CO is widely used as a tracer of molecular gas. However, there is now mounting evidence that gas phase carbon is depleted in the disk around TW Hya. Previous efforts to quantify this depletion have been hampered by uncertainties regarding the radial thermal structure in the disk. Here we present resolved ALMA observations of 13CO 3-2, C18O 3-2, 13CO 6-5, and C18O 6-5 emission in TW Hya, which allow us to derive radial gas temperature and gas surface density profiles, as well as map the CO abundance as a function of radius. These observations provide a measurement of the surface CO snowline at ~30 AU and show evidence for an outer ring of CO emission centered at 53 AU, a feature previously seen only in less abundant species. Further, the derived CO gas temperature profile constrains the freeze-out temperature of CO in the warm molecular layer to < 21 K. Combined with the previous detection of HD 1-0, these data constrain the surface density of the warm H2 gas in the inner ~30 AU. We find that CO is depleted by two orders of magnitude from R=10-60 AU, with the small amount of CO returning to the gas phase inside the surface CO snowline insufficient to explain the overall depletion. Finally, this new data is used in conjunction with previous modeling of the TW Hya disk to constrain the midplane CO snowline to 17-23 AU.
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