Gas and dust temperature in pre-stellar cores revisited: New limits on
  cosmic-ray ionization rate
  We develop a self-consistent model for the equilibrium gas temperature and
size-dependent dust temperature in cold, dense pre-stellar cores, assuming an
arbitrary power-law size distribution of dust grains. Compact analytical
expressions applicable to a broad range of physical parameters are derived and
compared with predictions of the commonly used standard model. It is suggested
that combining the theoretical results with observations should allow us to
constrain the degree of dust evolution and the cosmic-ray ionization rate in
dense cores, and to help in discriminating between different regimes of
cosmic-ray transport in molecular clouds. In particular, assuming a canonical
MRN distribution of grain sizes, our theory demonstrates that the gas
temperature measurements in the pre-stellar core L1544 are consistent with an
ionization rate as high as $\sim 10^{-16}$ s$^{-1}$, an order of magnitude
higher than previously thought.
