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Abstract

With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown gravitational waveforms from coalescing compact binaries by combining both descriptions into one complete hybrid signal. It is important to estimate the error of such waveforms. Previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. There are two outstanding issues that make it difficult to determine the minimum simulation length necessary to produce suitably accurate hybrids: (1) the relevant criteria for a signal search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model. For discrete hybrids this optimization is not possible. (2) these calculations require that NR waveforms already exist, while ideally we would like to know the necessary length before performing the simulation. Here we overcome these difficulties by developing a general procedure that allows us to estimate hybrid mismatch errors without numerical data, and to optimize them over all physical parameters. Using this procedure we find that, contrary to some earlier studies, ~10 NR orbits before merger allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning binaries, even with high mass-ratio (>20) are well modeled for astrophysically reasonable component masses. In addition, the parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the Advanced detector era, and begin to assess the limits of the science that can be done with them.