Fermi-bubble Bulk and Edge Analysis Reveals Dust, Cooling Breaks, and Cosmic-Ray Diffusion, Facilitating a Self-consistent Model

The full, radio to γ -ray spectrum of the Fermi bubbles is shown to be consistent with standard strong-shock electron acceleration at the bubble edge, without the unnatural energy cutoffs and unrealistic electron cooling of previous studies, if the ambient interstellar radiation is strong; the γ -ray cooling break should then have a microwave counterpart, undetected until now. Indeed, a broadband bubble-edge analysis uncovers a pronounced downstream dust component, which masked the anticipated ∼35 GHz spectral break, and the same overall radio softening consistent with Kraichnan diffusion previously reported in γ -rays. A self-consistent bulk and edge model implies a few Myr old bubbles, with fairly uniform radiation fields and enhanced magnetization near the edge.