# A Resolution Study of Magnetically Arrested Disks

## TL;DR

This study examines the numerical convergence of simulations of magnetically arrested disks around spinning black holes, finding some flow properties converge while small-scale turbulence and emission variability do not.

## Contribution

It provides a detailed analysis of convergence in GRMHD simulations of black hole accretion disks using Athena++, highlighting which aspects are reliable and which require higher resolution.

## Key findings

- Accretion rate and large-scale flow structure are converged.
- Jet energy and spin energy extraction efficiency are converged.
- Small-scale turbulence and emission variability are not fully converged.

## Abstract

We investigate numerical convergence in simulations of magnetically arrested disks around spinning black holes. Using the general-relativistic magnetohydrodynamics code Athena++, we study the same system at four resolutions (up to an effective 512 by 256 by 512 cells) and with two different spatial reconstruction algorithms. The accretion rate and general large-scale structure of the flow agree across the simulations. This includes the amount of magnetic flux accumulated in the saturated state and the ensuing suppression of the magnetorotational instability from the strong field. The energy of the jet and the efficiency with which spin energy is extracted via the Blandford-Znajek process also show convergence. However the spatial structure of the jet shows variation across the set of grids employed, as do the Lorentz factors. Small-scale features of the turbulence, as measured by correlation lengths, are not fully converged. Despite convergence of a number of aspects of the flow, modeling of synchrotron emission shows that variability is not converged and decreases with increasing resolution even at our highest resolutions.