The last phase of a binary black hole coalescence is accompanied by a damped, late train of gravitational radiation known as the ringdown phase of the merger. At sufficiently late times, this emission can be described as a sum of discrete modes arising from linear perturbation theory around the final Kerr state : the quasi-normal modes (QNMs) of this Kerr black hole. Each spheroidal harmonic mode of the radiation admits an infinite discrete set of QNM complex frequencies, known as a fundamental tone and overtones. As a consequence of the black hole no-hair theorem, these frequencies can be computed uniquely from the two parameters (mass and spin) of the final black hole. The measure of these frequencies in a ringdown signal then enables a test of this prediction of general relativity by comparing the results either to the inspiral phase of the radiation or between different QNMs.
It has recently been suggested [M. Giesler, M. Isi, M.A. Scheel, S.A. Teukolsky, PRX 9, 041060 (2019), arXiv:1903.08284] that ringdown signals may be modelled by QNMs already from the merger onwards provided a large enough number of overtones is considered, potentially allowing for the analysis of a substantially louder signal than at later times. I will present the results of further tests of this claim in two different regimes.
The first approach focuses on the local dynamics of the common horizon formed during a head-on merger. This dynamics is related to the gravitational radiation and also expected to be described by QNMs at late times, and we could in this case benefit from very precise numerical relativity data that enables a study of multiple harmonics. We indeed find a good match of QNM decompositions with large enough number of overtones for each of these harmonics. I will discuss whether this should be interpreted as an early validity of the linear picture. The second investigation comes back to numerical waveforms and probes the continued improvement of the model’s match and recovery of the final mass and spin as increasingly large numbers of overtones are included. I will in particular discuss the stability of the recovery of the individual tones in the model and the resulting prospects for QNM-based tests of general relativity.