Merging black holes in dwarf galaxies: calculating binary black hole coalescence time-scales from simulations for LISA detection

Supermassive black holes (SMBHs) merging in dwarf galaxies will be detectable by the Laser Interferometer Space Antenna (LISA) in the mid-2030s. Previous cosmological hydrodynamic simulations have shown the prediction of massive BHs merging in dwarf galaxies, but these simulations are limited by their resolution and cannot follow BH pairs all the way to coalescence. We calculate the delay time between BH pairing and merger based on the properties of the BHs and their host galaxies, and use these properties to calculate gravitational wave strains for eleven different binary BHs that merge inside dwarf galaxies from eight cosmological simulations. This delay time calculation accounts for dynamical friction due to gas and stars, loss-cone scattering, and hardening of the binary due to gravitational radiation. Out of the eleven BH mergers in the simulations, five BH pairs will merge within 0.8-8 Gyr of forming a close pair and could be observed by LISA, and the remaining six are unresolved due to resolution limitations of the simulation. As all five of the resolved close pairs merge within a Hubble time, we make the broad estimate that close SMBH pairs in dwarf galaxies will merge and be detectable by LISA, but this estimate depends on either the presence of gas during orbital decay or a solution to the dynamical buoyancy problem in cored potentials.