Abstract: The diffusive propagation of nonrelativistic cosmic ray (CR) protons undergoing energy losses by ionization in a dense homogeneous infinitely extended interstellar molecular cloud (MC) is investigated in a spatially one-dimensional geometry. The steady-state transport equation for the differential number density of nonrelativistic CR protons is solved with the boundary condition that at the edge of cloud it agrees with the interstellar CR number density. The derived CR proton density distribution in the MC sensitively depends on two characteristic length scales determined by the ratio of the time scales for diffusive propagation and ionization losses. In the edge region where 0 less than or equal Z less than or euqal Z_0 = 1.47 * 10^(-4) pc the ionization time scale is much longer than the diffusion time scales for all CR momenta, so here the CR proton density distribution equals the incoming interstellar CR proton distribution. For intermediate penetration depths Z_0 less than Z less than or equal Z_1 = 2.33 pc only CR with low momenta are affected by the ionization losses, whereas at large penetration depths Z greater than Z_1 CRs at all momenta are affected by the ionization losses. This leads to different momentum spectra and spatial distributions of the CR protons and their total density in these three regions. Consequently, nonrelativistic CRs inside MCs lose energy by ionizing and heating the molecular gas at small penetration depths Z less than Z_1 = 2.33 pc, whereas at large penetration depths Z greater than Z_1 they are collectively dissipated by the streaming instability. MCs with thicknesses much greater than Z_1 are an efficient sink of nonrelativistic CRs.
Cosmic rays and MHD turbulence generation in interstellar molecular clouds
Reinhard Schlickeiser (University of Bochum) // March 17, 2016
Abstract: The diffusive propagation of nonrelativistic cosmic ray (CR) protons undergoing energy losses by ionization in a dense homogeneous infinitely extended interstellar molecular cloud (MC) is investigated in a spatially one-dimensional geometry. The steady-state transport equation for the differential number density of nonrelativistic CR protons is solved with the boundary condition that at the edge of cloud it agrees with the interstellar CR number density. The derived CR proton density distribution in the MC sensitively depends on two characteristic length scales determined by the ratio of the time scales for diffusive propagation and ionization losses. In the edge region where 0 less than or equal Z less than or euqal Z_0 = 1.47 * 10^(-4) pc the ionization time scale is much longer than the diffusion time scales for all CR momenta, so here the CR proton density distribution equals the incoming interstellar CR proton distribution. For intermediate penetration depths Z_0 less than Z less than or equal Z_1 = 2.33 pc only CR with low momenta are affected by the ionization losses, whereas at large penetration depths Z greater than Z_1 CRs at all momenta are affected by the ionization losses. This leads to different momentum spectra and spatial distributions of the CR protons and their total density in these three regions. Consequently, nonrelativistic CRs inside MCs lose energy by ionizing and heating the molecular gas at small penetration depths Z less than Z_1 = 2.33 pc, whereas at large penetration depths Z greater than Z_1 they are collectively dissipated by the streaming instability. MCs with thicknesses much greater than Z_1 are an efficient sink of nonrelativistic CRs.