Estimating the possible QPOs of [formula omitted] from the parameters of a hairy Kerr black hole

Abstract

In this paper, we study the dynamics of the shock cone formed around a hairy Kerr black hole due to Bondi-Hoyle-Lyttleton (BHL) accretion and investigate the quasi-periodic oscillations (QPO) behaviors resulting from the black hole-cone interaction, aiming to predict the QPO frequencies that may occur around the M87∗ black hole. To achieve this, we use the hairy Kerr black hole parameters consistent with the observed shadow parameters of M87∗ as initial conditions in numerical simulations, revealing the structure of the resulting shock cone and QPOs in a strong gravitational field. Numerical calculations show that the deviation of the hairy Kerr black hole from the Kerr metric and the hair parameters significantly influence the complex behavior of the resulting QPOs. It is found that the Lense-Thirring effect and the pressure modes trapped within the cone lead to the excitation of QPOs. The hair parameter has been observed to suppress the resulting QPO frequencies. The Lense-Thirring effect, in a strong gravitational field with a black hole spin parameter of a/M>0.7, also suppresses other modes and generates high-frequency QPOs. It is predicted that the QPO frequencies observed around the M87∗ black hole could span a wide range from nHz to mHz. Using both Kerr and hairy Kerr gravities, the QPO frequencies formed around the M87∗ black hole can be explained. Especially in cases where the black hole is spinning rapidly, power spectrum density (PSD) analyses have shown very distinct low-frequency QPOs and resonance conditions in both gravities. By comparing the results obtained from numerical calculations with observational and analytical results, we discuss the observability of the QPO frequencies that may occur around the M87∗ black hole.