Testing the space-time geometry around black hole candidates with the analysis of the broad K$\alpha$ iron line

TL;DR

This paper investigates whether the broad Kα iron line in X-ray spectra can be used to test if black hole candidates are described by the Kerr metric, potentially confirming General Relativity's predictions about strong gravity near black holes.

Contribution

It demonstrates that analyzing the broad Kα iron line can effectively constrain deviations from the Kerr geometry independently of the black hole's spin.

Findings

The broad iron line shape is sensitive to space-time geometry.

Analysis can distinguish Kerr from non-Kerr black holes.

Method provides bounds on deviations from Kerr geometry.

Abstract

Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but there is not yet clear evidence that the geometry of the space-time around these objects is really described by the Kerr metric. In order to confirm the Kerr black hole hypothesis, we have to observe strong gravity features and check that they are in agreement with the ones predicted by General Relativity. In this paper, I study the broad K$\alpha$ iron line, which is often seen in the X-ray spectrum of both stellar-mass and super-massive black hole candidates and whose shape is supposed to be strongly affected by the space-time geometry. As found in previous studies in the literature, there is a strong correlation between the spin parameter and the deformation parameter; that is, the line emitted around a Kerr black hole with a certain spin can be very similar to the one coming from the space-time around a non-Kerr object with a quite different spin. Despite that, the analysis of the broad K$\alpha$ iron line is potentially more powerful than the continuum-fitting method, as it can put an interesting bound on possible deviations from the Kerr geometry independently of the value of the spin parameter and without additional measurements.