Rapid sinking and efficient mergers of supermassive black holes in compact high-redshift galaxies

We present a cosmological zoom-in simulation targeting the high redshift compact progenitor phase of massive galaxies, with the most massive galaxy reaching a stellar mass of $M_{\star}=8.5\times 10^{10} \ M_{\odot}$ at $z=5$. The dynamics of supermassive black holes (SMBHs) is modelled from seeding down to their coalescence at sub-parsec scales due to gravitational wave (GW) emission by utilising a new version of the KETJU code, which combines regularised integration of sufficiently massive SMBHs with a dynamical friction subgrid model for lower-mass SMBHs. All nine massive galaxies included in this study go through a gas-dominated phase of early compaction in the redshift range of $z\sim 7-9$, starting at stellar masses of $M_\star\gtrsim 10^8\ \mathrm{M}_\odot$ and ending at a few times $M_{\star}\sim 10^9\ \mathrm{M}_\odot$. The sizes, masses and broad band fluxes of these compact systems are in general agreement with the population of systems observed with JWST known as `Little Red Dots'. In the compact phase, the stellar and SMBH masses grow rapidly, leading to a sharp decline in the central gas fractions. The outer regions, however, remain relatively gas-rich, leading to subsequent off-centre star formation and size growth. Due to the very high central stellar densities ($\rho_{\star}\gtrsim 10^{13}\,\mathrm{M_\odot/kpc^3}$), the SMBHs merge rapidly, typically just $\sim 4-35\ \mathrm{Myr}$ after the SMBH binaries have become bound. Combining KETJU with the phenomenological PhenomD model resolves the complete evolution of the GW emission from SMBH binaries through the Pulsar Timing Array frequency waveband up to the final few orbits that produce GWs observable with the future LISA mission.