Inversely synthesizing the core mass function of high-mass star-forming regions from the canonical initial mass function

Many studies have revealed that the core mass function (CMF) in high-mass star-forming regions is top-heavy. In this work, we start from the canonical initial mass function (IMF) to inversely synthesize the observed CMFs of high-mass star formation regions, taking into account variations in multiplicity and mass conversion efficiency from core to star (ϵcore). To match the observed CMFs, cores of different masses should have varying ϵcore, with ϵcore increasing as the core mass decreases. However, the multiplicity fraction does not affect the synthesized CMFs. To accurately fit the high-mass end of the CMF, it is essential to determine whether the CMF shows a slope transition from the low-mass end to the high-mass one. If the CMF truly undergoes a slope transition but observational biases obscure it, leading to a combined fit with a shallower slope, this could artificially create a top-heavy CMF.