Detection template families for gravitational waves from the final stages of binary–black-hole inspirals: Nonspinning case

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses $m=5\mathrm{}–{20M}_{\odot },$ moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post-Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is $\gtrsim 0.95$ (corresponding to an event rate loss $\lesssim 15\%)$ and we estimate that the discretization of the template family, for $\sim {10}^4$ templates, increases the loss to $\lesssim 20\%.$