From the CMF to the IMF: Beyond the Core-Collapse Model
  Observations have indicated that the prestellar core mass function (CMF) is
similar to the stellar initial mass function (IMF), except for an offset
towards larger masses. This has led to the idea that there is a one-to-one
relation between cores and stars, such that the whole stellar mass reservoir is
contained in a gravitationally-bound prestellar core, as postulated by the
core-collapse model, and assumed in recent theoretical models of the stellar
IMF. We test the validity of this assumption by comparing the final mass of
stars with the mass of their progenitor cores in a high-resolution
star-formation simulation that generates a realistic IMF under physical
conditions characteristic of observed molecular clouds. Using a definition of
bound cores similar to previous works we obtain a CMF that converges with
increasing numerical resolution. We find that the CMF and the IMF are closely
related in a statistical sense only; for any individual star there is only a
weak correlation between the progenitor core mass and the final stellar mass.
In particular, for high mass stars only a small fraction of the final stellar
mass comes from the progenitor core, and even for low mass stars the fraction
is highly variable, with a median fraction of only about 50%. We conclude that
the core-collapse scenario and related models for the origin of the IMF are
incomplete. We also show that competitive accretion is not a viable
alternative.
