The metallicity dependence of the stellar initial mass function

Dust is important for star formation because it is the crucial component that couples gas to stellar radiation fields, allowing radiation feedback to influence gas fragmentation and thus the stellar initial mass function (IMF). Variations in dust abundance therefore provide a potential avenue by which variation in galaxy metallicity might affect the IMF. In this paper we present a series of radiation-magnetohydrodynamic simulations in which we vary the metallicity and thus the dust abundance from 1% of Solar to 3$\times$ Solar, spanning the range from the lowest metallicity dwarfs to the most metal-rich early-type galaxies found in the local Universe. We design the simulations to keep all dimensionless parameters constant so that the interaction between feedback and star-forming environments of varying surface density and metallicity is the only factor capable of breaking the symmetry between the simulations and modifying the IMF, allowing us to cleanly isolate and understand the effects of each environmental parameter. We find that at a fixed surface density more metal-rich clouds tend to form a slightly more bottom-heavy IMF than metal-poor ones, primarily because in metal-poor gas radiation feedback is able to propagate further, heating somewhat larger volumes of gas. However, shifts in IMF with metallicity at a fixed surface density are much smaller than shifts with surface density at fixed metallicity; metallicity-induced IMF variations are too small to explain the variations in mass-to-light ratio reported in galaxies of different mass and metallicity. We, therefore, conclude that metallicity variations are much less important than variations in surface density in driving changes in the IMF and that the latter rather than the former are most likely responsible for the IMF variations found in early-type galaxies.