Resolving numerical star formation: a cautionary tale

Resolution studies of test problems set baselines and help define minimum resolution requirements, however, resolution studies must also be performed on scientific simulations to determine the effect of resolution on the specific scientific results. We perform a resolution study on the formation of a protostar by modelling the collapse of gas through 14 orders of magnitude in density. This is done using compressible radiative non-ideal magnetohydrodynamics. Our suite consists of an ideal magnetohydrodynamics (MHD) model and two non-ideal MHD models, and we test three resolutions for each model. The resulting structure of the ideal MHD model is approximately independent of resolution, although higher magnetic field strengths are realised in higher resolution models. The non-ideal MHD models are more dependent on resolution, specifically the magnetic field strength and structure. Stronger magnetic fields are realised in higher resolution models, and the evolution of detailed structures such as magnetic walls are only resolved in our highest resolution simulation. In several of the non-ideal MHD models, there is an off-set between the location of the maximum magnetic field strength and the maximum density, which is often obscured or lost at lower resolutions. Thus, understanding the effects of resolution on numerical star formation is imperative for understanding the formation of a star.