Bridging Scales in Black Hole Accretion and Feedback: Subgrid Prescription from First Principles

Abstract Understanding how supermassive black holes (BHs) couple to their host galaxies across a vast spatial and temporal dynamic range remains a central challenge in galaxy evolution. Using the multizone framework—designed to capture a bidirectional inflow–outflow from the event horizon to the Bondi scale—we present a suite of long-duration GRMHD simulations spanning BH spins ∣ a * ∣ = 0–0.9 and Bondi radii R B / r g = 4 × 10 2 –2 × 10 6 . From these simulations we derive spin-dependent subgrid prescriptions from first principles, applicable to hot accretion flows with low Eddington ratios ( f Edd ≲ 10 −3 ), for adoption in cosmological simulations and semianalytic models. We provide compact analytic fits for the time-averaged accretion rate M ̇ ( R B , a * ) and feedback power E ̇ fb ( R B , a * ) with respect to the Bondi rate M ̇ B , which are largely insensitive to the initial gas configuration and magnetic field strength. To capture intrinsic time variability, we also quantify the full distributions of M ̇ and feedback efficiency η , both well described by lognormal statistics, with widths that increase toward larger R B . We further measure self-consistent spin evolution in the hot accretion mode, finding that the spin-up parameter varies as s ( a * ) ≃ −3.7 a * , which implies a very long spin-down timescale t s ≃ 12(10 −3 / f Edd ) Gyr. Thus, BH spins are effectively frozen during phases of quiescent accretion. Compared to conventional small-domain GRMHD calculations, our simulations, which reach dynamical equilibrium across horizon to galaxy scales, yield systematically different long-term accretion, feedback, and spin properties, cautioning against direct extrapolation from small-scale GRMHD simulations when constructing galactic-scale subgrid models.