Extreme mass ratio inspirals into black holes surrounded by matter: Resonance crossings

TL;DR

This paper compares different methods for calculating gravitational wave fluxes in EMRIs and investigates the effects of orbital resonances, providing new numerical techniques to improve modeling accuracy and efficiency.

Contribution

It systematically compares flux calculation approaches and introduces novel numerical methods to analyze resonance crossings in EMRIs.

Findings

Quadrupole fluxes agree well with Teukolsky results across various orbits.

Resonance crossings significantly affect orbital evolution in EMRIs.

New numerical methods reduce computational costs for resonance analysis.

Abstract

The forthcoming space-based gravitational-wave observatory Laser Interferometer Space Antenna (LISA) should enable the detection of Extreme Mass Ratio Inspirals (EMRIs), in which a stellar-mass compact object gradually inspirals into a supermassive black hole while emitting gravitational waves. Modeling the waveforms of such systems is a challenging task, requiring precise computation of energy and angular momentum fluxes as well as proper treatment of orbital resonances, during which two fundamental orbital frequencies become commensurate. In this work, we perform a systematic comparison of fluxes derived from three approaches: the quadrupole formula, post-Newtonian approximations, and time-domain solutions of the Teukolsky equation. We show that quadrupole-based fluxes remain in good agreement with Teukolsky results across a broad range of orbital configurations, including perturbed orbits. Building on these insights, we explore the dynamical impact of resonance crossings within the adiabatic approximation. By introducing novel numerical methods, we reduce computational costs and uncover diverse resonance-crossing behaviors. These results contribute to the effort to understand theoretically and model adequately resonance crossings during an EMRI.