Massive black hole binaries ( MBHBs ) form as a consequence of galaxy mergers .
However , it is still unclear whether they typically merge within a Hubble time , and how accretion may affect their evolution .
These questions will be addressed by pulsar timing arrays ( PTAs ) , which aim to detect the GW background ( GWB ) emitted by MBHBs during the last Myrs of inspiral .
Here we investigate the influence of differential accretion on MBHB merger rates , chirp masses and the resulting GWB spectrum .
We evolve a MBHB sample from the Illustris hydrodynamic cosmological simulation using semi-analytic models and for the first time self-consistently evolve their masses with binary accretion models .
In all models , MBHBs coalesce with median total masses up to 1.5 \times 10 ^ { 8 } M _ { \odot } , up to 3 - 4 times larger than in models neglecting accretion .
In our model with the largest plausible impact , the median mass ratio of coalescing MBHBs increases by a factor 3.6 , the coalescence rate by 52.3 \% , and the GWB amplitude by a factor 4.0 , yielding a dimensionless GWB strain A _ { yr ^ { -1 } } = 1 \times 10 ^ { -15 } .
Our model that favours accretion onto the primary MBH reduces the median mass ratio of coalescing MBHBs by a factor of 2.9 , and yields a GWB amplitude A _ { yr ^ { -1 } } = 3.1 \times 10 ^ { -16 } .
This is nearly indistinguishable from our model neglecting accretion , despite higher MBHB masses at coalescence . We further predict binary separation and mass ratio distributions of stalled MBHBs in the low-redshift universe , and find that these depend sensitively on binary accretion models .
This presents the potential for combined EM and GW observational constraints on merger rates and accretion models of MBHB populations .