APPLYING NUMERICAL RELATIVITY TO GRAVITATIONAL WAVE ASTRONOMY
APPLYING NUMERICAL RELATIVITY TO GRAVITATIONAL WAVE ASTRONOMY
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Date
2008-03-12
Authors
McWilliams, Sean Thomas
Advisor
Shawhan, Peter
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Abstract
General relativity predicts the existence of gravitational waves produced by
the motion of massive objects. The inspiral, merger, and ringdown of black hole
binaries is expected to be one of the brightest sources in the gravitational wave sky.
Interferometric detectors, such as the current ground-based Laser Interferometer
Gravitational Wave Observatory (LIGO) and the future space-based Laser Interferometer
Space Antenna (LISA), measure the influx of gravitational radiation from
the whole sky. Each physical process that emits gravitational radiation will have a
unique waveform, and prior knowledge of these waveforms is needed to distinguish a
signal from the noise inherent in the interferometer. In the strong field regime of the
merger, only numerical relativity, which solves the full set of Einstein's equations
numerically, has been able to provide accurate waveforms.
We present a comprehensive study of the nonspinning portion of parameter
space for which we have generated accurate simulations of the late inspiral through
merger and ringdown, and a comparison of those results with predictions from the
adiabatic Taylor-expanded post-Newtonian (PN) and effective-one-body (EOB) PN
approximations. We then focus on data analysis questions using the equal-mass
nonspinning as well as the 2:1, 4:1, and 6:1 mass ratio nonspinning black hole binary
(BHB) waveforms. We construct a full waveform by combining our results from
numerical relativity with a highly accurate Taylor PN approximation, and use it
to calculate signal-to-noise ratios (SNRs) for several detectors. We measure the
mass ratio scaling of the waveform amplitude through the inspiral and merger, and
compare our observations with predictions from PN. Lastly, we turn our focus to
parameter estimation with LISA, and investigate the increased accuracy with which
parameters can be measured by including both the merger and inspiral waveforms,
compared to estimates without numerical waveforms which can only incorporate the
inspiral. We use the equal mass, nonspinning waveform as a test case and assess the
parameter uncertainty by means of the Fisher matrix formalism.