Formation of the cosmic-ray halo: The role of nonlinear Landau damping

TL;DR

This paper develops a nonlinear model of the Galactic cosmic-ray halo, highlighting how nonlinear Landau damping influences the size of the halo and the propagation of cosmic rays, aligning well with observations.

Contribution

It introduces a self-consistent model incorporating nonlinear Landau damping to determine the cosmic-ray halo size and propagation regions, a novel approach in cosmic-ray physics.

Findings

Halo size increases with energy due to NL damping effects.

Proton spectrum matches observational data.

Estimated halo height is about 1 kpc for GeV protons.

Abstract

We present a nonlinear model of self-consistent Galactic halo, where the processes of cosmic ray (CR) propagation and excitation/damping of MHD waves are included. The MHD-turbulence, which prevents CR escape from the Galaxy, is entirely generated by the resonant streaming instability. The key mechanism controlling the halo size is the nonlinear Landau (NL) damping, which suppresses the amplitude of MHD fluctuations and, thus, makes the halo larger. The equilibrium turbulence spectrum is determined by a balance of CR excitation and NL damping, which sets the regions of diffusive and advective propagation of CRs. The boundary $z_{cr}(E)$ between the two regions is the halo size, which slowly increases with the energy. For the vertical magnetic field of $\sim 1~\mu G$, we estimate $z_{cr} \sim 1$ kpc for GeV protons. The derived proton spectrum is in a good agreement with observational data.