The effect of differential accretion on the Gravitational Wave Background and the present day MBH Binary population

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. \textbf{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.}