Measuring the Binary Black Hole Mass Spectrum with an Astrophysically Motivated Parameterization

Gravitational-wave detections have revealed a previously unknown population of stellar mass black holes with masses above 20 M-circle dot. These observations provide a new way to test models of stellar evolution for massive stars. By considering the astrophysical processes likely to determine the shape of the binary black hole mass spectrum, we construct a parameterized model to capture key spectral features that relate gravitational-wave data to theoretical stellar astrophysics. In particular, we model the signature of pulsational pair-instability supernovae, which are expected to cause all stars with initial mass 100 M circle dot less than or similar to M less than or similar to 150 M-circle dot to form similar to 40 M-circle dot black holes. This would cause a cutoff in the black hole mass spectrum along with an excess of black holes near 40 M-circle dot. We carry out a simulated data study to illustrate some of the stellar physics that can be inferred using gravitational-wave measurements of binary black holes and demonstrate several such inferences that might be made in the near future. First, we measure the minimum and maximum stellar black hole mass. Second, we infer the presence of a peak due to pair-instability supernovae. Third, we measure the distribution of black hole mass ratios. Finally, we show how inadequate models of the black hole mass spectrum lead to biased estimates of the merger rate and the amplitude of the stochastic gravitational-wave background.