The observable prestellar phase of the IMF
The fragmentation of molecular clouds into dense filaments and cores provides important clues to understand the process of star formation. The observed similarities between the mass function of prestellar cores (CMF) and the stellar initial mass function (IMF) suggest that the IMF is already largely determined in the gas phase, in the sense that each prestellar core produces a single stellar system with a (nearly mass-independent) fraction of its mass. However, theoretical arguments show that the CMF may differ significantly from the IMF. In this work, we study the relation between the CMF and the IMF, as predicted by the IMF model of Padoan and Nordlund. We show that the observed CMF should provide strong evidence of the power-law slope of the IMF above one solar mass. We also find that the CMF should continue to rise monotonically towards smaller masses, as found in most (sub-)mm surveys. The CMF peak found in only a few surveys may be an artifact related to the survey incompleteness, rather than a probe of the IMF peak that one could use to estimate the local efficiency of star formation. Because most observed prestellar cores are still being assembled, their mass is often smaller than the mass of the stellar systems they will eventually generate. The procedure of selecting a core subsample with masses larger than half their Bonnor-Ebert mass is helpful in eliminating a large fraction of cores that will never collapse into stars.