Learning about compact binary merger: The interplay between numerical relativity and gravitational-wave astronomy

Activities in data analysis and numerical simulation of gravitational waves have to date largely proceeded independently. In this work we study how waveforms obtained from numerical simulations could be effectively used within the data analysis effort to search for gravitational waves from black hole binaries. To this end we analyze the cross-correlation between different numerical waveforms weighted by the detector's noise. This allow us to propose measures to quantify the accuracy of numerical waveforms for the purpose of data analysis, study how sensitive the analysis is to errors in the waveforms, and propose a way to efficiently encode the waveform's information for its use as a member of the template bank. We estimate that ∼100 templates (and ∼10 simulations with different mass ratios) are needed to detect waves from nonspinning binary black holes with total masses in the range 100M ≤M≤400M using initial LIGO. Of course, many more simulation runs will be needed to confirm that the correct physics is captured in the numerical evolutions. From this perspective, we also discuss sources of systematic errors in numerical waveform extraction and provide order of magnitude estimates for the computational cost of simulations that could be used to estimate the cost of parameter space surveys. Finally, we discuss what information from near-future numerical simulations of compact binary systems would be most useful for enhancing the detectability of such events with contemporary gravitational-wave detectors and emphasize the role of numerical simulations for the interpretation of eventual gravitational-wave observations.