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

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, 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.

Cosmic-ray electron transport in the galaxy M 51

“…CRE diffusionDeflections of CREs in the Galactic magnetic field introduce diffusive transport behavior, which is characterized by the diffusion tensor D that enters the transport equation. It is known that in galaxies spatial diffusion can be anisotropic or isotropic dependent on the environment(Sampson et al 2022). In the absence of detailed knowledge for the three-dimensional modeling of diffusion tensor and their relation for M51, especially at the low particle energies, where predictions of the classical scattering relation break(Reichherzer et al 2022b), we assume scalar diffusion.…”

Ion alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays

“…Gas density fluctuations can occur on scales much smaller than the correlation scale of the magnetic field (e.g., ion fluctuations down to less than AU scales, Armstrong et al, 1995). A detailed experimental study of diffusion for streaming cosmic rays is beyond the scope of this study, and is presented with great detail in Sampson et al (2022). In this study we explore the ionic Alfvén wave fluctuations in a compressible, magnetized turbulent medium across a broad range of plasma parameters describing the diffuse, warm atomic medium to dense (possibly sub-Alfvénic- Li et al, 2013;Federrath et al, 2016;Hu et al, 2019;Heyer et al, 2020;Hwang et al, 2021;Hoang et al, 2021;Skalidis et al, 2021b) highly-supersonic molecular clouds, highlighting the role of compressibility in the generation of the inhomogeneities in ionic Alfvén wave speeds.…”

“…However, to first order, a slight asymmetry in the scattering distribution develops such that there is a bulk velocity along the field, v stream , that approaches the ion Alfvén speed, v A,ion B / 4πχρ , where B is the magnitude of the local magnetic field, ρ is the gas density and χ is the ionization fraction by mass. The asymmetry corresponds to an advective process whereby the population of scattering cosmic rays move down CR pressure gradients and along the field lines (Caprioli et al, 2009;Bell, 2013;Krumholz et al, 2020;Xu and Lazarian, 2021a;Bustard and Zweibel, 2021;Sampson et al, 2022). Throughout this study, we will refer to CRs that have selfconfined to stream at close to v A,ion as SCRs (streaming cosmic rays).…”

Cosmic Ray Interstellar Propagation Tool using Itô Calculus (criptic): software for simultaneous calculation of cosmic ray transport and observational signatures

“…on which B is measured is not assumed to be smaller that the turbulent dissipation scale, and thus there may be turbulent fluctuations in the magnetic field on top of the large-scale guide field B; this will often be the case in galactic or cosmological simulations, for example, where the simulation resolution is insufficient to resolve the magnetic dissipation scale. Thus we wish to leave open the possibility that, while CRs do not diffuse perpendicular to magnetic field lines (to leading order), the field lines themselves can wander perpendicular to the large-scale guide field, and this will induce an effective diffusion in the CRs perpendicular to the large-scale guide field (Beattie et al 2022;Sampson et al 2022).…”

“…can be used to solve a wide range of problems in CR transport. In Sampson et al (2022), we have already applied it to the problem of determining an effective transport theory for CRs that stream through a turbulent plasma. This application exploits -'s ability to model transport through an arbitrary, time-dependent background -in this case the output of an MHD turbulence simulation.…”