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 ℓ is then a direct reflection of interstellar turbulence, from which one expects C ℓ ∝ ℓ −γ−1 for ℓ ≫ 1, where γ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law γ = 5/3 with a convection velocity dispersion of 20 km s−1 on the scale of 10 pc.