Analyzing black-hole ringdowns. (arXiv:2107.05609v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Isi_M/0/1/0/all/0/1">Maximiliano Isi</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Farr_W/0/1/0/all/0/1">Will M. Farr</a>
A perturbed black hole rings down by emitting gravitational waves in tones
with specific frequencies and durations. Such tones encode prized information
about the geometry of the source spacetime and the fundamental nature of
gravity, making the measurement of black hole ringdowns a key goal of
gravitational wave astronomy. However, this task is plagued by technical
challenges that invalidate the naive application of standard data analysis
methods and complicate sensitivity projections. In this paper, we provide a
comprehensive account of the formalism required to properly carry out ringdown
analyses, examining in detail the foundations of recent observational results,
and providing a framework for future measurements. We build on those insights
to clarify the concepts of ringdown detectability and resolvability — touching
on the drawbacks of both Bayes factors and naive Fisher matrix approaches —
and find that overly pessimistic heuristics have led previous works to
underestimate the role of ringdown overtones for black hole spectroscopy. We
put our framework to work on the analysis of a variety of simulated signals in
colored noise, including analytic injections and a numerical relativity
simulation consistent with GW150914. We demonstrate that we can use tones of
the quadrupolar angular harmonic to test the no-hair theorem at current
sensitivity, with precision comparable to published constraints from real data.
Finally, we assess the role of modeling systematics, and project measurements
for future, louder signals. We release ringdown, a Python library for analyzing
black hole ringdowns using the the methods discussed in this paper, under a
permissive open-source license at https://github.com/maxisi/ringdown
A perturbed black hole rings down by emitting gravitational waves in tones
with specific frequencies and durations. Such tones encode prized information
about the geometry of the source spacetime and the fundamental nature of
gravity, making the measurement of black hole ringdowns a key goal of
gravitational wave astronomy. However, this task is plagued by technical
challenges that invalidate the naive application of standard data analysis
methods and complicate sensitivity projections. In this paper, we provide a
comprehensive account of the formalism required to properly carry out ringdown
analyses, examining in detail the foundations of recent observational results,
and providing a framework for future measurements. We build on those insights
to clarify the concepts of ringdown detectability and resolvability — touching
on the drawbacks of both Bayes factors and naive Fisher matrix approaches —
and find that overly pessimistic heuristics have led previous works to
underestimate the role of ringdown overtones for black hole spectroscopy. We
put our framework to work on the analysis of a variety of simulated signals in
colored noise, including analytic injections and a numerical relativity
simulation consistent with GW150914. We demonstrate that we can use tones of
the quadrupolar angular harmonic to test the no-hair theorem at current
sensitivity, with precision comparable to published constraints from real data.
Finally, we assess the role of modeling systematics, and project measurements
for future, louder signals. We release ringdown, a Python library for analyzing
black hole ringdowns using the the methods discussed in this paper, under a
permissive open-source license at https://github.com/maxisi/ringdown
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