Impulsive Spot Heating and Thermal Explosion of Interstellar Grains
  Revisited
  The problem of impulsive heating of dust grains in cold, dense interstellar
clouds is revisited theoretically, with the aim to better understand leading
mechanisms of the explosive desorption of icy mantles. It is rigorously shown
that if the heating of a reactive medium occurs within a sufficiently localized
spot (e.g., heating of mantles by cosmic rays), then the subsequent thermal
evolution is characterized by a single dimensionless number $\lambda$. This
number identifies a bifurcation between two distinct regimes: When $\lambda$
exceeds a critical value (threshold), the heat equation exhibits the explosive
solution, i.e., the thermal (chemical) explosion is triggered. Otherwise,
thermal diffusion causes the deposited heat to spread over the entire grain --
this regime is commonly known as the whole-grain heating. The theory allows us
to find a critical combination of the physical parameters that govern the
explosion of icy mantles due to impulsive spot heating. In particular, the
calculations suggest that heavy cosmic ray species (e.g., iron ions) colliding
with dust are able to trigger the explosion. Based on the recently calculated
local cosmic-ray spectra, the expected rate of the explosive desorption is
estimated. The efficiency of the desorption, which affects all solid species
independent of their binding energy, is shown to be comparable with other
cosmic-ray desorption mechanisms typically considered in the literature. Also,
the theory allows us to estimate maximum abundances of reactive species that
may be stored in the mantles, which provides important constraints on available
astrochemical models.
