Turbulent diffusion of streaming cosmic rays in compressible, partially ionized plasma

Matt L. Sampson, James R. Beattie, Mark Krumholz, Roland Crocker, Christoph Federrath, Amit Seta

Abstract:

Cosmic rays (CRs) are a dynamically important component of the interstellar medium (ISM) of galaxies. The ∼GeV CRs that
carry most CR energy and pressure are likely confined by self-generated turbulence, leading them to stream along magnetic
field lines at the ion Alfvén speed. However, the consequences of self-confinement for CR propagation on galaxy scales
remain highly uncertain. In this paper, we use a large ensemble of magnetohydrodynamical turbulence simulations to quantify
how the basic parameters describing ISM turbulence – the sonic Mach number, M (plasma compressibility), Alfvén Mach
number, MA0 (strength of the large-scale field with respect to the turbulence), and ionisation fraction by mass, 𝜒 – affect the
transport of streaming CRs. We show that the large-scale transport of CRs whose small-scale motion consists of streaming
along field lines is well described as a combination of streaming along the mean field and superdiffusion both along (parallel
to) and across (perpendicular to) it; MA0 drives the level of anisotropy between parallel and perpendicular diffusion and 𝜒
modulates the magnitude of the diffusion coefficients, while in our choice of units, M is unimportant except in the sub-Alfvénic
(MA0 . 0.5) regime. Our finding that superdiffusion is ubiquitous potentially explains the apparent discrepancy between CR
diffusion coefficients inferred from measurements close to individual sources compared to those measured on larger, Galactic
scales. Finally, we present empirical fits for the diffusion coefficients as a function of plasma parameters that may be used as
sub-grid recipes for global interstellar medium, galaxy or cosmological simulations.