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).Comment: Accepted by MNRAS, 15 pages, 8 figure
