Resonant jumps induced by stationary tidal perturbation: a two-for-one deal

TL;DR

This paper investigates how stationary tidal perturbations cause resonance jumps in EMRIs, providing a Hamiltonian-based relation between changes in conserved quantities, relevant for gravitational wave detection.

Contribution

It introduces a Hamiltonian formulation linking resonance jumps in Carter constant and angular momentum due to stationary tidal perturbations in Kerr spacetime.

Findings

Derived a closed-form relation between Carter constant and angular momentum jumps.

Confirmed the relation's consistency with previous tidal resonance models.

Highlights the impact of environmental effects on EMRI orbital evolution.

Abstract

Extreme-mass-ratio inspirals (EMRIs) are promising target sources for space-based interferometers such as LISA, Taiji, and Tianqin. Depending on the astrophysical environment, such as close perturbers or an accretion disk, EMRI orbital evolution may deviate from the predictions of general relativity in vacuum. In particular, we focus on the resonance jumps, i.e., the changes of the conserved quantities induced by a stationary perturbation to the background Kerr geometry. Using Hamiltonian formulation, we provide a closed relation between the jump in Carter constant and that in the axial component of angular momentum. It is also shown that the obtained relation is consistent with the fitting formulae computed for the tidal resonance in previous works.