Abstract
It is possible to infer the mass and spin of the remnant black hole from binary black hole mergers by comparing the ringdown gravitational wave signal to results from studies of perturbed Kerr spacetimes. Typically these studies are based on the fundamental quasinormal mode of the dominant $\ell=m=2$ harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find that the fundamental mode alone is insufficient to recover the true underlying mass and spin, unless the analysis is started very late in the ringdown. Including higher overtones associated with this $\ell=m=2$ harmonic resolves this issue, and provides an unbiased estimate of the true remnant parameters. Further, including overtones allows for the modeling of the ringdown signal for all times beyond the peak strain amplitude, indicating that the linear quasinormal regime starts much sooner than previously expected. A model for the ringdown beginning at the peak strain amplitude can exploit the higher signal-to-noise ratio in detectors, reducing uncertainties in the extracted remnant quantities. Tests of the no-hair theorem should consider incorporating overtones in the analysis.
Highlights
The end state of astrophysical binary black hole (BBH) mergers is a perturbed single BH characterized by two parameters: the final remnant mass Mf and spin angular momentum Sf [1,2,3]
Using a superposition of quasinormal modes (QNMs), we model the ringdown portion of the l 1⁄4 m 1⁄4 2 mode of the numerical relativity waveform Simulating eXtreme Spacetimes (SXS):BBH:0305, which is consistent with GW150914
We find that with enough included overtones, the QNMs provide an excellent description for the GW strain for all times beyond the peak amplitude of the complex strain h
Summary
The end state of astrophysical binary black hole (BBH) mergers is a perturbed single BH characterized by two parameters: the final remnant mass Mf and spin angular momentum Sf [1,2,3]. The multiple start times used in the analysis reflect an uncertainty about when the fundamental mode becomes a valid description for the ringdown, as there is noticeable disagreement between the measured mode and the GR prediction at early times. This result raises the following question: At what point in the ringdown does perturbation theory become relevant?. The inclusion of QNM overtones provides a highaccuracy description of the ringdown as early as the time of the peak strain amplitude, where the high signal-to-noise ratio (SNR) can be exploited to significantly reduce the uncertainty in the extracted remnant properties
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