Sensitive limits on the water abundance in cold low-mass molecular cores

We present Submillimeter Wave Astronomy Satellite observations of water vapor in two cold starless clouds, B68 and core D in rho Ophiuchi. Sensitive nondetections of the 1(10)-1(01) transition of o-H2O are reported for each source. Both molecular cores have been previously examined by detailed observations that have characterized the physical structure. Using these rather well-defined physical properties and a Monte Carlo radiation transfer model, we have removed one of the largest uncertainties from the abundance calculation and set the lowest water abundance limit to date in cold low-mass molecular cores. These limits are x(o-H2O) <3 x 10(-8) (relative to H-2) and x(o-H2O) < in 8 x 10(-9) in B68 and rho Oph D, respectively. Such low abundances 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, these limits are well below theoretical predictions and appear to support the suggestion that most of the water in dense low-mass cores is frozen onto the surfaces of cold dust grains.