Molecular Gas and Star Formation in the Cartwheel
  Atacama Large Millimeter/submillimeter Array (ALMA) 12CO(J=1-0) observations
are used to study the cold molecular ISM of the Cartwheel ring galaxy and its
relation to HI and massive star formation (SF). CO moment maps find
$(2.69\pm0.05)\times10^{9}$ M$_{\odot}$ of H$_2$ associated with the inner ring
(72%) and nucleus (28%) for a Galactic I(CO)-to-N(H2) conversion factor
($\alpha_{\rm CO}$). The spokes and disk are not detected. Analysis of the
inner ring's CO kinematics show it to be expanding ($V_{\rm exp}=68.9\pm4.9$ km
s$^{-1}$) implying an $\approx70$ Myr age. Stack averaging reveals CO emission
in the starburst outer ring for the first time, but only where HI surface
density ($\Sigma_{\rm HI}$) is high, representing $M_{\rm
H_2}=(7.5\pm0.8)\times10^{8}$ M$_{\odot}$ for a metallicity appropriate
$\alpha_{\rm CO}$, giving small $\Sigma_{\rm H_2}$ ($3.7$ M$_{\odot}$
pc$^{-2}$), molecular fraction ($f_{\rm mol}=0.10$), and H$_2$ depletion
timescales ($\tau_{\rm mol} \approx50-600$ Myr). Elsewhere in the outer ring
$\Sigma_{\rm H_2}\lesssim 2$ M$_{\odot}$ pc$^{-2}$, $f_{\rm mol}\lesssim 0.1$
and $\tau_{\rm mol}\lesssim 140-540$ Myr (all $3\sigma$). The inner ring and
nucleus are H$_2$-dominated and are consistent with local spiral SF laws.
$\Sigma_{\rm SFR}$ in the outer ring appears independent of $\Sigma_{\rm H_2}$,
$\Sigma_{\rm HI}$ or $\Sigma_{\rm HI+H_2}$. The ISM's long confinement in the
robustly star forming rings of the Cartwheel and AM0644-741 may result in
either a large diffuse H$_2$ component or an abundance of CO-faint low column
density molecular clouds. The H$_2$ content of evolved starburst rings may
therefore be substantially larger. Due to its lower $\Sigma_{\rm SFR}$ and age
the Cartwheel's inner ring has yet to reach this state. Alternately, the outer
ring may trigger efficient SF in an HI-dominated ISM.
