Multi-Zone Modeling of Black Hole Accretion and Feedback in 3D GRMHD: Bridging Vast Spatial and Temporal Scales

Simulating accretion and feedback from the horizon scale of supermassive black holes (SMBHs) out to galactic scales is challenging because of the vast range of scales involved. Elaborating on H. Cho et al., we describe and test a "multizone" technique, which is designed to tackle this difficult problem in three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. While short-timescale variability should be interpreted with caution, the method is demonstrated to be well-suited for finding dynamical steady states over a wide dynamic range. We simulate accretion on a nonspinning SMBH ($a_* = 0$) using initial conditions and the external galactic potential from a large-scale galaxy simulation and achieve a steady state over eight decades in radius. As found in H. Cho et al., the density scales with radius as $\rho \propto r^{-1}$ inside the Bondi radius $R_B$, which is located at $R_B=2\times 10^5 \,r_g$ ($\approx 60\,{\rm pc}$ for M87), where $r_g$ is the gravitational radius of the SMBH; the plasma-$\beta$ is ~ unity, indicating an extended magnetically arrested state; the mass accretion rate $\dot{M}$ is $\approx 1\%$ of the analytical Bondi accretion rate $\dot{M}_B$ and there is continuous energy feedback out to $\approx 100R_B$ (or beyond $>\,{\rm kpc}$) at a rate $\approx 0.02 \dot{M}c^2$. Surprisingly, no ordered rotation in the external medium survives as the magnetized gas flows to smaller radii, and the final steady solution is very similar to when the exterior has no rotation. Using the multizone method, we simulate GRMHD accretion over a wide range of Bondi radii, $R_{\rm B} \sim 10^2 - 10^7\,r_{\rm g}$, and find that $\dot{M}/\dot{M}_B\approx (R_B/6\, r_g)^{-0.5}$.