Temperature fluctuations in interstellar grains. I - Computational method and sublimation of small grains

A technique is presented for calculating the temperature distribution of interstellar dust grains in the presence of a radiation field or collisional heating by a hot gas, or both. The distribution functions are computed for grain sizes ranging from 0.02 micron to 2.5 A for graphite and silicate grains. Five different radiation fields are considered: one and three times the 'average' interstellar radiation in the solar neighborhood, the radiation field 0.3 pc from a B3V star appropriate for visual reflection nebulae, and the radiation fields in interstellar clouds at optical depths corresponding to visual extinctions of A(V) = 0.25 mag and A(V) = 0.50 mag. For the interstellar radiation field in the solar neighborhood, a minimum grain size N(crit) of roughly 23 for graphite grains and N(crit) of roughly 37 for silicate grains, where N(crit) is the number of atoms in a grain for which the lifetime against sublimation is 10 to the 13th s.