A chemical solver to compute molecule and grain abundances and non-ideal
  MHD resistivities in prestellar core collapse calculations
  We develop a detailed chemical network relevant to the conditions
characteristic of prestellar core collapse. We solve the system of
time-dependent differential equations to calculate the equilibrium abundances
of molecules and dust grains, with a size distribution given by size-bins for
these latter. These abundances are used to compute the different non-ideal
magneto-hydrodynamics resistivities (ambipolar, Ohmic and Hall), needed to
carry out simulations of protostellar collapse. For the first time in this
context, we take into account the evaporation of the grains, the thermal
ionisation of Potassium, Sodium and Hydrogen at high temperature, and the
thermionic emission of grains in the chemical network, and we explore the
impact of various cosmic ray ionisation rates. All these processes
significantly affect the non-ideal magneto-hydrodynamics resistivities, which
will modify the dynamics of the collapse. Ambipolar diffusion and Hall effect
dominate at low densities, up to n_H = 10^12 cm^-3, after which Ohmic diffusion
takes over. We find that the time-scale needed to reach chemical equilibrium is
always shorter than the typical dynamical (free fall) one. This allows us to
build a large, multi-dimensional multi-species equilibrium abundance table over
a large temperature, density and ionisation rate ranges. This table, which we
make accessible to the community, is used during first and second prestellar
core collapse calculations to compute the non-ideal magneto-hydrodynamics
resistivities, yielding a consistent dynamical-chemical description of this
process.
