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

## TL;DR

This study uses Monte Carlo simulations to explore how different coronal geometries in black hole X-ray binaries influence observed spectra, aiming to distinguish these geometries through spectral and polarimetric analysis.

## Contribution

It introduces a simulation-based approach to differentiate coronal geometries in black hole binaries using spectral fitting and polarimetric predictions.

## Key findings

- Lamppost model incompatible with hard state due to dominant disk emission.
- Sandwich and spherical models can produce similar spectra, but polarimetry can distinguish them.
- Coronal size effects are significant in lower-spin black holes.

## 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.