Detectability of avoided crossings in black hole ringdowns

TL;DR

This study assesses the challenges of detecting nearly degenerate black hole quasinormal modes with avoided crossings using Bayesian methods, highlighting difficulties in resolving individual modes but potential for identifying collective signatures.

Contribution

It introduces a Bayesian framework to analyze the detectability of avoided crossings in black hole ringdowns with different waveform models, emphasizing the observational challenges.

Findings

Resolving individual QNM frequencies is difficult even with optimistic data.

Collective signatures of avoided crossings can be detected if AC modes dominate the signal.

Detection is hindered by contamination from other modes and the close proximity of frequencies.

Abstract

Quasinormal modes (QNMs) of black holes can exhibit avoided crossings (ACs), in which specific QNM frequencies approach each other while their amplitudes are enhanced and acquire nearly opposite phases, leading to characteristic interference. Resolving such closely spaced modes through black hole spectroscopy is observationally challenging. In this paper, we investigate the detectability of nearly degenerate QNMs in the presence of an AC within a Bayesian framework using three waveform models. We examine how the inference of the complex frequencies and amplitudes depends on the separation between the two QNM frequencies and on the choice of template waveform. We find that resolving the individual QNM frequencies is difficult even under optimistic conditions. On the other hand, collective waveform signatures associated with ACs may still be identified through complementary waveform descriptions, provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed.