Diffusive versus Free-streaming Cosmic-Ray Transport in Molecular Clouds

Abstract

Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume the CRs to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD turbulence present in the medium. We discuss the conditions under which CR diffusion can operate in a molecular cloud, calculate the local CR spectrum and ionization rate in both a free-streaming and diffusive propagation model, and highlight the different results from the two models. We also apply these two models to the propagation through the ISM to obtain the spectrum seen by Voyager 1, and show that such a spectrum favors a diffusive propagation model.

Impact of Low-Energy Cosmic Rays on Star Formation

“…3.1.2, the value of n H D 0 does not depend on N for a constant ionisation fraction and is determined by the velocity exponent λ of the turbu-lent spectrum. Silsbee and Ivlev (2019) showed that condition (51) is expected to hold for N 8×10 19 cm −2 for a Kolmogorov spectrum and for N 3×10 18 cm −2 for a Kraichnan spectrum. At higher column densities, the ion density is expected to drop dramatically when there are insufficient UV photons to keep carbon ionised.…”

“…it is possible to obtain simple analytical expressions for the local spectrum and corresponding ionisation rate as a function of column density. The loss function in the energy range relevant for ionisation in molecular clouds can be well approximated by (Padovani et al, 2018b;Silsbee and Ivlev, 2019)…”

“…(1) is the total column density of hydrogen atoms. Therefore, N in Silsbee and Ivlev (2019) is a factor of 1.67 higher than that in Padovani et al (2018b), which is taken into account in the value of L 0 .…”

“…MHD turbulence in these regions can resonantly scatter the pitch angles of penetrating CRs (Kulsrud and Pearce, 1969), leading to spatial diffusion. The spectrum of MHD turbulence determines the magnitude of the CR diffusion coefficient and its dependence on the particle energy (Schlickeiser et al, 2016;Silsbee and Ivlev, 2019). However, MHD turbulence can also be driven by anisotropy in the CR distribution function (Skilling and Strong, 1976;Morlino and Gabici, 2015;Ivlev et al, 2018), which arises in response to CR absorption in dense cores.…”

“…where ρ i is the ion mass density and v 2 turb is their mean squared turbulent velocity. Then, for a power-law turbulent spectrum with v turb (k) ∝ k −λ , the diffusion coefficient scales as (Silsbee and Ivlev, 2019)…”