The Morphology of the Galactic Dark Matter Synchrotron Emission with Self-Consistent Cosmic Ray Diffusion Models

A generic prediction in the paradigm of weakly interacting dark matter is the production of relativistic particles from dark matter pair-annihilation in regions of high dark matter density. Ultra-relativistic electrons and positrons produced in the center of the Galaxy by dark matter annihilation should produce a diffuse synchrotron emission. While the spectral shape of the synchrotron dark matter haze depends on the particle model (and secondarily on the galactic magnetic fields), the morphology of the haze depends primarily on (1) the dark matter density distribution, (2) the galactic magnetic field morphology, and (3) the diffusion model for high-energy cosmic-ray leptons. Interestingly, an unidentified excess of microwave radiation with characteristics similar to those predicted by dark matter models has been claimed to exist near the galactic center region in the data reported by the WMAP satellite, and dubbed the "WMAP haze". In this study, we carry out a self-consistent treatment of the variables enumerated above, enforcing constraints from the available data on cosmic rays, radio surveys and diffuse gamma rays. We outline and make predictions for the general morphology and spectral features of a "dark matter haze" and we compare them to the WMAP haze data. We also characterize and study the spectrum and spatial distribution of the inverse Compton emission resulting from the same population of energetic electrons and positrons. We point out that the spectrum and morphology of the radio emission at different frequencies is a powerful diagnostics to test whether a galactic synchrotron haze indeed originates from dark matter annihilation.