A New Constraint on the Relative Disorder of Magnetic Fields between Neutral Interstellar Medium Phases

Utilizing Planck polarized dust emission maps at 353 GHz and new large-area maps of the neutral hydrogen (HI) cold neutral medium (CNM) fraction ($f_\mathrm{CNM}$), we investigate the relationship between dust polarization fraction ($p_{353}$) and $f_\mathrm{CNM}$ in the diffuse high latitude ($|b|>30^{\circ}$) sky. We find that the correlation between $p_{353}$ and $f_\mathrm{CNM}$ is qualitatively distinct from the $p_{353}$-HI column density ($N_\mathrm{H\,I}$) relationship. At low column densities ($N_\mathrm{H\,I}<4\times10^{20}~\mathrm{cm^{-2}}$) where $p_{353}$ and $N_\mathrm{H\,I}$ are uncorrelated, there is a strong positive $p_{353}$-$f_\mathrm{CNM}$ correlation. We fit the $p_{353}$-$f_{\rm CNM}$ correlation with data-driven models to constrain the degree of magnetic field disorder between phases along the line-of-sight. We argue that an increased magnetic field disorder in the warm neutral medium (WNM) relative to the CNM best explains the positive $p_{353}$-$f_\mathrm{CNM}$ correlation in diffuse regions. Modeling the CNM-associated dust column as being maximally polarized, with a polarization fraction $p_{\rm CNM} \sim$ 0.2, we find that the best-fit mean polarization fraction in the WNM-associated dust column is 0.22$p_{\rm CNM}$. The model further suggests that a significant $f_{\rm CNM}$-correlated fraction of the non-CNM column (an additional ~18.4% of the HI mass on average) is also more magnetically ordered, and we speculate that the additional column is associated with the unstable medium (UNM). Our results constitute a new large-area constraint on the average relative disorder of magnetic fields between the neutral phases of the ISM, and are consistent with the physical picture of a more magnetically aligned CNM column forming out of a disordered WNM.