To study the evolution of high mass cores, we have searched for evidence of collapse motions in a large sample of starless cores in the Orion molecular cloud. We used the Caltech Submillimeter Observatory telescope to obtain spectra of the optically thin (H13CO+) and optically thick (HCO+) high density tracer molecules in 27 cores with masses $>$ 1 Ms. The red- and blue-asymmetries seen in the line profiles of the optically thick line with respect to the optically thin line indicate that 2/3 of these cores are not static. We detect evidence for infall (inward motions) in 9 cores and outward motions for 10 cores, suggesting a dichotomy in the kinematic state of the non-static cores in this sample. Our results provide an important observational constraint on the fraction of collapsing (inward motions) versus non-collapsing (re-expanding) cores for comparison with model simulations.
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