Small-Scale Anisotropies of Cosmic Rays from Turbulent Flow

Abstract

Within the classical convection--diffusion approximation, we show that the angular distribution of cosmic rays (CRs) in a highly turbulent flow may exhibit significant small-scale anisotropies. The CR intensity angular power spectrum $C_{\ell }$ is then a direct reflection of interstellar turbulence, from which one expects $C_{\ell }\propto {\ell }^{-{\hat{I}}^3-1}$ for $\ell \gg 1$, where ${\hat{I}}^3$ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law ${\hat{I}}^3=5/3$ with a convection velocity dispersion of 20 km/s on the scale of 10 pc.

Accepted for publication in ApJL