Demystifying flux eruptions: Magnetic flux transport in magnetically arrested disks

Abstract

Magnetically arrested disks (MADs) are a compelling model for explaining variability in low-luminosity active galactic nuclei (AGN), including horizon-scale outbursts like those observed in Sagittarius A*. MADs experience powerful flux eruptions-episodic ejections of magnetic flux from the black hole horizon-that may drive the observed luminosity variations. In this work, we develop and validate a new formalism describing large-scale magnetic field transport in general relativistic magnetohydrodynamic simulations of MADs with geometrical thicknesses of $h/R=0.1$ and $h/R=0.3$. We introduce a net flux transport velocity, $v_\Phi$, which accounts for both advective and diffusive processes. We show that MADs maintain a statistical quasi-steady state where advection and diffusion nearly balance. Flux eruptions appear as small deviations from this equilibrium, with $v_\Phi/V_k\ll1$, where $V_k$ is the local Keplerian velocity. Using this framework, we analytically derive a recurrence timescale for flux eruptions, $t_{\rm rec}\sim1500\, r_g/c$. This timescale closely matches simulation results. The smallness of $v_\Phi$ explains the long recurrence times of flux eruptions compared to other system timescales. We also take a closer look at the diffusion of the magnetic field by performing the first measurement of turbulent resistivity in MADs. We then estimate the turbulent magnetic Prandtl number, defined as the ratio of turbulent viscosity to turbulent resistivity. We find $\mathcal{P}_m\sim3$, consistent with shearing-box simulations of magneto rotational instability-driven turbulence. While flux eruptions excite large-scale non-axisymmetric modes and locally enhance turbulent resistivity, magnetic field diffusion is dominated by smaller-scale turbulent motions. These results provide new insight into the nature of AGN variability and the fundamental physics of magnetic field transport.