Dust coagulation feedback on magnetohydrodynamic resistivities in
  protostellar collapse
  The degree of coupling between the gas and the magnetic field during the
collapse of a core and the subsequent formation of a disk depends on the
assumed dust size distribution. We study the impact of grain-grain coagulation
on the evolution of magnetohydrodynamic (MHD) resistivities during the collapse
of a prestellar core. We use a 1-D model to follow the evolution of the dust
size distribution, out-of-equilibrium ionization state and gas chemistry during
the collapse of a prestellar core. To compute the grain-grain collisional rate,
we consider models for both random and systematic, size-dependent, velocities.
We include grain growth through grain-grain coagulation and ice accretion, but
ignore grain fragmentation. Starting with a MRN (Mathis et al. 1977) size
distribution, we find that coagulation in grain-grain collisions generated by
hydrodynamical turbulence is not efficient at removing the smallest grains, and
as a consequence does not affect much the evolution of the Hall and ambipolar
diffusion MHD resistivities which still severly drop during the collapse like
in models without coagulation. The inclusion of systematic velocities, possibly
induced by the presence of ambipolar diffusion, increases the coagulation rate
between small and large grains, removing small grains earlier in the collapse
and therefore limiting the drop in the Hall and ambipolar diffusion
resistivities. At intermediate densities ($n_{\rm H} \sim 10^8\,$cm$^{-3}$),
the Hall and ambipolar diffusion resistivities are found to be higher by 1 to 2
orders of magnitude in models with coagulation than in models where coagulation
is ignored, and also higher than in a toy model without coagulation where all
grains smaller than $0.1\,{\mu}$m would have been removed in the parent cloud
before the collapse. When grain drift velocities induced by ambipolar diffusion
are included, dust coagulation ... (abridged)
