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.
