Journal
PHYSICAL REVIEW D
Volume 97, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.97.044048
Keywords
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Funding
- NSF [PHY-1607130, AST-1716715]
- FCT under the IF2014 Programme [IF/00797/2014/CP1214/CT0012]
- European Union's H2020 ERC Consolidator Grant Matter and strong-field gravity: New frontiers in Einstein's theory [MaGRaTh-646597]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development Innovation
- National Science Foundation [PHY-1701284]
- Air Force Research Laboratory [10-RI-CRADA-09]
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie [690904]
- COST Action [CA16104]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1607130] Funding Source: National Science Foundation
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The relaxation of a distorted black hole to its final state provides important tests of general relativity within the reach of current and upcoming gravitational wave facilities. In black hole perturbation theory, this phase consists of a simple linear superposition of exponentially damped sinusoids (the quasinormal modes) and of a power-law tail. How many quasinormal modes are necessary to describe waveforms with a prescribed precision? What error do we incur by only including quasinormal modes, and not tails? What other systematic effects are present in current state-of-the-art numerical waveforms? These issues, which are basic to testing fundamental physics with distorted black holes, have hardly been addressed in the literature. We use numerical relativity waveforms and accurate evolutions within black hole perturbation theory to provide some answers. We show that (i) a determination of the fundamental l = m = 2 quasinormal frequencies and damping times to within 1% or better requires the inclusion of at least the first overtone, and preferably of the first two or three overtones; (ii) a determination of the black hole mass and spin with precision better than 1% requires the inclusion of at least two quasinormal modes for any given angular harmonic mode (l, m). We also improve on previous estimates and fits for the ringdown energy radiated in the various multipoles. These results are important to quantify theoretical (as opposed to instrumental) limits in parameter estimation accuracy and tests of general relativity allowed by ringdown measurements with high signal-to-noise ratio gravitational wave detectors.
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