Polycyclic Aromatic Hydrocarbons, the Anomalous Microwave Emission, and Their Connection to the Cold Neutral Medium

Using new large area maps of the cold neutral medium (CNM) fraction, $f_{\rm CNM}$, we investigate the relationship between the CNM, the abundance of polycyclic aromatic hydrocarbons (PAHs), and the anomalous microwave emission (AME). We first present our $f_{\rm CNM}$ map based on full-sky HI4PI data, using a convolutional neural network to covert the spectroscopic HI data to $f_{\rm CNM}$. We demonstrate that $f_{\rm CNM}$ is strongly correlated with the fraction of dust in PAHs as estimated from mid- and far-infrared dust emission. In contrast, we find no correlation between $f_{\rm CNM}$ and the amount of AME per dust emission, nor between $f_{\rm CNM}$ and the AME peak frequency. These results suggest PAHs preferentially reside in cold, relatively dense gas, perhaps owing to enhanced destruction in more diffuse media. The lack of correlation between $f_{\rm CNM}$ and AME peak frequency is in tension with expectations from theoretical models positing different spectral energy distributions of AME in the cold versus warm neutral medium. We suggest that different PAH abundances and emission physics in different interstellar environments may explain the weaker than expected correlation between 12$\mu$m PAH emission and AME even if PAHs are the AME carriers.