A Localized Current-Sheet Magnetic-Diffusion and Heating Prescription for Ideal-GRMHD Simulations of M87*-like Accretion Flows

Abstract

Ideal-GRMHD calculations provide the bulk accretion flows used in black-hole emission models. A localized dissipation prescription can add a resolved map of current-sheet activity while retaining that dynamical reference. We implement such a prescription in Athena++, using a smooth threshold on the dimensionless current proxy $α_J$ to select the magnetic-diffusion coefficient. The constrained-transport update is coupled to a conservative energy-flux correction. Gas heating follows from primitive recovery; $q_{Ohm}=ηJ^2$ is recorded as a diagnostic, without a second energy source. Static Fourier and traveling Alfvén tests measure the evolved thermal gain, and an open-boundary Schwarzschild test closes the Killing-energy ledger. The relative total-energy residual is below $2\times10^{-15}$ in these tests. A two-resolution Harris matrix gives localized rate exponents $0.510\pm0.027$ and $0.488\pm0.028$, consistent with $1/2$ over the specified early interval. The $η=10^{-3}$ rate exceeds the same-resolution ideal control by a factor of 5.96. In matched axisymmetric M87*-like runs, localized diffusion changes the early mean magnetic flux, accretion rate, and normalized flux by less than $0.02\%$, with a radial-density distance of $0.005\%$. During the late active phase, a common-restart on/off comparison keeps these mean shifts below $1.6\%$, within the intrinsic temporal variability, and gives a density distance of $0.29\%$. Uniform diffusion at the tested coefficient reduces the raw flux and accretion rate by $85\%$ and $99.8\%$. These comparisons establish a spatially selective diffusion prescription with explicit energy accounting and a quantified, small bulk-flow response.