Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*

TL;DR

This paper investigates the shadows of hairy Kerr black holes, incorporating additional parameters, and uses EHT observations of M87* to constrain these models, finding that such black holes can match observed shadow features.

Contribution

It provides a detailed analysis of how hair parameters affect black hole shadows and derives observational bounds from M87* data, extending the understanding of non-Kerr black holes.

Findings

Hairy Kerr black holes have smaller, more distorted shadows than Kerr black holes.

Shadow parameters constrain the hair and spin parameters, fitting M87* observations.

Hairy Kerr black holes are viable astrophysical black hole candidates.

Abstract

The recently obtained hairy Kerr black holes, due to additional sources or surrounding fluid, like dark matter, with conserved energy-momentum tensor, have a deviation $\alpha$ and primary hair $l_0$, apart from rotation parameter $a$ and mass $M$. In the wake of the \textit{Event Horizon Telescope} (\textit{EHT}) observations of the supermassive black hole M87*, a recent surge in interest in black hole shadows suggests comparing the black holes in general relativity (GR) and modified theories of gravity (MoG) to assess these models' differences. Motivated by this, we take on an extensive study of the rotating hairy Kerr black holes, which encompasses, in particular cases, the Kerr black hole ($\alpha=0$). We investigate ergosphere and shadows of the black holes to infer that their size and shape are affected due to the $l_0$ and are found to harbour a richer chaotic structure. In particular, the hairy Kerr black holes possess smaller size but more distorted shadows when compared with Kerr black holes. We also estimate the parameters $l_0$ and $a$ associated with hairy Kerr black holes using the shadow observables. The inferred circularity deviation $\Delta C \leq 0.1$ for the M87* black hole is satisfied, whereas shadow angular diameter $\theta_{d}=42 \pm 3 \mu as$, within $1 \sigma$ region, for a given choice of $\alpha$, places bounds on the parameters $a$ and $l_0$. Interestingly, the shadow axial ratio obeying $1< D_x \lesssim 4/3$ is in agreement with the \textit{EHT} results and thus eventuates in the hairy Kerr black holes being suitable candidates for astrophysical black holes.