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Cosmic-ray and X-ray Heating of Interstellar Clouds and Protoplanetary Disks

Cosmic-ray and X-ray heating are derived from the electron energy loss calculations of Dalgarno, Yan and Liu for hydrogen-helium gas mixtures. These authors treated the heating from elastic scattering and collisional de-excitation of rotationally excited hydrogen molecules. Here we consider the heating that can arise from all ionization and excitation processes, with particular emphasis on the reactions of cosmic-ray and X-ray generated ions with the heavy neutral species, which we refer to as chemical heating. In molecular regions, chemical heating dominates and can account for 50 per cent of the energy expended in the creation of an ion pair. The heating per ion pair ranges in the limit of negligible electron fraction from about 4.3 eV for diffuse atomic gas, to about 13 eV for the moderately dense regions of molecular clouds and to about 18 eV for the very dense regions of protoplanetary disks. An important general conclusion of this study is that cosmic-ray and X-ray heating depends on the physical properties of the medium, i.e., on the molecular and electron fractions, the total density of hydrogen nuclei, and to a lesser extent on the temperature. It is also noted that chemical heating, the dominant process for cosmic-ray and X-ray heating, plays a role in UV irradiated molecular gas.