Angular Power Spectrum of TeV-PeV Cosmic Ray Anisotropies

Abstract: Simulations of the cosmic-ray (CR) anisotropy down to TeV energies are presented, using turbulence parameters consistent with those inferred from observations of the interstellar medium. We compute the angular power spectra $C_{\ell}$ of the CR anisotropy obtained from the simulations. We demonstrate that the amplitude of the large scale gradient in the CR density profile affects only the overall normalisation of the $C_{\ell}$s, without affecting the shape of the angular power spectrum. We show that the power spectrum depends on CR energy, and that it is sensitive to the location of the observer at small $\ell$. It is found to flatten at large $\ell$, and can be modelled by a broken power-law, exhibiting a break at $\ell \approx 4$. Our computed power spectrum at $\sim 10\,$TeV fits well HAWC and IceCube measurements. Moreover, we calculate all coefficients of the spherical harmonics and compute the component of the angular power spectrum projected onto the direction of the local magnetic field line. We find that deviations from gyrotropy become increasingly important at higher CR energies and larger values of $\ell$.