Striking the right tone: towards a selfconsistent framework for measuring black hole ringdowns
Abstract
The ringdown portion of a binary black hole merger consists of a sum of modes, each containing an infinite number of tones that are exponentially damped sinusoids. In principle, these can be measured as gravitationalwaves with observatories like LIGO/Virgo/KAGRA, however in practice it is unclear how many tones can be meaningfully resolved. We investigate the consistency and resolvability of the overtones of the quadrupolar l = m = 2 mode by starting at late times when the gravitational waveform is expected to be wellapproximated by the l m n = 220 tone alone. We present a Bayesian inference framework to measure the tones in numerical relativity data. We measure tones at different start times, checking for consistency: we classify a tone as stably recovered if and only if the 95% credible intervals for amplitude and phase at time t overlap with the credible intervals at all subsequent times. We test the first four overtones of the fundamental mode and find that the 220 and 221 tones can be measured consistently with the inclusion of additional overtones. The 222 tone measurements can be stabilised when we include the 223 tone, but only in a narrow time window, after which it is too weak to measure. The 223 tone recovery appears to be unstable, and does not become stable with the introduction of the 224 tone. Within our framework, the ringdown of the fundamental mode of binary black hole waveforms can be selfconsistently described by three to four tones, which are stable from 10 M after the peak strain. However, additional tones are not obviously required because the fit amplitudes are consistent with zero. We conclude that recent claims of overtone detection are not necessarily an exercise in overfitting; the observed tones can be selfconsistently modelled, although, not until ~ 10 M from peak strain with our fourtone model.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.02819
 arXiv:
 arXiv:2402.02819
 Bibcode:
 2024arXiv240202819C
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 13 pages, 8 figures, 2 tables