Formation of the Cosmic-Ray Halo: The Role of Nonlinear Landau Damping

Abstract

Abstract We present a nonlinear model of a self-consistent Galactic halo, where the processes of cosmic-ray (CR) propagation and excitation/damping of MHD waves are included. The MHD turbulence that 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 ∼1 μG, we estimate z cr ∼ 1 kpc for GeV protons. The derived proton spectrum is in a good agreement with observational data.