d). In Figure 5, we show the variation of the TCAF model fitted mass of the BH, the evolution of the shock location (X_s), and the shock compression ratio (R) in panels (a), (b), and (c), respectively. In Figure 6, we plot the variation of Δχ² with the derived mass of the BH (M_BH) for observations with ObsIDs (a) 00885960000, (b) 00011107002, (c) 00011107007, and (d) 00896552000 taken from HS, HIMS, SS, and SIMS, respectively. The best-fitted parameters obtained from the TCAF model fitting to the source spectra during the outburst are presented in Table 1.

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3.5. Evolution of the Spectral State

3.6. Viscous Timescale

3.7. Estimation of the BH Mass

3.8. Estimation of Distance

We studied the evolution of the timing and the spectral properties of the newly discovered Galactic transient BHC MAXI J1348–630 during its 2019 outburst. We studied the BHC for a duration of about 4 months using data from Swift/XRT, Swift/BAT, and MAXI/GSC instruments. For the spectral analysis, we used the TCAF model-based fits file. From the TCAF model, we extracted flow parameters of the system such as the Keplerian disk accretion rate (${\dot{m}}_{d}$), the sub-Keplerian halo accretion rate (${\dot{m}}_{h}$), the shock location (X_s), and the shock compression ratio (R). We also estimated the mass of the BH from our spectral analysis. These parameters were obtained from each observation, collectively giving us an idea of accretion flow dynamics during the observational period.

It is to be noted that we used XRT (1–10 keV), GSC (7–20 keV), and BAT (15–150 keV) data to cover a broad energy range of 1–150 keV. It is best to use a broad energy range to obtain the flow parameters more accurately with TCAF. In general, without BAT, 1–10 keV XRT data or 1–20 keV XRT+GSC data were available for the spectral analysis. Therefore, part of the spectral information was missing when BAT data were absent. This is the case for any model and not just TCAF. However, the TCAF model handles both narrowband and broadband data better than any phenomenological model. TCAF calculates all the model parameters self-consistently. Therefore, we do not expect the fitting result to be changed abruptly with or without BAT. We checked it by removing BAT data from broadband spectra (when XRT+BAT was used). We found that the results did not change significantly without BAT. As an example, on the first observation (ObsID 00885807000), we obtained $\dot{{m}_{d}}\,=\,0.36$, $\dot{{m}_{h}}=0.41$, X_s = 274, R = 3.07 for χ²/dof = 312/287 with 1–150 keV XRT+GSC+BAT data. When we removed BAT data, we obtained $\dot{{m}_{d}}=0.36$, $\dot{{m}_{h}}=0.41$, X_s = 272, R = 3.06 for ${\chi }^{2}$/dof = 254/231 with 1–20 keV XRT+GSC data. The fit result and statistics did not change significantly when we did not use BAT data.

MAXI J1348–630 went into its first outburst in 2019. The source was discovered on 2019 January 26 (MJD 58,509.45). The outburst continued for ∼4 months. Both the soft and the hard X-ray intensities increased in the rising phase of the outburst, although at different rates. Hard X-ray flux (15–50 keV BAT) showed a rapid rise and reached its peak flux on 2019 February 3 (MJD 58,517.67). After that, BAT flux declined. The soft X-ray (2–4 keV GSC) flux increased monotonically and achieved peak value on 2019 February 9 (MJD 58,523.5). On that day, the BHC entered the SS. The intermediate period (from MJD 58,517.67 to MJD 58,523.5) belongs to two intermediate spectral states (rising HIMS and SIMS). In the declining phase, the X-ray flux slowly decreased. Depending on the rising (slow) and decreasing (slow) variation of the total X-ray flux (2–10 keV GSC), it appears that the nature of the outburst is an SRSD type (see Debnath et al. 2010).

We identified the spectral states into two independent ways: (i) from the evolution of the HRs, the soft X-ray flux, and the hard X-ray flux; and (ii) from the variation of the TCAF model fitted spectral parameters. However, to mark the exact state transition days, we used both methods. For example, the source entered in the SS from the SIMS (ris.) on MJD 58,523.5. However, no spectral data were available on that day. Spectral data were available on MJD 58,524.53, and the source was clearly in the SS on that day. Similarly, the transition day from HIMS (dec.) to HS (dec.) was marked from the evolution of HRs. During the outburst, MAXI J1348–630 showed all four usual spectral states in the following sequence: HS (ris.) → HIMS (ris.) → SIMS (ris.) → SS → SIMS (dec.) → HIMS (dec.) → HS (dec.).

MAXI J1348–630 was in the HS when the outburst started. The sub-Keplerian halo accretion rate was higher than the Keplerian disk accretion rate in this state. A strong shock was found at a significant distance from the BH. Both accretion rates increased as the outburst progressed. We see the peak of the halo accretion rate on the transition day from HIMS (ris.) to SIMS (ris.) (2019 February 7; MJD 58,521.07). The Keplerian disk accretion rate increased more rapidly than the sub-Keplerian halo accretion rate from this transition day. More supply in the disk matter cooled the CENBOL in a faster way as the source moved to the SIMS (ris.) and SS. In the SS, the total accretion rate achieved its peak value on 2019 February 10 (MJD 58,524.53). Then, the source entered the declining phase. Both accretion rates decreased slowly. The source remained in the softer states (SIMS and SS) for a long time (∼2.5 months). We have also noticed that in the present outburst of MAXI J1348–630, the duration of the SIMS (dec.) was much longer compared to the SS and other spectral states. Generally, we see longer SS in the outbursting BHCs. As the outburst progressed, the shock became strong and receded from the BH starting from the SS-to-SIMS (dec.) transition day (2019 February 19; MJD 58,533.54). The ARR also increased slowly. This trend continued in the declining HIMS and HS too. In general, the ARR increased in the HS of the declining phase as the spectra became hard.

Unlike many outbursting candidates, we did not observe QPOs on each day of observation during the 2019 outburst of MAXI J1348–630. We detected LFQPOs only in two observations in the rising phase of the outburst. The QPOs were detected on 2019 January 29 and 30 at frequencies of 0.57 ± 0.04 Hz and 0.66 ± 0.04 Hz with Q-values of 4.5 ± 0.4 and 2.8 ± 0.3, respectively. Chen et al. (2019) also found an evolving QPO on 2019 January 30 with maximum centroid frequency of 0.71 ± 0.01 Hz with FWHM of 0.16 ± 0.04 Hz from HXMT observation. They studied roughly for the full-day observation. Thus, we feel that our findings are consistent with their reports. No QPO was observed in the declining phase of the outburst. The shock oscillations are believed to be the reason behind these QPOs. Since Type C LFQPOs occur as a result of resonance between cooling and infall timescales (Molteni et al. 1996), rapid deterioration of Q-value indicates that the flow went off the resonance very quickly. Type A or Type B QPOs are observed sporadically in the SIMS owing to a weakly oscillating shock. This weak shock oscillation could be due to either a weakly resonating CENBOL (for Type B) or a shockless centrifugal barrier (for Type A) (Ryu et al. 1997). In the present system, such QPOs were not observed.

We checked whether the resonance condition is satisfied during the outburst. The resonance condition is satisfied when the infall (compressional heating) timescale (t_in) of the post-shock matter matches with the cooling timescale (t_c) of the post-shock matter (Molteni et al. 1996; Chakrabarti et al. 2015, hereafter CMD15). As far as the resonance condition is concerned, the ratio has to be strictly 1 to have resonance by definition. However, since the CENBOL is not oscillating as a single entity (rather, different parts are oscillating with slightly different frequency), the resonance condition is achieved when the ratio is on the order of unity. CMD15 showed that if the ratio is between 0.5 and 1.5, i.e., within 50% of unity, the resonance is satisfied. However, this limit is not rigid. Even outside of this range, some oscillation may occur, and instead of Type C QPOs, one may also see Type B or Type A QPOs. As the ratio deviates, chances of finding QPOs with a significant decrease of rms are reduced, as we saw here. Jana et al. (2020b) applied this method to investigate the reason behind the nonobservation of LFQPOs during the 2015 outburst of V404 Cygni. For the present object too, we followed the CMD15 procedure to calculate t_c and t_in. We find that the resonance condition was satisfied only during three observations, i.e., on 2019 January 29 (MJD 58,512.43), 2019 January 30 (MJD 58,513.11), and 2019 February 1 (MJD = 58,515.75), with the ratio being 0.94, 0.79, and 0.60, respectively. The cooling times (t_c) for three observations are 1.20, 0.96, and 0.67 s, respectively. The infall times (t_in) are 1.28, 1.22, and 1.12 s for MJD 58,512.43, MJD 58,513.11, and MJD 58,515.75, respectively. The QPOs were indeed observed only in two observations, on MJD 58,512.43 and MJD 58,513.11. On MJD 58,515.75, nonobservation of the QPO could be due to weak satisfaction of the resonance condition. In other observations, QPOs were not observed, as the resonance condition was not satisfied owing to efficient cooling processes. Such observation is consistent with the expectation from a purely theoretical point of view.

Low viscous sub-Keplerian flow has low angular momentum, whereas the Keplerian disk has high angular momentum and viscosity. Thus, the sub-Keplerian halo moves faster than the Keplerian disk, which moves in the viscous timescale. Thus, the sub-Keplerian flow rate achieves its peak earlier than the Keplerian disk rate. The time difference of reaching the maxima of the sub-Keplerian halo accretion rate and the Keplerian disk accretion rate is the viscous timescale of the Keplerian component. Jana et al. (2016) calculated the viscous timescale for MAXI J1836–194 during its 2011 outburst as ∼10 days using this method. In the same way, viscous timescales are also calculated for a few other BHCs (Mondal et al. 2017). During the 2019 outburst of MAXI J1348–630, the sub-Keplerian halo accretion rate became maximum on 2019 February 7 (MJD 58,521.07), and the Keplerian disk accretion rate became maximum on 2019 February 10 (MJD 58,524.53). This suggests that the viscous timescale for the outburst is ∼3.5 days.

During the spectral analysis, we found that the hydrogen column density (N_H) varied between 0.58 × 10²² cm⁻² and 3.24 × 10²² cm⁻² during the outburst. It is observed that N_H may change in different spectral states owing to the radio activity and the outflowing matter from the disk (Sreehari et al. 2019). If the accretion rate is high, there could be outflow from the disk due to radiation pressure (Radhika et al. 2016a). This disk may lead to the variable N_H (Radhika et al. 2016a, 2016b). In MAXI J1348–630, the super-Eddington accretion rate was observed, which could lead to disk wind and hence variable N_H.

We observed the Fe emission line in 11 out of a total of 27 observations in our analysis. The Fe line was detected in the rising phases of HS, HIMS, and SIMS, and in the SS. In the declining phase, no Fe line was detected except for one observation. In general, the Fe line was detected when the Keplerian disk rate was high. This suggests that the Fe line may be associated with the Keplerian disk. This could be the reason for nondetection of the Fe line in the declining phase when the Keplerian disk receded and the disk rate decreased. In our observation, the line energy varied between 6.06 and 6.95 keV. The observed line around ∼6.9 keV might be the Fe xxvi line. The observed broad lines could be a possible blend of several Fe lines, which could not be resolved individually.

Tominaga et al. (2020) estimated the mass of the BH from the result obtained from the tbabs*simpl*diskbb model. They calculated R_in from the diskbb normalization and equated with the innermost stable circular orbit (ISCO). From this, they calculated the mass of the BH to be >16 M_⊙. However, this method is not reliable, since the disk would extend up to ISCO or 3 r_s only in an ideal case, but often that is not achieved. Phenomenological model fitting gives a rough idea of the system parameters, but a physical model is required to study the dynamics of the system. Unlike the diskbb model, TCAF is a physical model, and all spectral parameters (including mass) are calculated self-consistently. In the TCAF model fits file, the mass of the BH is an important model input parameter, simply because the electron number density in CENBOL, the soft photon intensity from the Keplerian disk, the size of the CENBOL, etc., which are responsible for producing the spectrum, depend on the mass. Thus, it is possible to estimate the mass of the BH from the spectral analysis with the physical TCAF model. The mass of several Galactic BHCs and active galactic nuclei have already been estimated successfully from the spectral analysis with the TCAF model (Chatterjee et al. 2016, 2019; Jana et al. 2016; Molla et al. 2016; Bhattacharjee et al. 2017; Nandi et al. 2019). Jana et al. (2019) reported the mass of this BHC in the range of 8.5–11 M_⊙ from their preliminary analysis. In this paper, we estimated the mass of the BHC MAXI J1348–630 by keeping M_BH free while fitting the spectra with the TCAF model. Each observation gave us a best-fitted M_BH, which was found to vary between 8.44 and 9.72 M_⊙ (see the Appendix). This variation is the result of poor data quality and errors in fitting the data. For instance, fitting the peak of the multicolor blackbody depends on disk temperature T, and errors introduced are amplified four times, since M_BH  ∼ T⁻⁴. This is mainly contributing to the ∼4 times error in M_BH . From the variation of the model fitted M_BH, we calculated the average value of the mass as 9.1 M_⊙. We also checked the mass from Δχ²–M_BH plots. We kept mass frozen at different values and checked how Δχ² varied. From this, we find that the mass of the BHC MAXI J1348–630 is between 7.9 and 10.7 M_⊙ with 90% confidence. Combining these two methods, we conclude the mass of the BHC MAXI J1348–630 to be in the range of 7.9–10.7 M_⊙ or ${9.1}_{-1.2}^{+1.6}$ M_⊙.

We estimated the distance of the source from the hard-to-soft-state transition luminosity. It is observed that the soft-to-hard transition luminosity (L_t) is between 0.01L_Edd and 0.04L_Edd (Maccarone 2003; Tetarenko et al. 2016). From this method, the distance of MAXI J1910–057 was calculated to be >1.70 kpc (Nakahira et al. 2014). We calculated TCAF model fitted 1–10 keV luminosity as L = 1.24 × 10³⁷ (d/5) erg s⁻¹. We found that for d = 5–10, L_t/L_Edd = 0.01–0.042. This infers that the source distance is between 5 and 10 kpc. In another empirical relation, McClintock & Remillard (2009) showed that peak luminosity would be 0.2L_Edd–0.4L_Edd for three BHCs GRS 1915+105, GRO J1655–40, and XTE J1550–564. The peak luminosity of MAXI J1348–630 was observed on MJD 58,524.53 with L_peak = 1.90 × 10³⁹ (d/5) erg s⁻¹. From this, L_peak/L_Edd =  0.16, 0.23, and 0.41 for d = 5, 6, and 8 kpc, respectively. From this, the source distance is 5–8 kpc. Tominaga et al. (2020) estimated the source distance as 4–8 kpc using the same methods mentioned above. Our finding is consistent with the findings of Tominaga et al. (2020).

In the TCAF model, normalization N remains constant across the spectral states simply because it is just a scaling factor to convert the emitted spectrum to the TCAF spectrum (Molla et al. 2016, 2017). However, if a jet is present, normalization could vary, and N is observed to have a higher value (Jana et al. 2017, 2020a). In this case, emitted X-rays contain the contribution from the inner jet, which was theorized in TCAF. During the 2019 outburst of BHC MAXI J1348–630, normalization was not found to be a constant. This indicates the presence of the X-ray jets during the outburst. The disk–jet connection of the source will be studied and published elsewhere.

We studied MAXI J1348–630 during its 2019 outburst in detail. We used data of Swift/XRT, Swift/BAT, and MAXI/GSC in the combined broad energy range of 1–150 keV for our study. We find that the source went through all the usual spectral states. We presented how the flow parameters evolved during the outburst from TCAF fits of the spectra. We observed QPOs only in two observations when the stricter resonance condition between the heating and cooling timescales of the Compton cloud were found to be satisfied. We estimated the mass of MAXI J1348–630 as ${9.1}_{-1.2}^{+1.6}$ M_⊙. We also estimated the viscous timescale of the standard disk component to be ∼3.5 days during the outburst. From the state transition luminosity, we estimated the distance of the source as 5–10 kpc.

We thank an anonymous referee for his/her comments and suggestions on improving the quality of this manuscript. This work made use of XRT and BAT data supplied by the UK Swift Science Data Centre at the University of Leicester, and MAXI data were provided by RIKEN, JAXA, and the MAXI team. A.J. acknowledges the postdoctoral fellowship of the Physical Research Laboratory, Ahmedabad, funded by the Department of Space, Government of India. D.D. and A.J. acknowledge support from the DST/GITA-sponsored India-Taiwan collaborative project (GITA/DST/TWN/P-76/2017) fund. Research of D.D. and S.K.C. is supported in part by the Higher Education Dept. of the Govt. of West Bengal, India. S.K.C. and D.D. also acknowledge partial support from the ISRO-sponsored RESPOND project (ISRO/RES/2/418/17-18) fund. K.C. acknowledges support from the DST/INSPIRE Fellowship (IF170233). R.B. acknowledges support from the CSIR-UGC NET qualified UGC fellowship (2018 June, 527223). N.K. acknowledges support from the research fellowship from the Physical Research Laboratory, Ahmedabad, India, funded by the Department of Space, Government of India.

Initially, we kept the mass of the BH free while fitting with the TCAF model. Each spectrum gives us a best-fitted value of the mass. The variation of the mass is given in Table A1. From the variation, we estimated the mean value of the mass, which is 9.1 M_⊙. We kept the mass frozen at 9.1 M_⊙ and refitted all the spectra to get the final result. The final result is quoted in Table 1. In Table A1, we list the TCAF model fitted result when the mass of the BH was kept free. Note that Table A1 does not contain the final result.

Table A1.  Preliminary Spectral Analysis Result

Day	MBH a	$\dot{{m}_{d}}$ b	$\dot{{m}_{h}}$ b	XSc	R	N	${\chi }^{2}/\mathrm{dof}$
(MJD)	(M⊙ )	(${\dot{M}}_{\mathrm{Edd}}$)	(${\dot{M}}_{\mathrm{Edd}}$)	(rs)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
58,509.45	${9.07}_{-0.42}^{+0.53}$	${0.36}_{-0.02}^{+0.02}$	${0.41}_{-0.02}^{+0.03}$	${274}_{-3}^{+7}$	${3.06}_{-0.13}^{+0.12}$	${266}_{-24}^{+22}$	314/286
58,509.51	${8.82}_{-0.76}^{+0.62}$	${0.46}_{-0.02}^{+0.03}$	${0.52}_{-0.02}^{+0.02}$	${248}_{-9}^{+5}$	${2.49}_{-0.11}^{+0.12}$	${411}_{-22}^{+25}$	58 /52
58,510.05	${9.16}_{-0.61}^{+0.45}$	${0.55}_{-0.04}^{+0.06}$	${0.54}_{-0.03}^{+0.03}$	${224}_{-7}^{+4}$	${1.80}_{-0.11}^{+0.12}$	${292}_{-20}^{+16}$	317/264
58,511.58	${9.61}_{-0.66}^{+0.91}$	${0.57}_{-0.05}^{+0.04}$	${0.56}_{-0.05}^{+0.04}$	${215}_{-3}^{+6}$	${1.51}_{-0.03}^{+0.02}$	${195}_{-18}^{+21}$	299/261
58,512.43	${9.13}_{-0.38}^{+0.49}$	${0.62}_{-0.07}^{+0.05}$	${0.58}_{-0.01}^{+0.03}$	${208}_{-8}^{+6}$	${1.48}_{-0.16}^{+0.13}$	${336}_{-42}^{+34}$	327/265
58,513.11	${8.75}_{-0.72}^{+0.83}$	${0.64}_{-0.05}^{+0.04}$	${0.60}_{-0.04}^{+0.05}$	${205}_{-5}^{+4}$	${1.40}_{-0.11}^{+0.09}$	${163}_{-20}^{+14}$	725/582
58,515.75	${9.38}_{-0.55}^{+0.37}$	${0.72}_{-0.08}^{+0.07}$	${0.59}_{-0.03}^{+0.02}$	${187}_{-5}^{+4}$	${1.21}_{-0.04}^{+0.09}$	${861}_{-40}^{+57}$	358/296
58,517.67	${9.68}_{-0.87}^{+0.72}$	${0.73}_{-0.05}^{+0.08}$	${0.65}_{-0.05}^{+0.03}$	${166}_{-5}^{+4}$	${1.14}_{-0.09}^{+0.10}$	${284}_{-44}^{+30}$	223/180
58,521.07	${9.64}_{-0.88}^{+0.71}$	${0.99}_{-0.09}^{+0.10}$	${0.73}_{-0.02}^{+0.04}$	${94}_{-4}^{+3}$	${1.06}_{-0.04}^{+0.05}$	${125}_{-29}^{+20}$	137/127
58,523.00	${9.10}_{-0.57}^{+0.73}$	${1.34}_{-0.08}^{+0.08}$	${0.71}_{-0.03}^{+0.05}$	${61}_{-5}^{+3}$	${1.10}_{-0.03}^{+0.07}$	${164}_{-24}^{+16}$	128/129
58,524.53	${9.37}_{-0.62}^{+0.52}$	${1.60}_{-0.09}^{+0.10}$	${0.61}_{-0.05}^{+0.04}$	${51}_{-4}^{+3}$	${1.05}_{-0.06}^{+0.05}$	${307}_{-53}^{+43}$	235/208
58,527.44	${8.44}_{-0.47}^{+0.71}$	${1.35}_{-0.15}^{+0.10}$	${0.49}_{-0.05}^{+0.04}$	${65}_{-4}^{+5}$	${1.15}_{-0.14}^{+0.14}$	${79}_{-14}^{+12}$	125/132
58,530.29	${9.72}_{-0.81}^{+0.96}$	${1.43}_{-0.13}^{+0.05}$	${0.41}_{-0.05}^{+0.06}$	${71}_{-3}^{+2}$	${1.23}_{-0.10}^{+0.05}$	${86}_{-12}^{+13}$	142/135
58,531.35	${9.23}_{-0.75}^{+0.65}$	${1.27}_{-0.14}^{+0.12}$	${0.45}_{-0.05}^{+0.02}$	${83}_{-5}^{+5}$	${1.24}_{-0.15}^{+0.09}$	${43}_{-9}^{+13}$	130/135
58,533.54	${9.27}_{-0.63}^{+0.87}$	${1.10}_{-0.08}^{+0.06}$	${0.45}_{-0.04}^{+0.05}$	${95}_{-3}^{+4}$	${1.33}_{-0.09}^{+0.11}$	${58}_{-14}^{+12}$	253/223
58,535.80	${8.50}_{-0.61}^{+0.92}$	${1.08}_{-0.12}^{+0.10}$	${0.43}_{-0.02}^{+0.02}$	${98}_{-4}^{+5}$	${1.41}_{-0.12}^{+0.08}$	${121}_{-11}^{+11}$	267/223
58,550.49	${8.91}_{-0.60}^{+0.71}$	${0.78}_{-0.06}^{+0.07}$	${0.30}_{-0.02}^{+0.03}$	${133}_{-4}^{+4}$	${1.37}_{-0.10}^{+0.05}$	${302}_{-46}^{+40}$	268/211
58,553.87	${9.10}_{-0.49}^{+0.62}$	${0.64}_{-0.06}^{+0.03}$	${0.32}_{-0.01}^{+0.02}$	${137}_{-6}^{+2}$	${1.44}_{-0.10}^{+0.09}$	${476}_{-43}^{+40}$	251/217
58,559.13	${8.73}_{-0.50}^{+0.88}$	${0.50}_{-0.03}^{+0.02}$	${0.29}_{-0.04}^{+0.01}$	${147}_{-6}^{+5}$	${1.54}_{-0.11}^{+0.11}$	${824}_{-61}^{+46}$	959/890
58,562.04	${8.99}_{-0.64}^{+0.79}$	${0.41}_{-0.05}^{+0.04}$	${0.22}_{-0.02}^{+0.02}$	${150}_{-7}^{+5}$	${1.47}_{-0.05}^{+0.10}$	${323}_{-32}^{+41}$	1024/879
58,574.38	${9.38}_{-0.33}^{+0.55}$	${0.30}_{-0.02}^{+0.03}$	${0.16}_{-0.01}^{+0.01}$	${155}_{-6}^{+5}$	${1.55}_{-0.12}^{+0.13}$	${95}_{-14}^{+19}$	901/884
58,577.25	${9.00}_{-0.49}^{+0.68}$	${0.26}_{-0.03}^{+0.01}$	${0.17}_{-0.02}^{+0.02}$	${165}_{-4}^{+7}$	${1.83}_{-0.12}^{+0.13}$	${299}_{-24}^{+25}$	282/266
58,585.20	${9.25}_{-0.33}^{+0.22}$	${0.15}_{-0.02}^{+0.01}$	${0.13}_{-0.02}^{+0.02}$	${164}_{-4}^{+7}$	${2.00}_{-0.11}^{+0.09}$	${391}_{-35}^{+41}$	1171/891
58,588.72	${8.48}_{-0.52}^{+0.59}$	${0.12}_{-0.01}^{+0.01}$	${0.12}_{-0.01}^{+0.01}$	${169}_{-8}^{+7}$	${2.25}_{-0.13}^{+0.11}$	${209}_{-22}^{+12}$	988/891
58,597.04	${8.62}_{-0.67}^{+0.75}$	${0.13}_{-0.02}^{+0.01}$	${0.11}_{-0.01}^{+0.00}$	${184}_{-6}^{+5}$	${2.30}_{-0.14}^{+0.12}$	${285}_{-25}^{+33}$	965/899
58,615.97	${8.70}_{-0.53}^{+0.71}$	${0.07}_{-0.01}^{+0.01}$	${0.09}_{-0.01}^{+0.01}$	${194}_{-9}^{+5}$	${2.51}_{-0.12}^{+0.14}$	${125}_{-15}^{+13}$	689/916
58,618.74	${8.94}_{-0.47}^{+0.54}$	${0.07}_{-0.01}^{+0.02}$	${0.09}_{-0.01}^{+0.01}$	${180}_{-7}^{+6}$	${2.94}_{-0.15}^{+0.12}$	${282}_{-41}^{+26}$	703/891

Notes.

^aTCAF model fitted/derived parameters are mentioned in Columns (2)–(7). TCAF model fitted mass is given in M_⊙. ^bAccretion rates ($\dot{{m}_{d}}$ and $\dot{{m}_{h}}$) are in Eddington accretion rate (${\dot{M}}_{\mathrm{Edd}}$). ^cShock location is in Schwarzschild radius (r_s). Best-fitted values of ${\chi }^{2}$ and degrees of freedom are mentioned in Column (8) as ${\chi }^{2}/\mathrm{dof}$. Errors are obtained using the "err" task in XSPEC with 90% confidence. The horizontal lines separate different spectral states.

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