We performed very deep searches for 2 ground-state water transitions in 13 protoplanetary disks with the HIFI instrument on-board the Herschel Space Observatory , with integration times up to 12 hours per line .
Two other water transitions that sample warmer gas were also searched for with shallower integrations .
The detection rate is low , and the upper limits provided by the observations are generally much lower than predictions of thermo-chemical models with canonical inputs .
One ground-state transition is newly detected in the stacked spectrum of AA Tau , DM Tau , LkCa 15 , and MWC 480 .
We run a grid of models to show that the abundance of gas-phase oxygen needs to be reduced by a factor of at least { \sim } 100 to be consistent with the observational upper limits ( and positive detections ) if a dust-to-gas mass ratio of 0.01 were to be assumed .
As a continuation of previous ideas , we propose that the underlying reason for the depletion of oxygen ( hence the low detection rate ) is the freeze-out of volatiles such as water and CO onto dust grains followed by grain growth and settling/migration , which permanently removes these gas-phase molecules from the emissive upper layers of the outer disk .
Such depletion of volatiles is likely ubiquitous among different disks , though not necessarily to the same degree .
The volatiles might be returned back to the gas phase in the inner disk ( { \lesssim } 15 AU ) , which is consistent with current constraints .
Comparison with studies on disk dispersal due to photoevaporation indicates that the timescale for volatile depletion is shorter than that of photoevaporation .