APPLYING NUMERICAL RELATIVITY TO GRAVITATIONAL WAVE ASTRONOMY

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.