Small-Scale Anisotropies of Cosmic Rays from Turbulent Flow

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 $C_{\mathrm{\ell }}$ is then a direct reflection of interstellar turbulence, from which one expects $C_{\mathrm{\ell }}\propto {\mathrm{\ell }}^{-\gamma -1}$ for $\mathrm{\ell }\gg 1$, 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 $\gamma =5\mathrm{/}3$ with a convection velocity dispersion of 20 km/s on the scale of 10 pc.