Impulsive Spot Heating and Thermal Explosion of Interstellar Grains Revisited

Abstract: 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.