Free-Free Optical Depth

Free-free emission, thermal bremsstrahlung from the Galaxy's ionized gas, should be the best-behaved foreground in the microwave sky: its physics is textbook, its spectrum is nearly flat and precisely known, and its amplitude should be predictable from hydrogen-alpha emission maps once dust absorption is corrected, since both signals come from the same ionized plasma (Dickinson et al. 2003).

The prediction and the radio sky disagree. Matching the observed radio brightness to the H-alpha-derived optical depth requires electron temperatures that are sometimes unphysically high, and that show gradients with Galactic latitude that standard photo-ionization equilibrium does not produce; depending on region, the radio free-free runs brighter or fainter than the H-alpha ledger allows (Planck Collaboration 2016). The component-separation degeneracy compounds the physics problem: free-free's flat spectrum is easily confused with the anomalous microwave emission in joint fits, so errors in either component contaminate the other, leaving residuals in cleaned CMB maps whose attribution remains ambiguous. The diagnosis options mirror the rest of the foreground sector: unmodeled ionized-gas populations, departures from photo-ionization equilibrium, or template errors that happen to organize spatially.

The standing is part of the joint foreground bottleneck: the best-understood emission mechanism in the inventory still fails its cross-check against its own tracer, in the same regions where every other component model also strains.

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