The measurable impact of the 2pN spin-dependent accelerations on the jet precession of M87$^\ast$

TL;DR

This paper analytically calculates second post-Newtonian order spin-dependent accelerations in the Kerr metric and explores their effects on jet precession, providing new insights into the dynamics around supermassive black holes like M87*.

Contribution

It introduces new second-order spin-dependent accelerations in the Kerr metric and analyzes their impact on jet precession, extending previous models of black hole dynamics.

Findings

Precession effects are about 20% of Lense-Thirring precession.

Second-order spin effects are measurable in jet precession.

Parameter space for M87* jet precession is characterized.

Abstract

Motivated by recent accurate measurements of disk/jet coprecessions around some galactic supermassive black holes, the accelerations experienced by an uncharged, spinless object in the Kerr metric, written in harmonic coordinates, are analytically calculated up to the formal second post-Newtonian order. To such a level, some new accelerations make their appearance. They are proportional to even and odd powers of the hole's angular momentum. Their counterparts are not known where the primary is a material body. After expressing them in a coordinate-independent, vector form valid for any orientations of the hole's spin axis in space, their orbital effects are perturbatively worked out in terms of the particle's Keplerian orbital elements. The resulting expressions, averaged over one orbital revolution, are valid for generic shapes and inclinations of the orbit. The orbital plane's precession proportional to the first power of the hole's angular momentum and to the reciprocal of the fourth power of the speed of light amounts to about twenty per cent of the corresponding Lense-Thirring effect. The latter is believed to be the cause of the accurately measured disk/jet precessional phenomenology, currently measured to a few per cent accuracy. Although at a lesser extent, also the precession proportional to the second power of the hole's spin and to the reciprocal of the fourth power of the speed of light is measurable. Allowed domains in the parameter space of the jet precession around M87$^\ast$ are displayed.