A lack of constraints on the cold opaque HI mass: HI spectra in M31 and M33 prefer multi-component models over a single cold opaque component

Previous work has argued that atomic gas mass estimates of galaxies from 21 cm HI emission are systematically low due to a cold opaque atomic gas component. If true, this opaque component necessitates a ~35% correction factor relative to the mass from assuming optically-thin HI emission. These mass corrections are based on fitting HI spectra with a single opaque component model that produces a distinct "top-hat" shaped line profile. Here, we investigate this issue using deep, high spectral resolution HI VLA observations of M31 and M33 to test if these top-hat profiles are instead superpositions of multiple HI components along the line-of-sight. We fit both models and find that >80% of the spectra strongly prefer a multi-component Gaussian model while <2% prefer the single opacity-corrected component model. This strong preference for multiple components argues against previous findings of lines-of-sight dominated by only cold HI. Our findings are enabled by the improved spectral resolution (0.42 km/s), whereas coarser spectral resolution blends multiple components together. We also show that the inferred opaque atomic ISM mass strongly depends on the goodness-of-fit definition and is highly uncertain when the inferred spin temperature has a large uncertainty. Finally, we find that the relation of the HI surface density with the dust surface density and extinction has significantly more scatter when the inferred HI opacity correction is applied. These variations are difficult to explain without additionally requiring large variations in the dust properties. Based on these findings, we suggest that the opaque HI mass is best constrained by HI absorption studies.