The interplay between ambipolar diffusion and Hall effect on magnetic field decoupling and protostellar disc formation

Non-ideal MHD effects have been shown recently as a robust mechanism of averting the magnetic braking "catastrophe" and promoting protostellar disc formation. However, the magnetic diffusivities that determine the efficiency of non-ideal MHD effects are highly sensitive to microphysics. We carry out non-ideal MHD simulations to explore the role of microphysics on disc formation and the interplay between ambipolar diffusion (AD) and Hall effect during the protostellar collapse. We find that removing the smallest grain population ($\lesssim$10 nm) from the standard MRN size distribution is sufficient for enabling disc formation. Further varying the grain sizes can result in either a Hall-dominated or an AD-dominated collapse; both form discs of tens of AU in size regardless of the magnetic field polarity. The direction of disc rotation is bimodal in the Hall dominated collapse but unimodal in the AD-dominated collapse. We also find that AD and Hall effect can operate either with or against each other in both radial and azimuthal directions, yet the combined effect of AD and Hall is to move the magnetic field radially outward relative to the infalling envelope matter. In addition, microphysics and magnetic field polarity can leave profound imprints both on observables (e.g., outflow morphology, disc to stellar mass ratio) and on the magnetic field characteristics of protoplanetary discs. Including Hall effect relaxes the requirements on microphysics for disc formation, so that prestellar cores with cosmic-ray ionization rate of $\lesssim$2--3$\times10^{-16}$ s$^{-1}$ can still form small discs of $\lesssim$10 AU radius. We conclude that disc formation should be relatively common for typical prestellar core conditions, and that microphysics in the protostellar envelope is essential to not only disc formation, but also protoplanetary disc evolution.