Universal radial scaling of large-scale black hole accretion for magnetically arrested and rocking accretion disks

Accretion onto supermassive black holes (BHs) can launch relativistic outflows and jets that inject energy and momentum into their surroundings. Understanding how such feedback shapes large-scale accretion is key to bridging observations from galactic scales (e.g., the Bondi radius, ${r}_{\mathrm{B}}$) down to event horizon scales (${r}_{\mathrm{g}}$), spanning five to six orders of magnitude. To address this challenge directly, we treat the spatial scale separation as a free parameter, varying it across two to four orders of magnitude. We perform a suite of the longest contiguous 3D general relativistic magnetohydrodynamic simulations to date ($t\ensuremath{\le}4\ifmmode\times\else\texttimes\fi{}{10}^{6}{r}_{\mathrm{g}}/c$), modeling Bondi-like accretion of rotating, nonrelativistic gas with weak vertical magnetic fields onto a rapidly spinning BH, achieving inflow equilibrium out to $r\ensuremath{\gtrsim}{10}^{3}{r}_{\mathrm{g}}$. We find that, regardless of scale separation or ambient gas rotation, all simulations reach a magnetically arrested disk (MAD) state in which the BH becomes magnetically saturated. In this state, the mass inflow rate follows a universal radial scaling relative to the Bondi rate: ${\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{M}}_{\mathrm{in}}(r)/{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{M}}_{\mathrm{B}}\ensuremath{\sim}(r/{r}_{\mathrm{B}}{)}^{s}$ with $s=0.66\ifmmode\pm\else\textpm\fi{}0.03$. The MAD state self-regulates through jets, outflows, and magnetic flux eruptions that can ultimately disrupt coherent angular momentum inflow, giving rise to a rocking accretion disk (RAD) state. This RAD state features chaotically oriented inflows, weak intermittent jets, and a steeper inflow slope of $s=0.87\ifmmode\pm\else\textpm\fi{}0.05$, along with significantly weaker outflows. For rapidly spinning BHs, the MAD and RAD BH accretion rates become comparable at typical scale separations, ${r}_{\mathrm{B}}/{r}_{\mathrm{g}}\ensuremath{\gtrsim}{10}^{5}$. The weaker outflows in the RAD state allow large-scale inflows to resume, eventually restoring the MAD state and enabling a repeating MAD-RAD cycle. We find that the MAD-RAD timescales can last from a few to hundreds of Bondi timescales, ${t}_{\mathrm{B}}\ensuremath{\sim}0.2\text{ }\text{ }\mathrm{Myr}\ifmmode\times\else\texttimes\fi{}({r}_{\mathrm{B}}/{10}^{5}{r}_{\mathrm{g}}{)}^{3/2}\ifmmode\times\else\texttimes\fi{}({M}_{\mathrm{BH}}/{10}^{9}{M}_{\ensuremath{\bigodot}})$, where ${M}_{\mathrm{BH}}$ is the BH mass, potentially setting the duty cycle of jetted active galactic nucleus outbursts, like M87*.