Infrared emission from interstellar dust. I. Stochastic heating of small grains

We present a method for calculating the infrared emission from a population of dust grains heated by starlight, including very small grains for which stochastic heating by starlight photons results in high-temperature transients. Because state-to-state transition rates are generally unavailable for complex molecules, we consider model polycyclic aromatic hydrocarbon (PAH), graphitic, and silicate grains with realistic vibrational mode spectra and realistic radiative properties. The vibrational density of states is used in a statistical-mechanical description of the emission process. Unlike previous treatments, our approach fully incorporates multiphoton heating effects, important for large grains or strong radiation fields. We discuss how the "temperature" of the grain is related to its vibrational energy. By comparing with an "exact" statistical calculation of the emission process, we determine the conditions under which the "thermal" and the "continuous cooling" approximations can be used to calculate the emission spectrum. We present results for the infrared emission spectra of PAH grains of various sizes heated by starlight. We show how the relative strengths of the 6.2, 7.7, and 11.3 mum features depend on grain size, starlight spectrum and intensity, and grain charging conditions. We show results for grains in the "cold neutral medium" and "warm ionized medium" and representative conditions in photodissociation regions. Our model results are compared to observed ratios of emission features for the Milky Way and other galaxies and for the M17 and NGC 7023 photodissociation regions.