Compact substructure is expected to arise in a starless core as mass becomes concentrated in the central region likely to form a protostar. Additionally, multiple peaks may form if fragmentation occurs. We present ALMA Cycle 2 observations of 60 starless and protostellar cores in the Ophiuchus molecular cloud. We detect eight compact substructures which are >15 arcsec from the nearest Spitzer YSO. Only one of these has strong evidence for being truly starless after considering ancillary data, e.g., from Herschel and X-ray telescopes. An additional extended emission structure has tentative evidence for starlessness. The number of our detections is consistent with estimates from a combination of synthetic observations of numerical simulations and analytical arguments. This result suggests that a similar ALMA study in the Chamaeleon I cloud, which detected no compact substructure in starless cores, may be due to the peculiar evolutionary state of cores in that cloud.
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