No abstract

The stellar initial mass function (IMF) is commonly assumed to be an invariant probability density distribution function of initial stellar masses. These initial stellar masses are generally represented by the canonical IMF, which is defined as the result of one star formation event in an embedded cluster. As a consequence, the galaxy-wide IMF (gwIMF) should also be invariant and of the same form as the canonical IMF; gwIMF is defined as the sum of the IMFs of all star-forming regions in which embedded clusters form and spawn the galactic field population of the galaxy. Recent observational and theoretical results challenge the hypothesis that the gwIMF is invariant. In order to study the possible reasons for this variation, it is useful to relate the observed IMF to the gwIMF. Starting with the IMF determined in resolved star clusters, we apply the IGIMF-theory to calculate a comprehensive grid of gwIMF models for metallicities, [Fe/H] ∈ (−3, 1), and galaxy-wide star formation rates (SFRs), SFR ∈ (10−5, 105) M⊙ yr−1. For a galaxy with metallicity [Fe/H] < 0 and SFR > 1 M⊙ yr−1, which is a common condition in the early Universe, we find that the gwIMF is both bottom light (relatively fewer low-mass stars) and top heavy (more massive stars), when compared to the canonical IMF. For a SFR < 1 M⊙ yr−1 the gwIMF becomes top light regardless of the metallicity. For metallicities [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 life of the galaxy and that it evolves into a bottom heavy gwIMF in the metal-enriched galactic centre. Using the gwIMF grids, we study the SFR−Hα relation and its dependency on metallicity and the SFR. We also study the correction factors to the Kennicutt SFRK − Hα 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 gas-consumption timescales and for the main sequence of galaxies. We explicitly discuss Leo P and ultra-faint dwarf galaxies.

Here we present a full description of the integrated galaxy-wide initial mass function (IGIMF) theory in terms of the optimal sampling and compare it with available observations. Optimal sampling is the method we use to discretize the IMF deterministically into stellar masses. Evidence indicates that nature may be closer to deterministic sampling as observations suggest a smaller scatter of various relevant observables than random sampling would give, which may result from a high level of self-regulation during the star formation process. We document the variation of IGIMFs under various assumptions. The results of the IGIMF theory are consistent with the empirical relation between the total mass of a star cluster and the mass of its most massive star, and the empirical relation between the star formation rate (SFR) of a galaxy and the mass of its most massive cluster. Particularly, we note a natural agreement with the empirical relation between the IMF power-law index and the SFR of a galaxy. The IGIMF also results in a relation between the SFR of a galaxy and the mass of its most massive star such that, if there were no binaries, galaxies with SFR < 10 −4 M /yr should host no Type II supernova events. In addition, a specific list of initial stellar masses can be useful in numerical simulations of stellar systems. For the first time, we show optimally sampled galaxy-wide IMFs (OSGIMF) that mimic the IGIMF with an additional serrated feature. Finally, a Python module, GalIMF, is provided allowing the calculation of the IGIMF and OSGIMF dependent on the galaxy-wide SFR and metallicity.

A scenario for the formation of multiple co-eval populations separated in age by about 1 Myr in very young clusters (VYCs, ages less than 10 Myr) and with masses in the range 600 − 20000 M is outlined. It rests upon a converging inflow of molecular gas building up a first population of pre-main sequence stars. The associated just-formed O stars ionise the inflow and suppress star formation in the embedded cluster. However, they typically eject each other out of the embedded cluster within 10 6 yr, that is before the molecular cloud filament can be ionised entirely. The inflow of molecular gas can then resume forming a second population. This sequence of events can be repeated maximally over the life-time of the molecular cloud (about 10 Myr), but is not likely to be possible in VYCs with mass < 300 M , because such populations are not likely to contain an O star. Stellar populations heavier than about 2000 M are likely to have too many O stars for all of these to eject each other from the embedded cluster before they disperse their natal cloud. VYCs with masses in the range 600 − 2000 M are likely to have such multi-age populations, while VYCs with masses in the range 2000 − 20000 M can also be composed solely of co-eval, mono-age populations. More massive VYCs are not likely to host sub-populations with age differences of about 1 Myr. This model is applied to the Orion Nebula Cluster (ONC), in which three well-separated pre-main sequences in the color-magnitude diagram of the cluster have recently been discovered. The mass-inflow history is constrained using this model and the number of OB stars ejected from each population are estimated for verification using Gaia data. As a further consequence of the proposed model, the three runaway O star systems, AE Aur, µ Col and ι Ori, are considered as significant observational evidence for stellar-dynamical ejections of massive stars from the oldest population in the ONC. Evidence for stellar-dynamical ejections of massive stars in the currently forming population is also discussed.

Growing evidence in recent years suggests a systematic variation of the stellar initial mass function (IMF), being top-heavy for starburst galaxies and possibly bottom-heavy for massive ellipticals. Galaxy chemical evolution simulations adopting an invariant canonical IMF face difficulty in simultaneously reproducing the metallicity and α-enhancement of the massive elliptical galaxies. Applying a variable IMF that changes with time is a promising solution, however, it is non-trivial to couple a variable IMF theory with the existing galaxy evolution codes. Here we present the first open source simulation code which recalculates the galaxy-wide IMF at each time step according to the Integrated-Galactic-IMF (IGIMF) theory where the galaxy-wide IMF depends on the galactic star formation rate and metallicity. The resulting galaxy-wide IMF and metal abundance evolve with time. With this pilot work, we explore the effect of the IGIMF theory on galaxy chemical evolution in comparison with an invariant IMF.

The galaxy-wide stellar initial mass function (gwIMF) of a galaxy in dependence on its metallicity and star formation rate can be calculated by the integrated galactic IMF (IGIMF) theory. This theory has been applied in a study of the chemical evolution of the ultra-faint dwarf (UFD) satellite galaxies, but failed to reproduce the data. Here, we find that the IGIMF theory is naturally consistent with the data. We applied the time-evolving gwIMF, which was calculated at each time step. The number of type Ia supernova explosions that forms per unit stellar mass was renormalised according to the gwIMF. The chemical evolution of Boötes I, one of the best-observed UFD, was calculated. Our calculation suggests a mildly bottom-light and top-light gwIMF for Boötes I, and that this UFD has the same gas-consumption timescale as other dwarfs, but was quenched about 0.1 Gyr after formation. This is consistent with independent estimations, and it is similar to Dragonfly 44. The recovered best-fitting input parameters in this work are not covered in previous work, creating a discrepancy between our conclusions. In addition, a detailed discussion of the uncertainties is presented to address the dependence of the chemical evolution model results on the applied assumptions. This study demonstrates the power of the IGIMF theory in understanding star formation in extreme environments and shows that UDFs are a promising pathway to constrain the variation of the low-mass stellar IMF.

Previous studies of the stellar mean metallicity and [Mg/Fe] values of massive elliptical (E) galaxies suggest that their stars were formed over a very short timescale that cannot be reconciled with estimates from stellar population synthesis (SPS) studies and with hierarchical assembly. Applying the previously developed chemical evolution code, GalIMF, which allows an environment-dependent stellar initial mass function (IMF) to be applied to the integrated galaxy initial mass function theory instead of an invariant canonical IMF, the star formation timescales (SFT) of E galaxies are re-evaluated. The code’s uniqueness lies in it allowing the galaxy-wide IMF and associated chemical enrichment to evolve as the physical conditions in the galaxy change. The calculated SFTs become consistent with the independent SPS results if the number of type Ia supernovae (SNIa) per unit stellar mass increases for more massive E galaxies. This is a natural outcome of galaxies with higher star formation rates producing more massive star clusters, spawning a larger number of SNIa progenitors per star. The calculations show E galaxies with a stellar mass ≈109.5 M⊙ to have had the longest mean SFTs of ≈2 Gyr. The bulk of more massive E galaxies were formed faster (SFT ≈ 1 Gyr) leading to domination by M dwarf stars and larger dynamical mass-to-light ratios as observed, while lower mass galaxies tend to lose their gas supply more easily due to their shallower potential and therefore also have similarly-short mean SFTs. This work achieves, for the first time, consistency of the SFTs for early-type galaxies between chemical-enrichment and SPS modelling. Equally, it leads to an improved understanding of how the star formation environment may affect the total number of SNIa per unit stellar mass formed.

Recent observational and theoretical studies indicate that the stellar initial mass function (IMF) varies systematically with the environment (star formation rate -SFR, metallicity). Although the exact dependence of the IMF on those properties is likely to change with improving observational constraints, the reported trend in the shape of the IMF appears robust. We present the first study aiming to evaluate the effect of the IMF variations on the measured cosmic SFR density (SFRD) as a function of metallicity and redshift, f SFR (Z,z). We also study the expected number and metallicity of white dwarf, neutron star and black hole progenitors under different IMF assumptions. Applying the empirically driven IMF variations described by the integrated galactic IMF (IGIMF) theory, we correct f SFR (Z,z) obtained by Chruslinska & Nelemans (2019) and find lower SFRD at high redshifts as well as a higher fraction of metal-poor stars being formed. In the local Universe, our calculation applying the IGIMF theory suggests more white dwarf and neutron star progenitors in comparison with the universal IMF scenario, while the number of black hole progenitors remains unaffected.