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 ($\epsilon_{\rm core}$). To match the observed CMFs, cores of different masses should have varying $\epsilon_{\rm core}$, with $\epsilon_{\rm core}$ 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.