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

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.

The effect of the environment-dependent IMF on the formation and metallicities of stars over the cosmic history

“…To combine the two methods, one needs to convert one metallicity measure to the other, which is not a straightforward procedure. However, we note that the metallicity dependence of the IMF has only a secondary effect on the correction factors calculated by Jeřábková et al (2018) and so the exact form of the relation does not have a strong effect on our results. For the purpose of this study we assume an example relation between [O/H] and [Fe/H] as shown in Fig.…”

“…Such corrections to the Kennicutt (1998) relation were recently calculated by Jeřábková et al (2018). Using the PyPegase python wrapper 4 , Jeřábková et al (2018) combined the GalIMF code (Yan et al 2017(Yan et al , 2019a which computes the galaxy-wide IMF(S FR, [Fe/H]) with PEGASE.2 stellar population synthesis code (Fioc & Rocca-Volmerange 1999;Fioc et al 2011) to produce the Hα flux for a given stellar population assuming a constant star formation history (SFH). For the purpose of this paper we extended previous calculations for a larger parameter space of SFRs (10 −5 M /yr, 10 3 M /yr) and [Fe/H] metallicities (-5,1).…”

“…To model the non-universal, environment dependent IMF we rely on the description provided by the IGIMF theory (Weidner et al 2013b;Yan et al 2017;Jeřábková et al 2018). The IGIMF uses empirically derived prescriptions for the formation of stars on pc/embedded cluster scales to build-up galaxywide stellar populations.…”

“…We note that the SFMR constructed that way is not directly based on any particular tracer at higher z, nevertheless, we use the matallicity dependent correction of the Hαbased SFR at all redshifts to obtain a rough estimate of the effect of the non-universal IMF on the f SFR (Z,z). Kroupa (2001) IMF (SFR K01 ) and the corresponding correction factors (K K01−IGIMF3 ) used to correct that SFR for the environment dependent IMF (described by the IGIMF3 model from Jeřábková et al (2018)). Different lines show the dependence of the correction factor on metallicity (represented by [Fe/H]).…”

“…The metallicity dependence of the IMF in Jeřábková et al (2018) is parametrised using the relative iron abundance (relative to solar; [Fe/H]), while the observations used in ChN19 provide the oxygen abundance Z O/H (Z O/H =12+log 10 (O/H)). To combine the two methods, one needs to convert one metallicity measure to the other, which is not a straightforward procedure.…”