ACCRETION FLOW DYNAMICS OF MAXI J1836-194 DURING ITS 2011 OUTBURST FROM TCAF SOLUTION

Compact objects such as neutron stars, black holes, etc. are characterized by electromagnetic radiations emitted from the accretion disks, forms due to the accreting matter supplied by their companions. Some of these objects are transient binaries in nature and are very interesting to study using X-rays as they undergo rapid evolutions in their spectral and timing properties. Several works are present 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 variation of timing and spectral properties of these objects during their X-ray outbursts. It also has been reported by several authors that these objects exhibit different spectral states (e.g., hard, hard-intermediate, soft-intermediate and soft) during their outbursts (see Debnath et al. 2013 and references therein). Low-frequency quasi-periodic oscillations (QPOs) are often observed in the power-density spectra (PDS) of some of these spectral states (see Remillard & McClintock 2006 for a review). In the literature many authors (Belloni et al. 2005; Debnath et al. 2013 and references therein) have reported that model-extracted physical parameters undergo a hysteresis loop during their spectral evolution through an entire epoch of the outburst of these transient black hole candidates (BHCs).

It is well-known that the emitted spectrum of radiation coming from BHCs is multicolor in nature and contains both nonthermal and thermal components. The thermal component is the multicolor blackbody radiation from the standard Keplerian disk (Novikov & Thorne 1973; Shakura & Sunyaev 1973) and the other is the power-law component that originates from a "Compton" cloud (Sunyaev & Titarchuk 1980, 1985), a repository of hot electrons whose thermal energy is transferred to low-energy photons from the standard disk by repeated Compton scatterings to produce high-energy X-rays. In the two-component advective flow (TCAF) solution of Chakrabarti & Titarchuk (1995, hereafter CT95; see also, Chakrabarti 1997), the so-called "Compton cloud" or "hot corona" is actually the CENtrifugal pressure supported Boundary Layer (CENBOL) that automatically forms behind the centrifugal barrier due to the pileup of the low viscosity (lesser than critical viscosity) and low angular momentum optically thin matter known as sub-Keplerian (halo) accretion component. An axisymmetric shock (Chakrabarti 1990, 1996; Ryu et al. 1997) defines the outer boundary of the CENBOL. Okuda et al. (2007) showed that this shock is stable even for non-axisymmetric perturbations. In TCAF another component of the accretion flow is the viscous optically thick and geometrically thin Keplerian (disk) component which is submerged inside the sub-Keplerian (halo) component. CENBOL being much hotter in general, the Keplerian disk is naturally truncated at the shock location close to the black hole. This Keplerian flow settles down to a standard SS73 disk when cooling is efficient (see Giri & Chakrabarti 2013; Giri 2015 and references therein).

Recently, after the inclusion of TCAF solution in HEASARC's spectral analysis software package XSPEC (Arnaud 1996) as a local additive table model (Debnath et al. 2014; hereafter DCM14; Mondal et al. 2014; hereafter MDC14; Debnath et al. 2015a; hereafter DMCM15; Debnath et al. 2015b; hereafter DMC15), which requires only five physical parameters (including mass) to fit a spectrum from a BHC, an accurate picture of the accretion flow dynamics around several transient BHCs (e.g., H 1743-322, GX 339-4, MAXI J1659-152) during their X-ray outbursts was obtained. From the TCAF model fitted spectrum one cannot only directly obtain information about instantaneous accretion rates of the two components but also crucial information on shock parameters (instantaneous shock location X_s and shock strength β = 1/R, where R is the shock compression ratio) which allow us to estimate frequencies of the dominating QPOs (if observed in PDS; see, DCM14). Various spectral states are observed during an outburst phase of a transient BHC and can be characterized by interesting variations of the accretion rate ratio (ARR) and QPOs (shape, frequency, Q value, and rms%). This motivated us to study the accretion flow dynamics of the newly discovered Galactic BHC MAXI J1836-194 during its very first outburst in 2011 with TCAF, particularly because of its very low orbital timescale.

The transient BHC MAXI J1836-194 has a short orbital period of <4.9 hr and a low disk inclination angle (4°–15°; Russell et al. 2014). The source located at R.A. = 18^h35^m4343, decl. = −19°19'121 was first observed simultaneously by SWIFT/BAT and MAXI/GSC on 2011 August 29 (Negoro et al. 2011). Miller-Jones et al. (2011), on the basis of X-ray spectral analysis and the observation of a radio jet when a transition from hard to soft state occurs, suggested the source to be a potential BHC. Reis et al. (2012) suggested the source to be a highly rotating BHC with a spin parameter of a = 0.88 ± 0.03. VLT optical spectral study of the binary system by Russell et al. (2014) suggests that the mass and the distance of the source to be 4–12 M_⊙ and 4–10 kpc, respectively. They also computed the mass and the radius of the companion donor main sequence star to be <0.65 M_⊙ and <0.59 R_⊙, respectively. On the contrary, Cenko et al. (2011) concluded the companion to be a high-massive Be star on the basis of their optical spectroscopic study and system as a high-mass X-ray binary.

MAXI J1836-194 showed its first X-ray flaring activity on 2011 August 29 (Modified Julian Day, i.e., MJD = 55802) and it continued for  ∼2 months. During this outburst period the source was studied extensively in multi-energy bands such as various X-ray (Ferrigno et al. 2012; Reis et al. 2012; Radhika et al. 2014) and radio observatories (Yang et al. 2012; Russell et al. 2013). An evolving radio jet was also observed by Russell et al. (2013). We study timing and spectral properties of the BHC during the entire phase of the outburst using RXTE Proportional Counter Array (PCA) archival data. In the present work we give the TCAF fitted spectral analysis results to study accretion flow dynamics around the BHC during its 2011 outburst and discuss how the ARR values and nature of QPOs (if present) vary with spectral states. We also compare our TCAF model fitted spectral results with that of the combined disk blackbody (DBB) and power-law (PL) model fitted results.

The paper is organized in the following way. In Section 2 we briefly discuss observation and data analysis procedures using the HEASARC's HeaSoft software package. In Section 3 we present spectral analysis results using the TCAF solution-based fits file as a local additive table model in XSPEC. We also fitted spectra with the DBB model plus the PL model and compared analysis results with those of the TCAF fitted spectral results to demonstrate the strength of the TCAF fits to understand different spectral states and their correlation with temporal properties. We show that on some days there are clear indications of unresolved double peaked iron lines. Finally in Section 4 a brief discussion on the results and concluding remarks are presented.

RXTE/PCA monitored the source two days after its discovery on a daily basis (Strohmayer & Smith 2011) except for a crucial ∼5 days gap during MJD = 55813 − 18 in the rising phase of the outburst. Here we study achival data of 35 observational IDs starting from the first PCA observed day, 2011 August 31 (MJD = 55804), to 2011 November 24 (MJD = 55889) using XSPEC version 12.8. To analyze the data we follow the standard data analysis technique of the RXTE/PCA instrument as presented in Debnath et al. (2013, 2015b).

For timing analysis we use the PCA Science Binned mode (FS3f*.gz) data with a maximum timing resolution of 125 μs to generate light curves for a well-calibrated Proportional Counter Unit 2 (PCU2; including all six layers) in 2–25 keV (0–59 channels) and 2–15 keV (0–35 channels). To generate the PDS "powspec" routine of the XRONOS package is used to compute rms fractional variability on 2–15 keV light curves of 0.01 sec time bin. To find centroid frequencies of QPOs we fit PDS with Lorentzian profiles and use the "fit err" command to get error limits.

For spectral analysis we use the Standard2 mode Science Data (FS4a*.gz) of the PCA instrument. The 2.5–25 keV background subtracted Proportional Counter Unit 2 (PCU2) spectra are fitted with both the TCAF-based model fits file and combined DBB and PL model components in XSPEC. The individual DBB model and PL model components fluxes are obtained by using the convolution model "cflux" technique. To achieve the best spectral fits, a Gaussian line of peak energy around 6.5 keV (iron line emission) is used except for the five observations (see Table 1) where we fitted the data with the LAOR model (Laor 1991). We fit the data with line energies at ∼7.1 keV and with emissivity indices around ∼3.5 (see Table 2). Hydrogen column density (N_H) was kept frozen at 2.0 × 10²¹ atoms cm⁻² (Kennea et al. 2011) for absorption model wabs. For the entire outburst we also use a fixed 1.0% systematic instrumental error for the spectral analysis. The XSPEC command "err" is used to find 90% confidence "+ve" and "−ve" error values for the model fitted parameters after achieving the best fit based on reduced the chi-square value (χ²_red ∼ 1). In Table 1 average values of these two ± errors are mentioned in the superscripts of the parameter values. In Table 2 we present combined TCAF and LAOR model fitted LAOR parameters for five spectra, where the LAOR model is found to be more useful to deal with the Fe line instead of the single Gaussian ∼6.5 keV.

Table 1.  2.5–25 keV Combined DBB plus PL and TCAF Model Fitted Spectral Parameters with QPOs

Obs. Id	MJD	Tin	Γ	DBBfa	PLf†	DBB Norm.	$\dot{{m}_{d}}$	$\dot{{m}_{h}}$	ARR	Xs	R	Norm.	MBH	QPOb	${\chi }^{2}/\mathrm{dof}$
		(keV)					($\dot{M}$Edd)	($\dot{M}$Edd)		(rg)			(${M}_{\odot }$)	(Hz)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
X-01-00c	55804.52	${1.061}^{0.029}$	${1.647}^{0.018}$	${0.115}^{0.025}$	${1.078}^{0.012}$	${11.27}^{1.38}$	${2.057}^{0.023}$	${0.740}^{0.010}$	${0.360}^{0.009}$	${37.84}^{3.820}$	${1.072}^{0.017}$	${0.341}^{0.002}$	${10.49}^{0.22}$	${0.476}^{0.027}$	61.33/41
X-02-00c	55805.61	${1.066}^{0.023}$	${1.685}^{0.012}$	${0.164}^{0.027}$	${1.315}^{0.014}$	${15.63}^{1.62}$	${2.223}^{0.023}$	${0.805}^{0.013}$	${0.362}^{0.010}$	${35.93}^{2.230}$	${1.070}^{0.004}$	${0.347}^{0.002}$	${10.91}^{0.34}$	⋯	62.41/41
X-03-00d	55806.51	${0.963}^{0.037}$	${1.749}^{0.015}$	${0.188}^{0.018}$	${1.364}^{0.010}$	${31.25}^{2.46}$	${2.341}^{0.028}$	${0.853}^{0.003}$	${0.364}^{0.007}$	${35.23}^{1.511}$	${1.065}^{0.005}$	${0.349}^{0.027}$	${10.96}^{0.34}$	${0.895}^{0.050}$	44.93/38
X-03-01d	55808.33	${1.035}^{0.035}$	${1.758}^{0.018}$	${0.214}^{0.015}$	${1.536}^{0.011}$	${23.98}^{1.94}$	${2.380}^{0.012}$	${0.870}^{0.011}$	${0.366}^{0.007}$	${39.00}^{2.210}$	${1.057}^{0.005}$	${0.741}^{0.057}$	${9.99}^{0.31}$	⋯	28.58/38
X-03-02c	55810.29	${0.964}^{0.021}$	${1.710}^{0.015}$	${0.206}^{0.018}$	${1.715}^{0.011}$	${34.02}^{1.98}$	${2.395}^{0.004}$	${0.920}^{0.005}$	${0.384}^{0.003}$	${34.19}^{2.470}$	${1.053}^{0.009}$	${0.345}^{0.076}$	${10.87}^{0.37}$	$\cdots$	65.27/41
X-03-03d	55812.57	${0.907}^{0.018}$	${1.825}^{0.019}$	${0.263}^{0.012}$	${1.569}^{0.012}$	${60.71}^{1.66}$	${2.411}^{0.004}$	${0.853}^{0.005}$	${0.354}^{0.003}$	${39.01}^{1.118}$	${1.057}^{0.003}$	${0.542}^{0.087}$	${11.01}^{0.27}$	${1.531}^{0.066}$	53.50/38
Y-01-00c	55813.55	${0.971}^{0.039}$	${1.803}^{0.017}$	${0.179}^{0.014}$	${1.738}^{0.013}$	${280.24}^{17.9}$	${2.421}^{0.017}$	${0.848}^{0.012}$	${0.350}^{0.009}$	${32.51}^{2.510}$	${1.069}^{0.014}$	${0.343}^{0.017}$	${10.82}^{0.38}$	$\cdots$	43.90/41
Y-01-04c	55818.84	${0.713}^{0.021}$	${2.082}^{0.028}$	${0.307}^{0.015}$	${1.209}^{0.015}$	${290.72}^{17.0}$	${2.534}^{0.021}$	${0.617}^{0.003}$	${0.244}^{0.004}$	${47.00}^{2.360}$	${1.053}^{0.013}$	${2.073}^{0.186}$	${10.63}^{0.27}$	⋯	52.75/41
Y-01-05c	55819.20	${0.753}^{0.013}$	${2.062}^{0.015}$	${0.302}^{0.009}$	${1.220}^{0.008}$	${207.75}^{9.50}$	${2.547}^{0.028}$	${0.576}^{0.011}$	${0.226}^{0.007}$	${39.16}^{2.450}$	${1.058}^{0.015}$	${1.514}^{0.187}$	${10.89}^{0.23}$	${4.876}^{0.085}$	50.13/41
Y-02-03c	55820.40	${0.720}^{0.014}$	${2.076}^{0.018}$	${0.306}^{0.009}$	${1.127}^{0.009}$	${279.67}^{9.07}$	${2.537}^{0.014}$	${0.564}^{0.010}$	${0.222}^{0.006}$	${39.95}^{4.890}$	${1.057}^{0.015}$	${1.682}^{0.242}$	${10.89}^{0.23}$	${5.175}^{0.044}$	72.70/41
Y-02-00c	55821.85	${0.890}^{0.016}$	${1.964}^{0.019}$	${0.294}^{0.010}$	${1.164}^{0.009}$	${63.73}^{3.25}$	${2.447}^{0.011}$	${0.667}^{0.009}$	${0.273}^{0.005}$	${38.04}^{2.470}$	${1.057}^{0.016}$	${0.894}^{0.015}$	${10.58}^{0.33}$	${4.238}^{0.215}$	58.69/41
Y-02-01c	55822.83	${0.808}^{0.027}$	${2.014}^{0.027}$	${0.271}^{0.015}$	${1.179}^{0.014}$	${110.9}^{1.80}$	${2.345}^{0.026}$	${0.735}^{0.008}$	${0.313}^{0.007}$	${37.82}^{2.320}$	${1.055}^{0.009}$	${0.799}^{0.159}$	${10.98}^{0.54}$	${4.359}^{0.145}$	73.73/41
Y-02-04d	55823.81	${0.975}^{0.027}$	${1.871}^{0.025}$	${0.265}^{0.011}$	${1.189}^{0.013}$	${37.45}^{2.31}$	${2.341}^{0.024}$	${0.699}^{0.002}$	${0.299}^{0.003}$	${41.02}^{1.971}$	${1.058}^{0.071}$	${0.541}^{0.005}$	${10.91}^{0.15}$	⋯	28.93/38
Y-02-05d	55824.58	${0.895}^{0.032}$	${1.863}^{0.020}$	${0.184}^{0.012}$	${1.315}^{0.012}$	${45.70}^{2.08}$	${2.259}^{0.023}$	${0.791}^{0.004}$	${0.350}^{0.005}$	${31.19}^{1.214}$	${1.064}^{0.014}$	${0.315}^{0.031}$	${10.50}^{0.13}$	⋯	50.77/38
Y-02-02c	55825.94	${1.015}^{0.029}$	${1.769}^{0.019}$	${0.203}^{0.012}$	${1.255}^{0.011}$	${25.11}^{1.90}$	${2.237}^{0.046}$	${0.849}^{0.000}$	${0.380}^{0.008}$	${37.80}^{1.910}$	${1.060}^{0.001}$	${0.504}^{0.033}$	${10.86}^{0.49}$	${3.099}^{0.066}$	67.03/41
Y-02-06c	55826.60	${1.113}^{0.029}$	${1.746}^{0.030}$	${0.208}^{0.013}$	${1.267}^{0.013}$	${14.13}^{0.80}$	${2.157}^{0.028}$	${0.838}^{0.002}$	${0.389}^{0.006}$	${33.52}^{2.350}$	${1.065}^{0.010}$	${0.334}^{0.108}$	${10.78}^{0.11}$	${2.727}^{0.034}$	58.38/41
Y-03-04c	55827.33	${0.943}^{0.025}$	${1.793}^{0.026}$	${0.132}^{0.015}$	${1.261}^{0.014}$	${24.52}^{2.67}$	${2.085}^{0.028}$	${0.857}^{0.010}$	${0.411}^{0.011}$	${34.59}^{1.650}$	${1.060}^{0.008}$	${0.339}^{0.095}$	${11.01}^{0.24}$	${2.672}^{0.012}$	48.70/41
Y-03-01c	55829.80	${1.130}^{0.022}$	${1.725}^{0.024}$	${0.120}^{0.016}$	${1.270}^{0.015}$	${8.32}^{0.72}$	${1.958}^{0.049}$	${0.857}^{0.004}$	${0.438}^{0.013}$	${36.63}^{1.380}$	${1.058}^{0.003}$	${0.330}^{0.086}$	${10.62}^{0.15}$	${2.023}^{0.073}$	46.63/41
Y-03-05c	55830.89	${1.114}^{0.025}$	${1.701}^{0.030}$	${0.099}^{0.021}$	${1.272}^{0.018}$	${7.45}^{0.41}$	${1.902}^{0.036}$	${0.866}^{0.005}$	${0.455}^{0.011}$	${39.09}^{2.540}$	${1.051}^{0.003}$	${0.331}^{0.053}$	${11.00}^{0.41}$	⋯	51.52/41
Y-03-02c	55831.84	${1.128}^{0.026}$	${1.620}^{0.026}$	${0.096}^{0.017}$	${1.225}^{0.029}$	${6.60}^{0.92}$	${1.846}^{0.023}$	${0.869}^{0.006}$	${0.471}^{0.009}$	${39.99}^{1.780}$	${1.054}^{0.006}$	${0.313}^{0.050}$	${9.49}^{0.69}$	⋯	53.16/41
Y-03-03c	55832.81	${1.200}^{0.025}$	${1.629}^{0.020}$	${0.096}^{0.013}$	${1.222}^{0.011}$	${4.89}^{0.31}$	${1.934}^{0.029}$	${0.852}^{0.008}$	${0.441}^{0.011}$	${41.39}^{2.970}$	${1.063}^{0.009}$	${0.321}^{0.110}$	${10.70}^{0.58}$	⋯	34.85/41
Y-04-01c	55835.81	${1.195}^{0.028}$	${1.560}^{0.020}$	${0.076}^{0.012}$	${1.145}^{0.014}$	${3.95}^{0.26}$	${1.964}^{0.014}$	${0.843}^{0.007}$	${0.429}^{0.007}$	${46.34}^{3.280}$	${1.071}^{0.004}$	${0.330}^{0.031}$	${9.34}^{0.88}$	⋯	41.26/41
Y-04-02c	55836.78	${1.287}^{0.021}$	${1.523}^{0.025}$	${0.086}^{0.014}$	${1.101}^{0.013}$	${3.05}^{0.20}$	${1.957}^{0.015}$	${0.841}^{0.009}$	${0.430}^{0.008}$	${46.40}^{4.970}$	${1.073}^{0.009}$	${0.298}^{0.044}$	${9.49}^{0.91}$	${1.636}^{0.092}$	34.95/41
Y-04-04c	55838.83	${1.347}^{0.034}$	${1.488}^{0.038}$	${0.085}^{0.021}$	${1.023}^{0.018}$	${2.42}^{0.19}$	${1.910}^{0.035}$	${0.780}^{0.007}$	${0.408}^{0.011}$	${53.28}^{1.750}$	${1.067}^{0.021}$	${0.332}^{0.025}$	${9.49}^{0.78}$	⋯	36.53/41
Y-04-06c	55840.78	${1.270}^{0.039}$	${1.477}^{0.033}$	${0.080}^{0.016}$	${0.951}^{0.014}$	${3.04}^{0.14}$	${1.812}^{0.039}$	${0.756}^{0.007}$	${0.417}^{0.013}$	${49.84}^{2.120}$	${1.070}^{0.012}$	${0.293}^{0.007}$	${8.00}^{0.77}$	⋯	43.20/41
Y-05-00c	55842.79	${1.420}^{0.038}$	${1.496}^{0.037}$	${0.077}^{0.019}$	${0.860}^{0.019}$	${1.68}^{0.13}$	${1.817}^{0.033}$	${0.716}^{0.011}$	${0.394}^{0.013}$	${50.91}^{2.560}$	${1.070}^{0.015}$	${0.280}^{0.008}$	${8.79}^{0.89}$	${1.449}^{0.074}$	58.38/41
Y-05-01c	55843.76	${1.468}^{0.040}$	${1.487}^{0.033}$	${0.079}^{0.016}$	${0.827}^{0.016}$	${1.46}^{0.12}$	${1.823}^{0.039}$	${0.680}^{0.001}$	${0.373}^{0.009}$	${53.44}^{2.840}$	${1.070}^{0.012}$	${0.280}^{0.057}$	${9.45}^{0.52}$	⋯	44.12/41
Y-05-04c	55844.86	${1.259}^{0.034}$	${1.528}^{0.039}$	${0.055}^{0.018}$	${0.864}^{0.015}$	${2.18}^{0.18}$	${1.827}^{0.022}$	${0.648}^{0.009}$	${0.355}^{0.009}$	${57.40}^{4.230}$	${1.071}^{0.005}$	${0.323}^{0.074}$	${9.45}^{0.67}$	${0.368}^{0.029}$	40.58/41
Y-05-06c	55847.80	${1.237}^{0.038}$	${1.536}^{0.049}$	${0.032}^{0.023}$	${0.762}^{0.016}$	${1.39}^{0.10}$	${1.831}^{0.014}$	${0.663}^{0.006}$	${0.362}^{0.006}$	${61.04}^{2.470}$	${1.070}^{0.009}$	${0.299}^{0.042}$	${8.16}^{0.87}$	⋯	47.60/41
Y-06-02c	55850.87	${1.377}^{0.037}$	${1.504}^{0.046}$	${0.048}^{0.027}$	${0.673}^{0.021}$	${1.22}^{0.08}$	${1.784}^{0.017}$	${0.642}^{0.002}$	${0.360}^{0.004}$	${60.38}^{3.110}$	${1.069}^{0.015}$	${0.269}^{0.074}$	${8.26}^{0.75}$	⋯	35.71/41
Y-07-00	55856.47	${1.194}^{0.035}$	${1.586}^{0.042}$	${0.016}^{0.027}$	${0.541}^{0.014}$	${0.77}^{0.07}$	${1.668}^{0.013}$	${0.566}^{0.004}$	${0.339}^{0.005}$	${75.16}^{1.740}$	${1.069}^{0.008}$	${0.270}^{0.027}$	${7.54}^{0.41}$	⋯	69.54/44
Y-08-00	55862.87	${1.542}^{0.030}$	${1.379}^{0.034}$	${0.053}^{0.023}$	${0.403}^{0.020}$	${0.78}^{0.06}$	${1.665}^{0.015}$	${0.491}^{0.002}$	${0.295}^{0.004}$	${96.45}^{3.450}$	${1.076}^{0.004}$	${0.251}^{0.011}$	${7.51}^{0.64}$	⋯	52.25/44
Y-08-05	55867.08	${1.474}^{0.033}$	${1.395}^{0.031}$	${0.042}^{0.015}$	${0.384}^{0.012}$	${0.76}^{0.04}$	${1.583}^{0.016}$	${0.460}^{0.015}$	${0.291}^{0.013}$	${135.48}^{4.450}$	${1.084}^{0.005}$	${0.251}^{0.016}$	${7.72}^{0.72}$	⋯	51.72/44
Y-09-02	55871.06	${1.649}^{0.032}$	${1.399}^{0.040}$	${0.038}^{0.037}$	${0.318}^{0.026}$	${0.40}^{0.06}$	${1.530}^{0.013}$	${0.457}^{0.012}$	${0.299}^{0.011}$	${162.37}^{7.870}$	${1.084}^{0.012}$	${0.250}^{0.007}$	${7.76}^{0.83}$	⋯	65.29/44
Y-10-01	55877.63	${1.612}^{0.046}$	${1.481}^{0.032}$	${0.020}^{0.024}$	${0.296}^{0.016}$	${0.34}^{0.05}$	${1.486}^{0.018}$	${0.422}^{0.002}$	${0.284}^{0.006}$	${199.24}^{4.510}$	${1.089}^{0.009}$	${0.258}^{0.002}$	${7.57}^{0.65}$	⋯	64.36/44

Notes. Average values of 90% confidence ± values obtained using the "err" task in XSPEC are placed as superscripts of fitted parameter values. X = 96371-03 and Y = 96438-01 are the prefixes of observation Ids. Blank lines mark transitions between different spectral states.

^aDBBf and PLf represent combined DBB and PL model fitted fluxes in the 2.5–25 keV band for the DBB and PL model components, respectively, in units of ${10}^{-9}\;\mathrm{erg}\;{\mathrm{cm}}^{-2}\;{s}^{-1}$. $\dot{{m}_{h}}$ (in Eddington rate unit), $\dot{{m}_{d}}$ (in Eddington rate unit), X_s (in units of Schwarzschild radius), and R are TCAF fitted Keplerian disk, sub-Keplerian halo, shock location and compression ratio values respectively. Norm. and M_BH are TCAF fitted normalization and BH mass values, respectively. ^bFrequencies of the dominating QPO in Hz are mentioned. dof means degrees of freedom of the spectral model fits. The values of ${\chi }^{2}$ and dof of the TCAF model fitted spectra are mentioned in Column 16. The ratio is the ${\chi }_{\mathrm{red}}^{2}$. ^cSpectra are fitted with additional Gaussian lines of energy ∼6.5 keV. ^dSpectra are fitted with an additional LAOR component with the TCAF model. T_in, and Γ values indicate combined DBB and PL model fitted DBB temperatures in keV and PL photon indices, respectively.

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Table 2.  Combined LAOR plus TCAF Spectral Fitted LAOR Parameters

obs. Id	MJD	Line Energy	Index	Rin	Rout	Inclination	LAOR Norm.
		(keV)		(${r}_{g})$	(rg)	(Degree)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
X-03-00	55806.51	${7.14}^{0.08}$	${3.49}^{0.02}$	${3.02}^{0.61}$	${358.154}^{9.97}$	${4.00}^{0.03}$	${0.0042}^{0.0001}$
X-03-01	55808.33	${7.11}^{0.12}$	${3.50}^{0.02}$	${3.04}^{0.57}$	${330.13}^{12.79}$	${4.12}^{0.02}$	${0.0049}^{0.0001}$
X-03-03	55812.57	${7.15}^{0.10}$	${3.47}^{0.02}$	${3.59}^{0.48}$	${378.62}^{14.21}$	${4.10}^{0.04}$	${0.0047}^{0.0002}$
Y-02-04	55823.81	${7.17}^{0.14}$	${3.62}^{0.02}$	${3.33}^{0.51}$	${351.10}^{11.71}$	${4.07}^{0.03}$	${0.0046}^{0.0004}$
Y-02-05	55824.58	${7.04}^{0.18}$	${3.61}^{0.14}$	${3.24}^{0.42}$	${297.32}^{10.33}$	${4.09}^{0.07}$	${0.0054}^{0.0002}$

Note. average values of 90% confidence ± values obtained using the "err" task in XSPEC are placed as superscripts of fitted parameter values. X = 96371-03 and Y = 96438-01 are the prefixes of observation Ids.

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To fit the spectra using the TCAF-based model additive table fits file, one needs to supply five model input parameters such as (i) black hole mass (M_BH) in solar mass (M_⊙) unit, (ii) Keplerian accretion rate ($\dot{{m}_{d}}$ in Eddington rate ${\dot{M}}_{\mathrm{Edd}}$), (iii) sub-Keplerian accretion rate ($\dot{{m}_{h}}$ in ${\dot{M}}_{\mathrm{Edd}}$), (iv) location of the shock (X_s in Schwarzschild radius r_g = $2{{GM}}_{\mathrm{BH}}/{c}^{2}$), and (v) compression ratio (R = ${\rho }_{+}/{\rho }_{-}$, where ρ₊ and ρ₋ are post- and pre-shock densities respectively) of the shock. The model normalization value is a fraction of $\frac{{r}_{g}^{2}}{4\pi {D}^{2}}\mathrm{sin}(i)$, where "D" is the source distance (in 10 kpc unit) and "i" is the disk inclination angle. To fit a black hole spectrum with the TCAF model we create an additive table model fits file (TCAF.fits) using theoretical model spectra that are generated by varying five input parameters in the modified CT95 code. Basically the governing equations are taken from CT95 as far as hydrodynamics and radiative transfer are concerned. However, the shock strength and the equation to get shock height were generalized to capture features with a wider range of accretion rates (see, DCM14 and DMC15). In this paper, for the spectral analysis of MAXI J1836-194 with the TCAF we keep mass a free parameter and find that it comes out to be in the range of 7.5–11 M_⊙.

Our recent study shows that the accretion flow dynamics around a transient BHC can be well understood by the analysis of the spectral and temporal behaviors of the BHC during its outburst under the TCAF model paradigm. Here the spectral analysis results based on the TCAF model are presented. We also compare the DBB model plus the PL model fitted results with that of the TCAF model fitted spectral analysis results. It is to be noted that the combined PL and DBB model fitted spectral analysis only provides gross properties of the accretion disk such as fluxes from different thermal and nonthermal components, whereas the TCAF model goes one step further. The TCAF model extracts detailed physical flow parameters such as two types of accretion rates and the Compton cloud properties. Furthermore, transitions between different spectral states are more conspicuous when described in terms of the fitted parameters as we shall also see in the case of  the present object. Thus, studying accretion dynamics around BHCs with a TCAF solution-based fits file provides certain definite advantages.

To study the timing and spectral properties of MAXI J1836-194 during its current outburst, RXTE/PCA data for 35 observations spread over the entire period of the 2011 outburst are used. We first studied X-ray count rate variation over the entire outburst phase with PCU2 light curves from all observations in the 2–25 keV energy band (see Figure 1(a)). From the nature of this outburst profile we may define the source as belonging to a fast-rise and slow-decay (FRSD) type rather than to a complete outbursting slow-rise and slow-decay (SRSD) type such as GRO J1655-40, GX 339-4, etc. (Debnath et al. 2010). QPOs are found for only 14 observations out of total of 35. For spectral study we initially fitted spectra with the combined PL and DBB model components. The spectral model fitted parameters such as DBB temperature (T_in in keV), PL photon index (Γ), and fluxes from both model components are obtained. All the spectra are then refitted with the current version (v0.3) of our TCAF model fits file in XSPEC to extract the accretion flow parameters such as Keplerian disk rate (${\dot{m}}_{d}$), sub-Keplerian halo rate (${\dot{m}}_{h}$), shock location (X_s), and the compression ratio (R) of the shock.

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3.1. Spectral Analysis with the TCAF Solution and with Combined DBB and PL models

Spectral fit with the conventional DBB plus PL model, which provides us with a rough estimate of the flux contributions coming from both nonthermal (from PL) and thermal (from DBB) processes around a BH. It gives us a rough idea about the evolution of spectral states by monitoring the variations of T_in, Γ factors, and flux contribution from both model components. However, variations of the TCAF fitted/derived parameters (such as two types of accretion rates, ${\dot{m}}_{d}$ and ${\dot{m}}_{h}$; shock parameters, X_s and R; and ARR) provide us with a clear picture of the geometry and the accretion flow dynamics around the BH during the outburst phase. In Table 1 all these spectral fitted/derived parameters are mentioned in a tabular form with estimated errors in superscript. Most importantly, since the entire flow dynamics are determined by these few parameters only we do not need to change the normalization constant from day to day. The uncertainty in normalization merely reflects the uncertainty in mass measurements.

Figures 1–4 show variations of QPO frequencies, X-ray intensities, and spectral (with DBB plus PL model components and the TCAF model) fitted and derived parameters. In Figure 1(a) a variation of the background subtracted PCU2 count rate in the 2–25 keV energy band with the time (day in MJD) is shown. In Figure 1(c) the variation of the TCAF model fitted total accretion rates (${\dot{m}}_{d}$ plus ${\dot{m}}_{h}$) in the energy band of 2.5–25 keV are shown. To compare with the PCU2 rates and with the total accretion rates in Figure 1(b) the total flux variation of the DBB plus PL model fitted spectra of 2.5–25 keV are shown. Here we observe that the variation of the TCAF fitted total flow rate (Figure 1(c)) is different from the count rate or total flux variations in Figures 1(a)–(b), especially in the early stages of the outburst. In Figure 1(d) variation of accretion rate ratio, i.e., ARR (defined as the ratio between the sub-Keplerian halo rate with the Keplerian disk rate, i.e., ${\dot{m}}_{h}$/${\dot{m}}_{d}$) is shown. In Figure 1(e) we show QPO frequencies (only dominating primary) with the day (in MJD). From the variations of these physical flow parameters, QPO frequencies, etc., only two spectral classes such as hard (HS), and hard-intermediate (HIMS) are observed during the entire phase of the current outburst of MAXI J1836-194. Note that softer states such as soft-intermediate (SIMS) and soft state (SS) are absent in contrast to what most of the other outburst sources exhibited (see, e.g., Nandi et al. 2012; Debnath et al. 2013). A similar result of no SS was observed by Debnath et al. (2015a) for another MAXI source, namely MAXI J1659-152 (during its 2010 outburst). The sequence in the present source appears to be HS (rising) $\to$ HIMS (rising) $\to$ HIMS (declining) $\to$ HS (declining).

In Figures 2(a)–(b) the variation of the DBB temperature (T_in in keV) and the power-law photon index (Γ) with the day (MJD) are shown. In Figures 2(c)–(d) the TCAF model fitted shock location (X_s in r_g unit) and compression ratio (R) are plotted with the day (in MJD). In Figures 3(a)–(b) the variations of DBB flux from the DBB plus PL model fits and the TCAF model fitted Keplerian disk rate with the day (MJD) are compared. Similarly in Figures 3(c)–(d) we compare variations of the PL flux with the sub-Keplerian halo rate from these respective models. Clearly one can observe "some" similarities in each pair of these compared quantities, but not totally since the PL flux is a function of the disk rate as well.

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Figure 4 shows plots of (a) hardness intensity diagram and (b) ARR and 2–15 keV PCU2 count rate drawn to find a correlation between temporal and spectral properties of the BHC and judge their behavior vis-a-vis classifications. There is clearly a hysteresis behavior. This will be discussed in detail in Section 3.3. In Figure 5 the TCAF model fitted combined spectra (top panel) and residuals for four spectra of observation Ids: 96371-03-03-01 (MJD = 55808.34, black online), 96438-01-01-04 (MJD = 55818.85, red online), 96438-01-02-04 (MJD = 55823.82, blue online), and 96438-01-06-02 (MJD = 55850.87, orange online) selected from different regions, i.e., states of the outburst are shown. Plots (i) and (iv) are for hard states and plots (ii) and (iii) are for hard-intermediate states of rising and declining phases, respectively. We observe that in plots (i) and (iii) the fits are better with an additional LAOR model described iron line component which appears to be unresolved double lines (Fabian et al. 1989; Stella 1990). In plots (ii) and (iv) we required only a single Gaussian to model the single iron lines.

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To check correlation among spectral fitted parameters, in Figures 6(a)–(d), we make comparative plots of (i) total (DBB plus PL) flux versus total flow rate (${\dot{m}}_{d}$ plus $\dot{{m}_{h}}$), (ii) ARR versus QPO frequency, (iii) $\dot{{m}_{h}}$ versus $\dot{{m}_{d}}$, and (iv) PL photon index Γ versus $\dot{{m}_{h}}$. In Figure 6(a), correlation is expected. In Figure 6(b), no correlation is expected in any obvious sense and the QPOs are related to resonance effects between cooling timescale (a function of $\dot{{m}_{h}}$ and $\dot{{m}_{d}}$) and infall timescale (a function of X_s and R). In Figure 6(c), weak coupling between the two rates ($\dot{{m}_{h}}$ and $\dot{{m}_{d}}$) is due to the fact that at least a fraction of the disk rate is the bi-product of the halo rate mediated by viscosity. In Figure 6(d), a weak coupling of rising of Γ with $\dot{{m}_{h}}$ was expected even from the basic work of CT95 when $\dot{{m}_{d}}$ is almost constant and small. We made statistical analysis using two correlation methods such as Spearman Rank (SR) and Pearson Linear (LP), and found that total fluxes are strongly correlated with total accretion rates (SR coefficient SR_e = 0.964, LP coefficient LP_e = 0.976), no or weak anti-correlation between the ARR and QPO frequency (SR_e = −0.008, LP_e = −0.363), and a weak correlation between two types ($\dot{{m}_{h}}$, and $\dot{{m}_{d}}$) of accretion rates (SR_e = −0.336, LP_e = −0.418), and PL photon index Γ with halo ($\dot{{m}_{h}}$) rate (SR_e = 0.271, LP_e = 0.221). We also find that Γ and the ARR are weakly anti-correlated with each other (SR_e = −0.278, LP_e = −0.404) as expected from the argument given above.

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3.2. Evolution of Spectral and Temporal Properties During the Outburst

3.3. ARR-intensity Diagram (ARRID): A Correlation Between Timing and Spectral Properties

We study the evolution of the spectral and temporal properties of a Galactic transient BHC MAXI J1836-194 during its first (2011) X-ray outburst using RXTE PCU2 data. For spectral evolution study, we use two models (TCAF and DBB plus PL models) applied to a total of 35 observations. A combined PL and DBB model fit provides us with a rough estimate of thermal (DBB) and nonthermal (PL) flux contributions as well as an idea about the disk temperatures (T_in) and PL photon indices (Γ). The TCAF model (v0.3) fit provides us with physical accretion flow parameters such as the Keplerian disk ($\dot{{m}_{d}}$), sub-Keplerian halo ($\dot{{m}_{h}}$) rates, the shock location (X_s), and the shock compression ratio (R; see, Figures 1–3). In Table 1 detailed spectral analysis results with observed QPO frequencies are presented. The variation of these model fitted parameters with the ARR (a ratio between $\dot{{m}_{h}}$ to $\dot{{m}_{d}}$) and properties of QPOs (if observed) provide us with a better understanding of the accretion flow dynamics around the BHC during its outburst.

So far we have successfully studied the accretion flow dynamics of three Galactic BHCs (H 1743-322, GX 339-4, and MAXI J1659-194) during their X-ray outbursts from our spectral study with the TCAF model (see MDC14, DMC15, DMCM15). A strong correlation between spectral and timing properties are found for these sources giving rise to transitions between different spectral states. Generally four (HS, HIMS, SIMS, and SS) spectral states are observed during an outburst of transient BHC in the sequence of HS $\to$ HIMS $\to$ SIMS $\to$ SS $\to$ SIMS $\to$ HIMS $\to$ HS. According to CT95, Ebisawa et al. (1996), an outburst of transient BHCs is triggered due to a sudden rise in viscosity at the outer edge of the disk and the declining phase begins when the viscosity is turned off at the outer edge (CT95; Ebisawa et al. 1996). If the viscosity does not rise above a critical value (Chakrabarti 1990), the Keplerian component does not form and as a result we may miss soft states (SS) altogether during an outburst (DMCM15). The resulting event could be termed a "failed" outburst.

The QPOs (generally type "C") are found to evolve monotonically in rising/declining hard and hard-intermediate spectral states (Chakrabarti et al. 2005, 2008; Debnath et al. 2010, 2013; Nandi et al. 2012). We also observed a local maximum of the ARR on the transition day of HS $\rightleftharpoons$ HIMS and of evolving QPO frequency on HIMS $\rightleftharpoons$ SIMS transition day (MDC14, DMC15, DMCM15). QPOs are observed sporadically on and off during SIMS and are absent in SS (Debnath et al. 2008, 2013; Nandi et al. 2012). During the rising hard state, the ARR is found to increase monotonically with a rise in the halo rate and reaches its maximum on the HS-HIMS transition day and the shock is found to move in gradually weakening it strength. In rising HIMS the shock further moves in rapidly due to shrinking of the CENBOL size. This may be due to the rapid rise in the thermally cooler Keplerian disk rate, which reaches its maximum on the HIMS-SIMS transition day. Also, on the transition day the shock compression ratio (R) becomes approximately unity. During this process the ARR rapidly reduces to a lower value on the transition day. During rising SIMS, the ARR is observed at a lower value with very little variation and generally type B or A QPOs are observed sporadically. The origin of these QPOs is assumed to be different and may be due to non-satisfaction of the Rankine–Hugoniot condition to form a stable shock location (Ryu et al. 1997; Chakrabarti et al. 2015). A strong jet may be found during this phase of the outburst that may be due to the cooling down of the base of the CENBOL with a sudden rise in the Keplerian matter contributions. The cooling reduces sound speed, making the upper part of the jet become supersonic quite abruptly. In the soft state the ARR reduces further with a clear dominance of the Keplerian component. In the declining SIMS the contribution of the Keplerian component starts to decrease and sporadic appearances of QPOs are seen. The ARR varies in a similar way as rising SIMS. On the declining SIMS-HIMS transition day the maximum value of the QPO frequency could be found. In the process, during the declining HIMS the ARR rises rapidly and reaches its maximum value on the HIMS-HS transition day. QPO frequencies are observed to decrease continuously in a rapid manner with an outward movement of shock and a rise in compression ratios. In the declining hard state, both ARR and QPO frequency decrease with time with a rapid outward movement of shock. At the same time a decrease in both components of accretion rates could be observed.

The present analysis of the outburst data reveals a great deal of surprises. Depending on the nature of the variation of the TCAF model fitted or derived parameters ($\dot{{m}_{d}},$ $\dot{{m}_{h}},$ ARR, X_s, R, etc.) and nature the of QPOs (if present), only two spectral classes, namely, hard (HS), and hard-intermediate (HIMS), are observed during the entire phase of the current outburst of MAXI J1836-194. These spectral states are observed in the sequence of HS (rising) $\to$ HIMS (rising) $\to$ HIMS (declining) $\to$ HS (declining). The so-called "q"-diagram does not show a "q" shape at all (see Figure 4(a)). In the ARRID diagram (Figure 4(b)) the evolution of the 2–25 keV PCU2 count rate with the ARR, which hints at a hysteresis behavior, strongly justifies our spectral classification. Different branches of the plot appear to be related to different spectral states. We clearly see that the ARR has a local maximum on transition days of HS $\rightleftharpoons$ HIMS. This plot provides us with a better understanding of the strong correlation between spectral and temporal properties. In MDC14 a similar type of correlation between different spectral states was also found for Galactic BHC H 1743-322 during its 2010 outburst.

A peculiarity of this outburst of MAXI J1836-194 is that QPOs are not seen every day although there is a general trend similar to other outbursts: increasing frequency during the rising phase and decreasing frequency in the declining phase of the outburst. Also, we have not found any signature of the soft and soft-intermediate spectral states. The source started and ended from/to hard spectral states via two hard-intermediate spectral states during the entire phase of the outburst. Furthermore, the spectral indices in few observation of hard states are very low (i.e., spectra are super-hard). The unusual behavior of the source during this outburst may be due to a shorter orbital period of the binary system which makes the disk very small in size and it is possibly immersed in the wind or the excretion disk of the companion; this would be the case if the companion is a Be Star, for instance (Cenko et al. 2011). During most of this outburst the source was covered with low angular momentum matter which is not necessarily a part of the accretion disk. The non-observation of QPOs on a regular basis is also explained since resonance conditions for QPOs would be difficult to fulfill in the presence of such extraneous matter (see Molteni et al. 1996; Chakrabarti et al. 2015; Mondal et al. 2015) which is not included in the TCAF solution.

For a detailed analysis of  the TCAF extracted parameters, one may be able to estimate the viscous timescale using time differences between peaks of the Keplerian disk and sub-Keplerian halo component rates during rising or declining phases of an outburst of a transient BHC. MAXI J1836-194 shows double humps for both of the accretion rates during the entire phase of the current outburst. During the rising phase the halo rate attains its maximum value on  MJD = 55810, whereas the disk rate attains its peak after ∼10 days when the halo reaches its first minimum. Again, during the declining phase the halo rate starts to increase and attains its second peak on MJD = 55826. At the same time the disk rate attains its second peak on MJD = 55836, which is coincidentally exactly after ∼10 day interval. The observed time gaps between the peaks of $\dot{{m}_{h}}$ and $\dot{{m}_{d}}$ in both the rising and declining phases suggests that the viscous timescale of MAXI J1836-194 during 2011 outburst could be around of ∼10 days.

Recently, Shaposhnikov & Titarchuk (2009) have found that the scaling method of the PL photon Index (Γ) versus the QPO frequency diagram is a powerful tool to predict the mass of an unknown BHC. For that one needs a sufficient number of observations, especially at the bending and horizontal saturation branches of the diagram. This method is not useful to predict the mass of the current BHC MAXI J1836-192 since there are only two observations of QPOs (4.35 and 5.17 Hz) at the saturation level and no QPOs in the region where the slope turns into the saturation level for higher frequencies and indices. So we obtain the mass of the unknown BH from our TCAF fits.

To further emphasize the advantage of the TCAF fits, we wish to emphasize that the model normalization is the normalization of the whole spectrum and that it arises out of the difference between the calculated spectrum at the disk frame and the observer's frame which includes the idiosyncrasies of the instruments. Once the spectrum is calculated using certain inner edges and other parameters there is no way that a normalization constant should contain the disk parameters anymore. Strangely, our precision fitting with the TCAF model does not require one to vary the normalization constant as in other models. This is because the TCAF solution normalization depends on the source distance (D) and the disk inclination angle (i) for a given mass of the black hole all intrinsic properties of the disk (such as the inner edge of the disk) which are used inside normalization in other models are all used up to obtain the spectrum itself. Indeed, we get excellent fits keeping the normalization constant within a narrow range as it should be for the current source MAXI J1836-194 and the source MAXI J1659-152 during its 2010 outburst (Molla et al. 2016). On the other hand, the normalization required for diskbb varies from day to day. These are given in Table 1. This nonconstancy has been variously explained by the change of the inner edge of the disk, which we find intriguing since the truncated disk information should have already been used to fit the data in the first place. Our model normalization is found to vary in a narrow range of 0.25–0.35, (DBB model normalization shows wild variation in the range of 0.34–291) except for five observations around the transition day between two HIMS when a prominent jet is observed (see, Russell et al. 2013). The deviation of the normalization in these days reflects the non-inclusion of a contribution from the jet in the current version (v0.3) of the TCAF model fits file. During the spectral fitting, as we kept mass of the BH as a free parameter, the M_BH is found in the range of 7.5–11 M_⊙. The detailed method of the prediction of the BH mass from the TCAF fitting are discussed in Molla et al. (2016).

In the future, we will make a detailed spectral and temporal study of other similar short orbital period BHCs (for 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 the flow dynamics of these sources also follow a similar trend.

A.J. and D.D. acknowledge support from the ISRO-sponsored RESPOND project fund (ISRO/RES/2/388/2014-15). D.D. also acknowledges support from the DST-sponsored Fast-track Young Scientist project fund (SR/FTP/PS-188/2012). A.A.M. and S.M. acknowledge the support of the MoES-sponsored junior research fellowship and postdoctoral fellowship respectively.