Possible Coronal Geometry in the Hard and Soft State of Black Hole X-ray Binaries from MONK Simulations

TL;DR

This paper uses the MONK Monte Carlo ray-tracing code to simulate X-ray spectra from three plausible coronal geometries (sandwich, spherical, lamppost) around a Kerr black hole, aiming to distinguish hard and soft states in black hole X-ray binaries. By fitting the simulated NuSTAR data with the simplified model $\text{simplcut}*\text{kerrbb}$ and evaluating disk emission fractions and photon indices $\Gamma$, the authors map the viable parameter spaces for each geometry and state, revealing degeneracies between geometry and spectral shape. They find that sandwich and spherical geometries can reproduce both hard and soft states, while lamppost geometries remain disk-dominated and inconsistent with the hard state unless the corona is unusually extended; polarization predictions from IXPE show promise for breaking these degeneracies. The work also explores the impact of inclination, spin, and coronal temperature on spectral fits and discusses consistency with analytical models like compTT, highlighting the value of polarization data for constraining coronal geometry in BHXRBs. These results inform future modeling and interpretation of high-energy spectra and motivate continued use of IXPE-type polarimetry to refine corona geometry in accreting black hole systems.

Abstract

Understanding the coronal geometry in different states of black hole X-ray binaries is important for more accurate modeling of the system. However, it is difficult to distinguish different geometries by fitting the observed Comptonization spectra. In this work, we use the Monte Carlo ray-tracing code MONK to simulate the spectra for three simple corona toy models widely proposed in observational studies: sandwich, spherical, and lamppost, varying their optical depth and size (height). By fitting the simulated NuSTAR observations with the simplcut*kerrbb model, we infer the possible parameter space for the hard state and soft state of different coronal geometries. The influence of the disk inclination angle, black hole spin and coronal temperature is discussed. We find that in the lamppost model, if we exclude the case of a very extended corona, the disk emission is always dominant, making the lamppost geometry incompatible with the hard state. While the sandwich and spherical models can produce similar spectra in both the hard and soft states, the simulated IXPE polarimetric spectra show the potential to break this degeneracy. Geometrical effects arising from the limited size of the corona become evident in lower-spin black holes and affect the spectral fitting, where the larger ISCO reduces the corona coverage of the inner disk.

Figures (12)

• Figure 1: The coronal geometries considered in our study. The upper left panel is the sandwich corona, which is two parallel layers with a certain thickness above and below the disk. The upper right panel is the spherical corona, which is a central sphere around the black hole. The lower panel is the lamppost corona, which is a sphere of finite radius ($=2~R_g$ in our simulations) along the black hole spin axis.
• Figure 2: The data, best-fit model and residuals of the fit of the simulated disk emission of a $10~M_{\odot}$, $a_*=0.998$ black hole accreting at 10% of the Eddington mass accretion rate, observed from 10 kpc and $60^{\circ}$. The model kerrbb can fit well the simulated spectrum, with $\chi^2/d.o.f.=135.23/124=1.09$.
• Figure 3: Sandwich corona. The change of the disk fraction (the left panel) and $\Gamma$ (the right panel) with the optical depth ($\tau=n_{\rm{e}}\sigma_{\rm{T}}h$, where $h=h_{\rm{max}}-h_{\rm{min}}$ is the thickness of the corona) and outer corona radius ($R_{\rm{out}}$), observed at $i=60^{\circ}$. We produce the simulation over a $6 \times 5$ grid ($\tau=0.1,0.3,0.5,0.7,0.9$ while $R_{\rm{out}}=10, 14, 18, 22, 26, 30~R_{\rm{g}}$) and perform a 2D interpolation to get the continuous trend and draw the contour lines. The upper triangle and lower triangle show the selected soft-state and hard-state spectra of the sandwich corona in Fig. \ref{['pol_compare']}. Throughout the paper, the color bars of all the contour plots are the same.
• Figure 4: Spherical corona. The change of the disk fraction (the left panel) and $\Gamma$ (the right panel) with the optical depth ($\tau=n_{\rm{e}}\sigma_{\rm{T}}R$) and corona radius ($R$), observed at $i=60^{\circ}$. We produce the simulations over a $5 \times 5$ grid ($\tau=1.0,1.5,2.0,2.5,3.0$ while $R=6, 12, 18, 24, 30~R_{\rm{g}}$) and perform a 2D interpolation to get the continuous trend and draw the contour lines. The upper triangle and lower triangle show the selected soft-state and hard-state spectra of the spherical corona in Fig. \ref{['pol_compare']}.
• Figure 5: Lamppost corona. The change of the disk fraction (the left panel) and $\Gamma$ (the right panel) with the optical depth ($\tau=n_{\rm{e}}\sigma_{\rm{T}}R$, where $R=2~R_{\rm{g}}$) and corona height ($h$) above the disk, observed at $i=60^{\circ}$. We do the simulation on a $5 \times 5$ grid ($\tau=1,2,3,4,5$ while $h=1,2,3,4,5~R_{\rm{g}}$) and do a 2D interpolation to get the continuous trend and draw the contour lines. The shadowed region indicates the spectra with $\sigma_{\Gamma}$ larger than 0.2.