Cosmic ray and plasma coupling for isothermal supersonic turbulence in the magnetized interstellar medium

TL;DR

This study investigates how cosmic rays influence magnetized, turbulent interstellar plasmas, revealing regimes of coupling and decoupling that affect turbulence properties and cosmic ray heating.

Contribution

It introduces a two-moment CRMHD model to dynamically analyze cosmic ray and plasma interactions, identifying regimes of coupling and their effects on turbulence and heating.

Findings

Coupled regime reduces Mach number and density fluctuations.

Decoupled regime shows negligible CR-plasma interactions.

CR heating occurs via structures in compressible velocity fields.

Abstract

Cosmic rays (CRs) are an integral part of the non-thermal pressure budget in the interstellar medium (ISM) and are the leading-order ionization mechanism in cold molecular clouds. We study the impacts that different microphysical CR diffusion coefficients and streaming speeds have on the evolution of isothermal, magnetized, turbulent plasmas, relevant to the cold ISM. We utilized a two-moment CR magnetohydrodynamic (CRMHD) model, allowing us to dynamically evolve both CR energy and flux densities with contributions from Alfv\'enic streaming and anisotropic diffusion. We identify $\textit{coupled}$ and $\textit{decoupled}$ regimes, and define dimensionless Prandtl numbers $\rm{Pm_c}$ and $\rm{Pm_s}$, which quantify whether the plasma falls within these two regimes. In the coupled regime -- characteristic of slow streaming ($\rm{Pm_s} < 1$) and low diffusion ($\rm{Pm_c} < 1$) -- the CR fluid imprints upon the plasma a mixed equation of state between $P_{\rm{c}} \propto \rho^{4/3}$ (relativistic fluid) and $P_{\rm{c}} \propto \rho^{2/3}$ (streaming), where $P_{\rm{c}}$ is the CR pressure, and $\rho$ is the plasma density. By modifying the sound speed, the coupling reduces the turbulent Mach number, and hence the amplitude of the density fluctuations, whilst supporting secular heating of the CR fluid. In contrast, in the decoupled regime ($\rm{Pm_s} > 1$ or $\rm{Pm_c} > 1$) the CR fluid and the plasma have negligible interactions. We further show that CR heating is enabled by coherent structures within the compressible velocity field, with no impact on the turbulence spectrum of incompressible modes.