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.