Self-consistent theory of cosmic ray penetration into molecular clouds: relativistic case

TL;DR

This paper develops a universal analytical model for relativistic cosmic ray penetration into molecular clouds with increasing density, revealing stronger modulation effects and aligning well with recent gamma-ray observations.

Contribution

It introduces a self-consistent, density-dependent model for CR self-modulation in molecular clouds, extending previous work to the relativistic case with analytical solutions.

Findings

CR self-modulation is stronger with higher density boundaries.

The model's predictions match recent gamma-ray observations.

Boundaries of the diffusion zone are at lower densities than previously assumed.

Abstract

We study penetration of interstellar cosmic rays (CRs) into molecular clouds surrounded by nonuniform diffuse envelopes. The present work generalizes our earlier model of CR self-modulation (Ivlev et al. 2018, Dogiel et al. 2018), in which the value for the envelope's gas density where CRs excite MHD waves was treated as a free parameter. Now, we investigate the case where the density monotonically increases toward the center. Assuming that CRs are relativistic, we obtain a universal analytical solution which does not depend on the particular shape of gas distribution in the envelope, and self-consistently derive boundaries of the diffusion zone formed within the envelope, where CRs are scattered at the self-excited waves. The values of the gas density at the boundaries are found to be substantially smaller than those assumed in the earlier model, which leads to a significantly stronger modulation of penetrating CRs. We compute the impact of CR self-modulation on the gamma-ray emission, and show that the results of our theoretical model are in excellent agreement with recent observations of nearby giant molecular clouds by Yang et al. (2023).