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Observations have indicated that the prestellar core mass function (CMF) issimilar to the stellar initial mass function (IMF), except for an offsettowards larger masses. This has led to the idea that there is a one-to-onerelation between cores and stars, such that the whole stellar mass reservoir iscontained in a gravitationally-bound prestellar core, as postulated by thecore-collapse model, and assumed in recent theoretical models of the stellarIMF. We test the validity of this assumption by comparing the final mass ofstars with the mass of their progenitor cores in a high-resolutionstar-formation simulation that generates a realistic IMF under physicalconditions characteristic of observed molecular clouds. Using a definition ofbound cores similar to previous works we obtain a CMF that converges withincreasing numerical resolution. We find that the CMF and the IMF are closelyrelated in a statistical sense only; for any individual star there is only aweak correlation between the progenitor core mass and the final stellar mass.In particular, for high mass stars only a small fraction of the final stellarmass comes from the progenitor core, and even for low mass stars the fractionis highly variable, with a median fraction of only about 50%. We conclude thatthe core-collapse scenario and related models for the origin of the IMF areincomplete. We also show that competitive accretion is not a viablealternative.

From the CMF to the IMF: Beyond the Core-Collapse Model