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We have developed a model which describes the co‐evolution of the mass function of dense gravitationally bound cores and of the stellar mass function in a protocluster clump. In the model, dense cores are injected, at a uniform rate, at different locations in the clump and evolve under the effect of gas accretion. Gas accretion on to the cores follows a time‐dependent accretion rate that describes accretion in a turbulent medium. Once the accretion time‐scales of cores of a given age, of a given mass and located at a given distance from the centre of the protocluster clumps exceed their contraction time‐scales, they are turned into stars. The stellar initial mass function (IMF) is thus built up from successive generations of cores that undergo this accretion‐collapse process. We also include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the wind's energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). The ONC is the only known cluster for which a well‐determined IMF exists for masses ranging from the sub‐stellar regime to very massive stars. Our model is able to reproduce both the shape and normalization of the ONC's IMF and the mass function of dense submillimetre cores in Orion. The complex features of the ONC's present‐day IMF, namely a shallow slope in the mass range of  ∼[0.3–2.5] M ⊙  , a steeper slope in the mass range of  ∼[2.5–12] M ⊙   and a nearly flat tail at the high‐mass end, are reproduced. The model predicts a ‘rapid’ star formation process with an age spread for the stars of  2.3 × 10 5   yr which is consistent with the fact that 80 per cent of the ONC's stars have ages of  ≲0.3  Myr. The model also predicts a primordial mass segregation with the most massive stars being born in the region between two and four times the core radius of the cluster. In parallel, the model also reproduces, at the time the IMF is set and star formation quenched, the mass distribution of dense cores in the Orion star‐forming complex. We study the effects of varying some of the model parameters on the resulting IMF and we show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps' and cores' physical properties exist.

The IMF of stellar clusters: effects of accretion and feedback