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% 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 ∼4.3 eV for diffuse atomic gas to ∼13 eV for the moderately dense regions of molecular clouds and to ∼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.