Measuring the binary black hole mass spectrum with an astrophysically motivated parameterization

At the end of their lives stars more than ten times more masses than the sun collapse into a black hole. Theoretical estimates of the exact mass black hole a given star will form is uncertain due to difficulty simulating these complex systems. Stars in binaries are yet more difficult to model. There are, however, predictions which can generically be extracted from simulations. For example, if two stars initially have more mass but one contains more metals[^1], the higher metallicity star will form a less massive black hole.

Another generic prediction of stellar simulations is that stars which are more massive than some threshold mass undergo a series of violent pulsations. These pulsations are due to spontaneous formation of electron-positron pairs from the high energy photons inside the star. This leads to a reduction in the internal pressure and contraction of the star, leading to higher temperatures and more pair production. Eventually the pair production stabilises and the pulse stops. There may then be additional periods of instability before the final explosion and formation of a black hole. This process is known as a pulsational pair-instability supernova. For more massive stars the initial period of instability does not stop and the entire star is blown apart and no black hole forms in a pair-instability supernova.

The masses at which (pulsational) pair-instability supernovae occur depend on the specific internal physics of the star. We expect most black holes formed through pulsational pair-instability supernovae to be distributed about some fiducial mass. In this work we develop a model which includes this phenomenology and show that within the lifetime of current gravitational-wave detectors we will be able to measure the black hole mass distribution and by extension the details of pulsational pair-stability supernovae.

[^1]: Confusingly, when astronomers talk about metals, we mean everything except Hydrogen and Helium.