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 harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find, in agreement with previous findings, 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 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. This result implies that the spacetime is well described as a linearly perturbed black hole with a fixed mass and spin as early as the peak. 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. These results should be taken into consideration when testing the no-hair theorem.
- Received 13 April 2019
- Revised 14 August 2019
DOI:https://doi.org/10.1103/PhysRevX.9.041060
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The final fate of a pair of black holes is a violent collision that results in a single black hole that “rings down” like a struck bell. Each merger produces a black hole that emanates gravitational waves with specific pitches and decay rates that serve as a unique black hole fingerprint. Using computer simulations of merging black holes, we show that overtones, an often-ignored set of tones considered to be unimportant, can provide a precise estimate of the black hole’s mass and spin. The key to measuring the overtones is to look much earlier in the signal, at a time previously assumed to be too complex to model. By listening to black hole mergers, we can test how closely the detected tones agree with those predicted by Einstein’s theory of gravity.
The no-hair theorem conjectures that a black hole is described by just its mass and spin, and that the measurement of two tones is sufficient to test this claim. Much effort has gone into preparing to conduct this test with future detectors, as much more sensitive detectors are required to carry out a test that neglects overtones. We show that the overtones provide the multiple tones required and that these are measurable with current detectors. This means we can put the no-hair theorem to the test today, roughly 15 years ahead of schedule.
In previous work, we carried out this test using existing gravitational-wave data and found good agreement with Einstein’s theory of ringing black holes. As detection sensitivity improves, so too will the precision with which we can put Einstein to the test.
