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The power-law emission and reflection component provide valuable insights into the accretion process around a black hole. In this work, thanks to the broadband spectra coverage of \emph{the Nuclear Spectroscopic Telescope Array}, we study the spectral properties for a sample of low-mass black hole X-ray binaries (BHXRBs). We find that there is a positive correlation between the photon index $\Gamma$ and the reflection fraction $R$ (the ratio of the coronal intensity that illuminates the disk to the coronal intensity that reaches the observer), consistent with previous studies, but except for MAXI J1820+070. It is quite interesting that this source also deviates from the well-known ``V"-shaped correlation between the photon index $\Gamma$ and the X-ray luminosity log$L_{\rm X}$, when it is in the bright hard state. More specifically, the $\Lambda$-shaped correlation between $\Gamma$ and log$L_{\rm X}$ is observed, as the luminosity decreases by a factor of 3 in a narrow range from $\sim 10^{38}$ to $10^{37.5}$ $\rm erg~s^{-1}$. Furthermore, we discover a strong positive correlation between $R$ and the X-ray luminosity for BHXRBs in the hard state, which puts a constraint on the disk-corona coupling and the evolution., Comment: 18 pages, 9 figures, 3 tables, Accepted for publication in ApJ

We report results on the joint-fit of the NuSTAR and HXMT data for the black hole X-ray binary candidate MAXI J1535-571. The observations were obtained in 2017 when the source evolved through the hard, hard-intermediate and soft-intermediate states over the rising phase of the outburst. After subtracting continuum components, X-ray reflection signatures are clearly showed in those observations. By modeling the relativistic reflection in detail, we find that the inner radius $R_{\rm{in}}$ is relatively stable with $R_{\rm{in}}\lesssim 1.55 R_{\rm{g}}$ during the three states, which implies that the inner radius likely extends to the innermost stable circular orbit even in the bright hard state. When adopting $R_{\rm{in}} = R_{\rm{ISCO}}$, the spin parameter is constrained to be $0.985_{-0.004}^{+0.002}$ at 90% confidence (statistical only). The best-fitting results reveal that the inclination of the inner accretion disc is $\sim70-74$ degrees, which notably conflicts with the apparent orientation of the ballistic jet ($\leqslant$45 degrees). In addition, both the photon index and the electron temperature increase during the transition from hard to soft state. It seems that the corona evolves from dense low-temperature in the LHS to tenuous high-temperature after the state transition, which indicates that the state transition is accompanied by the evolution of the coronal properties., Comment: 11 pages, 5 figures, 3 tables; Publicated in MNRAS. We update Fig. 5 in paper which does not affect conclusions

Cygnus X-1 is a well-studied persistent black hole X-ray binary. Recently, the three parameters needed to estimate the black hole spin of this system, namely the black hole mass $M$, the orbital inclination $i$ and the source distance $D$, have been updated. In this work we redetermine the spin parameter using the continuum-fitting technique for those updated parameter values. Based on the assumption that the spin axis of the black hole is aligned with the orbital plane, we fit the thermal disk component to a fully relativistic thin accretion disk model. The error in the spin estimate arising from the combined observational uncertainties is obtained via Monte Carlo (MC) simulations. We demonstrate that, without considering the counteracting torque effect, the new spin parameter is constrained to be a$_* > 0.9985$ (3$\sigma$), which confirms that the spin of the black hole in Cygnus X-1 is extreme., Comment: ApJ published

MAXI J1820+070 is a newly-discovered black hole X-ray binary, whose dynamical parameters, namely the black hole mass, the inclination angle and the source distance, have been estimated recently. \emph{Insight}-HXMT have observed its entire outburst from March 14th, 2018. In this work, we attempted to estimate the spin parameter~$a_*$, using the continuum-fitting method and applying a fully-relativistic thin disk model to the soft-state spectra obtained by \emph{Insight}-HXMT. It is well know that $a_*$ is strongly dependent on three dynamical parameters in this method, and we have examined two sets of parameters. Adopting our preferred parameters: $M$ = $8.48^{+0.79}_{-0.72}~M_\odot$, $i=63^\circ\pm3^\circ$ and $D=2.96\pm0.33$ kpc, we found a slowly-spinning black hole of $a_*=0.14 \pm 0.09$ ($1\sigma$), which give a prograde spin parameter as majority of other systems show. While it is also possible for the black hole to have a retrograde spin (less than 0) if different dynamical parameters are taken.

4U 1543-47 is a low mass X-ray binary which harbours a stellar-mass black hole located in our Milky Way galaxy. In this paper, we revisit 7 data sets which were in the Steep Power Law state of the 2002 outburst. The spectra were observed by the Rossi X-ray Timing Explorer. We have carefully modelled the X-ray reflection spectra, and made a joint-fit to these spectra with relxill, for the reflected emission. We found a moderate black hole spin, which is $0.67_{-0.08}^{+0.15}$ at 90% statistical confidence. Negative and low spins (< 0.5) at more than 99% statistical confidence are ruled out. In addition, our results indicate that the model requires a super-solar iron abundance: $5.05_{-0.26}^{+1.21}$, and the inclination angle of the inner disc is $36.3_{-3.4}^{+5.3}$ degrees. This inclination angle is appreciably larger than the binary orbital inclination angle (~21 degrees); this difference is possibly a systematic artefact of the artificially low-density employed in the reflection model for this X-ray binary system., Comment: Accepted for publication in MNRAS

We 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% 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., Comment: Accepted for publication in MNRAS