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

摘要

We discuss the extraction of information from detected binary black hole(BBH) coalescence gravitational waves, focusing on the merger phase that occursafter the gradual inspiral and before the ringdown. Our results are: (1) Ifnumerical relativity simulations have not produced template merger waveformsbefore 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 wavesshould typically be just barely visible in the noise for initial and advancedLIGO interferometers. (2) We derive an optimized (maximum likelihood) methodfor extracting a best-fit merger waveform from the noisy detector output; one"perpendicularly projects" this output onto a function space (specified usingwavelets) that incorporates our prior knowledge of the waveforms. An extensionof the method allows one to extract the BBH's two independent waveforms fromoutputs of several interferometers. (3) If numerical relativists produce codesfor generating merger templates but running the codes is too expensive to allowan extensive survey of the merger parameter space, then a coarse survey of thisparameter space, to determine the ranges of the several key parameters and toexplore several qualitative issues which we describe, would be useful for dataanalysis purposes. (4) A complete set of templates could be used to test thenonlinear dynamics of general relativity and to measure some of the binaryparameters. We estimate the number of bits of information obtainable from themerger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate theinformation loss due to template numerical errors or sparseness in the templategrid, and infer approximate requirements on template accuracy and spacing.