Measuring black hole spins with x-ray reflection spectroscopy: A GRMHD outlook

TL;DR

This paper evaluates the reliability of X-ray reflection spectroscopy for black hole spin measurements by juxtaposing GRMHD-informed thin-disk simulations with synthetic NuSTAR data. By deriving electron density and ionization profiles from GRMHD, and testing a sequence of reflection-model configurations (including lamppost and broken power-law emissivity profiles) against jet-like corona geometries, the work reveals that current models robustly recover spins only for fast-rotating BHs and when the corona is compact; extended or jet-like coronas challenge spin recovery. It also demonstrates that incorporating realistic ionization and density structures can both help and hinder spin determination, depending on disk size and ionization profile. The findings emphasize the need for more advanced accretion-disk and coronal geometries in reflection models and suggest that reliable spins may be confined to fast rotators with compact coronas, guiding future modeling and observational strategies.

Abstract

X-ray reflection spectroscopy has evolved as one of the leading methods to measure black hole spins. However, the question is whether its measurements are subjected to systematic biases, especially considering the possible discrepancy between the spin measurements inferred with this technique and those from gravitational wave observations. In this work, we use general relativistic magnetohydrodynamic (GRMHD) simulations of thin accretion disks around spinning black holes for modeling the accretion process, and then we simulate NuSTAR observations to test the capability of modern reflection models in recovering the input spins. For the first time, we model the electron density and ionization profiles from GRMHD-simulated disks. Our study reveals that current reflection models work well only for fast-rotating black holes. We model the corona as the base of the jet and we find that reflection models with lamppost emissivity profiles fail to recover the correct black hole spins. Reflection models with broken power-law emissivity profiles perform better. As we increase the complexity of the simulated models, it is more difficult to recover the correct input spins, pointing toward the need to update our current reflection models with more advanced accretion disks and coronal geometries.

Figures (12)

• Figure 1: A sketch of the disk-corona model.
• Figure 2: Normalized density profile of the initial configuration of the accretion disk around a black hole of $a_* = 0.5$. The gray lines represent magnetic field lines.
• Figure 3: Normalized density profile of the accretion disk around a black hole of $a_* = 0.5$, averaged over $7500~t_g$ -- $15000~t_g$. The gray lines represent magnetic field lines.
• Figure 4: Corona and disk geometry obtained from the simulations and ray tracing for the simulation with black hole spin $a_* = 0.5$. The boundary of the corona is marked by the pink line. The surface of the accretion disk is marked by the green line. Outer edge of the disk for all cases lies $\sim 188~r_g$. The color map is the normalized density as in Fig. \ref{['fig:avg_disk']}.
• Figure 5: Photon flux from the corona illuminating the disk (left columns), electron density (central columns), and ionization parameter (right columns) obtained from ray tracing onto GRMHD disks for different spins. The black dotted vertical lines mark the radial values of the horizon ($r_{\rm H}$) and the innermost stable circular orbit ($r_{\rm ISCO}$). In the right columns, the red dashed horizontal lines show the highest value of ionization in the xillverCp model viz. $\log\xi = 4.7$. In the central and right columns, the orange dashed curves denote the electron density and ionization parameter profiles when the electron density profile is calculated from the GRMHD simulations for $r < 20~r_g$ and is constant with the value at $r = 20~r_g$ for larger radii (setup M6).