Cosmic-ray ionisation in collapsing clouds
  Cosmic rays (CR) play an important role in dense molecular cores, affecting
their thermal and dynamical evolution and initiating the chemistry. Several
studies have shown that the formation of protostellar discs in collapsing
clouds is severely hampered by the braking torque exerted by the entrained
magnetic field on the infalling gas, as long as the field remains frozen to the
gas. We examine the possibility that the concentration and twisting of the
field lines in the inner region of collapse can produce a significant reduction
of the ionisation fraction. To check whether the CR ionisation rate (CRir) can
fall below the critical value required to maintain good coupling, we first
study the propagation of CRs in a model of a static magnetised cloud varying
the relative strength of the toroidal/poloidal components and the mass-to-flux
ratio. We then follow the path of CRs using realistic magnetic field
configurations generated by numerical simulations of a rotating collapsing
core. We find that an increment of the toroidal component of the magnetic
field, or, in general, a more twisted configuration of the field lines, results
in a decrease in the CR flux. This is mainly due to the magnetic mirroring
effect that is stronger where larger variations in the field direction are
present. In particular, we find a decrease of the CRir below 10^-18 s-1 in the
central 300-400 AU, where density is higher than about 10^9 cm-3. This very low
value of the CRir is attained in the cases of intermediate and low
magnetisation (mass-to-flux ratio lambda=5 and 17, respectively) and for
toroidal fields larger than about 40% of the total field. Magnetic field
effects can significantly reduce the ionisation fraction in collapsing clouds.
We provide a handy fitting formula to compute approximately the attenuation of
the CRir in a molecular cloud as a function of the density and the magnetic
configuration.
