Data from the Five College Radio Astronomy Observatory CO Mapping Survey of the Taurus molecular cloud are combined with extinction data for a sample of 292 background field stars to investigate the uptake of CO from the gas to icy grain mantles on dust within the cloud. On the assumption that the reservoir of CO in the ices is well represented by the combined abundances of solid CO and solid CO2 (which forms by oxidation of CO on the dust), we find that the total column density (gas + solid) correlates tightly with visual extinction (Av) over the range 5 < Av < 30 mag, i.e., up to the highest extinctions covered by our sample. The mean depletion of gas-phase CO increases monotonically from negligible levels for Av < 5 to approximately 30 percent at Av = 10 and 60 percent at Av = 30. As these results refer to line-of-sight averages, they must be considered lower limits to the actual depletion at loci deep within the cloud, which may approach 100 percent. We show that it is plausible for such high levels of depletion to be reached in dense cores on timescales of order 0.6 Myr, comparable with their expected lifetimes. Dispersal of cores during star formation may be effective in maintaining observable levels of gaseous CO on the longer timescales estimated for the age of the cloud.
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