We present Spitzer observations of a sample of 12 starless cores selected to have prominent 24 micron shadows. The Spitzer images show 8 and 24 micron shadows and in some cases 70 micron shadows; these spatially resolved absorption features trace the densest regions of the cores. We have carried out a 12CO (2-1) and 13CO (2-1) mapping survey of these cores with the Heinrich Hertz Telescope (HHT). We use the shadow features to derive optical depth maps. We derive molecular masses for the cores and the surrounding environment; we find that the 24 micron shadow masses are always greater than or equal to the molecular masses derived in the same region, a discrepancy likely caused by CO freeze--out onto dust grains. We combine this sample with two additional cores that we studied previously to bring the total sample to 14 cores. Using a simple Jeans mass criterion we find that ~ 2/3 of the cores selected to have prominent 24 micron shadows are collapsing or near collapse, a result that is supported by millimeter line observations. Of this subset at least half have indications of 70 micron shadows. All cores observed to produce absorption features at 70 micron are close to collapse. We conclude that 24 micron shadows, and even more so the 70 micron ones, are useful markers of cloud cores that are approaching collapse.
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