Spherical inspirals of spinning bodies into Kerr black holes

TL;DR

This paper develops a model for spinning bodies inspiraling into Kerr black holes, highlighting the importance of secondary spin effects on gravitational wave signals for LISA detection.

Contribution

It introduces a flux-driven framework for spherical inspirals of spinning bodies into Kerr black holes, incorporating recent solutions for spinning test particles and analyzing waveform impacts.

Findings

Secondary spin significantly affects gravitational waveforms.

Neglecting secondary spin causes large waveform mismatches.

Spherical orbits remain spherical under radiation reaction at linear spin order.

Abstract

Extreme mass-ratio inspirals (EMRIs), consisting of a stellar-mass compact object spiraling into a massive black hole, are key sources for future space-based gravitational wave observatories such as LISA. Accurate modeling of these systems requires incorporating the spin effects of both the primary and secondary bodies, particularly for waveforms at the precision required for LISA detection and astrophysical parameter extraction. In this work, we develop a framework for modeling flux-driven spherical inspirals (orbits of approximately constant Boyer-Lindquist radius) of a spinning secondary into a Kerr black hole. We leverage recently found solutions for the motion of spinning test particles and compute the associated gravitational wave fluxes to linear order in the secondary spin. Next, we show that spherical orbits remain spherical under radiation reaction at linear order in spin, and derive the evolution of the orbital parameters throughout the inspiral. We implement a numerical scheme for waveform generation in the frequency domain and assess the impact of the secondary spin on the gravitational wave signal. In contrast to quasi-circular inspirals, we find that neglecting the secondary spin in spherical inspirals induces large mismatches in the waveforms that will plausibly be detectable by LISA.