Production of atomic hydrogen by cosmic rays in dark clouds
  The presence of small amounts of atomic hydrogen, detected as absorption dips
in the 21 cm line spectrum, is a well-known characteristic of dark clouds. The
abundance of hydrogen atoms measured in the densest regions of molecular clouds
can be only explained by the dissociation of H$_2$ due to cosmic rays. We want
to assess the role of Galactic cosmic rays in the formation of atomic hydrogen,
by using recent developments in the characterisation of the low-energy spectra
of cosmic rays and advances in the modelling of their propagation in molecular
clouds. We model the attenuation of the interstellar cosmic rays entering a
cloud and compute the dissociation rate of molecular hydrogen due to collisions
with cosmic-ray protons and electrons as well as fast hydrogen atoms. We
compare our results with the available observations. The cosmic-ray
dissociation rate is entirely determined by secondary electrons produced in
primary ionisation collisions. These secondary particles constitute the only
source of atomic hydrogen at column densities above $\sim10^{21}$ cm$^{-2}$. We
also find that the dissociation rate decreases with column density, while the
ratio between the dissociation and ionisation rates varies between about 0.6
and 0.7. From comparison with observations we conclude that a relatively flat
spectrum of interstellar cosmic-ray protons, as the one suggested by the most
recent Voyager 1 data, can only provide a lower bound for the observed atomic
hydrogen fraction. An enhanced spectrum of low-energy protons is needed to
explain most of the observations. Our findings show that a careful description
of molecular hydrogen dissociation by cosmic rays can explain the abundance of
atomic hydrogen in dark clouds. An accurate characterisation of this process at
high densities is crucial for understanding the chemical evolution of
star-forming regions.
