The Anisotropy of the Extragalactic Radio Background from Dark Matter Annihilation

Observations of the extragalactic radio background have uncovered a significant isotropic emission across multiple frequencies spanning from 22 MHz to 10 GHz. The intensity of this non-thermal emission component significantly exceeds the expected contribution from known astrophysical sources. Interestingly, models have indicated that the annihilation of dark matter particles may reproduce both the flux and spectrum of the excess. However, the lack of a measurable anisotropy in the residual emission remains challenging for both dark matter and standard astrophysical interpretations of the ARCADE-2 data. We calculate the expected synchrotron anisotropy from dark matter annihilation and show that these models can produce very small anisotropies, though this requires galaxy clusters to have large substructure contributions and strong magnetic fields. We show that this constraint can be significantly relaxed, however, in scenarios where electrons produced via dark matter annihilation can be efficiently reaccelerated by Alfv\'en waves in the intra-Cluster medium. Our analysis indicates that any source capable of explaining the intensity and isotropy of the extragalactic radio excess must have a spatial extension far larger than typical for baryons in galaxies, suggesting a novel physics interpretation.