The Anomalous Microwave Emission is the foreground that refused its assignments: a broad excess of diffuse Galactic radiation peaking between 10 and 60 GHz, discovered by COBE and mapped by WMAP and Planck, that fits neither synchrotron nor thermal dust spectra. The community's working hypothesis is spinning dust, electric dipole radiation from nanometer-scale grains spun to tens of gigahertz, with polycyclic aromatic hydrocarbons the favored carriers (Dickinson et al. 2018).
The hypothesis works in outline and strains in detail. The grain size distributions, dipole moments, and environmental dependencies required to fit the observed spectra vary uncomfortably from region to region; the expected correlation between AME strength and PAH abundance, the natural test of the carrier identification, comes back inconsistent across sightlines (Hensley et al. 2016); and the polarization is the standing puzzle: aligned spinning grains should polarize their emission at the few-percent level, yet observed AME polarization sits below one percent, among the least polarized emissions in the sky. Each mismatch is absorbable alone; together they suggest the grain rotation physics is being driven by something the local-environment models do not contain.
The standing matters beyond the interstellar medium, because AME is a CMB foreground: B-mode searches at these frequencies need the component modeled correctly, making the anomaly's resolution a practical requirement for precision cosmology.