Systematic investigation of the expected gravitational wave signal from
  supermassive black hole binaries in the pulsar timing band
  In this letter we carry out the first systematic investigation of the
expected gravitational wave (GW) background generated by supermassive black
hole (SMBH) binaries in the nHz frequency band accessible to pulsar timing
arrays (PTAs). We take from the literature several estimates of the redshift
dependent galaxy mass function and of the fraction of close galaxy pairs to
derive a wide range of galaxy merger rates. We then exploit empirical black
hole-host relations to populate merging galaxies with SMBHs. The result of our
procedure is a collection of a large number of phenomenological SMBH binary
merger rates consistent with current observational constraints on the galaxy
assembly at z<1.5. For each merger rate we compute the associated GW signal,
eventually producing a large set of estimates of the nHz GW background that we
use to infer confidence intervals of its expected amplitude. When considering
the most recent SMBH-host relations, accounting for ultra-massive black holes
in brightest cluster galaxies, we find that the nominal $1\sigma$ interval of
the expected GW signal is only a factor of 3-to-10 below current PTA limits,
implying a non negligible chance of detection in the next few years.
