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

Abstract

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.

Cosmic ray feedback in galaxies and galaxy clusters

“…Beattie et al. ( 2022 ) study compressible MHD turbulence simulations and find that for sub-Alfvénic turbulence, the probability density function of the ionic Alfvén velocity only depends on the density fluctuations that result from shocks forming parallel to the magnetic field. By contrast, for super-Alfvénic turbulence, the correlations between magnetic and density fluctuations are more complex.…”

Mirror Acceleration of Cosmic Rays in a High-β Medium

“…) The interaction of CRs with the ubiquitous turbulent magnetic fields causes their diffusion and stochastic acceleration (Schlickeiser 2002;Marcowith et al 2020;Liu & Jokipii 2021). The advances achieved recently in theoretically understanding (Goldreich & Sridhar 1995;Lazarian & Vishniac 1999), simulating (e.g., Cho & Vishniac 2000;Maron & Goldreich 2001;Cho & Lazarian 2002;Beresnyak 2014), and observationally measuring (e.g., Lazarian et al 2018;Hu et al 2019Hu et al , 2022aYuen et al 2022) magnetohydrodynamic (MHD) turbulence bring significant changes to the standard paradigm of CR diffusion and acceleration (e.g., Chandran 2000;Yan & Lazarian 2002Xu & Yan 2013;Lazarian & Yan 2014;Comisso & Sironi 2018;Xu & Lazarian 2018;Sioulas et al 2020aSioulas et al , 2022bFornieri et al 2021;Lazarian & Xu 2021;Nättilä & Beloborodov 2021;Zhdankin 2021;Beattie et al 2022;Maiti et al 2022, Hu et al 2022bKempski & Quataert 2022;Lemoine 2022;Kempski et al 2023;Lemoine 2023;Sampson et al 2023).…”