Sensitive Limits on the Water Abundance in Cold Low-Mass Molecular Cores

We present SWAS observations of water vapor in two cold star-less clouds, B68and Core D in rho Ophiuchus. Sensitive non-detections of the 1(10)-1(01)transition of o-H2O are reported for each source. Both molecular cores havebeen previously examined by detailed observations that have characterized thephysical structure. Using these rather well defined physical properties and aMonte-Carlo radiation transfer model we have removed one of the largestuncertainties from the abundance calculation and set the lowest water abundancelimit to date in cold low-mass molecular cores. These limits are < 3 x 10^{-8}(relative to H2) and < 8 x 10^{-9} in B68 and rho Oph D, respectively. Such lowabundances confirm the general lack of ortho-water vapor in cold (T < 20 K)cores. Provided that the ortho/para ratio of water is not near zero, theselimits are well below theoretical predictions and appear to support thesuggestion that most of the water in dense low-mass cores is frozen onto thesurfaces of cold dust grains.Comment: 12 pages, 3 figures, accepted by Astrophysical Journal Letter