Dynamical quasinormal mode excitation

TL;DR

This paper develops an analytical model for the excitation of quasinormal modes during black hole mergers, capturing waveform features and late-time behavior, and predicts mode amplitudes for generic inspiral configurations.

Contribution

It introduces a Green's function approach to model time-dependent QNM excitation for generic orbits, including late-time amplitude predictions, extending prior work to more general binary configurations.

Findings

QNM signals propagate along hyperboloidal slices.

Waveform consists of activation and impulsive terms.

Late-time amplitudes match numerical solutions.

Abstract

We study the dynamical excitation of quasinormal modes (QNMs) through the plunge, merger and ringdown of an extreme-mass-ratio-inspiral into a Schwarzschild black hole, for generic orbital configurations. We work out the QNM causality condition, crucial to eliminate amplitude divergences and to incorporate horizon redshift effects. We then use it to derive a model of the time-dependent QNM excitation via a Green's function approach, driven by the point-particle source on a given trajectory. Our model predicts that: i) QNMs propagates along hyperboloidal slices in the minimal gauge; ii) the signal is composed of an ``activation'' term, depending on the source past history, and a local ``impulsive'' term; iii) amplitudes grow in time in an ``activation function'' fashion, and the waveform displays a stationary ringdown regime at times $\sim 10-20M$ after its peak; iv) at these late times, an infinite tower of non-oscillatory, exponentially-damped terms appear: the redshift terms. The model is in good agreement with numerical solutions, capturing the main waveform features after the peak. Additional components of the Green's function are required to complement the QNM description and reproduce the plunge-merger waveform. We predict the late-time, stationary amplitude of the quadrupolar mode as a function of eccentricity, in agreement with accurate numerical solutions, marking the first time that QNM amplitudes are predicted for generic binary configurations. Our work provides a first solid step towards analytically modeling the inspiral's imprint onto ringdown signals, generalizable to include higher orders in the mass ratio, black hole spin, non-vacuum configurations and corrections to the Einstein-Hilbert action.