The impact of the metallicity and star formation rate on the time-dependent galaxy-wide stellar initial mass function

TL;DR

This paper investigates how galaxy metallicity and star formation rate influence the galaxy-wide stellar initial mass function (gwIMF), revealing that the gwIMF varies from top-heavy to bottom-heavy depending on these factors, challenging the assumption of invariance.

Contribution

The study applies the IGIMF theory to model the gwIMF across a range of metallicities and SFRs, demonstrating its variability and implications for galaxy evolution.

Findings

gwIMF is top-heavy at low metallicity and high SFR

gwIMF becomes top-light at low SFR regardless of metallicity

Massive elliptical galaxies likely had top-heavy gwIMFs early on

Abstract

The stellar initial mass function (IMF) is commonly assumed to be an invariant probability density distribution function of initial stellar masses being represented by the canonical IMF. As a consequence the galaxy-wide IMF (gwIMF), defined as the sum of the IMFs of all star forming regions, should also be invariant. Recent observational and theoretical results challenge the hypothesis that the gwIMF is invariant. In order to study the possible reasons for this variation we use the IMF determined in resolved star clusters and apply the IGIMF-theory to calculate a grid of gwIMF models for metallicities, -3<[Fe/H]<1, and galaxy-wide star formation rates, $10^{-5}$<SFR<$10^{5}\,\mathrm{M_{\odot}/yr}$. For a galaxy with metallicy [Fe/H]$<0$ and SFR$\,> 1\,M_\odot$/yr, which is a common condition in the early Universe, we find that the gwIMF is top-heavy (more massive stars), when compared to the canonical IMF. For a SFR $< 1\,\mathrm{M_{\odot}/yr}$ the gwIMF becomes top-light regardless of the metallicity. For metallicities $\mathrm{[Fe/H]} > 0$ the gwIMF can become bottom-heavy regardless of the SFR. The IGIMF models predict that massive elliptical galaxies should have formed with a gwIMF that is top-heavy within the first few hundred Myr of the galaxy's life and that it evolves into a bottom-heavy gwIMF in the metal-enriched galactic center. We study the SFR$-$H$\alpha$ relation, its dependency on metallicity and the SFR, the correction factors to the Kennicutt SFR$_{\rm K}-$H$\alpha$ relation, and provide new fitting functions Late-type dwarf galaxies show significantly higher SFRs with respect to Kennicutt SFRs, while star forming massive galaxies have significantly lower SFRs than hitherto thought. This has implications for the gas-consumption time scales and for the main sequence of galaxies. The Leo P and ultra-faint dwarf galaxies are discussed explicitly. [abridged]