We present a direct comparison of a chemical/physical model to multitransitional observations of C18O and 13CO towards the Barnard 68 pre-stellar core. These observations provide a sensitive test for models of low UV field photodissociation regions and offer the best constraint on the gas temperature of a pre-stellar core. We find that the gas temperature of this object is surprisingly low (~7-8 K), and significantly below the dust temperature, in the outer layers (Av < 5 mag) that are traced by C18O and 13CO emission. As shown previously, the inner layers (Av > 5 mag) exhibit significant freeze-out of CO onto grain surfaces. Because the dust and gas are not fully coupled, depletion of key coolants in the densest layers raises the core (gas) temperature, but only by ~1 K. The gas temperature in layers not traced by C18O and 13CO emission can be probed by NH3 emission, with a previously estimated temperature of ~10-11 K. To reach these temperatures in the inner core requires an order of magnitude reduction in the gas to dust coupling rate. This potentially argues for a lack of small grains in the densest gas, presumably due to grain coagulation.
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