Nonlinear diffusion of cosmic rays escaping from supernova remnants: Cold partially neutral atomic and molecular phases

Aims: We aim to elucidate cosmic ray (CR) propagation in the weakly ionized environments of supernova remnants (SNRs) basing our analysis on the cosmic ray cloud (CRC) model.
Methods: We solved two transport equations simultaneously: one for the CR pressure and one for the Alfvén wave energy density where CRs are initially confined in the SNR shock. Cosmic rays trigger a streaming instability and produce slab-type resonant Alfvén modes. The self-generated turbulence is damped by ion-neutral collisions and by noncorrelated interaction with Alfvén modes generated at large scales.
Results: We show that CRs leaking in cold dense phases such as those found in cold neutral medium (CNM) and diffuse molecular medium (DiM) can still be confined over distances of a few tens of parsecs from the CRC center for a few thousand years. At 10 TeV, CR diffusion can be suppressed by two or three orders of magnitude. This effect results from a reduced ion-neutral collision damping in the decoupled regime. We calculate the grammage of CRs in these environments. We find that in both single and multi-phase setups at 10 GeV, CNM and DiM media can produce grammage in the range 10-20 g cm^-2 in the CNM and DiM phases. At 10 TeV, because of nonlinear propagation the grammage increases to values in the range 0.5-20 g cm^-2 in these two phases. We also present preliminary calculations in inhomogeneous interstellar medium combining two or three different phases where we obtain the same trends.