IMPULSIVE SPOT HEATING AND THERMAL EXPLOSION OF INTERSTELLAR GRAINS REVISITED

ABSTRACT The problem of the impulsive heating of dust grains in cold, dense interstellar clouds is revisited theoretically with the aim of better understanding the leading mechanisms of the explosive desorption of icy mantles. We rigorously show that if the heating of a reactive medium occurs within a sufficiently localized spot (e.g., the heating of mantles by cosmic rays (CRs)), then the subsequent thermal evolution is characterized by a single dimensionless number λ. This number identifies a bifurcation between two distinct regimes: when λ 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 whole-grain heating. The theory allows us to find a critical combination of physical parameters that govern the explosion of icy mantles due to impulsive spot heating. In particular, our calculations suggest that heavy CR species (e.g., iron ions) colliding with dust are able to trigger the explosion. Based on recently calculated local CR spectra, we estimate the expected rate of explosive desorption. The efficiency of the desorption, which in principle affects all solid species independent of their binding energy, is shown to be comparable to other CR desorption mechanisms typically considered in the literature. Also, the theory allows us to estimate the maximum abundances of reactive species that may be stored in the mantles, which provides important constraints on the available astrochemical models.