Neutral gas phase distribution from HI morphology: phase separation with scattering spectra and variational autoencoders

Unraveling the multi-phase structure of the diffuse interstellar medium (ISM) as traced by neutral hydrogen (HI) is essential to understanding the lifecycle of the Milky Way. However, HI phase separation is a challenging and under-constrained problem. The neutral gas phase distribution is often inferred from the spectral line structure of HI emission. In this work, we develop a data-driven phase separation method that extracts HI phase structure solely from the spatial morphology of HI emission intensity structures. We combine scattering spectra (SS) statistics with a Gaussian-mixture variational autoencoder (VAE) model to: 1. derive an interpretable statistical model of different HI phases from their multi-scale morphological structures; 2. use this model to decompose the 2D channel maps of GALFA-HI emission in diffuse high latitude ($|b|>30$\degree) regions over narrow velocity channels ($\Delta v=3$ km/s) into cold neutral medium (CNM), warm neutral medium (WNM), and noise components. We integrate our CNM map over velocity channels to compare it to an existing map produced by a spectrum-based method, and find that the two maps are highly correlated, while ours recovers more spatially coherent structures at small scales. Our work illustrates and quantifies a clear physical connection between the HI morphology and HI phase structure, and unlocks a new avenue for improving future phase separation techniques by making use of both HI spectral and spatial information to decompose HI in 3D position-position-velocity (PPV) space. These results are consistent with a physical picture where processes that drive HI phase transitions also shape the morphology of HI gas, imprinting a sparse, filamentary CNM that forms out of a diffuse, extended WNM.