Testing the Kerr Nature of Black Hole Candidates using Iron Line Spectra in the CPR Framework

TL;DR

This study assesses the potential of iron Kα line spectra to test the Kerr black hole hypothesis by constraining deviations using the CPR parametrization, highlighting the importance of high-quality data and specific geometric perturbations.

Contribution

It extends previous work by applying the CPR framework to analyze the iron line's ability to detect deviations from Kerr geometry across various spins and inclinations.

Findings

Iron line profiles can constrain certain deviations from Kerr geometry.

High-quality data and specific conditions enhance the detection of relativistic effects.

Some perturbations are more detectable than others in the iron line spectrum.

Abstract

The iron K$\alpha$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around these objects. In this paper, we extend previous work using the iron K$\alpha$ line to test the Kerr black hole hypothesis. We adopt the Cardoso-Pani-Rico parametrization and we test the possibility of constraining possible deviations from the Kerr solution that can be obtained from observations across the range of black hole spins and inclination angles. We confirm previous claims that the iron K$\alpha$ line is potentially a quite powerful probe for testing the Kerr metric given sufficiently high quality data and with systematics under control, especially in the case of fast-rotating black holes and high inclination angles since both conditions serve to maximize relativistic effects. We find that some geometric perturbations from Kerr geometry manifest more strongly in the iron line profile than others. While the perturbation parameter $\epsilon^t_3$ can be well constrained by the iron line profile, an orthogonal data set is necessary to constrain departures from Kerr geometry in $\epsilon^r_3$.