Massive Black Hole Binaries from the TNG50-3 Simulation: II. Using Dual AGNs to Predict the Rate of Black Hole Mergers

Dual active galaxy nuclei (dAGNs) trace the population of post-merger galaxies and are the precursors to massive black hole (MBH) mergers, an important source of gravitational waves that may be observed by LISA. In Paper I of this series, we used the population of nearly 2000 galaxy mergers predicted by the TNG50-3 simulation to seed semi-analytic models of the orbital evolution and coalescence of MBH pairs with initial separations of about 1 kpc. Here, we calculate the dAGN luminosities and separation of these pairs as they evolve in post-merger galaxies, and show how the coalescence fraction of dAGNs changes with redshift. We find that because of the several Gyr long dynamical friction timescale for orbital evolution, the fraction of dAGNs that eventually end in a MBH merger grows with redshift and does not pass 50% until a redshift of 1. However, dAGNs in galaxies with bulge masses >10^10 solar masses, or comprised of near-equal mass MBHs, evolve more quickly and have higher than average coalescence fractions. At any redshift, dAGNs observed with small separations (> 0.7 kpc) have a higher probability of merging in a Hubble time than more widely separated systems. As found in Paper I, radiation feedback effects can significantly reduce the number of MBH mergers, and this could be manifested as a larger than expected number of widely separated dAGNs. We present a method to estimate the MBH coalescence rate as well as the potential LISA detection rate given a survey of dAGNs. Comparing these rates to the eventual LISA measurements will help determine the efficiency of dynamical friction in post-merger galaxies.