Formation of the cosmic-ray halo: Galactic spectrum of primary cosmic rays

TL;DR

This paper presents a self-consistent one-dimensional model of the Galactic cosmic-ray halo that explains its size and spectrum without relying heavily on MHD turbulence, matching observed spectral features.

Contribution

It introduces a novel mechanism where increasing Alfven velocity with distance causes turbulent redshift, shaping the cosmic-ray halo and spectrum.

Findings

The model reproduces the spectral break at ~0.6 TeV.

The calculated spectrum aligns with observations up to ~10 TeV.

Halo size depends on energy, transitioning from diffusion to advection.

Abstract

A self-consistent model of a one-dimensional cosmic-ray (CR) halo around the Galactic disk is formulated with the restriction to a minimum number of free parameters. It is demonstrated that the turbulent cascade of MHD waves does not necessarily play an essential role in the halo formation. Instead, an increase of the Alfven velocity with distance to the disk leads to an efficient generic mechanism of the turbulent redshift, enhancing CR scattering by the self-generated MHD waves. As a result, the calculated size of the CR halo at lower energies is determined by the halo sheath, an energy-dependent region around the disk beyond which the CR escape becomes purely advective. At sufficiently high energies, the halo size is set by the characteristic thickness of the ionized gas distribution. The calculated Galactic spectrum of protons shows a remarkable agreement with observations, reproducing the position of spectral break at ~ 0.6 TeV and the spectral shape up to ~ 10 TeV.