The no-hair theorems at work in M87$^\ast$

TL;DR

This paper demonstrates how the no-hair theorems, combined with Lense-Thirring precession and quadrupole effects, can explain the observed jet precession in M87* and constrains the black hole's spin and accretion disk parameters.

Contribution

It introduces a comprehensive model incorporating quadrupole moments and Lense-Thirring precession to better match observational data of M87*'s jet precession.

Findings

Reproduces observed jet precession time series with high spin parameter.

Shows quadrupole effects are significant in black hole dynamics.

Constrains black hole spin and accretion disk radius based on model fitting.

Abstract

Recently, a perturbative calculation to the first post-Newtonian order has shown that the analytically worked out Lense-Thirring precession of the orbital angular momentum of a test particle following a circular path around a massive spinning primary is able to explain the measured features of the jet precession of the supermassive black hole at the centre of the giant elliptical galaxy M87. It is shown that also the hole's mass quadrupole moment $Q_2$, as given by the no-hair theorems, has a dynamical effect which cannot be neglected, as, instead, done so far in the literature. New allowed regions for the hole's dimensionless spin parameter $a^\ast$ and the effective radius $r_0$ of the accretion disk, assumed tightly coupled with the jet, are obtained by including both the Lense-Thirring and the quadrupole effects in the dynamics of the effective test particle modeling the accretion disk. One obtains that, by numerically integrating the resulting averaged equations for the rates of change of the angles $\eta$ and $\phi$ characterizing the orientation of the orbital angular momentum with $a^\ast = +0.98$ and $r_0=14.1$ gravitational radii, it is possible to reproduce, both quantitatively and qualitatively, the time series for them recently measured with the Very Long Baseline Interferometry technique. Instead, the resulting time series produced with $a^\ast = -0.95$ and $r_0=16$ gravitational radii turn out to be out of phase with respect to the observationally determined ones, while maintaining the same amplitudes.