Hybrid GRMHD and force-free simulations of black hole accretion

We present a new approach for stably evolving general relativistic magnetohydrodynamic (GRMHD) simulations in regions where the magnetization σ =b²/ρ c² becomes large. GRMHD codes typically struggle to evolve plasma above σ ≈ 100 in simulations of black hole accretion. To ensure stability, GRMHD codes will inject mass density artificially to the simulation as necessary to keep the magnetization below a ceiling value σ ₘₐₓ. We propose an alternative approach where the simulation transitions to solving the equations of general relativistic force-free electrodynamics (GRFFE) above a magnetization σ ₜᵣₐₙₛ. We augment the GRFFE equations in the highly magnetized region with approximate equations to evolve the decoupled field-parallel velocity and plasma energy density. Our hybrid scheme is explicit and easily added to the framework of standard-volume GRMHD codes. We present a variety of tests of our method, implemented in the GRMHD code koral, and we show results from a 3D hybrid GRMHD + GRFFE simulation of a magnetically arrested disc (MAD) around a spinning black hole. Our hybrid MAD simulation closely matches the average properties of a standard GRMHD MAD simulation with the same initial conditions in low magnetization regions, but it achieves a magnetization σ ≈ 10⁶ in the evacuated jet funnel. We present simulated horizon-scale images of both simulations at 230 GHz with the black hole mass and accretion rate matched to M87*. Images from the hybrid simulation are less affected by the choice of magnetization cut-off σ cut imposed in radiative transfer than images from the standard GRMHD simulation.