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

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 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.