No tension between assembly models of supermassive black hole binaries and pulsar observations

Abstract: Pulsar timing arrays (PTAs) are presently the only means to search for the gravitational wave stochastic background from supermassive black hole binary populations, considered to be within the grasp of current or near future observations. However, the stringent upperlimit set by the Parkes PTA (Shannon et al. 2013, 2015) has been interpreted as excluding at $> 90\%$ confidence the current paradigm of binary assembly through galaxy mergers and hardening via stellar interactions, suggesting evolution is accelerated (by stars and/or gas) or stalled. Using Bayesian hierarchical modelling, we consider implications of this upperlimit for a comprehensive range of astrophysical scenarios, without invoking stalling nor more exotic physical processes. We find they are fully consistent with the upperlimit, but (weak) bounds on population parameters can be inferred. Bayes factors between models vary between $\approx 1.03$ -- $5.81$ and Kullback-Leibler divergences between characteristic amplitude prior and posterior lie between $0.37$ -- $0.85$. Considering prior astrophysical information on galaxy merger rates, recent upwards revisions of the black hole-galaxy bulge mass relation (Kormendy & Ho 2013) are disfavoured at $1.6\sigma$ against lighter models (e.g. Shankar et al. 2016). We also show, if no detection is achieved once sensitivity improves by an order of magnitude, the most optimistic scenario is disfavoured at $3.9\sigma$.