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.
