Massive black hole binary systems and the NANOGrav 12.5 year results

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported evidence for the presence of a common stochastic signal across their array of pulsars. The origin of this signal is still unclear. One of the possibilities is that it is due to a stochastic gravitational wave background (SGWB) in the $\sim 1-10\,{\rm nHz}$ frequency region. Taking the NANOGrav observational result at face value, we show that this signal would be fully consistent with a SGWB produced by an unresolved population of in-spiralling massive black hole binaries (MBHBs) predicted by current theoretical models. Considering an astrophysically agnostic model we find that the MBHB merger rate is loosely constrained to the range $10^{-11} - 2$ $\mathrm{Mpc}^{-3}\,\mathrm{Gyr}^{-1}$. Including additional constraints from galaxy pairing fractions and MBH-bulge scaling relations, we find that the MBHB merger rate is $10^{-5} - 5\times10^{-4}$ $\mathrm{Mpc}^{-3}\,\mathrm{Gyr}^{-1}$, the MBHB merger time-scale is $\le 3\,\mathrm{Gyr}$ and the norm of the $M_\mathrm{BH}-M_\mathrm{bulge}$ relation $\ge 1.2\times 10^{8}\,M_\odot$ (all intervals quoted at 90\% confidence). Regardless of the astrophysical details of MBHB assembly, this result would imply that a sufficiently large population of massive black holes pair up, form binaries and merge within a Hubble time.