Recipes for Jet Feedback and Spin Evolution of Black Holes with Strongly-Magnetized Super-Eddington Accretion Disks

A spinning black hole accreting from a disk of strongly magnetized plasma via a magnetically arrested disk is known to produce an efficient electromagnetic jet powered by the black hole's spin energy. We present general relativistic radiative magnetohydrodynamic simulations of magnetically arrested systems covering a range of sub- to super-Eddington accretion rates. Using the numerical results from these simulations, we develop formulae to describe the magnetization, jet efficiency, and spin evolution of an accreting black hole as a function of its spin and accretion rate. A black hole with near-Eddington accretion experiences a mild degree of spin-down because of angular momentum loss through the jet, leading to an equilibrium spin of 0.8 rather than 1.0 at the Eddington limit. As the accretion rate increases above Eddington, the spin-down effect becomes progressively stronger, ultimately converging on previous predictions based on non-radiative simulations. In particular, spin evolution drives highly super-Eddington systems toward a black hole spin near zero. The formulae developed in this letter may be applied to galaxy and cosmological scale simulations that include black holes. If magnetically arrested disk accretion is common among supermassive black holes, the present results have broad implications for active galactic nucleus feedback and cosmological spin evolution.