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^{-\gamma -1} $ for $ \ell\gg 1 $, where $ \gamma $ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law $ \gamma =5/3 $ with a convection velocity dispersion of 20 km/s on the scale of 10 pc.