Massive black hole binary inference with pulsar timing array searches for gravitational waves

Massive black holes reside at the centre of most galaxies. During galaxy mergers, the massive black holes at the centres of each galaxy are believed to form binaries, which can emit gravitational waves in the nano-Hertz frequency band. Pulsar timing arrays are being used to search for the gravitational wave background from many massive binary black hole binaries throughout cosmic time. No detection has yet been made, however pulsar timing arrays are placing upper limits on the strength of the gravitational wave background from these sources. As upper limits improve with sensitivity, we can make comparisons to astrophysical models of the population of massive black hole binaries. A lack of detection could indicate that either these binaries stall before reaching gravitational wave emission or are accelerated through the band. Using Bayesian hierarchical modeling we consider implications of this upper limit for a range of astrophysical scenarios, without invoking stalling, nor more exotic physical processes. We find these models to be consistent so far, however as sensitivity improves the most optimistic predictions will become disfavored.