The Relationship between CO Emission and Visual Extinction Traced by
  Dust Emission in the Magellanic Clouds
  To test the theoretical understanding that finding bright CO emission depends
primarily on dust shielding, we investigate the relationship between CO
emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and
expressed as "$A_V$") across the Large Magellanic Cloud, the Small Magellanic
Cloud, and the Milky Way. We show that at our common resolution of 10 pc
scales, $I_{\rm CO}$ given a fixed line-of-sight $A_V$ is similar across all
three systems despite the difference in metallicity. We find some evidence for
a secondary dependence of $I_{\rm CO}$ on radiation field; in the LMC, $I_{\rm
CO}$ at a given $A_V$ is smaller in regions of high $T_{\rm dust}$, perhaps
because of an increased photodissociating radiation field. We suggest a simple
but useful picture in which the CO-to-H$_2$ conversion factor (\xco) depends on
two separable factors: (1) the distribution of gas column densities, which maps
to an extinction distribution via a dust-to-gas ratio; and (2) the dependence
of $I_{\rm CO}$ on $A_V$. Assuming that the probability distribution function
(PDF) of local Milky Way clouds is universal, this approach predicts a
dependence of \xco\ on $Z$ between $Z^{-1}$ and $Z^{-2}$ above about a third
solar metallicity. Below this metallicity, CO emerges from only the high column
density parts of the cloud and so depends very sensitively on the adopted PDF
and the H$_2$/{\sc Hi} prescription. The PDF of low metallicity clouds is thus
of considerable interest and the uncertainty associated with even an ideal
prescription for \xco\ at very low metallicity will be large.
