When did the initial mass function become bottom-heavy?

The characteristic mass that sets the peak of stellar initial function (IMF) is closely linked to thermodynamic behaviour interstellar gas, which controls how gas fragments as it collapses under gravity. As Universe has grown in metal abundance over cosmic time, this evolved from a primordial regime dominated by competition between compressional heating and molecular hydrogen cooling modern where dominant process dense protostellar radiation feedback, transmitted dust-gas collisions. In paper we map out primordial-to-modern transition constructing model for thermodynamics collapsing, dusty clouds at wide range metallicities. We show begins metallicity $Z\sim 10^{-4} \rm{Z_\odot}$, passes through an intermediate stage line $Z \sim 10^{-3}\,\rm{Z_{\odot}}$, then transitions dust- feedback-dominated 10^{-2} \rm{Z_\odot}$. low pressure environments like Milky Way, accompanied dramatic change mass, $\sim 50\,\rm{M_\odot}$ 10^{-6}\,\rm{Z_{\odot}}$ 0.3\,\rm{M_\odot}$ once feedback dominate, marks appearance bottom-heavy Way IMF. high typical massive elliptical galaxies, modern, dust-dominated falls 0.1\,\rm{M_{\odot}}$, thus providing explanation more IMF observed these galaxies. conclude key driver variations extension,