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, M A0 (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; M A0 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 (M A0 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.

We present, the Cosmic Ray Interstellar Propagation Tool using Itô Calculus, a new open-source software package to simulate the propagation of cosmic rays through the interstellar medium and to calculate the resulting observable non-thermal emission. C solves the Fokker-Planck equation describing transport of cosmic rays on scales larger than that on which their pitch angles become approximately isotropic, and couples this to a rich and accurate treatment of the microphysical processes by which cosmic rays in the energy range ∼MeV to ∼PeV lose energy and produce emission. C is deliberately agnostic as to both the cosmic ray transport model and the state of the background plasma through which cosmic rays travel. It can solve problems where cosmic rays stream, diffuse, or perform arbitrary combinations of both, and the coefficients describing these transport processes can be arbitrary functions of the background plasma state, the properties of the cosmic rays themselves, and local integrals of the cosmic ray field itself (e.g., the local cosmic ray pressure or pressure gradient). The code is parallelised using a hybrid OpenMP-MPI paradigm, allowing rapid calculations exploiting multiple cores and nodes on modern supercomputers. Here we describe the numerical methods used in the code, our treatment of the microphysical processes, and the set of code tests and validations we have performed.

The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from ∼ GeV − TeV are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfvén waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfvén velocity. The transport of streaming CRs is therefore sensitive to ionic Alfvén velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfvénic turbulence, as applies for a strongly magnetized ISM, the ionic Alfvén velocity probability density function (PDF) is determined solely by the density fluctuations from shocked gas forming parallel to the magnetic field, and we develop analytical models for the ionic Alfvén velocity PDF up to second moments. For super-Alfvénic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfvén velocity PDF. We discuss the implications of these findings for underlying “macroscopic” diffusion mechanisms in CRs undergoing the streaming instability, including modeling the macroscopic diffusion coefficient for the parallel transport in sub-Alfvénic plasmas. We also describe how, for highly-magnetized turbulent gas, the gas density PDF, and hence column density PDF, can be used to access information about ionic Alfvén velocity structure from observations of the magnetized ISM.