Magnetohydrodynamic turbulence and the associated spatial diffusion tensor of cosmic rays in dynamical galactic halos

¹ Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik IV, 44780 Bochum, Germany
² Ruhr Astroparticle and Plasma Physics Center (RAPP Center), 44780 Bochum, Germany
³ Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Astronomisches Institut (AIRUB), 44780 Bochum, Germany
⁴ Department of Mathematics, University of Waikato, Hamilton 3240, New Zealand

^★ Corresponding author: jk@tp4.rub.de

Received: 23 January 2025
Accepted: 23 April 2025

Abstract

Context. A detailed understanding of cosmic-ray transport in galactic halos is essential for explaining various observations, such as the radio continuum measurements of synchrotron radiation from energetic electrons. Of central importance is the spatial diffusion tensor of cosmic rays, which can be computed in an ab initio manner if the turbulence in the background medium is known.

Aims. The study aimed to establish a suitable framework to compute the evolution of magnetohydrodynamic (MHD) turbulence and, hence, the diffusion tensor in the dynamical halos of galaxies.

Methods. The Reynolds-averaged single-fluid MHD equations were solved numerically on a cylindrical grid, assuming axial symmetry and fixed boundary conditions on a central ellipsoid representing the galaxy. The physical properties of both large-scale MHD and small-scale turbulent quantities, including the coefficients of parallel and perpendicular diffusion, were extracted from the resulting steady state.

Results. Hydrodynamic validation revealed a persistent instability of the near-axis flow, which could be traced to the galaxy’s gravitating mass. The results for the evolution of MHD turbulence in a galactic halo – using parameters approximating those of NGC 4631 – enabled an ab initio computation of the spatial diffusion tensor of cosmic rays through the application of a state-of-the-art nonlinear theory.

Conclusions. The simulation results reveal variation in turbulence quantities, (i.e., fluctuation energy, correlation scale, and cross helicity) in a dynamical halo. Furthermore, the corresponding diffusion tensor of cosmic rays exhibits significant variation throughout such a halo.