Non-ideal magnetohydrodynamics vs turbulence I: Which is the dominant process in protostellar disc formation?

Non-ideal magnetohydrodynamics (MHD) is the dominant process. We investigate the effect of magnetic fields (ideal and non-ideal) and turbulence (sub- and transsonic) on the formation of circumstellar discs that form nearly simultaneously with the formation of the protostar. This is done by modelling the gravitational collapse of a 1~M$_\odot$ gas cloud that is threaded with a magnetic field and imposed with both rotational and turbulent velocities. We investigate magnetic fields that are parallel/anti-parallel and perpendicular to the rotation axis, two rotation rates and four Mach numbers. Disc formation occurs preferentially in the models that include non-ideal MHD where the magnetic field is anti-parallel or perpendicular to the rotation axis. This is independent of the initial rotation rate and level of turbulence, suggesting that subsonic turbulence plays a minimal role in influencing the formation of discs. Aside from first core outflows which are influenced by the initial level of turbulence, non-ideal MHD processes are more important than turbulent processes during the formation of discs around low-mass stars.