In this paper we present the results of a systematic investigation of anentire population of starless dust cores within a single molecular cloud.Analysis of extinction data shows the cores to be dense objects characterizedby a narrow range of density. Analysis of C18O and NH3 molecular-lineobservations reveals very narrow lines. The non-thermal velocity dispersionsmeasured in both these tracers are found to be subsonic for the large majorityof the cores and show no correlation with core mass (or size). Thermal pressureis thus the dominate source of internal gas pressure and support for most ofthe core population. The total internal gas pressures of the cores are found tobe roughly independent of core mass over the entire range of the core massfunction (CMF) indicating that the cores are in pressure equilibrium with anexternal source of pressure. This external pressure is most likely provided bythe weight of the surrounding Pipe cloud within which the cores are embedded.Most of the cores appear to be pressure confined, gravitationally unboundentities whose nature, structure and future evolution are determined by only afew physical factors which include self-gravity, the fundamental processes ofthermal physics and the simple requirement of pressure equilibrium with thesurrounding environment. The observed core properties likely constitute theinitial conditions for star formation in dense gas. The entire core populationis found to be characterized by a single critical Bonnor-Ebert mass. This masscoincides with the characteristic mass of the Pipe CMF indicating that mostcores formed in the cloud are near critical stability. This suggests that themass function of cores (and the IMF) has its origin in the physical process ofthermal fragmentation in a pressurized medium.
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