When did the initial mass function become bottom-heavy?

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