Evidence for Low Universal Equilibrium Black Hole Spin in Luminous Magnetically Arrested Disks

Abstract

Relativistic collimated outflows, or jets, provide a crucial mode of active galactic nucleus feedback. Although jets extract their energy from the black hole (BH) rotation, their effect on the BH spin is poorly understood. Because the spin controls radiative and mechanical BH feedback, lack of first-principles models for spin evolution limits our ability to interpret observations, including the recent LIGO-Virgo-KAGRA spin constraints. Particularly important are luminous disks, which rapidly grow and strongly torque their BHs. Jetless and weakly magnetized standard luminous disks spin up their BHs to near-maximum spin, $a_{eq,NT}=0.998$. However, sufficient large-scale vertical magnetic flux can cause the inner disk to enter a magnetically arrested disk (MAD) state, whose jets can efficiently extract BH rotational energy and significantly spin down the BH. Lowell et al. (2024) found that nonradiative, thick MADs spin down their BHs to very low $a_{eq,MAD}^{thick}=0.07$. Their analytic model predicted that luminous, thin MADs also spin down their BHs to low $a_{eq,MAD}^{thin}\sim0.3\text{-}0.5$. To test this prediction, we perform 3D general relativistic (radiation) magnetohydrodynamic (GR(R)MHD) simulations of MADs across a wide range of BH spin ($-0.9\le{}a\le0.99$) and disk thickness ($0.03\le{}h/r\le0.3$, which corresponds to Eddington ratio, $0.35\le{}\dot{m}/\dot{m}_{Edd}\le\infty$). We find that luminous, thin MADs ($0.03\le{}h/r\le0.1$) efficiently spin down their BHs to a low universal equilibrium spin value, $a_{eq,MAD}^{thin}\approx0.3$: a maximally spinning BH ($a=1$) spins down to $a=0.5$ after accreting just $25\%$ of its initial mass. Our results follow quadratic convergence, $a_{eq,MAD}^{fit}\simeq0.3-2.7(h/r)^2\to0.3$ as $h/r\to0$, which we attribute to the aggressive cooling that renders disk thermodynamics irrelevant and magnetic forces insensitive to thermal $h/r$.