Repeated Ringing of the Black Hole's Bell: Quasi-Normal Bursts from Highly Eccentric, Extreme Mass-Ratio Binaries

TL;DR

This paper investigates the origin and behavior of quasi-normal bursts in high-eccentricity black hole binaries, revealing their frequency evolution and decay over time due to overtone excitation.

Contribution

It provides a detailed analysis showing that QNB frequencies evolve towards the dominant quasi-normal mode, resolving previous puzzles about their lower observed frequencies.

Findings

QNB frequency approaches the dominant QNM exponentially over time.

QNB amplitude decays inversely with time.

Overtone excitation explains the QNB behavior.

Abstract

Recent studies of scalar and gravitational waveforms from high-eccentricity, extreme mass-ratio black hole binaries show the presence of quasi-normal bursts (QNB) -- lingering high frequency decaying oscillations (also known as ``wiggles'') -- soon after each periapsis passage. One puzzle associated with these QNB is that in the case of a nearly-extreme rotating central black hole the frequency of the QNB has been found to be in a range which is lower than the corresponding range of relevant quasi-normal modes. We reproduce these results using a different approach and perform a detailed analysis to find evidence for the resolution of the puzzle and for the origin of the QNB. We find that the QNB frequency as measured at future null infinity evolves in (retarded) time and approaches the dominant quasi-normal frequency exponentially in time. We also show that the QNB amplitude decays inversely in (retarded) time. We discuss the time dependence of both the QNB waveform frequency and its amplitude and argue that this behavior arises as a result of the excitation of many quasi-normal overtones and the summation thereof.