Set them free: extending RAMCOAL to model massive black hole triplets in hydrodynamical simulations of galaxies

Massive black hole binaries (MBHBs), and the higher-order multiples produced by repeated galaxy mergers, spend part of their lives in dynamical regimes that cosmological simulations cannot resolve, even though these regimes set their merger delays, spins, recoils, and host-galaxy context. We extend the RAMCOAL framework to follow such subgrid massive black hole triplets directly within hydrodynamical galaxy simulations. As in the original staged binary model, the black holes start as sink particles, pass through a dynamical-friction phase, and settle into bound binaries that harden through stellar scattering, gas torques, circumbinary-disc coupling, and gravitational-wave emission. When a hierarchical triplet becomes chaotic, RAMCOAL maps the encounter onto a library of three-body outcomes from direct N-body experiments and updates the surviving system, following the resulting mergers, exchanges, and ejections together with the accretion and spin evolution of each black hole. Using isolated-galaxy tests with contrasting geometries, we show that the encounter geometry alone can change which pair finally merges, and after how long. We demonstrate the first triplet MBH dynamical evolution all the way to coalescence inside a live hydrodynamical simulation. This establishes an end-to-end capability to predict triplet-driven MBH coalescences self-consistently coupled to the evolving host galaxy. Because each MBHB coalescence carries its environmental history through the subgrid phase, RAMCOAL offers a route toward merger catalogues that link the gravitational-wave signatures of coalescing black holes to the galaxies in which they form.