The role of cosmic rays on magnetic field diffusion and the formation of
  protostellar discs
  The formation of protostellar discs is severely hampered by magnetic braking,
as long as magnetic fields remain frozen in the gas. The latter condition
depends on the levels of ionisation that characterise the innermost regions of
a collapsing cloud. The chemistry of dense cloud cores and, in particular, the
ionisation fraction is largely controlled by cosmic rays. The aim of this paper
is to evaluate whether the attenuation of the flux of cosmic rays expected in
the regions around a forming protostar is sufficient to decouple the field from
the gas, thereby influencing the formation of centrifugally supported disc. We
adopted the method developed in a former study to compute the attenuation of
the cosmic-ray flux as a function of the column density and the field strength
in clouds threaded by poloidal and toroidal magnetic fields. We applied this
formalism to models of low- and high-mass star formation extracted from
numerical simulations of gravitational collapse that include rotation and
turbulence. For each model we determine the size of the magnetic decoupling
zone, where collapse or rotation motion becomes unaffected by the local
magnetic field. In general, we find that decoupling only occurs when the
attenuation of cosmic rays is taken into account with respect to a calculation
in which the cosmic-ray ionisation rate is kept constant. The extent of the
decoupling zone also depends on the dust grain size distribution and is larger
if large grains (of radius $\sim 10^{-5}$ cm) are formed by compression and
coagulation during cloud collapse. We conclude that a realistic treatment of
cosmic-ray propagation and attenuation during cloud collapse may lead to a
value of the resistivity of the gas in the innermost few hundred AU around a
forming protostar that is higher than generally assumed.
