Resolution analysis of magnetically arrested disk simulations

Polarisation measurements by the Event Horizon Telescope from M87$^{\ast}$ and Sgr A$^\ast$ suggest that there is a dynamically strong, ordered magnetic field, typical of what is expected of a magnetically arrested accretion disk (MAD). In such disks the strong poloidal magnetic field can suppress the accretion flow and cause episodic flux eruptions. Recent work shows that General Relativistic Magnetohydrodynamic (GRMHD) MAD simulations feature dynamics of turbulence and mixing instabilities that are becoming resolved at higher resolutions. We perform a convergence study of MAD states exceeding the status quo by an order of magnitude in resolution. We use existing 3D simulations performed with the H-AMR code, up to resolution of 5376 x 2304 x 2304 in a logarithmic spherical-polar grid. We find consistent time-averaged disk properties across all resolutions. However, higher resolutions reveal signs of inward angular momentum transport attributed to turbulent convection, particularly evident when mixing instabilities occur at the surfaces of flux tubes during flux eruptions. Additionally, we see wave-like features in the jet sheath, which become more prominent at higher resolutions, that may induce mixing between jet and disk. At higher resolutions, we observe the sheath to be thinner, resulting in increased temperature, reduced magnetisation, and greater variability. Those differences could affect the dissipation of energy, that would eventually result in distinct observable radiative emission from high-resolution simulations. With higher resolutions, we can delve into crucial questions about horizon-scale physics and its impact on the dynamics and emission properties of larger-scale jets.