# Constraining the Johannsen deformation parameter $\epsilon_3$ with black hole X-ray data

## TL;DR

This paper uses X-ray reflection spectroscopy data from multiple black holes to test the Kerr black hole hypothesis by constraining the Johannsen deformation parameter $$, finding results consistent with Kerr and setting strong limits.

## Contribution

It extends previous work by analyzing diverse X-ray data to place observational constraints on the Johannsen deformation parameter $$, testing deviations from the Kerr metric.

## Key findings

- All measurements of  are consistent with the Kerr metric.
- Strong constraints on  obtained from Ark 564 and MCG-6-30-15.
- Results support the Kerr black hole hypothesis.

## Abstract

We extend our previous work on tests of the Kerr black hole hypothesis using X-ray reflection spectroscopy and we infer observational constraints on the Johannsen deformation parameter $\epsilon_3$. We analyze a NuSTAR observation of the stellar-mass black hole in GS 1354-645, Suzaku data of the supermassive black holes in Ark 564, 1H0419-577, and PKS 0558-504, and some simultaneous XMM-Newton and NuSTAR observations of the supermassive black hole in MCG-6-30-15. All our measurements of $\epsilon_3$ are consistent with the Kerr metric and we find quite strong constraints from Ark 564 and MCG-6-30-15. We discuss the implications of our results and the next steps to improve our tests.