Angular power spectrum of the galactic synchrotron radiation

Abstract

We calculate the angular power spectrum of the galactic synchrotron radiation induced by the small scale fluctuations of the magnetic field and the cosmic ray electron density. Using the observed interstellar magnetic field spectrum, which is consistent with the Komolgorov turbulence model at the relevant scales, we find that $C_l \propto l^{-3.7}$. We estimate the cosmic ray electron density fluctuation spectrum with an injection-diffusion model, the shape of the angular power spectrum in this model depends on the correlations between the injection sources. For Poisson distribution of sources, $C_l \propto l^{-4}$. We discuss the implications for the interpretation of cosmic microwave background (CMB) data and the impact on future 21 cm tomography experiments.