Signatures of Circumbinary Disk Dynamics in Multi-Messenger Population Studies of Massive Black Hole Binaries

We investigate the effect of cutting-edge circumbinary disk (CBD) evolutionmodels on massive black hole binary (MBHB) populations and the gravitationalwave background (GWB). We show that CBD-driven evolution leaves a tell-talesignature in MBHB populations, by driving binaries towards an equilibriumeccentricity that depends on binary mass ratio. We find high orbitaleccentricities (e_ b∼ 0.5) as MBHBs enter multi-messenger observablefrequency bands. The CBD-induced eccentricity distribution of MBHB populationsin observable bands is independent of the initial eccentricity distribution atbinary formation, erasing any memory of eccentricities induced in thelarge-scale dynamics of merging galaxies. Our results suggest that eccentricMBHBs are the rule rather than the exception in upcoming transient surveys,provided that CBDs regularly form in MBHB systems. We show that the GWBamplitude is sensitive to CBD-driven preferential accretion onto the secondary,resulting in an increase in GWB amplitude A_ yr^-1 by over 100% withjust 10% Eddington accretion. As we self consistently allow for binaryhardening and softening, we show that CBD-driven orbital expansion does notdiminish the GWB amplitude, and instead increases the amplitude by a smallamount. We further present detection rates and population statistics of MBHBswith M_ b≳ 10^6 M_⊙ in LISA, showing that most binarieshave equal mass ratios and can retain residual eccentricities up to e_ b∼ 10^-3 due to CBD-driven evolution.