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In a seminal paper, Parker showed the vertical stratification of the interstellar medium (ISM) is unstable if magnetic fields and cosmic rays provide too large a fraction of pressure support. Cosmic ray acceleration is linked to star formation, so Parker’s instability and its nonlinear outcomes are a type of star formation feedback. Numerical simulations have shown the instability can significantly restructure the ISM, thinning the thermal gas layer and thickening the magnetic field and cosmic ray layer. However, the timescale on which this occurs is rather long (∼0.4 Gyr). Furthermore, the conditions for instability depend on the model adopted for cosmic ray transport. In this work, we connect the instability and feedback problems by examining the effect of a single, spatially and temporally localized cosmic ray injection on the ISM over ∼1 kpc³scales. We perform cosmic ray magnetohydrodynamic simulations using theAthena++code, varying the background properties, dominant cosmic ray transport mechanism, and injection characteristics between our simulation runs. We find robust effects of buoyancy for all transport models, with disruption of the ISM on timescales as short as 100 Myr when the background equilibrium is dominated by cosmic ray pressure.

 

Cosmic rays have been shown to be extremely important in the dynamics of diffuse gas in galaxies, helping to maintain hydrostatic equilibrium, and serving as a regulating force in star formation. In this paper, we address the influence of cosmic rays on galaxies by re-examining the theory of a cosmic ray Eddington limit, first proposed by Socrates et al. and elaborated upon by Crocker et al. and Huang & Davis. A cosmic ray Eddington limit represents a maximum cosmic ray energy density above which the interstellar gas cannot be in hydrostatic equilibrium, resulting in a wind. In this paper, we continue to explore the idea of a cosmic ray Eddington limit by introducing a general framework that accounts for the circumgalactic environment and applying it to five galaxies that we believe to be a good representative sample of the star-forming galaxy population, using different cosmic ray transport models to determine what gives each galaxy the best chance to reach this limit. We show that, while an Eddington limit for cosmic rays does exist, for our five galaxies, the limit either falls at star formation rates that are much larger or gas densities that are much lower than each galaxy’s measured values. This suggests that cosmic ray pressure is not the main factor limiting the luminosity of starburst galaxies.

 

Understanding the time-scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic ray transport in turbulent magnetic fields. We show that the diffusion time-scales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to numerical simulations. Very good agreement for a large parameter space is found, transforming classical scattering relation predictions into a computational prescription for the perpendicular component. We discuss and compare these findings, in particular, the time-scales to become diffusive with the time-scales that particles reside in astronomical environments, the so-called escape time-scales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the time-scales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.

 

Abstract Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is two-fold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmic-ray signatures. One of the most important aspects in the modeling of cosmic-ray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By taking the wave spectrum boundaries into account, we quantify cosmic-ray diffusion parallel and perpendicular to the guide field direction at turbulence levels above 5% of the total magnetic field. We apply our results of the parallel and perpendicular diffusion coefficient to the Milky Way. We show that simple purely diffusive transport is in conflict with observations of the inner Galaxy, but that just by taking a Galactic wind into account, data can be matched in the central 5 kpc zone. Further comparison shows that the outer Galaxy at $$>5$$ > 5  kpc, on the other hand, should be dominated by perpendicular diffusion, likely changing to parallel diffusion at the outermost radii of the Milky Way. 

ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.