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A detailed study on the reflection component for the black hole candidate MAXI J1836−194

01 Apr 2020-Monthly Notices of the Royal Astronomical Society (Oxford Academic)-Vol. 493, Iss: 2, pp 2178-2187

AbstractWe present a detailed spectral analysis of the black hole candidate MAXI J1836−194. The source was caught in the intermediate state during its 2011 outburst by Suzaku and RXTE. We jointly fit the X-ray data from these two missions using the relxill model to study the reflection component, and a steep inner emissivity profile indicating a compact corona as the primary source is required in order to achieve a good fit. In addition, a reflection model with a lamp-post configuration (relxilllp), which is normally invoked to explain the steep emissivity profile, gives a worse fit and is excluded at 99 per cent confidence level compared to relxill. We also explore the effect of the ionization gradient on the emissivity profile by fitting the data with two relativistic reflection components, and it is found that the inner emissivity flattens. These results may indicate that the ionization state of the disc is not constant. All the models above require a supersolar iron abundance higher than ∼4.5. However, we find that the high-density version of reflionx can describe the same spectra even with solar iron abundance well. A moderate rotating black hole (a* = 0.84–0.94) is consistently obtained by our models, which is in agreement with previously reported values.

Topics: Emissivity (56%), Rotating black hole (53%), Reflection (physics) (50%)

Summary (2 min read)

Introduction

  • Key words: accretion, accretion discs – black hole physics – relativistic processes – X-rays: individual: MAXI J1836−194.
  • In addition, the disc ionization state can also affect the profile of the reflection emissivity, but it has not been discussed substantially in the previous studies.

2 DATA SE L E C T I O N A N D R E D U C T I O N

  • The authors searched the HEASARC data archive, and found one Suzaku and 74 RXTE observations in total.
  • For XIS, before extracting spectral products, the authors used the correction tools3 described in Yamada et al. (2012) to correct the mean position shift of the source, and to estimate the level of pile-up for XIS0 and XIS3.
  • Then, the authors used XISRMFGEN and XISARFGEN to generate the new ancillary response files and redistribution matrix files for both XIS0 and XIS3, respectively.

3 SPECTRAL A NA LY SI S AND RESULTS

  • The fitted value for the parameters in Model 2 are listed here.
  • It is suggested that the constant ionization in current models may lead to a steep emissivity index.

4 D ISCUSSION

  • The authors analysed the broad-band X-ray data of MAXI J1836−194 in the intermediate state, using the simultaneously observed X-ray data from Suzaku and RXTE.
  • The unabsorbed Eddington ratio is approximately 11 per cent in which the accretion disc is geometrically thin and optically thick, suggesting that the inner edge of the disc has already reached the ISCO radius.
  • As can be seen from Fig. 3, all the four models can fit the data well, giving acceptable fits.
  • The fact that the index of the powerlaw component is ∼2, together with the disc fraction of 26 per cent, implies that the source is in the intermediate state.
  • For Model 3, this may be due to the more contribution from thermal emission, while for Model 4, it is led by the more contribution from the reflection (see Fig. 2) at soft X-ray band.

4.1 Steep inner emissivity index

  • The authors showed the contour plot for the spin and the emissivity index for Model 1 in the right-hand panel in Fig.
  • The steep inner index may be explained with a compact corona close to the black hole.
  • The steep emissivity profile might be caused by the simple assumption of a constant ionization along the radius in the reflection model.
  • The total reflection is stronger than that in other models.

4.2 High iron abundance

  • Model 1 and Model 3 require an extremely supersolar iron abundance.
  • The authors showed the contour plot for the spin and the iron abundance for Model 1 in the left-hand panel in Fig.
  • Moreover, it provides the best fit among their four models.
  • The authors noticed that the ionization state decreases, which follows its relationship with density (see the formula in Section 1).

4.3 Spin constraints

  • The authors thank the valuable discussions with Dr. Erlin Qiao.
  • This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Centre , which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.

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MNRAS 493, 2178–2187 (2020) doi:10.1093/mnras/staa401
Advance Access publication 2020 February 12
A detailed study on the reflection component for the black hole candidate
MAXI J1836194
Yanting Dong,
1,2
Javier A. Garc
´
ıa,
3,4
Zhu Liu ,
1
Xueshan Zhao,
1,2
Xueying Zheng
1,2
andLijunGou
1,2
1
The National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
2
University of Chinese Academy of Sciences, No.19(A) Yuquan Road, Shijingshan District, Beijing 100049, China
3
Cahill Centre for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
4
Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Sternwartstr 7, D-96049 Bamberg, Germany
Accepted 2020 February 6. Received 2020 February 6; in original form 2019 December 15
ABSTRACT
We present a detailed spectral analysis of the black hole candidate MAXI J1836194. The
source was caught in the intermediate state during its 2011 outburst by Suzaku and RXTE.
We jointly fit the X-ray data from these two missions using the relxill model to study
the reflection component, and a steep inner emissivity profile indicating a compact corona
as the primary source is required in order to achieve a good fit. In addition, a reflection
model with a lamp-post configuration (relxilllp), which is normally invoked to explain
the steep emissivity profile, gives a worse fit and is excluded at 99 per cent confidence level
compared to relxill. We also explore the effect of the ionization gradient on the emissivity
profile by fitting the data with two relativistic reflection components, and it is found that the
inner emissivity flattens. These results may indicate that the ionization state of the disc is
not constant. All the models above require a supersolar iron abundance higher than 4.5.
However, we find that the high-density version of reflionx can describe the same spectra
even with solar iron abundance well. A moderate rotating black hole (a
= 0.84–0.94) is
consistently obtained by our models, which is in agreement with previously reported values.
Key words: accretion, accretion discs black hole physics relativistic processes X-rays:
individual: MAXI J1836194.
1 INTRODUCTION
Galactic X-ray binaries are believed to be powered by accretion
on to stellar-mass black holes or neutron stars. The gases in
accretion disc emit thermal radiation in UV/X-ray band (Shakura &
Sunyaev 1973). Some fraction of the thermal photons from the
disc are then inverse Compton scattered by energetic electrons in
the hypothetically hot corona, producing a hard X-ray spectrum in
the form of power law, i.e. N (E) E
. A fraction of the high-
energy photons will irradiate the cold accretion disc, generating
the so-called X-ray reflection component (Fabian et al. 1989). The
main features of the reflection spectrum are the fluorescent Fe K α
emission line at energies of 6.4–6.97 keV (depend on the ionization
state of the disc) and the Compton hump at 20–30 keV (Young,
Ross & Fabian 1999).
The profile of the reflection spectrum will be smeared due to
the effects of Doppler shift, special relativity, and general relativity
if it comes from the inner region of the accretion disc (Fabian
E-mail: ytdong@nao.cas.cn (YD); lgou@nao.cas.cn (LG)
et al. 2000). Observationally, the most prominent effect is that
the intrinsically narrow Fe K α line is broadened and skewed to
an asymmetric shape. The profile of the broad line, especially
the red wing of the line, is directly linked to the inner radius of
the accretion disc which is thought to be at the innermost stable
circular orbit (ISCO), i.e. R
in
= R
ISCO
. Thus, by modelling the
broad iron line, we can deduce the spin of the black hole based
on the relation between the spin and the ISCO (Bardeen, Press &
Teukolsky 1972). However, the line profile is readily affected by
the subtraction of continuum and other components. Therefore,
Reynolds (2014) pointed out that a more accurate measurement of
the spin can be achieved by modelling the full reflection spectrum.
The spin is one of the two key parameters to make a full description
of a black hole. So far, we have measured dozens of stellar-mass
black hole spins via X-ray reflection fitting method (Brenneman &
Reynolds 2006; Brenneman et al. 2011; Lohfink et al. 2012; Miller
et al. 2013; Walton et al. 2013, 2019;Garc
´
ıa et al. 2015; Walton
et al. 2016;Wangetal.2017; Garc
´
ıa et al. 2018b; Tomsick et al.
2018;Xuetal.2018;Tripathietal.2019).
The geometry of the corona, which is still unclear, will affect the
profile of the reflection spectrum. Particularly, it has a significant
C
2020 The Author(s)
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Reflection study of MAXI J1836194 2179
Tab le 1 . Details of the observations.
Mission Instrument ObsID MJD Start time End time Exp. Count rate
a
(in 2011) (in 2011) (s) (cts s
1
)
Suzaku XIS 906003010 55818.43 Sep 14, 10:12:23 Sep 15, 10:50:14 19440 113.7
PIN 35463 1.3
RXTE PCA 96438010104 55818.84 Sep 14, 20:12:00 Sep 14, 20:31:44 1024 100.7
PCA 96438010105 55819.16 Sep 15, 03:56:32 Sep 15, 05:52:48 4240 102.1
a
Count rate is measured in 1.2–10.0, 15.0–50.0, and 3.0–25.0 keV for XIS, PIN, and PCA, respectively.
impact on the emissivity profile of the reflection spectrum. The
reflection emissivity profile is described by (r) r
q
,whereq is
the emissivity index. It is normally assumed to be a broken power
law with q = q
in
, r = R
br
,andq = q
out
,whereR
br
, q
in
,andq
out
are the
break radius, the emissivity index in the inner region, and in the outer
region, respectively. In most cases, the break radius is usually hard
to be constrained, and the emissivity index was only assumed to be a
single value fixed at 3 (Novikov & Thorne 1973; Shakura & Sunyaev
1973; Reynolds & Begelman 1997) due to limited photon statistics.
Of course, a good constraint on the break radius and emissivity
index is also obtained for a number of systems [both active galactic
nuclei (AGNs) and binary systems], showing a steep inner index
(q
in
> 3) and small break radius (R
br
< 6R
g
1
), such as 1H0419-577
(Jiang et al. 2019), 1H0707-495 (Fabian & Wilkins 2011; Fabian
et al. 2012), IRAS 13224-3809 (Fabian et al. 2018), and Mrk 335
(Fabian et al. 2014; Wilkins & Gallo 2015), as well as for black
hole binaries, such as XTE J1752223 (Garc
´
ıa et al. 2018b), Cyg
X-1 (Wilkins et al. 2012), GRS 1915105 (Miller et al. 2013), and
MAXI J1535571 (Xu et al. 2018). The steep emissivity profile is
usually explained with an extremely compact corona locating close
to the black hole, in which case a large fraction of the power-law
emission will be focused towards the inner region as a result of light-
bending effect (Miniutti & Fabian 2004;Dauseretal.2013). The
X-ray reflection emission profile has been successfully reproduced
by lamp-post model (Duro et al. 2016;Garc
´
ıa et al. 2018b).
In addition, the disc ionization state can also affect the profile of
the reflection emissivity, but it has not been discussed substantially
in the previous studies. The ionization state of the disc at radius
r is defined as ξ (r) = 4πF
X
(r)/n
e
(r), where F
X
is the flux of the
irradiation and n
e
(r) is the electron density of the disc at radius r
(Fabian et al. 2000). As illustrated in Svoboda et al. (2012, see their
fig. 3), the strong radius dependence of F
X
will naturally lead to
the radial decrease of the disc ionization for any reasonable density
profile of the disc. However, the ionization is always assumed to be
constant in current reflection models. The simulations by Svoboda
et al. (2012) and Kammoun et al. (2019) indicated that the ignorance
of the ionization gradient will lead to an increase in the emissivity
index.
In this work, we made a detailed study on the reflection spectrum
of the stellar-mass black hole candidate MAXI J1836194. The
source was discovered as an X-ray transient by the MAXI/GSC (Ne-
goro et al. 2011)andSwift/XRT (Kennea et al. 2011) on 2011 August
30. The coordinate of MAXI J1836194 provided by Swift/XRT
is RA/Dec. (J2000) = 278.93097/-19.32004. It was identified as a
black hole candidate by studying its multiband properties (Miller-
Jones et al. 2011; Nakahira et al. 2011; Rau, Greiner & Sudilovsky
2011; Strohmayer & Smith 2011). MAXI J1836194 was active
1
R
g
is the gravitational radius and is defined to be R
g
= GM/c
2
,whereG is
the gravitational constant, M is the mass of the black hole, and c is the speed
of light.
for about three months. However, it did not enter a soft state which
suggested that this source experienced a failed outburst. L
´
opez et al.
(2019) inferred its companion as an M2 main-sequence star or later
based on its near-infrared and optical properties. Low-frequency
quasi-periodic oscillations are detected with Rossi X-ray Timing
Explorer (RXTE) during the outburst (Jana et al. 2016).
MAXI J1836194 was reported to have a spin parameter of
a
= 0.88 ± 0.03 at 90 per cent confidence level by Reis et al.
(2012), using one Suzaku spectrum during the intermediate state
from its 2011 outburst. A relativistically broadened iron line was
clearly shown. Reis et al. (2012) used a relativistic blurring model
relconv to convolve with the reflection model refbhb (Ross &
Fabian 2007), in which the thermal emission of the disc and the
reflection emission are included in a self-consistent way. They
reported a steep broken power-law emissivity profile with q
in
>
7.3, q
out
= 3.19
+0.07
0.05
,andR
br
= 3.6
+0.2
0.1
R
g
.
In this paper, we re-analysed this Suzaku observation along
with two simultaneous spectra taken by RXTE. A much more
sophisticated reflection model, namely relxill (Dauser et al.
2014;Garc
´
ıa et al. 2014), is used. The model relxill is the
combination of the ionized reflection produced by xillver
(Garc
´
ıa & Kallman 2010;Garc
´
ıa, Kallman & Mushotzky 2011;
Garc
´
ıa et al. 2013) and relativistic broadening based on relline
(Dauser et al. 2010, 2013). The remarkable characteristic of this
model is that the reflected flux can be calculated for each point on
the disc, of which the light-bending effect is also taken into account.
We explore the steep power-law index using the configurations with
lamp-post and the ionization gradient, respectively, and also explore
the effect of disc density on reflection spectrum.
The paper is organized as follows. We describe the observation
and data reduction in Section 2, including both Suzaku and RXTE
data. We present the detailed spectral analysis and results in
Section 3. We make discussions and conclusions in Sections 4 and
5, respectively.
2 DATA SELECTION AND REDUCTION
We searched the HEASARC data archive, and found one Suzaku
and 74 RXTE observations in total. The Suzaku observation was
carried out on 2011 September 14 (MJD 55818.43). The RXTE
observations started on 2011 August 31 (MJD 55804.46) and ended
on November 30 (MJD 55895.93). Ferrigno et al. (2012) and Jana
et al. (2016) systematically studied MAXI J1836194 using RXTE
observations. In our work, only two RXTE observations (MJD
55818.84 and MJD 55819.16), which were simultaneously observed
with Suzaku, were selected. The two spectra are in the intermediate
state with the similar flux. Their hardness ratios, defined as the count
rate at the energy band of 8.6–18 keV to that at 5–8.6 keV, were
calculated to be 0.65 (Garc
´
ıa et al. 2015). We listed the information
including the ObsID, the start time, the end time, the exposure time,
and the count rate of adopted observations in Table 1.
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2180 Y. Dong et al.
2.1 Suzaku observation
There is one X-ray Imaging Spectrometer (XIS, Koyama et al.
2007) and one Hard X-ray detector (HXD, Takahashi et al. 2007)
onboard Suzaku. The XIS consists of four CCDs. Since one of
them, XIS2, had broken down in 2006 November, the remaining
three, namely XIS0, XIS1, and XIS3, were operated in the ‘0.5s
burst mode’. The window size and editing mode were 1/4 window
and 3 × 3/5 × 5, respectively. The HXD consisting of Si PIN photo-
diodes and GSO scintillation counters was operated in the ‘normal’
mode. The observation was performed at XIS nominal position.
Following Reis et al. (2012), we only analysed the XIS0, XIS3, and
PIN data. The archival data have been reprocessed and rescreened
using the Suzaku pipeline (version 3.0.22.44) with the calibration
data base hxd20110913, xis20160607, and xrt20110630. The latest
calibration products of XIS on 2018 August 23 only improved the
redistribution matrices around the Si-K edge which will be ignored
in our analysis. We generated the cleaned event files with
HEASOFT
version 6.19 following the Suzaku data analysis guide.
2
For XIS, before extracting spectral products, we used the correc-
tion tools
3
described in Yamada et al. (2012) to correct the mean
position shift of the source, and to estimate the level of pile-up for
XIS0 and XIS3. New attitude files were generated and were used
as input for
XISCOORD to create new cleaned event files. Unlike the
pile-up estimation in Reis et al. (2012) in which they reported a
maximum pile-up fraction of 2 per cent using the script PILE
EST
4
(Davis 2001), we evaluated that the pile-up fraction of the source
is larger than 3 per cent within the circle with a radius of 22.8 pixel
(1 per cent at 58.7 pixel) from the source centre for XIS0 and larger
than 3 per cent within the circle with a radius of 26.0 pixel (1 per cent
at 60.6 pixel) for XIS3, respectively. The pile-up correction tool also
created relevant region files. Yamada et al. (2012) recommended
using the X-ray events from the region outside the radius with pile-
up fraction of 3 per cent or 1 per cent for spectral analysis. Here, we
extracted spectra from an annular region that excluded events with
pile-up fraction higher than 3 per cent.
The background spectra were extracted from a circular region
with a radius of 100 arcsec, which is away from the source but still
on the same chip. Then, we used
XISRMFGEN and XISARFGEN to
generate the new ancillary response files and redistribution matrix
files for both XIS0 and XIS3, respectively. Finally, in order to
increase the signal-to-noise ratio (S/N), we combined their spectra,
backgrounds, and response files. We added systematic errors of
1 per cent to the spectrum to take into account the calibration
uncertainties.
For HXD, the spectrum (12–70 keV) observed by PIN diodes is
used, while the spectrum (40–600 keV) detected by GSO scintilla-
tors is abandoned due to the low S/N. We obtained the appropriate
response file (ae
hxd pinxinome11 20110601.rsp) and the non-X-
ray background (NXB) file from the HXD team (Fukazawa et al.
2009). We extracted the background spectrum based on the NXB
file and the total spectrum based on the cleaned events from the
same good-time intervals. The 7 per cent dead time of the observed
spectrum was corrected. The contribution from the cosmic X-
ray background (CXB), which contributes 5 per cent of the PIN
background, was estimated by simulation with ‘fakeit’ command
in
XSPEC, in which the model Boldt (1987) and the ‘flat’ response
2
https://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/
3
http://www-x.phys.se.tmu.ac.jp/syamada/ana/suzaku
4
https://space.mit.edu/ASC/software/suzaku/pest.html
(ae hxd pinflate11 20110601.rsp) were used. Furthermore, the nor-
malization of the model was adjusted so that the contribution from
CXB is 5 per cent. Then, the NXB and CXB were added together
to obtain the total background spectrum.
For XIS data, due to the calibration issues below 1.0 keV, we
only use the data in the 1.2–10.0 keV energy range. The 1.6–2.0
and 2.2–2.4 keV energy ranges are also excluded due to the Si K
and the Au M edge at 1.8 and 2.2 keV, respectively. For HXD
PIN data, we restrict its energy range between 15.0 and 50.0 keV.
When both spectra are simultaneously fitted, a normalization factor
of 1.16 is adopted as advised in the Suzaku data analysis guide.
2.2 RXTE observations
The standard RXTE products (the source, background, and response
files) which were reduced from observations MJD 55818.84 and
MJD 55819.16, were downloaded from the HEASARC data archive.
The PCA spectra are used, while the HEXTE data are discarded
due to the low S/N. The PCA were extracted from PCU2, the best-
calibrated detector. As a tradition, we added 0.6 per cent systematic
uncertainties and rebinned the spectra with at least 25 photons within
each bin. Following the spectral analysis of PCA spectra, we restrict
our analysis in the energy range of 3.0–25.0 keV (Miller et al. 2009).
3 SPECTRAL ANALYSIS AND RESULTS
All spectra were analysed using
XSPEC version 12.9.0g (Arnaud
1996). In order to model the Galactic absorption, we used the
TBabs (Wilms, Allen & McCray 2000) model. The solar abun-
dances from Wilms et al. (2000) and the photoelectric cross-sections
from Verner et al. (1996) were adopted. We fixed the column density
to 0.2 × 10
22
cm
2
(Kennea et al. 2011), which was given by fitting
the Swift/XRT observation. All uncertainties calculated for specified
parameters in this paper are at 90 per cent confidence level (χ
2
=
2.71), unless noted particularly.
3.1 Preliminary Suzaku spectral analysis
We performed preliminary spectral fits to Suzaku spectrum with a
model consisting of a power-law component (powerlaw)anda
multitemperature blackbody (diskbb, Mitsuda et al. 1984), in
specific, TBabs(diskbb+powerlaw). The 4–7 keV energy
band were excluded to avoid the contribution from the potential
broad Fe K α line. The best-fitting model as well as the ratio of the
model to data are shown in Fig. 1.ItisclearfromFig.1 that the
model does not fit the data well with χ
2
ν
= 1.444 (2924.13/2025). A
skewed broad iron line profile, iron absorption edge, and a Compton
hump are shown in the residues which could be the signature of the
disc reflection.
The best-fitting photon index of powerlaw is 2.22 ± 0.01 and
the temperature of diskbb is 0.439 ± 0.002 keV. The total 2.0–
20.0 keV unabsorbed flux is 1.8 × 10
9
erg cm
2
s
1
, 22 per cent
of which is attributed to the thermal emission. Reis et al. (2012)
reported a photon index of 2, which is slightly smaller than our
result. The fraction of the thermal emission in the total unabsorbed
flux (1.5 × 10
9
erg cm
2
s
1
) estimated in their paper is
26 per cent. Our steeper power law and higher flux may be attributed
to the pile-up correction process. Given a distance of 10 kpc and a
mass of 8 M
(Russell et al. 2014b), we calculated the Eddington
ratio L/L
Edd
to be 11 per cent, suggesting a geometrically thin and
optically thick accretion disc (McClintock et al. 2006). Thus, it is
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Reflection study of MAXI J1836194 2181
Figure 1. Unfolded Suzaku spectra fitted by ignoring the 4–7 keV energy
band, but including when plotted. In the top panel, the total, diskbb,and
powerlaw components are black, red, and green dotted lines, respectively.
In the bottom panel, the curvature in the data-to-model ratio plot shows the
clear signature of the disc reflection.
reasonable to assume that the inner radius of the disc is at the ISCO
(R
in
= R
ISCO
).
We also tried two other models, cutoffpl and nth-
Comp (Zdziarski, Johnson & Magdziarz 1996;
˙
Zycki, Done &
Smith 1999), to fit the data. The model cutoffpl is a phe-
nomenological power-law model with e-fold at high energies.
The model nthComp is a physically motivated thermal Comp-
tonization model in which the thermal seed photons from the
disc gain energies by interacting with electrons in the high-
temperature corona. The laor (Laor 1991)andsmedge (Ebi-
sawa et al. 1994) models were added to account for the reflec-
tion feature found in the ratio plot (Fig. 1). These two models
are TBabs
smedge(diskbb+cutoffpl+laor) (hereafter
M
off
)andTBabs
smedge(diskbb+nthComp+laor) (here-
after M
nth
), respectively. The central energy of the broad iron line
was constrained between 6.40 and 6.97 keV for the laor model,
including all the possible ionization states of iron. The edge could
change from 7.0 to 9.0 keV and the smearing width was fixed at
7keVforthesmedge model.
The M
off
and M
nth
can fit the data equally well with reduced
chi-square of 1.062 and 1.065 for the same degrees of freedom,
respectively. The best-fitting thermal temperature, normalization,
and photon index of the two models are in agreement with each
other, with kT
disc
= 0.433 ± 0.002 keV, N
disc
= 5842
+96
77
,and
= 2.156 ± 0.008 in M
off
,andkT
disc
= 0.433 ± 0.002 keV,
N
disc
= 5842
+109
104
,and = 2.150 ± 0.016 in M
nth
.Inbothcases,
the high-energy cut-off parameters are not constrained and only
upper limits (300 keV) can be given. An inner radius smaller than
2.9 R
g
in the laor model indicates that the reflection emission
arises from the innermost region around a rapidly rotating black
hole. Moreover, the normalization of the diskbb model could also
provide a measurement of the inner radius of the accretion disc
(R
in
= D
10kpc
[N
disc
/cos(i)]
1/2
,whereD
10kpc
is the source distance in
unit of 10 kpc). With the inclination angle of 4–15 deg (Russell et al.
2014a) and the source distance of 4–10 kpc (Russell et al. 2014b),
our fits (N
disc
= 5842
+109
104
) indicate that the inner disc extends to
2.58–6.44 R
g
, which is in agreement with the value obtained by
laor model.
3.2 Relativistic reflection models for Suzaku and RXTE spectra
In order to measure the spin of the black hole in MAXI J1836194,
we replaced the laor, smedge, and power-law models with the
relxill model to fit the reflection emission and the power-law
continuum. In addition, to better constrain the reflection component,
we extended the energy band to 15 keV by fitting the Suzaku and
RXTE simultaneously.
A multiplicative constant is included to account for the dif-
ferences in the flux calibration between the RXTE/PCA and the
Suzaku/XIS. The inclination angle i was bounded between 4 and
15 deg based on the optical measurements (Russell et al. 2014a).
The power-law continuum is described with the exponential cut-
off power-law. The inner radius R
in
is equal to R
ISCO
. The outer
radius R
out
is fixed at its default value: R
out
= 400 R
g
. We noted
that, as demonstrated in Section 3.1, changing it to a thermal
Comptonization model will not affect our results. The high-energy
cut-off E
cut
is equal to (2–3)kT
e
,inwhichkT
e
is the electron
temperature of the corona. E
cut
is fixed at its default value of
300 keV.
The power-law continuum was assumed to come from an ex-
tended corona (Model 1). A broken power-law emissivity profile
was adopted. The outer index was fixed at its canonical value (q
out
=
3), while the inner index q
in
and the break radius R
br
were set free.
This model gives a much better fit with χ
2
ν
= 1.002 (2118.76/2115),
compared to the initial fit with TBabs(diskbb+powerlaw) in
Section 3.1. The best-fitting results for each parameter can be found
in Table 2. The best-fitting model is shown in the top left panel in
Fig. 2. The residuals with 1σ of the best-fitting are shown in the top
two panels in Fig. 3.
The temperature and the normalization of the thermal emission
are 0.436
+0.003
0.002
keV and 5660
+129
168
, respectively. The photon index is
2.11
+0.02
0.01
. The inner index of the emissivity profile is 6.42
+1.10
1.83
and
the break radius is 4.45
+0.72
0.64
R
g
, implying that the corona is compact
and the flux of the reflected emission decreases dramatically within
the break radius. The best-fitting spin parameter is at a moderate
value of 0.88
+0.03
0.04
. The fit gives an upper limit of 9 deg for
the inclination angle. The iron abundance A
Fe
is 4.99
+1.02
0.68
.The
logarithmic ionization state is 3.67
+0.05
0.12
. The reflection fraction
which defines the photon fraction hitting the accretion disc (Dauser
et al. 2014) is 0.45
+0.12
0.06
. When the outer index is free, it is constrained
to be 3.31
+0.05
0.04
, and the inner index and the iron abundance only
obtained their lower limit of 7.46 and 7.29, respectively. The values
of the inner index and the iron abundance are too large to be
considered as physical. In any event, the value of the spin parameter
we cared most is not affected. Therefore, we will set the outer index
at 3 in the rest of the fits for simplicity.
In previous studies, a narrow Fe K α line, which could be
produced in the region far away from the central black hole, was
already detected in the X-ray spectra of some black hole X-ray
binaries, such as GX 339-4 (Garc
´
ıa et al. 2015)andCygX-1
(Tomsick et al. 2018). However, there is no clear evidence for
such a narrow line in the X-ray spectrum of MAXI J1836194
(see top two panels of Fig. 3). To further test the significance of
this component, we added the xillver model, which is used to
model unblurred reflection component, to Model 1. We found that
the inclusion of this component did not significantly improve the
fit with χ
2
ν
= 1.002 (2118.39/2114). The intensity of the relativistic
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2182 Y. Dong et al.
Tab le 2 . Best-fitting parameters with relativistic models.
Parameter Model 1 Model 2 Model 3 Model 4
Suzaku
Multitemperature blackbody
kT
disc
(keV) 0.436
+0.003
0.002
0.4380 (0.0004)
a
0.434 (0.003) 0.412
+0.010
0.002
N
disc
5660
+129
168
5588 (18) 5887
+164
191
6484
+477
715
Power-law continuum plus relativistic reflection
2.11
+0.02
0.01
2.109 (0.002) 2.00
+0.06
0.01
2.02
+0.01
0.02
h(R
g
) 2.36
+0.53
0.17
––
q
in
6.42
+1.10
1.83
–4.38
+0.57
0.59
> 5.95
R
br
(R
g
)4.45
+0.72
0.64
–5.34
+0.72
0.76
4.01
+0.36
0.29
a
0.88
+0.03
0.04
0.934 (0.005) 0.91
+0.03
0.04
0.88
+0.02
0.03
i (deg)
b
5
+4
15
1
4
+3
5
+3
A
Fe
4.99
+1.02
0.68
> 9.35 > 6.62 1(f)
c
log ξ
1
3.67
+0.05
0.12
3.63 (0.05) 4.23
+0.12
0.13
2.50
+0.11
0.09
R
ref
0.45
+0.12
0.06
1.33 (0.02) 0.65
+0.45
0.25
log ξ
2
3.47
+0.10
0.06
log n
e
–– > 21.83
N
cutoffpl
0.25 (0.01)
N
relxill
1
(×10
2
)0.38
+0.03
0.04
6.24
+1.96
0.01
0.21
+0.08
0.06
N
relxill
2
(×10
2
) 0.119
+0.08
0.02
N
reflionx hd
–– 1.17
+0.38
0.10
RXTE
Cross-Normalization constant (relative to Suzaku/XIS)
C 1.035
+0.004
0.005
1.035 (0.004) 1.034 (0.005) 1.035 (0.005)
χ
2
/ν 2118.76/2115 2144.58/2116 2107.01/2113 2093.68/2115
χ
2
ν
1.002 1.014 0.997 0.990
Notes. The best-fitting parameters obtained by modelling Suzaku and RXTE observa-
tions. Model 1 is TBabs
(disbkk + relxill) assuming an extended corona with
broken power-law emissivity profile. Model 2 is TBabs
(disbkk+relxilllp) as-
suming a lamp-post corona. Model 3 is TBabs
(disbkk+relxill
1
+relxill
2
),
namely we add another relativistic reflection component in Model 1. Model 4 is
TBabs(diskbb+cutoffpl+relconv
reflionx hd), in which the electron density
is a free parameter. For models relxill(lp) or relconv in Models 1, 2, and 4, the inner
radius R
in
is equal to R
ISCO
, and the outer radius R
out
is fixed at its default value: R
out
= 400
R
g
. In Model 3, in the first reflection (R1), R
in
is equal to R
ISCO
and R
out
is equal to R
br
;in
the second (R2), R
in
is equal to R
out
in R1, R
out
is equal to 400 R
g
, parameters q
in
, q
out
,and
R
br
are fixed at their default values, i.e. q
in
= 3, q
out
= 3, and R
br
= 15 R
g
,andlogξ
2
and
N
relxill
2
are free. The remaining common parameters are linked together for R1 and R2.
a
One digit enclosed in parentheses implies that the up error equal to the low.
b
The inclination angle pegs at its lower or upper limit (4–15 deg) we set.
c
The value followed by f in parentheses implied that it is fixed at some value.
reflection is also 30 times stronger than it. Additionally, it did not
affect the values of other parameters, such as the spin, the inclination
angle, and the iron abundance. Therefore, we did not include this
distant reflection in our fits.
As to the geometry of the corona, it is still unclear, but there
are two popular models: extended geometry (Wilkins & Fabian
2012) and lamp-post configuration (Matt, Perola & Piro 1991;
Martocchia & Matt 1996). In Model 1, we have assumed a broken
power-law emissivity to explore the extended corona, in which case
we found that a compact corona is required. In order to test the effect
of different geometry on the spin, we also tried to fit the data with a
lamp-post configuration using the model relxilllp (Model 2).
The lamp-post model leads to a slightly worse fit with χ
2
ν
= 1.014
(2144.58/2116) compared to Model 1. The best-fitting results of
Model 2 are shown in Table 2. The model components are shown
in the top right panel in Fig. 2 and the residuals with 1σ are shown
in the second top two panels in Fig. 3.
The fitted value for the parameters in Model 2 are listed here.
The temperature and the normalization of the thermal disc are
0.4380 ± 0.0004 keV and 5588 ± 18, respectively. The photon index
is 2.109 ± 0.002. The logarithmic ionization state is 3.63 ± 0.05.
These best-fitting parameters are consistent with the results found
in Model 1. The height of the point source is 2.36
+0.53
0.17
R
g
,which
indicates that a compact corona is located closely to the black
hole. The spin parameter of the black hole is 0.934 ± 0.005,
slightly higher than that in Model 1. The inclination angle is larger
than 14 deg but pegged at the upper limit of 15 deg. However,
the inclination angle was constrained to be 16–19 deg when
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