Gas-driven massive black hole binaries: signatures in the nHz gravitational wave background

Pulsar timing arrays (PTAs) measure nHz frequency gravitational waves (GWs) generated by orbiting massive black hole binaries (MBHBs) with periods between 0.1 and 10 yr. Previous studies on the nHz GW background assumed that the inspiral is purely driven by GWs. However, torques generated by a gaseous disc can shrink the binary much more efficiently than GW emission, reducing the number of binaries at these separations. We use simple disc models for the circumbinary gas and for the binary-disc interaction to follow the orbital decay of MBHBs through physically distinct regions of the disc, until GWs take over their evolution. We extract MBHB cosmological merger rates from the Millennium simulation, generate Monte Carlo realizations of a population of gas-driven binaries and calculate the corresponding GW amplitudes of the most luminous individual binaries and the stochastic GW background. For steady state alpha-discs witha alpha > 0.1, we find that the nHz GW background can be significantly modified. The number of resolvable binaries is however not changed by the presence of gas; we predict 1-10 individually resolvable sources to stand above the noise for a 1-50 ns timing precision. Gas-driven migration reduces predominantly the number of small total mass or unequal mass ratio binaries, which leads to the attenuation of the mean stochastic GW background, but increases the detection significance of individually resolvable binaries. The results are sensitive to the model of binary-disc interaction. The GW background is not attenuated significantly for time-dependent models of Ivanov, Papaloizou & Polnarev.