Self-consistent model of cosmic ray penetration into molecular clouds: Effect of energy losses

The theory of cosmic-ray (CR) penetration into dense molecular clouds developed recently for relativistic particles by Chernyshov (2024) is extended to nonrelativistic CRs. Interstellar CRs propagating into the clouds are able to resonantly excite magnetohydrodynamic waves in diffuse cloud envelopes. This leads to the self-modulation, such that particles are scattered off of the self-generated waves. In contrast to relativistic CRs, transport of lower-energy particles in the envelopes is generally heavily affected by ionization losses; furthermore, both CR protons and electrons contribute to wave excitation. We show that these effects have profound impact on the self-modulation, and can dramatically reduce CR spectra even for clouds with moderate column densities of a few times <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mn>21</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msup><a:mi>cm</a:mi><a:mrow><a:mo>−</a:mo><a:mn>2</a:mn></a:mrow></a:msup></a:math>.