Relationship between the Line Width of the Atomic and Molecular ISM in
  M33
  We investigate how the spectral properties of atomic (HI) and molecular
(H$_2$) gas, traced by CO(2-1), are related in M33 on $80$ pc scales. We find
the HI and CO(2-1) velocity at peak intensity to be highly correlated,
consistent with previous studies. By stacking spectra aligned to the velocity
of HI peak intensity, we find that the CO line width ($\sigma_{\rm
HWHM}=4.6\pm0.9$ km s$^{-1}$; $\sigma_{\rm HWHM}$ is the effective Gaussian
width) is consistently smaller than the HI line width ($\sigma_{\rm
HWHM}=6.6\pm0.1$ km s$^{-1}$), with a ratio of ${\sim}0.7$, in agreement with
Druard et al. (2014). The ratio of the line widths remains less than unity when
the data are smoothed to a coarser spatial resolution. In other nearby
galaxies, this line width ratio is close to unity which has been used as
evidence for a thick, diffuse molecular disk that is distinct from the thin
molecular disk dominated by molecular clouds. The smaller line width ratio
found here suggests that M33 has a marginal thick molecular disk. From
modelling individual lines-of-sight, we recover a strong correlation between HI
and CO line widths when only the HI located closest to the CO component is
considered. The median line width ratio of the line-of-sight line widths is
$0.56\pm0.01$. There is substantial scatter in the HI--CO(2-1) line width
relation, larger than the uncertainties, that results from regional variations
on $<500$ pc scales, and there is no significant trend in the line widths, or
their ratios, with galactocentric radius. These regional line width variations
may be a useful probe of changes in the local cloud environment or the
evolutionary state of molecular clouds.
