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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 0.1-10 yr. Previous studies on the nHz GW background assumed that the inspiral is purely driven by GWs. However, torques generated by a gaseous disk can shrink the binary much more efficiently than GW emission, reducing the number of binaries at these separations. We use simple disk models for the circumbinary gas and for the binary-disk interaction to follow the orbital decay of MBHBs through physically distinct regions of the disk, 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-disks with 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--disk interaction. The GW background is not attenuated significantly for time-dependent models of Ivanov, Papaloizou, & Polnarev (1999).