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 bidirectional inflow--outflow from the event horizon to the Bondi scale -- we present a suite of long-duration GRMHD simulations spanning BH spins $|a_{\ast }|=0$--0.9 and Bondi radii $R_B/r_g=4\times 10^2$--$2\times 10^6$. From these simulations we derive spin-dependent subgrid prescriptions from first principles, applicable to hot accretion flows with low-Eddington ratios ($f_{\mathrm{Edd}}\lesssim 10^{-3}$), for adoption in cosmological simulations and semi-analytic models. We provide compact analytic fits for the time-averaged accretion rate $\dot{M}(R_B,a_{\ast })$ and feedback power ${\dot{E}}_{\mathrm{fb}}(R_B,a_{\ast })$ with respect to the Bondi rate ${\dot{M}}_B$, 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 $\dot{M}$ and feedback efficiency $\eta$, 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 $s(a_{\ast })\simeq -3.7a_{\ast }$, which implies a very long spindown timescale $t_s\simeq 12(10^{-3}/f_{\mathrm{Edd}})\mathrm{Gyr}$. 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.

10 pages, 4 figures