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Previous work has argued that atomic gas mass estimates of galaxies from 21cm HI emission are systematically low due to a cold opaque atomic gascomponent. If true, this opaque component necessitates a ~35% correction factorrelative to the mass from assuming optically-thin HI emission. These masscorrections are based on fitting HI spectra with a single opaque componentmodel that produces a distinct "top-hat" shaped line profile. Here, weinvestigate this issue using deep, high spectral resolution HI VLA observationsof M31 and M33 to test if these top-hat profiles are instead superpositions ofmultiple HI components along the line-of-sight. We fit both models and findthat >80% of the spectra strongly prefer a multi-component Gaussian model while<2% prefer the single opacity-corrected component model. This strong preferencefor multiple components argues against previous findings of lines-of-sightdominated by only cold HI. Our findings are enabled by the improved spectralresolution (0.42 km/s), whereas coarser spectral resolution blends multiplecomponents together. We also show that the inferred opaque atomic ISM massstrongly depends on the goodness-of-fit definition and is highly uncertain whenthe inferred spin temperature has a large uncertainty. Finally, we find thatthe relation of the HI surface density with the dust surface density andextinction has significantly more scatter when the inferred HI opacitycorrection is applied. These variations are difficult to explain withoutadditionally requiring large variations in the dust properties. Based on thesefindings, we suggest that the opaque HI mass is best constrained by HIabsorption studies.

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