Mapping Inspiral Rates on Population Synthesis Parameters

Formation rates of compact object binaries are often derived from population synthesis calculations. However, such calculations depend sensitively on a relatively large number of model input parameters. Given the considerable uncertainty in those model parameters, the predicted inspiral rates for double compact objects observable by gravitational wave interferometric detectors have been shown to be uncertain by several orders of magnitude. Typically, inspiral rates are estimated for only a small set of models with a remarkably poor coverage of the highly multidimensional parameter space (primarily because of limited computer resources). Here, using as an example seven population synthesis model parameters, we show that it is possible to derive fits of double-compact object inspiral rates that depend simultaneously on all seven parameters. We find these fits to be accurate to 50% for binary black holes and to 40% for binary neutron stars. The availability of such fits implies that (1) depending on the problem of interest, it is not necessary to complete large numbers of computationally demanding population synthesis calculations and (2) for the first time, sufficient exploration of the relevant phase space and assessment of the uncertainties involved are not limited by computational resources and become feasible.