Quasinormal ringing of Kerr black holes. III. Excitation coefficients for equatorial inspirals from the innermost stable circular orbit

TL;DR

This paper develops a formalism to compute quasinormal mode excitation coefficients for Kerr black holes from equatorial inspirals, revealing that higher overtones are more prominent in rapidly spinning remnants, which improves gravitational wave detection prospects.

Contribution

It introduces a general frequency domain method to calculate excitation coefficients for quasinormal modes of Kerr black holes from equatorial inspirals, emphasizing spin dependence.

Findings

Higher overtones are more excited in rapidly rotating black holes.

Subdominant multipoles become significant for high spins.

Detection prospects for overtones improve with black hole spin.

Abstract

The remnant of a black hole binary merger settles into a stationary configuration by "ringing down" through the emission of gravitational waves that consist of a superposition of damped exponentials with discrete complex frequencies - the remnant black hole's quasinormal modes. While the frequencies themselves depend solely on the mass and spin of the remnant, the mode amplitudes depend on the merger dynamics. We investigate quasinormal mode excitation by a point particle plunging from the innermost stable circular orbit of a Kerr black hole. Our formalism is general, but we focus on computing the quasinormal mode excitation coefficients in the frequency domain for equatorial orbits, and we analyze their dependence on the remnant black hole spin. We find that higher overtones and subdominant multipoles of the radiation become increasingly significant for rapidly rotating black holes. This suggests that the prospects for detecting overtones and higher-order modes are considerably enhanced for highly spinning merger remnants.