Temperature fluctuations of interstellar dust grains

The temperatures of interstellar dust grains are analyzed using stochastic simulations, taking into account the grain composition and size and the discreteness of the photon flux. [...] The distribution of grain temperatures is calculated for a broad range of grain sizes and for different intensities of the interstellar radiation field, relevant to diffuse clouds and to PDRs. The dependence of the average grain temperature on its size is shown for different irradiation intensities. It is found that the average temperatures of grains with radii smaller than about 0.02 $\mu$m are reduced due to the fluctuations. The average temperatures of grains of radii larger than about 0.35 $\mu$m are also slightly reduced due to their more efficient emission of infrared radiation, particularly when exposed to high irradiation intensities. The average temperatures <T> of silicate and carbonaceous grains are found to depend on the radiation field intensity X_MMP according to <T>~X_MMP^gamma, where the exponent gamma depends on the grain size and composition. This fitting formula is expected to be useful in simulations of interstellar processes, and can replace commonly used approximations which do not account for the grain temperature fluctuations and for the detailed properties of interstellar dust particles. The implications of the results on molecular hydrogen formation are also discussed. It is concluded that grain-temperature fluctuations tend to reduce the formation rate of molecular hydrogen, and cannot account for the observations of H_2 in photon dominated regions, even in the presence of chemisorption sites.