The origin of the stellar initial mass function (IMF) is a fundamental issue in the theory of star formation. It is generally fit with a composite power law. Some clues on the progenitors can be found in dense starless cores that have a core mass function (CMF) with a similar shape. In the low-mass end, these mass functions increase with mass, albeit the sample may be somewhat incomplete; in the high-mass end, the mass functions decrease with mass. There is an offset in the turn-over mass between the two mass distributions. The stellar mass for the IMF peak is lower than the corresponding core mass for the CMF peak in the Pipe Nebula by about a factor of three. Smaller offsets are found between the IMF and the CMFs in other nebulae. We suggest that the offset is likely induced during a starburst episode of global star formation which is triggered by the formation of a few O/B stars in the multi-phase media, which naturally emerged through the onset of thermal instability in the cloud-core formation process. We consider the scenario that the ignition of a few massive stars photoionizes the warm medium between the cores, increases the external pressure, reduces their Bonnor?Ebert mass, and triggers the collapse of some previously stable cores. We quantitatively reproduce the IMF in the low-mass end with the assumption of additional rotational fragmentation.
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