Exploring Proxies for the Supermassive Black Hole Mass Function: Implications for Pulsar Timing Arrays

Abstract: Supermassive black holes (SMBHs) reside at the center of every massive galaxy in the local Universe with masses that closely correlate with observations of their host galaxy implying a connected evolutionary history. The population of binary SMBHs, which form following galaxy mergers, is expected to produce a gravitational wave background (GWB) detectable by pulsar timing arrays (PTAs). PTAs are starting to see hints of what may be a GWB, and the amplitude of the emerging signal is towards the higher end of model predictions. Simulated populations of binary SMBHs can be constructed from observations of galaxies and are used to make predictions about the nature of the GWB. The greatest source of uncertainty in these observation-based models comes from the inference of the SMBH mass function, which is derived from observed host galaxy properties. In this paper, I undertake a new approach for inferring the SMBH mass function starting from a velocity dispersion function rather than a galaxy stellar mass function. I argue that this method allows for a more direct inference by relying on a larger suite of individual galaxy observations as well as relying on a more "fundamental" SMBH mass relation. I find that the resulting binary SMBH population contains more massive systems at higher redshifts than previous models. Additionally, I explore the implications for the detection of individually resolvable sources in PTA data.