Massive black hole merger rates: the effect of kpc separation wandering and supernova feedback

We revisit the predictions for the merger rate of massive black hole binaries detectable by the Laser Interferometer Space Antenna (LISA) and their background signal for pulsar-timing arrays. We focus on the effect of the delays between the merger of galaxies and the final coalescence of black hole binaries, and on supernova feedback on the black hole growth. By utilizing a semi-analytic galaxy formation model, not only do we account for the driving the evolution of binaries at separations $\lesssim 1$ pc (gas-driven migration, stellar hardening and triple/quadruple massive black hole systems), but we also improve on previous studies by accounting for the time spent by black hole pairs from kpc down to pc separation. We also include the effect of supernova feedback, which may eject gas from the nuclear region of low-mass galaxies, thus hampering the growth of black holes via accretion and suppressing their orbital migration in circumbinary disks. Despite including these novel physical effects, we predict that the LISA detection rate should still be $\gtrsim 2 \mbox{yr}^{-1}$, irrespective of the model for the black hole seeds at high redshifts. Scenarios where black holes form from $\sim100 M_\odot$ seeds are more significantly impacted by supernova feedback. We also find that for detectable events, the merging black holes typically have mass ratios between $\sim 0.1$ and $1$. Predictions for the stochastic background in the band of pulsar-timing array experiments are instead rather robust, and show only a mild dependence on the model.