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

A Resolution Study of Magnetically Arrested Disks