Origin of the Cosmic Ray Galactic Halo Driven by Advected Turbulence and Self-Generated Waves

The diffusive paradigm for the transport of Galactic cosmic rays is central to our understanding of the origin of these high energy particles. However, it is worth recalling that the normalization, energy dependence, and spatial extent of the diffusion coefficient in the interstellar medium are fitted to the data and typically are not derived from more basic principles. Here, we discuss a scenario in which the diffusion properties of cosmic rays are derived from a combination of wave self-generation and advection from the Galactic disc, where the sources of cosmic rays are assumed to be located. We show for the first time that a halo naturally arises from these phenomena, with a size of a few kiloparsecs, compatible with the value that typically best fits observations in simple parametric approaches to cosmic ray diffusion. We also show that transport in such a halo results in a hardening in the spectra of primary cosmic rays at $\sim 300\mathrm{GV}$.

Figure 1

Wave spectrum as a function of $k$ with (solid lines) and without (dashed lines) the contribution of self-generated waves at different positions. At $z=0$, solid and dashed lines overlap around the injection peak at $k_0$. The dotted line shows the background turbulence we add to constrain diffusion velocity to be smaller than $c$.

Figure 2

Diffusion coefficient as a function of momentum for different values of $z$.

Figure 3

Spectrum of protons in the local ISM compared to observational data. The spatial dependence of the CR distribution function is shown in the inset for energies 10 GeV and 10 TeV.