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.
