Constraining astrophysical observables of galaxy and supermassive black hole binary mergers using pulsar timing arrays

We present an analytic model to describe the supermassive black hole binary ( SMBHB) merger rate in the Universe with astrophysical observables: galaxy stellar mass function, pair fraction, merger time-scale, and black hole-host galaxy relations. We construct observational priors and compute the allowed range of the characteristic spectrum h(c) of the gravitational wave background ( GWB) to be 10(-16) < h(c) < 10(-15) at a frequency of f = 1 yr(-1). We exploit our parametrization to tackle the problem of astrophysical inference from pulsar timing array ( PTA) observations. We simulate a series of upper limits and detections and use a nested sampling algorithm to explore the parameter space. Corroborating previous results, we find that the current PTA non-detection does not place significant constraints on any observables; however, either future upper limits or detections will significantly enhance our knowledge of the SMBHB population. If a GWB is not detected at a level of h(c)( f = 1 yr(-1)) = 10(-17), our current understanding of galaxy and SMBHB mergers is disfavoured at a 5 sigma level, indicating a combination of severe binary stalling, overestimating of the SMBH-host galaxy relations, and extreme dynamical properties of merging SMBHBs. Conversely, future detections of a Square Kilometre Array ( SKA)-type instrument will allow to constrain the normalization of the SMBHB merger rate in the Universe, the time between galaxy pairing and SMBHB merging, the normalization of the SMBH-host galaxy relations and the dynamical binary properties, including their eccentricity and density of stellar environment.