Orbital evolution of a particle around a black hole: II. Comparison of contributions of spin-orbit coupling and the self force

TL;DR

This paper analyzes the orbital evolution of a spinning particle around a Schwarzschild black hole, comparing the effects of spin-orbit coupling and the self force, and suggests simplified models for gravitational waveforms.

Contribution

It provides a comparison of spin-orbit and self force effects on orbital decay and proposes an approximation ignoring the self force for gravitational waveform modeling.

Findings

Orbit decay mainly driven by radiation reaction.

Spin force dominates conservative effects.

Ignoring the self force introduces small parameter estimation errors.

Abstract

We consider the evolution of the orbit of a spinning compact object in a quasi-circular, planar orbit around a Schwarzschild black hole in the extreme mass ratio limit. We compare the contributions to the orbital evolution of both spin-orbit coupling and the local self force. Making assumptions on the behavior of the forces, we suggest that the decay of the orbit is dominated by radiation reaction, and that the conservative effect is typically dominated by the spin force. We propose that a reasonable approximation for the gravitational waveform can be obtained by ignoring the local self force, for adjusted values of the parameters of the system. We argue that this approximation will only introduce small errors in the astronomical determination of these parameters.