Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates

Abstract

We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves, focusing on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are: (1) If numerical relativity simulations have not produced template merger waveforms before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves. For BBHs smaller than about 40 solar masses detected via their inspiral waves, the band pass filtering signal to noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (2) We derive an optimized (maximum likelihood) method for extracting a best-fit merger waveform from the noisy detector output; one "perpendicularly projects" this output onto a function space (specified using wavelets) that incorporates our prior knowledge of the waveforms. An extension of the method allows one to extract the BBH's two independent waveforms from outputs of several interferometers. (3) If numerical relativists produce codes for generating merger templates but running the codes is too expensive to allow an extensive survey of the merger parameter space, then a coarse survey of this parameter space, to determine the ranges of the several key parameters and to explore several qualitative issues which we describe, would be useful for data analysis purposes. (4) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary parameters. We estimate the number of bits of information obtainable from the merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.