Fluxes of Energetic Particles and the Ionization Rate in Very Dense Interstellar Clouds

Abstract

We investigate the propagation of the primary and secondary energetic protons, neutrons, electrons, and photons in a very dense cloud (protostar). Solving the one-dimensional transport equations we obtain the energy spectra and intensities of these particles as functions of the depth x (in g cm–2) from the surface of the protostar. The intensity of neutrons depends strongly on the density of the protostellar material because of the spontaneous decay. The secondary electrons and photons are mainly produced within the first 100-g cm–2 layer. At the depth x ≳ 100 g cm–2 the cascade processes become dominant, and all the intensities are attenuated exponentially with the characteristic lengths of 69 g cm–2 for nucleons and 100 g cm–2 for electrons and photons.

Using the calculated intensities we investigate the ionization rates of the hydrogen molecule by these particles. The ionization rate by protons decreases exponentially with the characteristic length of nucleons, 69 g cm–2. At x ≳ 150 g cm–2 electrons and photons are the main ionization sources, and the attenuation length of the ionization rate by them is 96 g cm–2. At x ≳ 1100 g cm–2 the ionization by radioactive elements in the protostellar material is more efficient than by the energetic particles. The most efficient element is 40K, and the total ionization rate by these elements is 6.9 × 10–23 s–1 (per hydrogen molecule) independent of the density.