RAMCOAL: Tracking on-the-fly massive black hole binary evolution and coalescence in galaxy simulations

The detection of gravitational waves (GWs) from massive black hole binary (MBHB) coalescence motivates the development of a subgrid model. We present RAMCOAL, integrated into the RAMSES code, which simulates the orbital evolution of MBHBs, while accounting for stellar and gaseous dynamical friction (DF), stellar scattering, circumbinary disk interactions, and GW emission at scales below the simulation resolution. Unlike post-processing approaches, RAMCOAL tracks the real-time evolution of MBHBs within hydrodynamical simulations of galaxies using local quantities to model the dynamics and accretion. This approach enables more accurate predictions of the GW signals and the properties of merging black holes. We validated RAMCOAL across isolated and merging galaxy setups at resolutions of 10, 50, and 100 pc, with and without black hole accretion and feedback. In addition, we tested the model in seven galaxy merger scenarios at 100 pc resolution. These tests demonstrated that RAMCOAL is largely resolution-independent and successfully captures the effects of DF from stars, dark matter, and gas, loss-cone scattering, viscous drag from circumbinary disks, and GW emission – all within a realistic galactic environment even at low resolution. With RAMCOAL, we can better estimate MBHB coalescence rates and the GW background, while providing insights into the electromagnetic counterparts of GW sources. This approach bridges the gap between electromagnetic observations and GW detection, offering a more comprehensive understanding of MBHB evolution in cosmological simulations.