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.