Trading oxygen for iron

M. Chruślińska; R. Pakmor; J. Matthee; T. Matsuno

doi:10.1051/0004-6361/202347602

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A&A, 686 (2024) A186

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Issue		A&A Volume 686, June 2024


Article Number		A186
Number of page(s)		27
Section		Extragalactic astronomy
DOI		https://doi.org/10.1051/0004-6361/202347602
Published online		14 June 2024

A&A, 686, A186 (2024)

I. The [O/Fe]–specific star formation rate relation of galaxies

M. Chruślińska¹, R. Pakmor¹, J. Matthee² and T. Matsuno³

¹ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
e-mail: mchruslinska@mpa-garching.mpg.de
² Department of Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, Zürich 8093, Switzerland
³ Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands

Received: 29 July 2023
Accepted: 20 March 2024

Abstract

Our current knowledge of the star-forming metallicity of galaxies relies primarily on gas-phase oxygen abundance measurements. However, these do not always allow an accurate description of differences in stellar evolution and feedback, which are driven by variations in iron abundance. α-elements (such as oxygen) and iron are produced by sources that operate on different timescales and the link between them is not straightforward. We explore the origin of the [O/Fe]–specific SFR (sSFR) relation, linking chemical abundances to galaxy formation timescales. This relation is adhered to by star-forming galaxies across redshifts according to cosmological simulations and basic theoretical expectations. Its apparent universality makes it suitable for trading the readily available oxygen for iron abundance. We show that the relation is determined by the relative iron production efficiency of core-collapse and type Ia supernovae and the delay-time distribution of the latter – uncertain factors that could be constrained empirically with the [O/Fe]–sSFR relation. We compile and homogenise a literature sample of star-forming galaxies with observational iron abundance determinations to place first constraints on the [O/Fe]–sSFR relation over a wide range of sSFR. The relation shows a clear evolution towards lower [O/Fe] with decreasing sSFR and a flattening above log₁₀(sSFR/yr) > − 9. These results are broadly consistent with expectations, but better constraints are needed to inform the models. We independently derive the relation from old Milky Way stars and find remarkable agreement between the two, as long as the recombination-line absolute oxygen abundance scale is used in conjunction with stellar metallicity measurements.

Key words: stars: abundances / stars: formation / supernovae: general / galaxies: abundances / galaxies: evolution / galaxies: star formation

© The Authors 2024

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model.

Open access funding provided by Max Planck Society.

1. Introduction

Oxygen is the most abundant metal in the Universe and it is relatively easily observable via strong optical emission lines (Tremonti et al. 2004; Kewley & Ellison 2008; Maiolino & Mannucci 2019; Kewley et al. 2019). These lines have been used to determine gas-phase abundances of oxygen relative to hydrogen (12 + log₁₀(O/H)) for large samples of star-forming galaxies up to z ≲ 3, and are now accessible at even higher redshifts with JWST (e.g. Jones et al. 2020; Arellano-Córdova et al. 2022; Curti et al. 2023; Katz et al. 2023; Nakajima et al. 2023).

However, it is the iron abundance that drives the differences in the lives and fates of massive stars at different metallicities and regulates their impact on the surroundings (Garcia et al. 2021; Eldridge & Stanway 2022; Chruślińska 2024; Vink 2022). Their evolution, as well as their final core and explosion properties, are strongly affected by radiation-driven winds, which scale with iron abundance due to its dominant role in setting the opacity in stellar atmospheres (Abbott 1982; Pauldrach et al. 1993; Vink et al. 2001; Kudritzki 2002; Vink & de Koter 2005; Sander & Vink 2020). By removing mass and angular momentum from stellar binaries and multiples, stellar winds further affect the orbit and evolution of such systems. Together with the effects of binary interactions, the iron abundance plays a decisive role in shaping the high-energy part of the galaxy spectra (particularly the UV continuum with absorption and wind features, and ionising radiation emitted by stellar populations; e.g. Leitherer et al. 2014; Stanway & Eldridge 2018; Götberg et al. 2019, 2020; Vink et al. 2023), which is particularly important for the HII region emission-line diagnostics (e.g. Steidel et al. 2016; Strom et al. 2018) and star formation rate diagnostics (Lee et al. 2002; Madau & Dickinson 2014). It is much more challenging to determine the iron abundances in star-forming material than it is the oxygen abundance, and iron abundances are presently available for only a limited number of galaxies. We review the methods used to determine oxygen and iron abundances in star-forming material, and discuss the related challenges in Sect. 3.1.

Those two elements are produced abundantly by sources that operate on different timescales and the link between them is not straightforward (Matteucci & Greggio 1986; Wheeler et al. 1989). Oxygen is promptly released to the interstellar medium via core-collapse supernovae (CCSNe), which come from massive star progenitors, reaching the core-collapse stage within a few to ≈50 Myr (Woosley et al. 2002; Heger et al. 2003; Janka et al. 2007; Schneider et al. 2021). Iron is also generously produced by type Ia supernovae (SN Ia). While the exact formation scenario of these latter events is a matter of ongoing debate, they are linked to thermonuclear explosions involving carbon–oxygen white dwarf(s) and come with a broad range of delays with respect to star formation of at least ∼40 Myr (i.e. the minimum time required to form a white dwarf; Greggio 2005; Maoz & Mannucci 2012; Wang & Han 2012; Maoz et al. 2014; Livio & Mazzali 2018). As a consequence, in young and highly star-forming environments, iron production is expected to lag behind that of oxygen. In such environments, the composition of the star-forming material may considerably deviate from the conventional solar abundance pattern. This is clear from the abundances recorded in old, metal-poor stars in the Milky Way (MW) and its satellites: their oxygen-to-iron ratios can exceed the reference solar value by more than five times (e.g. Gratton et al. 2000; Zhang & Zhao 2005; Tolstoy et al. 2009; Amarsi et al. 2019). Evidence of supersolar oxygen/α-element-to-iron abundance ratios has also been found in local (e.g. Izotov et al. 2006, 2018; Hernandez et al. 2017; Kojima et al. 2021; Gvozdenko et al. 2022; Senchyna et al. 2022) and high-redshift star-forming galaxies (e.g. Steidel et al. 2016; Strom et al. 2018, 2022; Sanders et al. 2020; Topping et al. 2020; Cullen et al. 2021) and in stellar populations of elliptical galaxies that formed in the high-redshift Universe (e.g. Thomas et al. 2010; Conroy et al. 2014). This implies that in certain environments the wind mass loss of hot, massive stars may be severely overestimated if the oxygen abundance is used as a proxy for their iron-group metallicity. This in turn has important consequences for their expected evolution, their explosion and compact object properties (and therefore also feedback and chemical enrichment), and the observable properties of the stellar population (galaxy spectra, ionising radiation, and certain emission line ratios) and related transients (various types of supernovae, long gamma-ray bursts, gravitational wave sources). Therefore, using the oxygen abundance as a proxy for the iron abundance (after scaling to the solar pattern, as commonly done in many areas of astronomy) can lead to important systematic errors that have so far remained largely unaccounted for.

Motivated by the need to establish a link between the readily available oxygen abundance and the essential but typically unknown star-forming iron abundance – which would be applicable across a wide range of galaxy properties –, we explore the relation between the star-forming [O/Fe]¹ ratio and the specific star formation rate (sSFR). One might expect the two quantities to be strongly related: sSFR = $\frac{SFR}{M_{*}}$ $\frac{\mathrm{SFR}}{M_{*}}$ is the ratio between the production rate of stars (a subset of which quickly explode as CCSNe) and the stellar mass accumulated over time (available for the continuous production of delayed SNe Ia). Therefore, to first degree, the sSFR sets the ratio between the rate of CCSNe and SNe Ia at a given time and [O/Fe]. A tight [O/Fe]–sSFR relation has indeed been found in the EAGLE cosmological simulations (Matthee & Schaye 2018) and within the semi-analytic gas-regulated galaxy evolution model (Kashino et al. 2022). We further discuss the origin of this relation and the main factors that are expected to shape it in Sect. 2.

In Sect. 2.5 we complement this qualitative discussion with a simple analytical description that allows us to reproduce the average [O/Fe]–sSFR relation resulting from the EAGLE (Schaye et al. 2015) and TNG cosmological simulations (Pillepich et al. 2018) and explain the origin of the differences between them.

The [O/Fe]–sSFR relation can be seen as a star-forming analogue of the well-known relic stellar [α/Fe]–[Fe/H] relation (Tolstoy et al. 2009; Amarsi et al. 2019), where both sSFR and [Fe/H] serve as some proxy for galaxy age. We show how we exploit this connection and roughly reconstruct the MW [O/Fe]–sSFR relation from its old disc stars in Sect. 3.2.

In Sect. 3.3, we present a collection of the available observational data characterising other star-forming galaxies and show how we select a subset of those that can be brought to a common baseline by accounting for systematic offsets (Sect. 3.4). We describe how we use this subset to empirically derive the [O/Fe]–sSFR relation (Sect. 4) and confront the result with theoretical expectations (Sect. 5). In Sect. 6 we reflect on the prospects of obtaining further constraints. We discuss the potential use of the [O/Fe]–sSFR relation to discriminate between the different theoretical SN Ia delay-time distributions, to infer the uncertain minimum delay at which they contribute significantly to enrichment, and to constrain the average CCSN iron yields.

Where relevant, we explicitly use either [X/H] = log₁₀(X/H)–log₁₀(X/H)_⊙ or 12 + log₁₀(X/H) notation to refer to the iron (X=Fe) or oxygen (X=O) abundance. We use Z_O (Z_Fe) to refer to oxygen (iron) abundance in a general sense. We assume solar reference abundances of 12+log₁₀(O/H)_⊙ = 8.83, 12+log₁₀(Fe/H)_⊙ = 7.5, and log₁₀(O/Fe)_⊙ = 1.33 dex from Grevesse & Sauval (1998) (GS98 hereafter).

2. Theoretical expectations

2.1. The sSFR of typical galaxies at different redshifts and their locations along the relation

The sSFR = $\frac{SFR}{M_{*}} = \frac{1}{τ_{SF}}$ $\frac{\mathrm{SFR}}{\mathrm{M}_{*}}=\frac{1}{\tau_{\mathrm{SF}}}$ defines a characteristic timescale τ_SF on which a galaxy grows to its current stellar mass if that growth happens at its current SFR. High sSFR values correspond to galaxies that are either young or forming stars more rapidly compared to their average star-forming activity in the past. For galaxies with regular star formation histories τ_SF can serve as some proxy for the age of their stellar population (the age increases towards the left side of the Fig. 1).

The typical sSFR of star-forming galaxies can be determined from the redshift-dependent star formation–mass relation (SFMR, also called the ‘main sequence’ of galaxies; e.g. Brinchmann et al. 2004; Salim et al. 2007; Speagle et al. 2014; Popesso et al. 2023). The range of the sSFR of main sequence (MS) galaxies at z ∼ 0 and z ∼ 2 is roughly indicated at the top of Fig. 1. For a given stellar mass, the SFRs of galaxies are higher at higher redshifts: a M_∗ ∼ 10¹⁰ M_⊙ MS galaxy at redshift z ≳ 3 has log₁₀(sSFR) ∼ –8.5 and this value drops to log₁₀(sSFR)≈ − 10 by z = 0 (Boogaard et al. 2018; Popesso et al. 2023). Therefore, the (upper) right corner of Fig. 1 is expected to be occupied by galaxies from the early Universe. Conversely, the typical low-redshift galaxies are expected to occupy the lower left corner of the relation. If the slope of the SFMR is close to unity, then all MS galaxies at a given redshift have similar sSFRs and occupy similar locations on the [O/Fe]–sSFR plane. In reality there is a σ_SFR ∼ 0.3 dex scatter in the SFR at fixed galaxy stellar mass around the SFRM and regular star-forming galaxies at any epoch always occupy a range of sSFR (e.g. Matthee & Schaye 2019). The redshift evolution of the normalisation of the SFMR is found to be relatively steep up to z ≲ 2–3, but much more gradual at higher redshifts (Weinmann et al. 2011). This means that the typical sSFR of MS galaxies does not increase much beyond this point if the current SFMR estimates are extrapolated to higher redshifts. Consequently, extremely high log₁₀(sSFR) ≳ −7.6 galaxies are either very low mass (M_∗ < 10⁶ M_⊙ at z ∼ 3 – the SFMR is essentially unconstrained at such low stellar masses even at low redshifts) and/or undergo a strong starburst phase.

Fig. 1.

Schematic illustration of the expected characteristics of the star-forming [O/Fe]–sSFR relation of galaxies. Young, high-redshift main sequence galaxies (with high sSFR) occupy the upper right part of the relation. Their chemical enrichment is dominated by prompt sources (CCSNe), which are expected to eject material with supersolar oxygen-to-iron abundance ratios. Below a certain sSFR (when the characteristic timescale τ_SF = 1/sSFR becomes comparable to the minimum SN Ia delay), SNe Ia begin to contribute significantly to the iron enrichment. As a result, old, low-redshift main sequence galaxies occupy the lower left part of the relation, with [O/Fe] approaching the solar ratio (orange dashed line). The exact shape of the relation depends on a number of uncertain factors (e.g. relative oxygen and iron yields, and rates and delays of different supernovae).

2.2. High sSFR: SN Ia-free regime

If the τ_SF timescale is short compared to the typical delay of SN Ia (τ_SF < τ_Ia; min, top-right corner of the Fig. 1), the enrichment is dominated by CCSNe. These latter phenomena pollute the interstellar medium with material with a relatively high supersolar [O/Fe] ratio (e.g. Tominaga et al. 2007; Heger & Woosley 2010; Nomoto et al. 2013; Sukhbold et al. 2016; Grimmett et al. 2018; Limongi & Chieffi 2018; Curtis et al. 2019; Ebinger et al. 2020). The most massive stars are the first to evolve and undergo core collapse. They are expected to eject material at higher [O/Fe] ratio than the lower mass CCSN progenitors, which may already lead to some evolution in the [O/Fe]-sSFR plane. We note that this is an extremely brief phase: all (single) stars massive enough to give rise to CCSN (≳7–8 M_⊙ at birth) are expected to explode or collapse within < 40–50 Myr following their formation. Whether some ‘typical’ [O/Fe] pattern is expected in this regime is unclear: τ_SF < 40 Myr implies log₁₀(sSFR) ≳ –7.6. As discussed above, such sSFR are not found for typical MS galaxies. The early enrichment is dominated by the most massive (rare), very metal-poor stellar progenitors. Such progenitors have been proposed to lead to a variety of explosions with very different properties from the regular CCSN (e.g. pair-instability supernovae El Eid & Langer 1986; Langer et al. 2007; Woosley 2017) and may eject matter with a different [O/Fe] (Heger & Woosley 2002; Nomoto et al. 2005; Heger & Woosley 2010; Grimmett et al. 2018; Takahashi et al. 2018), possibly leading to a large scatter in the rightmost part of the [O/Fe] – sSFR relation.

At slightly longer τ_SF the galaxy’s [O/Fe] may approach some population-averaged CCSN [O/Fe]_CCSN ratio. This expectation is guided by the existence of a plateau found for the stellar [α/Fe] – [Fe/H] relation at low [Fe/H] for the MW and local dwarf galaxies (where [Fe/H] serves as a proxy for the age of the galaxy playing an analogous role to the sSFR in Fig. 1, e.g. Tolstoy et al. 2009; Amarsi et al. 2019; Miglio et al. 2021). Theoretical CCSN yields (and hence the value of [O/Fe]_CCSN) are very uncertain, especially for the metal-poor CCSNe progenitors. Observational constraints on possible [O/Fe]_CCSN are therefore highly desirable.

2.3. The onset of SN Ia and a possible turnover

SN Ia start to contribute to the chemical enrichment of the interstellar gas at times longer than τ_Ia; min. The minimum theoretically feasible delay is set by the evolutionary timescale of the most massive white dwarf progenitor (leading to τ_Ia; min ≳ 40–50 Myr, or log₁₀(1/τ_Ia; min)≲–7.6). However, it could be longer than that depending on the assumed SN Ia formation scenario (e.g. Greggio 2010; Maoz et al. 2014; Liu et al. 2023). The mapping between the birth stellar mass and its final fate (i.e. white dwarf, neutron star/CCSN or black hole), which sets the timescales in the above considerations, is not straightforward. It is expected to depend on the metallicity of the progenitor star and can be altered by binary interactions. In particular, in the presence of binary interactions a fraction of CCSN can originate from lower mass stars and happen with delays longer than 50 Myr (Zapartas et al. 2017). SN Ia are thought to eject material with high iron and negligible oxygen abundances compared to average CCSN yields (Nomoto et al. 1997; Iwamoto et al. 1999; Lach et al. 2020). They act to reduce the galaxy’s [O/Fe], possibly leading to a break/change in the slope of the [O/Fe]-sSFR relation at sSFR = 1/τ_SF, corresponding to the timescale at which the SN Ia contribution becomes significant. Figure 2 compares some of the SN Ia delay time distributions (DTD) used in the literature, which predict considerably different SN Ia contributions at early times following the star formation. The possible turnover point would be expected at τ_SF relatively close to τ_Ia; min in the case of the conventionally assumed power-law SN Ia DTD, but it could be considerably longer than τ_Ia; min if the DTD has a different form.

Fig. 2.

Cumulative distribution functions of the example SN Ia DTD. The distributions were normalised to unity when integrated over the Hubble time. Solid lines correspond to single power-law-shaped DTD: brown – TNG cosmological simulations, black – fitted to the observed SN Ia volumetric rate by Maoz & Graur (2017). Dashed lines correspond to the exponential DTD: thick turquoise line – EAGLE cosmological simulations, thin blue line – Galaxy chemical evolution model from Schönrich & Binney (2009) with DTD parameters tuned to reproduce observed oxygen abundances. The black dotted line corresponds to the DTD used by Kashino et al. (2022), which follows the theoretical analytic formulation by Greggio (2005, 2010) allowing for a mixed contribution of different proposed SN Ia progenitors. The intersection with the horizontal dashed line indicates the median of each DTD. The vertical dashed line at 40 Myr marks the evolutionary timescale of an 8 M_⊙ star (i.e. roughly the minimum time needed to form a white dwarf).

2.4. Intermediate and low sSFR

At intermediate and low sSFRs, the relation between the [O/Fe] and sSFR is to first order governed by the relative rates of CCSN and SN Ia and their corresponding oxygen and iron yields, which are factors determined by stellar evolution and supernovae explosion properties. This is supported by the semi-analytical considerations from Kashino et al. (2022), who show that within the gas-regulator galaxy evolution framework (Lilly et al. 2013) the [O/Fe] – sSFR relation is independent of the model parameters related to large-scale processes in galaxy evolution (mass-loading factor, star formation efficiency) and is effectively determined by the abundance ratio produced by CCSN and SN Ia at any given time. We note that such ‘instantaneous’ [O/Fe] ratio might decrease faster than the abundance ratio in the star-forming material, where metals may accumulate and enter the star-forming phase with some delay rather than being reused immediately. In general, the slope of the [O/Fe]-sSFR relation can also be affected by inflows of metal-poor (or high [O/Fe]) material and/or feedback processes removing some fraction of the enriched matter from the star-forming material. Metal retention/feedback can in principle depend on the galaxy mass (e.g. Nelson et al. 2019a) and induce a secondary dependence of the [O/Fe]-sSFR relation on this property.

In the simplest scenario where the population-averaged supernova metal yields and the formation efficiencies are constant, other stellar sources contribute negligible O and Fe, potential inflowing material has zero metallicity, and star-forming [O/Fe] approaches the instantaneous production ratio, the [O/Fe]–sSFR relation can be readily derived from Eq. (12) from Kashino et al. (2022). This can be rewritten as follows:

$\begin{matrix} [O / Fe] & = {[O / Fe]}_{CCSN} \\ - {log}_{10} (1 + \frac{m_{Fe}^{Ia}}{m_{Fe}^{CCSN}} \frac{N_{Ia 0}}{k_{CCSN}} \frac{\int_{0}^{t} S F R (t^{'}) f_{Ia} (t - t^{'}) d t^{'}}{SFR}), \end{matrix}$ $\begin{aligned}{[\mathrm{O/Fe}]}&= {[\mathrm{O/Fe}]}_{\rm CCSN} \nonumber \\&\quad - \log _{10}\left( 1 + \frac{m^{\mathrm{Ia}}_{\mathrm{Fe}}}{m^{\mathrm{CCSN}}_{\mathrm{Fe}}} \frac{N_{\mathrm{Ia0}}}{k_{\rm CCSN}} \frac{\int _{0}^{t} SFR(t^\prime ) f_{\mathrm{Ia}}(t-t^\prime )\,\mathrm{d}t^\prime }{\mathrm{SFR}} \right), \end{aligned}$ (1)

where [O/Fe]_CCSN is the average CCSN oxygen to iron abundance ratio relative to solar, $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ and $m_{Fe}^{Ia}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}$ is the average iron mass ejected per CCSN or SN Ia event, respectively, k_CCSN is the CCSN formation efficiency (i.e. number of CCSN formed per unit stellar mass formed), N_Ia0 is the SN Ia formation efficiency (i.e. the Hubble time-integrated number of SN Ia formed per unit stellar mass) and f_Ia describes the SN Ia DTD normalised to unity when integrated over the Hubble time. The last term in the parenthesis in Eq. (1), i.e. the ratio of the time integral over the star formation history of the galaxy (∝M_*) modulated by the SNIa DTD to its current SFR masks the dependence on the sSFR.

For convenience, we define $C_{Ia / CC} : = \frac{m_{Fe}^{Ia}}{m_{Fe}^{CCSN}} \frac{N_{Ia 0}}{k_{CCSN}}$ $C_{\mathrm{Ia/CC}} \mathrel{\mathop:}\mkern-1.2mu= \frac{m^{\mathrm{Ia}}_{\mathrm{Fe}}}{m^{\mathrm{CCSN}}_{\mathrm{Fe}}} \frac{N_{\mathrm{Ia0}}}{k_{\mathrm{CCSN}}}$ . For a fixed SN Ia DTD, the slope of the relation is only sensitive to the relative iron yield of SN Ia and CCSN. Increasing the SN Ia formation efficiency or $m_{Fe}^{Ia}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}$ would have the same effect as lowering k_CCSN or $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ by the same amount and would act to steepen the relation. Increasing the oxygen yield per CCSN (i.e. increasing [O/Fe]_CCSN at fixed $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ ) would only change the overall normalisation of the relation without affecting its shape. In reality all k_CCSN, $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ and especially [O/Fe]_CCSN may vary with birth metallicity of stellar progenitors. With the example discussed in Sect. 2.5 we show that in such a case the [O/Fe]–sSFR relation can still be well described with fixed values of those parameters. However, their interpretation is much less straightforward. No clear dependence of SN Ia formation or metal yields on metallicity is predicted by current models (but see Cooper et al. 2009; Toonen et al. 2012). However, in principle such a dependence could be induced by environmental variations of the stellar IMF (Weidner & Kroupa 2005; Chruślińska et al. 2021).

Finally, the shape of the [O/Fe] – sSFR relation is sensitive to the SN Ia DTD. From Fig. 2 it is clear that the DTD used in the literature predict very different time evolution of the SN Ia rate. The power-law DTD (TNG and Maoz & Graur 2017 examples shown in Fig. 2) allows for a broader range of delay times at which SN Ia contribute compared to more concentrated exponential DTD (as in the EAGLE and Schönrich & Binney 2009 examples shown in Fig. 2). In the latter cases SN Ia start contributing at longer times following the star formation, but their contribution is rising more steeply. With such a DTD the expected turnover/change of slope in the [O/Fe]-sSFR relation would happen at lower sSFR but [O/Fe] would then decrease more steeply than in the power-law DTD scenario. This is evident in the Fig. 3, where we compare the [O/Fe]-sSFR relations resulting from the TNG and EAGLE simulations. We further discuss those examples in Sect. 2.5.

Fig. 3.

Star-forming [O/Fe] versus sSFR relation for simulated galaxies from the EAGLE cosmological simulations (turquoise contours) and TNG 100 cosmological simulations (brown contours). The contours enclose 50, 68, and 95 % of all central galaxies with log₁₀(M_*/M_⊙) = 9–10.5 at redshifts between 0 and 8. The solid turquoise line shows the fit to the relation in EAGLE from Matthee & Schaye (2018), while the dashed brown line shows our fit to the relation in TNG 100. The black dotted line shows the relation obtained by Kashino et al. (2022) for MS galaxies modeled within the gas-regulator framework.

We note that current galaxy simulations performed in the cosmological size box lack the resolution to reach very high sSFRs (log₁₀(sSFR) ≳ –8) and under-represent such galaxies relative to observations (Sparre et al. 2015; Rinaldi et al. 2022). As a result, the high sSFR region in Fig. 3 is not populated and the flattening of the [O/Fe] – sSFR relation (expected at log₁₀(sSFR) > − 8 and log₁₀(sSFR) > − 8.5 for TNG and EAGLE, respectively, given the SN Ia DTD assumptions used in the simulations) cannot be probed with such simulations.

2.5. Examples from cosmological simulations

The existence of a tight [O/Fe] – sSFR relation has been previously shown by Matthee & Schaye (2018) with the use of the EAGLE cosmological simulations (Crain et al. 2015; Schaye et al. 2015; McAlpine et al. 2016) and by Kashino et al. (2022) within the gas-regulator galaxy evolution semi-analytical model (Lilly et al. 2013). We show the corresponding relations, along with the results extracted from the TNG cosmological simulations (Pillepich et al. 2018; Nelson et al. 2019b) in Fig. 3. We plot several density contours indicating the locations of the EAGLE (using the Ref-L0100N1504 run) and TNG (using the TNG100-1 run) galaxies selected from the full simulation snapshots between redshifts 0 and 8. We select galaxies following the same criteria as Matthee & Schaye (2018) (central star-forming galaxies in the mass range log₁₀(M_*/M_⊙) = 9–10.5). Matthee & Schaye (2018) conclude that the simulated galaxies follow a fundamental plane linking SFR, M_* and [O/Fe] that is well described by the following fit at least up to redshift 2: [O/Fe] = −0.282 log₁₀(M_∗/10¹⁰ M_⊙) + 0.29 log₁₀(SFR/M_⊙ yr) + 0.023 where [O/Fe] assumes the GS98 reference solar scale and the constant value was adjusted accordingly². The corresponding relation for log₁₀M_* = 9.75 is shown as a thick solid turquoise line in Fig. 3. The fit to TNG-100 galaxies shown in Fig. 3 is described by: [O/Fe] = 0.037log₁₀(sSFR)² + 0.862log₁₀(sSFR)+5.12

The overall shape of the relation followed by the EAGLE galaxies at log₁₀(sSFR) ≲ –9 is very similar to the one found by Kashino et al. (2022), but significantly differs from the relation followed by the TNG-100 galaxies.

As anticipated in the previous section, those differences stem mostly from different assumptions about the SN Ia DTD (shown in Fig. 2). To illustrate this we consider mock MS galaxies; that is, galaxies that follow the evolving SFMR through cosmic time. Similarly to Kashino et al. (2022), we use this to determine average galaxy star formation histories and calculate their evolutionary tracks in the [O/Fe]-sSFR plane following Eq. (1). In panel a in Fig. 4 we show the result of this procedure when we use k_CCSN and N_Ia0, $m_{Fe}^{Ia}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}$ , SN Ia DTD and SFMR as in the EAGLE and TNG100-1 simulations (see Appendix A for more details). The CCSN metal yields (and therefore $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ and [O/Fe]_CCSN) used in the simulations vary with metallicity of the stellar population. We therefore cannot extract a single value for those parameters from the simulation settings. Instead, we choose their values in a way that allows to match the locations of galaxies from the corresponding simulations (indicated by density contours in Fig. 4). It can be seen that the corresponding evolutionary tracks of our mock MS galaxies reproduce the [O/Fe]–sSFR relations resulting from the simulairontions extremely well, despite the very simplistic assumptions that we made. This conclusion is not affected by the choice of the SFMR, which only shifts the locations of galaxies of different masses along the relation. This can be seen in panel b, where in all cases we use the same SFMR as Kashino et al. (2022) (see Sect. 5.2.1 and Fig. 15 therein). In panel c we show that when we additionally change the SN Ia DTD to the one used in the TNG simulations, the mock galaxies previously tracing the EAGLE-like relation start to follow the [O/Fe]–sSFR relation which resembles the one from the TNG simulations. If we further change [O/Fe]_CCSN to the same value as in TNG, the two sets of tracks overlap almost entirely (see panel d). The small difference in slope which remains between the brown and turquoise tracks in panel d results from the small difference in the ratio of the supernovae efficiencies $\frac{N_{Ia 0}}{k_{CCSN}}$ $\frac{N_{\mathrm{Ia0}}}{k_{\mathrm{CCSN}}}$ used in the EAGLE and TNG simulations.

Fig. 4.

Star-forming [O/Fe] – log₁₀(sSFR) relation for the simulated galaxies from the EAGLE cosmological simulations (turquoise contours), for the simulated galaxies from the TNG 100 cosmological simulations (brown contours), and those obtained by Kashino et al. (2022) (black dotted line). The contours enclose 50, 68 and 95 % of all central galaxies with log₁₀(M_*/M_⊙) = 9–10.5 at redshifts between 0 and 8. The thick solid lines show evolutionary tracks of MS galaxies along the relation calculated with Eq. (1) for different parameter choices. Squares/diamonds show the locations of galaxies of different masses (indicated by the symbol shading) at redshift 3.5/0. The tracks in panel a were calculated using the SFMR, DTD, $m_{Fe}^{Ia}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}$ , k_CCSN and N_Ia0 from the EAGLE (turquoise) or TNG (brown) simulations (see Appendix A). The remaining parameters are chosen to match the relation resulting from the EAGLE or TNG simulations, respectively. In panel b all tracks were caluclated with the same SFMR as in Kashino et al. (2022). In panel c we additionally change the DTD for turquoise tracks to the one used in the TNG simulations. In panel d we further change [O/Fe]_CCSN used to calculate the turquoise tracks to be the same as used to calculate the brown tracks.

We draw two conclusions from the comparison performed in this Section:

Despite the overall strong metallicity-dependence of CCSN yields (present in the yield tables used in both the EAGLE and TNG simulations), the average relation can be well reproduced using fixed values of $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ and [O/Fe]_CCSN.
The feedback model (which differs considerably between the two simulations) and other processes that are not captured by the simple description given by Eq. (1) but are accounted for in the simulations (e.g. galaxy mergers, gas recycling) do not have a major effect on the average [O/Fe]–sSFR relation.

This gives us a certain degree of confidence that the average [O/Fe]–sSFR relation may serve as a diagnostic of: (i) the relative iron production efficiency in SN Ia and CCSN, (ii) the SN Ia delay time distribution, and (iii) some sort of a cosmic average O/Fe abundance ratio produced per CCSN.

3. Observational data

Several methods are used to determine metallicity of the star-forming material. As we summarise in Sect. 3.1, different observational probes are suitable to infer iron-based (Z_Fe) and oxygen-based (Z_O) metallicity. Furthermore, different approaches are used at different redshifts and/or for different objects – especially in the case of iron. Both factors complicate the observational picture of the [O/Fe] evolution as a function of cosmic time or galaxy properties and particular attention needs to be paid to systematic uncertainties. We highlight the identified sources of such systematic offsets that have been quantified in the literature and that are specific to the methods introduced in Sect. 3.1. In Sect. 3.4 we summarise our attempt to correct for those and to bring the results compiled from the literature (see Sect. 3.3 and Appendix ) to a common baseline before combining them in Sect. 4.

3.1. Star-forming metallicity determination techniques

3.1.1. Stellar-based methods

The most intuitive approach to learn about the metallicity at which the stars are forming is to infer atmospheric abundances from spectra of individual massive (therefore recently formed) stars. Alternatively, one can rely on atmospheric abundance estimates derived from lower mass stars that either have very accurate age determinations or are members of young/open clusters. These methods are mostly restricted to the MW and its closest satellites, with the notable exception of AB-type blue supergiant (BSG) and red supergiant (RSG) based measurements. Especially the former are very bright, which makes it possible to obtain their high signal-to-noise ratio spectra in galaxies within a few Mpc (e.g. Przybilla et al. 2006; Bresolin et al. 2007, 2016, 2022; Kudritzki et al. 2008, 2016; Urbaneja et al. 2008; Hosek 2014; Davies et al. 2017; Liu et al. 2022). The observed spectra contain absorption lines from many elements and can be compared to a grid of line-blanketed models to determine metallicity (e.g. Kudritzki et al. 2008; Hosek 2014). Typically many iron-group (Fe, Cr) but also some α-element lines (e.g. Mg, Ca, Si, Ti) are included in the analysis. Therefore, the derived bulk metallicity may not be straightforwardly linked to iron or oxygen abundances. Nevertheless, it has been used in the literature as a proxy for both and compared with gas phase oxygen abundances (e.g Bresolin et al. 2016, 2022) or stellar-based iron measurements (e.g. Hosek 2014). Solar abundance pattern is assumed in the spectral models, which by construction does not allow to detect deviations from the solar ratios. Potential departures from the solar ratios are also difficult to infer from comparison with gas-phase oxygen abundances due to the known systematic uncertainty in the absolute value of such measurements: the BSG/RSG determinations typically fall within the range spanned by oxygen derivations obtained with different methods (e.g. Bresolin et al. 2016, 2022). Encouragingly, Garcia et al. (2014) find that the iron abundance of IC 1613 needs to be higher than approximately one-tenth solar estimated from its HII region oxygen abundances in order to match stellar spectra and wind properties, more in line with RSG based metallicities in this system. This suggests that RSG/BSG metallicities may reasonably probe iron abundances.

Finally, we note that while the surface iron abundance of massive stars is expected to be a good representation of the abundance of that element in the star-forming material, the surface oxygen abundance may be affected by evolutionary processes (in particular, strong rotation and mixing of the material processed in nuclear reactions may substantially lower birth oxygen abundance, e.g. Brott et al. 2011; Maeder et al. 2014).

3.1.2. Methods based on the UV emission of stellar populations

For more distant objects, rest-frame UV galaxy spectra can be used to obtain iron-based metallicity estimate (e.g. Heckman et al. 1998; Rix et al. 2004; Crowther et al. 2006; Sommariva et al. 2012; Cullen et al. 2019). This part of the spectrum is dominated by massive OB-type stars, and therefore reflects the star-forming metallicity. The UV continuum contains absorption features that can be linked to elements present in stellar photospheres (especially highly ionised iron) and stellar winds. The strength of the stellar winds and the associated line profiles are expected to be a strong function of metallicity (predominantly iron abundance due to its dominant contribution to opacity in radiation-driven winds, e.g. Kudritzki et al. 1987; Vink et al. 2001; Vink & de Koter 2005; Crowther et al. 2006). In practice, the metallicity is obtained by comparing the observed spectra with predictions of stellar population synthesis (SPS) and the result is inevitably model sensitive. The two SPS models that are most commonly used to derive the properties of high redshift galaxies (Starburst99, Leitherer et al. 2014 and BPASS, Stanway et al. 2016; Eldridge et al. 2017; Stanway & Eldridge 2018) are known to yield UV-continuum based metallicities that are systematically lower for BPASS models than for Starburst99 (S99, with the average offset of ∼0.1 dex, e.g. Chisholm et al. 2019; Cullen et al. 2019)³. BPASS models include the effects of binary evolution (in particular stripping of stellar outer layers in mass transfer) that tend to produce harder spectra for the same stellar population metallicity than single star based models (even when including rotation)⁴. Such harder ionisation fields as obtained when accounting for binary evolution effects help to reproduce the observed line ratios in high redshift galaxies, but even harder spectra than predicted by any existing SPS may be required to match the emission of the most metal poor objects (e.g. Steidel et al. 2016; Xiao et al. 2018; Nanayakkara et al. 2019; Strom et al. 2022; Eldridge & Stanway 2022; Senchyna et al. 2022; Katz et al. 2023). Furthermore, current models struggle with simultaneously reproducing wind and photospheric features in the UV spectra of young, highly star-forming galaxies (see Sect. 6.2 in Senchyna et al. 2022, for the extensive discussion). Senchyna et al. (2022) caution that UV stellar metallicity estimates relying primarily on wind line features (more easily detected at high redshifts than the photospheric features) may significantly bias the result towards higher values (see also Wofford et al. 2021).

Efficient absorption of UV-wavelengths in the Earth’s atmosphere means that obtaining UV spectra of local galaxies requires the use of space telescopes. Furthermore, typical local galaxies are UV-faint (i.e. have low SFR and declining star formation histories). Both factors result in this method being rarely applied in the local Universe (but see Senchyna et al. 2022, for the recent efforts). Conversely, rest-frame UV spectra of high redshift galaxies are much brighter and conveniently shifted to optical wavelengths for z ≳ 2 objects. Applying this technique still requires very good data quality (high-S/N continuum emission detection), and the UV-based iron metallicity is currently only available for a limited number of galaxies (Rix et al. 2004; Sommariva et al. 2012; Steidel et al. 2016; Topping et al. 2020; Cullen et al. 2019, 2021; Calabrò et al. 2021; Matthee et al. 2022).

Known source of systematic uncertainty. Choice of SPS model: we assume the average difference between Z_Fe derived with S99 and BPASS models Δ_SPS = 0.1 dex ( $Z_{Fe}^{S 99} = Δ_{SPS} + Z_{Fe}^{BPASS}$ $Z_{\mathrm{Fe}}^{\mathrm{S99}}=\Delta_{\mathrm{SPS}}+Z_{\mathrm{Fe}}^{\mathrm{BPASS}}$ ), unless the exact offset is known.

3.1.3. Gas-phase HII region-based methods: oxygen

The oxygen abundance is commonly inferred using optical emission lines from HII regions (see e.g. Peimbert et al. 2017; Kewley et al. 2019; Maiolino & Mannucci 2019 for the overview of methods and recent reviews). HII regions are ionised by neighbuoring massive stars, and are therefore suitable targets for investigations into the star-forming metallicity. The most direct approach requires detection of faint recombination lines and is mostly limited to nearby HII regions (e.g. Peimbert 1967; Esteban et al. 2014). The most commonly used alternative method relies on the fact that the electron temperature T_e of the gas is a sensitive probe of metallicity. For the same ionisation source, an HII region with higher metallicity has lower T_e due to more efficient cooling by metal line emission than its low metallicity counterpart. The line cooling is dominated by oxygen due to its high abundance and low excitation energies relative to other metals. T_e can thus be determined based on ratios of temperature-sensitive collisionally excited oxygen emission lines (e.g. [O III] 4363, 4959 and 5007). However, the suitable auroral lines are also challenging to detect. As a consequence, methods relying on strong-line proxies of auroral lines are commonly used. Estimates obtained with different strong-line calibrations lead to discrepant results (e.g. Kewley & Ellison 2008; Kewley et al. 2019; Maiolino & Mannucci 2019): the so-called ‘direct’ method (i.e. where the suitable collisionally excited T_e sensitive auroral lines are detected and T_e can be inferred directly) and methods based on empirical calibrations typically lead to lower oxygen abundances than theoretical calibrations. Notably, there is also a known discrepancy between the abundances based on the ‘direct’ method and the abundances inferred with OII recombination lines. The latter typically leads to ∼0.24 dex higher oxygen abundance inferred for the same region (this offset is often called the Abundance Discrepancy Factor ADF, e.g. Peimbert 1967; Esteban et al. 2014; Peimbert et al. 2017; Kewley et al. 2019; Chen et al. 2023; Méndez-Delgado et al. 2023). It is currently unclear which of the methods leads to the correct absolute oxygen abundance value and what is the origin of the differences between them (Chen et al. 2023; Méndez-Delgado et al. 2024). Steidel et al. (2016) and Sanders et al. (2020) find that in order to reproduce the observed HII region line ratios with photoionisation model grids using the ‘direct’ method oxygen abundances as input, they need to increase the empirically derived value. They suggest that adding ADF = 0.24 dex can solve this issue (at least when BPASS models are used to supply the ionisation field). This suggests that oxygen abundances inferred with recombination lines may be better suited for combining/comparing with stellar-based metallicity measurements (but see Bresolin et al. 2022). However, as discussed earlier, because stellar and gas-phase abundance measurements typically trace different elements, they may not be (and are not expected to be) consistent with each other in certain environments. While the exact oxygen abundance value is not important for establishing the existence of trends in metallicity evolution with redshift or with galaxy properties (e.g. the mass-metallicity relation; Tremonti et al. 2004) as long as consistent calibration is used for the entire sample, it is relevant for the discussion of the relative enrichment in different elements.

Known sources of systematic uncertainty. (i) Method used to translate the observed optical emission line ratios to oxygen abundance. While nearly all Z_O estimates used in this study are based on the ‘direct’ method (or empirical calibrationsn), they are still subject to the abundance discrepancy factor (ADF) – i.e. systematic uncertainty between the absolute Z_O value derived from recombination lines and T_e sensitive collisionally excited lines ( $Z_{O}^{RL} = Z_{O}^{CEL}$ $Z_{\mathrm{O}}^{\mathrm{RL}}=Z_{\mathrm{O}}^{\mathrm{CEL}}$ +ADF). We assume ADF = 0.24 dex, unless the exact offset is known.

(ii) Oxygen depletion onto dust grains: it is commonly assumed that dust depletion may lead to an underestimation of the true abundance of this element in the interstellar medium by up to ∼0.1 dex when derived from the gas phase. Therefore, we consider Δ_d = +0.1 dex dust correction uncertainty in Z_O.

3.1.4. Gas-phase HII region-based methods: iron

Iron lines are rarely detectable for HII regions, but in principle its gas-phase abundance can be derived from collisionally excited Fe III–Fe V lines, as has been done for the local low mass and very metal poor galaxies (e.g. Izotov & Thuan 1999; Izotov et al. 2006, 2018; Kojima et al. 2020). However, there are significant systematic uncertainties associated with the applied iron ionization correction factors (ICF, correcting the estimate for iron abundance in the ‘unseen’ ionisation states Stasińska & Izotov 2003; Rodríguez & Rubin 2005; Izotov et al. 2006; Kewley et al. 2019). In particular, ∼0.2 dex difference between the Fe²⁺ ICF resulting from the models of Stasińska & Izotov (2003) and Rodríguez & Rubin (2005) was found. Furthermore, iron is subject to severe depletion onto dust grains (Izotov et al. 2006; Rodríguez & Rubin 2005; Roman-Duval et al. 2021). Therefore, except for the most metal poor galaxies that typically have very little dust, gas-phase iron abundance estimates require substantial and uncertain depletion correction to reflect the true abundance of that element in the ISM. Finally, we note that the ADF uncertainty which affects the oxygen abundance (and T_e) derived with this method can also affect the iron abundance, because both quantities are used to estimate the iron abundance (e.g. Izotov et al. 2006). It is unclear how Z_Fe (and so [O/Fe]) is affected by this uncertainty and to our knowledge it has not been quantified in the literature.

Known sources of systematic uncertainty. Ionisation correction factors: all HII region-based Z_Fe that are quoted in our study use ICF from Stasińska & Izotov (2003) and may overestimate Z_Fe by Δ_ICF, Fe = 0.2 dex.

3.1.5. Indirect iron abundance determination

When neither iron lines nor UV continuum is observed, some constraints on the iron abundance can be inferred indirectly from HII region photoionisation models by considering metallicity of the input ionising source (supplied through SPS model) independently of the oxygen abundance when fitting for the observed line ratios (e.g. Strom et al. 2018, 2022; Sanders et al. 2020; Runco et al. 2021). This approach takes advantage of the fact that while gas cooling is dominated by oxygen, gas heating is to large extent determined by the abundance of iron due to its decisive role in setting the shape the ionising radiation field coming from massive stars. Since this method probes stellar rather than the gas-phase iron content, it does not require dust depletion corrections. The result is only sensitive to the ionising part of the model spectra, while the other stellar-based methods used to infer iron abundances rely on the UV continuum lines and wind features. While its downside is that it is indirect, it is a complimentary approach that allows for important consistency tests of the results derived with a given SPS model.

3.2. Milky Way-based [O/Fe]–sSFR relation

MW studies alone can provide constraints on different parts of the [O/Fe]-sSFR diagram. We discuss the MW data that can be used in this context below and show the resulting relation in Fig. 5. We put those results in the context of other star-forming galaxies in Fig. 6.

Fig. 5.

MW-based star-forming [O/Fe] versus sSFR relation. The big data point corresponds to the present-day MW, where the light grey extension of the error bars indicates the systematic uncertainty (see text and Table E.1). Grey points: [O/Fe] of the MW disc MS turn-off stars from GALAH DR3 with sSFR estimated from stellar ages assuming constant MW disc star formation history. Contours enclose 50%, 68%, and 95 % of stars in the diagram. Black empty squares indicate the average [O/Fe] of those stars grouped in 14 age bins (see Table B.1). Orange curves show part of the MW evolutionary track in the diagram reconstructed using binned ages and average [O/Fe] for different assumptions about the disc star formation history (see text for the details). The horizontal hatched bar at [O/Fe] ≈ 0.52 dex shows the average abundance ratio of the MW thick disc/halo dwarf stars with [Fe/H] < −2 from Amarsi et al. (2019) (x-axis value is arbitrary).

Fig. 6.

Observational estimates of the star-forming [O/Fe] versus sSFR for the MW (estimated at R_gal = 8 kpc and at 1.5 × R_e effective radius), nearby dwarf galaxies (LMC, SMC, IZw 18, Sextans A, NGC 3109), local galaxies with blue supergiant-based metallicity estimates from Bresolin et al. (2016, 2022), extremely metal-poor dwarf galaxies from Senchyna et al. (2022), Kojima et al. (2021), Thuan et al. (2022), and Izotov et al. (2018), and high-redshift star-forming galaxies/stacks from Steidel et al. (2016), Cullen et al. (2021), and Topping et al. (2020). For the remaining high-redshift estimates (marked with ^* in the legend), either the iron or oxygen abundance was inferred indirectly. Light grey extensions of the error bars indicate known sources of systematic uncertainty in the abundance determination (see text and Table E.1). Small orange points show the MW disc stars and orange curves indicate part of the MW disc evolutionary track in the diagram (see Sect. 3.2 and Fig. 5). Horizontal hatched bar at [O/Fe] ≈ 0.52 dex indicates the average abundance ratio of the MW thick disc/halo dwarf stars with [Fe/H] < –2 from Amarsi et al. (2019) (x-axis value is arbitrary). Only the offsets due to different reference solar abundances choices were corrected in this figure. Horizontal lines indicate zero points for different reference solar O and Fe abundance choices. There is a 0.14 dex offset between the Grevesse & Sauval (1998) (GS98, orange dashed line) scale used here and the commonly used Asplund et al. (2009) solar scale (black dashed line).

(i) Low sSFR: present-day Milky Way: star-forming spiral galaxies at low redshifts typically show negative radial metallicity gradients (e.g. Sánchez et al. 2014; Carton et al. 2018; Hernandez et al. 2019). The MW is no exception from this rule. To estimate its present-day [O/Fe], we combine the determination of the oxygen abundance gradient from Galactic HII regions obtained by Arellano-Córdova et al. (2020) and the determination of the iron abundance gradient from MW open clusters reported by Spina et al. (2022). Extragalactic metallicity estimates are typically representative of the metallicity at ∼1–1.5R_e effective radius (Kewley & Ellison 2008). For the local spiral galaxies the value at ∼1.5R_e is often quoted as representative of the integrated metallicity (Bresolin et al. 2016, 2022). Therefore, for comparison with other objects we use the [O/Fe] calculated at the Galactic radius R_gal = 6.8 kpc (≈1.5R_e for MW; Arellano-Córdova et al. 2020). We also indicate the [O/Fe] ratio at R_gal = 8 kpc, i.e. around the solar location (where it is best constrained).

(ii) Low/intermediate sSFR: MW disc evolutionary track: Photospheric abundances and age determinations available for a large sample of Galactic disc stars allow for a crude reconstruction of (part of) the MW evolutionary track in the [O/Fe] – log₁₀(sSFR) plane. To this end, we use [O/Fe] and stellar ages of main sequence turn-off stars from the third data release of the Galactic Archaeology with HERMES (GALAH) survey (Buder et al. 2021) and estimate the sSFR from stellar ages by assuming a MW disc star formation history as detailed below. Oxygen abundances for this sample were derived from the OI 777 nm triplet using the non-Local Thermodynamic Equilibrium (LTE) grids of departure coefficients (Amarsi et al. 2020). Stellar ages are provided in one of the value-added catalogues and estimated from T_eff, log₁₀(g), [Fe/H], [α/Fe], and photometric and astrometric information using the Bayesian Stellar Parameter Estimation code BSTEP (Sharma et al. 2018). We follow the quality cut and selection criteria of turn-off stars in the MW disc from Hayden et al. (2022)⁵

We group the data in 14 age bins and calculate the average [O/Fe] in each bin (see Table B.1). Stellar ages peak at around 6 Gyr and span roughly between t_* ≈ 2 Gyr and t_* ≈ 12.5 Gyr. We adopt the latter value as the limit on the formation time T_form of disc stars. The average [O/Fe] increases from 0.08 dex to 0.48 dex during this time. Assuming a constant disc SFR, the sSFR in each bin can be obtained by simply inverting the difference between T_form and the median stellar age (i.e. sSFR = 1/t_gal and t_gal = T_form − t_*, black squares in Fig. 5). Realistic MW disc star formation history estimates feature a burst/phase of rapid star formation followed by a decline to approximately constant SFR at a current level (Aumer & Binney 2009; Fantin et al. 2019; Bonaca et al. 2020). This means that the true sSFR can be expected to be lower than the one calculated with the constant disc SFR (i.e. the MW track in the [O/Fe] – log₁₀(sSFR) plane in Fig. 5 is likely leftwards of the one calculated with the constant SFR). To illustrate this, we also show the [O/Fe] – log₁₀(sSFR) tracks for which the sSFR is obtained assuming an exponentially declining SFH (SFR(t_gal) ∝e^{−t_gal/τ_MW} for t_gal < t_x and SFR = const at t_gal > t_x). We treat τ_MW and t_x as free parameters and use a range of values for which the calculated sSFR does not extend below the present-day MW constraints. We caveat that the sSFR assigned to the oldest stars (> 10 Gyr, with the highest [O/Fe]) is particularly uncertain, both because the average uncertainty in their age estimate is ≳1 Gyr (compared to ∼0.4 Gyr for stars with ages < 5Gyr), and because their sSFR is sensitive to the assumed T_form (if T_form is lower than assumed and the stars are younger, their assigned sSFR would be higher). Overall, the above considerations indicate that the MW-based [O/Fe]–sSFR relation may level off somewhere at log₁₀(sSFR) ≳ –9. While our estimate of the MW ‘evolutionary track’ should be taken with a grain of salt, it shows that a more careful analysis (beyond the scope of this study) can potentially provide valuable constraints.

(iii) High sSFR: metal-poor stars: Old, metal-poor stars are expected to hold a stable record the SN Ia-free [O/Fe]_CCSN ratio. Therefore, they can shed light on the enrichment level expected in the high sSFR part of the relation. To estimate this, we select MW thick disc/halo dwarf stars with oxygen and iron abundance determinations from Amarsi et al. (2019) and calculate the average [O/Fe] of stars with [Fe/H] < –2. We use the 3D-LTE iron abundance and the 3D non-LTE oxygen abundance estimate ([Fe/H]3L and [O/H]3N reported in Table 7 in Amarsi et al. 2019), as recommended by the authors. The resulting log₁₀(O/Fe)_CCSN ≈ 1.85 dex (which corresponds to [O/Fe]_CCSN ≈ 0.52 dex on our reference GS98 solar scale) is shown as a hatched horizontal bar in Fig. 5. The metallicity cut of [Fe/H] < –2 was chosen to ensure that the stars belong to the flat part of the [O/Fe] (or [α/Fe]) – [Fe/H] relation, see Fig. B.2). As discussed in Sect. 2, such a flattening is expected in the regime where the SN Ia contribution is subdominant. It is unclear to what range of sSFR it corresponds (the range of sSFR spanned by the horizontal bar in Fig. 5 is chosen arbitrarily).

3.3. Other star-forming galaxies

We collected literature estimates of the star-forming iron and oxygen abundances for galaxies spanning a wide range of sSFR. Their metal abundances were obtained with a range of methods described in Sect. 3.1. The compiled data and the references to original papers are given in Table E.1. In Fig. 6 we plot those results as reported (i.e. only correcting for solar scale differences). We indicate the known sources of systematic uncertainty that are relevant for each of those estimates in column 5 and/or in the comments in Table E.1 and show them as grey extensions to error bars in Fig. 6. We summarise how we correct for those offsets and how we select the sample to constrain the relation in Sect. 3.4. We briefly discuss the estimates shown in Fig. 6 below and refer the interested reader to Appendix for more details.

3.3.1. Low sSFR: Local star-forming galaxies

Objects with log₁₀(sSFR) < –9.5 in Fig. 6 correspond to local star-forming spiral and dwarf galaxies and probe a relatively typical low redshift galaxy population. Blue crosses in Fig. 6 mark galaxies with BSG-based metallicity estimates from Bresolin et al. (2016, 2022), assuming that those metallicity measurements can serve as a proxy of the iron abundance. As discussed in Sect. 3.1.1, this is not strictly correct, as those estimates provide the bulk metal mass fraction Z obtained from matching solar-scaled spectral model to multiple observed lines (mostly, but not only iron-group). It is unclear what is the error associated with this assumption. As we discuss in the Appendix D, whether we use this sample or not does not affect our main conclusions. However, currently it is the only method that could allow to extend the star-forming [O/Fe] estimates to relatively massive (and metal-rich) typical low-redshift spiral galaxies. See Appendix B.3 for the discussion of the remaining low sSFR galaxies.

3.3.2. Intermediate sSFR: High-redshift star-forming galaxies

Galaxies that occupy the intermediate sSFR range (roughly –9.5 ≲ log₁₀(sSFR) ≲ –8) are expected to be mostly high redshift MS objects. This is where the [O/Fe] is expected to show strong evolution. Several authors obtain iron abundance estimates using rest-UV spectra (individual or stacked) and ‘direct’ gas-phase oxygen abundances using rest-optical spectra of such galaxies at redshifts ≳2 (Steidel et al. 2016; Topping et al. 2020; Cullen et al. 2021, see Sect. 3.1.2 and Appendix B.4 for further details). All of those studies probe the intermediate galaxy stellar mass range log₁₀(M_*/M_⊙)∼9 – 10 and also provide the SFRs, which allows us to put their estimates on the [O/Fe]–sSFR plane. We note that SFRs estimated for individual galaxies in Cullen et al. (2021) (purple stars in Fig. 6) fall above the average z ∼ 3.4 MS (and have high log₁₀(sSFR) > –8).

We also indicate the z ∼ 2.2 estimate from Kashino et al. (2022) where the iron-based metallicity is obtained from stacked rest-UV galaxy spectra. However, the oxygen abundance is not measured directly but inferred from the ‘direct’ method mass-metallicity relation at a similar redshift obtained by Sanders et al. (2020). Finally, we show the results from Strom et al. (2018, 2022), Sanders et al. (2020), who estimate [O/Fe] with photoionisation models using only rest-frame oxygen optical emission lines as constraints (i.e. without any UV constraints, see Sect. 3.1.5). The results obtained by Sanders et al. (2020) show a substantial scatter and come with large errors/upper limits on the iron abundance (lower limits on [O/Fe]). Strikingly, some of them point to [O/Fe] > 1 and even despite the large uncertainties, clearly stand out from all the other estimates. In particular, the [O/Fe] estimate obtained by Sanders et al. (2020) for the KBSS-LM1 stack earlier analysed by Steidel et al. (2016) is > 1 dex higher than the value obtained by the latter authors. The reason behind this is unclear. In contrast, the estimates obtained by Strom et al. (2018, 2022) are well within the range of values covered by the other observational results summarised in this section. Strom et al. (2018) also analyse the KBSS-LM1 stack with their method. The value that they obtain for [O/Fe] ≈ 0.55 dex is somewhat higher (i.e. Fe abundance is lower), but consistent with the one reported by Steidel et al. (2016). We note that Strom et al. (2018, 2022) include a prior requiring [O/Fe] < 0.73 dex ([O/Fe] < 0.59 dex on our solar scale) and therefore by construction avoid such high values as quoted by Sanders et al. (2020). Given that the iron abundance is not directly constrained in those studies and it is unclear how to properly compare them with other estimates, we do not include those results in further analysis. Figure B.1 shows the [O/Fe]-sSFR plane when excluding the data with indirect Fe or O abundance estimates. This leaves only a few data points in the intermediate sSFR range, but the scatter is much reduced.

3.3.3. High sSFR: Very metal-poor local dwarf galaxies

Galaxies gathered in this section (IZw 18 and galaxy samples from Kojima et al. 2021 and Senchyna et al. 2022 – grey symbols and dark green circles in Fig. 6) are characterised by very low metal content and high sSFRs (log₁₀(sSFR) ≳ –8). Such properties are typical of the early rather than the local Universe, where they can be viewed as outliers. Those extreme local low-mass galaxies received a lot of attention precisely due to their potential to serve as testbed for future high redshift studies. Direct method HII region oxygen abundances are available for all of those galaxes. The iron abundance for the sample from Senchyna et al. (2022) is based on UV-continuum constraints. For the remaining objects iron abundance is derived from HII region lines following the method described in Izotov et al. (2006) (see Sect. 3.1.4 and Appendix B.5 for further details).

Given their properties (in particular their estimated young ages), especially the galaxies selected by Kojima et al. (2021) are not expected to be enriched by iron from SN Ia yet. Therefore, such objects can help to constrain the typical core-collapse [O/Fe]_CCSN ratio (or the potential plateau level of the [O/Fe]-sSFR relation). While for most of the galaxies in this sample the estimated [O/Fe] falls within the expected range (≳0.5–0.8 dex), two of them (J1631+4426 with abundances revised by Thuan et al. 2022 and J0811+4730 from Izotov et al. 2018) have [O/Fe] comparable to LMC and SMC. Early enrichment by very massive, rapidly rotating stars and rare Pair-Instability Supernovae were proposed as a possible explanation of their unexpected abundance ratios (Isobe et al. 2022; Goswami et al. 2022).

3.4. Selecting the final sample and bringing the data to the common baseline

The results shown in the previous section were obtained with a variety of methods and different modelling assumptions. Comparing them at face value may easily lead to erroneous conclusions. Here we discuss how we select the data that can be compared in a more consistent way in order to constrain the [O/Fe]–sSFR relation.

Firstly, we choose to use HII region based oxygen abundance estimates for all objects in our analysis, even if massive-star based estimates are available (mostly the case for MW and Magellanic Clouds). We do this for two main reasons: (i) as discussed in Sect. 3.1.1, the stellar atmospheric oxygen abundance may be significantly affected by processes related to stellar evolution; (ii) ‘direct’ HII region based oxygen metallicity estimates are now available for galaxies across redshifts and with different properties. The latter is advantageous, as it can reduce the impact of additional (possibly unidentified) systematics that can be introduced by combining results obtained with very different techinques.

We consider the following sources of systematic offsets between the results obtained in different studies and correct for them as outlined below:

Reference solar abundances. The correction is straightforward as long as the assumed solar reference abundances are reported in the original studies. There can be > 0.14 dex difference in [O/Fe] value depending solely on the choice of solar reference abundances (see horizontal lines in Fig. 6). Therefore, while the specific choice is not relevant for the conclusions, it is important to convert all measurements to a consistent solar scale. All abundances used in our study are converted to Grevesse & Sauval (1998) solar scale.

Uncertainty in the absolute value of the Z_O derived from the HII region optical emission lines (see Sect. 3.1.3). For the remainder of this paper, we refer to Z_O values obtained with the ‘direct’ method or with strong line methods based on empirical calibrations (which give similarly low values compared to recombination lines) as being on the collisionally excited line abundance scale. We correct for the systematic shift of ADF = 0.24 dex between the estimates reported on collisionally excited line and recombination line scales. If the exact offset is known, we use the ADF reported by the authors. We further consider Δ_d = +0.1 dex uncertainty due to dust depletion. Such dust correction has been explicitly added only to estimates reported by Senchyna et al. (2022). Not all data can be corrected for those offsets in a consistent way. As discussed in 3.1.4, it is unclear how to correct measurements where both Z_Fe and Z_O are based on HII region emission lines for ADF. For this reason, we do not use IZw18, J0811+4730 and the sample from Kojima et al. (2021) to characterise the [O/Fe]–sSFR relation. In any case, with the exception of IZw18, all these objects fall outside the sSFR range occupied by regular MS galaxies and cannot serve to constrain the relation in the part where it is expected to show the strongest and orderly evolution. We note that the oxygen abundance derived by Strom et al. (2018, 2022) is the only gas-phase Z_O reported here that is based on a theoretical calibration of the strong line method and may be subject to additional systematic differences with respect to other measurements. However, as discussed in the previous section, we exclude all estimates with indirect Z_Fe (this includes Strom et al. 2018, 2022) or Z_O determinations from further analysis.

Uncertainty in the absolute value of the Z_Fe derived from rest-frame UV galaxy spectra (see Sect. 3.1.2). Z_Fe is rarely derived with multiple SPS models and we assume Δ_SPS = 0.1 dex difference between the estimates relying on BPASS and S99 SPS models, unless the exact offset is known. Examples discussed in Cullen et al. (2021) and Senchyna et al. (2022) show that this offset can differ a lot from case to case and assuming fixed Δ_SPS is certainly a simplification. We exclude the low M_* stack from Cullen et al. (2021) from further analysis, as the difference between BPASS and S99 SPS models is Δ_SPS> 0.6 dex in this case and so [O/Fe] is very poorly constrained. The sample from Senchyna et al. (2022) shown in Fig. 6 relies on yet different set of SPS models (Charlot & Bruzual in prep., C&B hereafter). The comparison of [O/Fe] derived using S99 and C&B SPS shown in Fig. B.3 (see also Table 7 therein) shows that they are consistent within errors, except for the object HS1442+4250 (where S99 SPS leads to 0.36 dex lower Z_Fe). For easier comparison with other results used in this study, we report [O/Fe] based on S99 SPS in Table E.1. We estimate $Δ_{SPS}^{*}$ $\Delta_{\mathrm{SPS}}^{*}$ for this sample by taking the difference Δ_S99–C&B between S99-based and C&B-based Z_Fe values given in Table 7 in Senchyna et al. (2022). The results are given in Table E.1. We note that for all objects except J082555, C&B-based Z_Fe is higher than S99-based Z_Fe. Therefore, the offset between S99 and C&B is in the opposite direction than between S99 and BPASS-based Z_Fe, which we indicate be reporting $Δ_{SPS}^{*} =_{- Δ_{S99-C&B}}^{+ 0.1}$ $\Delta_{\mathrm{SPS}}^{*}=^{+0.1}_{-\Delta_{\mathrm{S99-C\& B}}}$ in the last column of Table E.1.

We do not apply Δ_SPS to the estimate from Steidel et al. (2016), as the reported value is averaged over the results obtained with BPASS and S99 models.

We can bring the data remaining in the sample that we choose for further analysis to several common baselines. In particular, we consider:

The high [O/Fe] baseline obtained by including Δ_d in all Z_O estimates, bringing all Z_O estimates to recombination line scale and all Z_Fe estimates derived with S99 SPS to BPASS scale.
The intermediate [O/Fe] baseline obtained by bringing all Z_O estimates to recombination line scale, all Z_Fe estimates derived with BPASS SPS to S99 SPS scale and subtracting Δ_d from dust-corrected Z_O estimates. This combination minimises the number of data points which require applying Δ_SPS (only data from Topping et al. 2020) and Δ_d corrections (only the sample from Senchyna et al. 2022). We consider additional variation (intermediate + Δ_d) by including Δ_d in all Z_O estimates.
The low [O/Fe] baseline obtained by subtracting Δ_d from dust-corrected Z_O estimates, bringing all Z_O estimates to collisionally excited line scale and all Z_Fe estimates derived with BPASS SPS to S99 scale.

As discussed in Sect. 3.1.1, it is unclear whether BSG-based metallicity estimates reported in the literature can be used as a measure of Z_Fe. Therefore, we exclude the sample from Bresolin et al. (2016, 2022) from our main analysis. This leaves us with 18 objects in the final sample. We summarise the results obtained when including the results from Bresolin et al. (2016, 2022) in the Appendix D. We note that for the NGC3109 (big light green circle in Fig. 6) Z_Fe estimate is also based on BSG (Hosek 2014). However, in this case BSG metallicity is also interpreted as such by the authors and we decide to include it in further analysis.

We caution that while we focus on issues related to abundance determinations, there are uncertainties associated with the SFR and M_* measurements as well. These include, among others, systematics due to the choice of the SFR tracer, IMF⁶, applied dust corrections or SPS model (used to estimate stellar mass in certain methods). Calibrations of the commonly used SFR proxies are metallicity (Z_Fe) dependent, which means that some of the uncertainties affect both [O/Fe] and sSFR. SFR and M_* for a given galaxy are often estimated in a separate analysis than its metal abundances. As a result, even though their derivation may rely on the same type of input information⁷, sSFR and abundances are not necessarily obtained with the same set of assumptions. It is beyond the scope of this study to correct for such factors. While it would be desirable to better quantify their effects on sSFR, they are unlikely to affect our main conclusions and with the current limited sample we can largely ignore these effects (Appendix C).

4. Results

4.1. The observed [O/Fe]–sSFR relation

The results obtained when bringing the data selected as described in Sect. 3.4 to the common ‘high [O/Fe]’ and ‘low [O/Fe]’ baselines are compared in Fig. 7. To better illustrate the evolution in [O/Fe]–sSFR plane, we group the data in three log₁₀(sSFR) bins and calculate the average < [O/Fe]_bin> in each bin. We choose the bins so that they contain the same number of data points (6). We assign split normal distribution to each data point (with mean and dispersion is set by its reported value and uncertainties) and draw 10⁵ values for each data point in a given bin to assess the uncertainty of < [O/Fe]_bin>. The resulting median < [O/Fe]_bin> and 0.13 th and 99.87 th percentiles (light coloured areas in Fig. 7) for each bin and baseline choice are reported in Table 1.

Fig. 7.

Star-forming [O/Fe] versus sSFR relation. Left/right panel: Data points (big circles) were shifted to a common high/low [O/Fe] baseline. The inner colour of the large circles indicates the stellar mass, and the outer colour indicates the bin to which the data point belongs. Values listed in the figure indicate the median [O/Fe] in each of the three equally populated log₁₀(sSFR) bins. The dark (light) area of each bin spans between 16–84 (0.13–99.87) percentiles of 10⁵ draws of the average [O/Fe]. The small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. Data with indirect O or Fe estimates are not shown. Thick horizontal lines indicate zero points for reference solar O and Fe abundance from Grevesse & Sauval (1998) (GS98) and Asplund et al. (2009) (A+09). The absolute [O/Fe] values are uncertain but there is a clear evolution towards lower [O/Fe] with decreasing log₁₀(sSFR) and no apparent secondary dependence on log₁₀(M_*) within the current sample. On the right hand side of the figure we summarise the average < [O/Fe]_bin> values found in the highest sSFR bin for different choices of the common baseline described in Sect. 3.4. The differences are equal to the sum of the average systematic offsets between the baselines. The yellow horizontal bar on the right shows the average < [O/Fe]_MW> of metal-poor dwarf stars in the MW from Amarsi et al. (2019). Baselines where Z_O measurements are placed on the collisionally excited line scale give < [O/Fe]_bin> which are inconsistent with this value.

Table 1.

Binned [O/Fe]–sSFR relation for different baseline choices.

There is a clear trend for [O/Fe] to decrease towards lower sSFR, independent of the choice of the common baseline. Our results can be broadly summarised as follows:

There is no evidence of [O/Fe] evolution between the two highest sSFR bins (corresponding to −6.5 > log₁₀(sSFR) > − 9) regardless of the baseline. This may hint at the existence of the expected flattening in the [O/Fe]–sSFR relation at high log₁₀(sSFR). In view of the small size of the current sample and the considerable uncertainties, we do not place a better constraint on the possible turnover point.
There is a clear increase in [O/Fe] between the lowest sSFR bin and the two remaining bins. In all cases, the offset is larger than the area spanned by the 99.8 and 0.13 percentiles of ⟨[O/Fe]_bin⟩ (light coloured areas in Fig. 7).
There is no clear secondary dependence on the galaxy stellar mass within the current sample.

The absolute ⟨[O/Fe]_bin⟩ value in each bin is uncertain:

(i)
⟨[O/Fe]_bin⟩ differs by 0.44 dex for the highest sSFR bins when the ‘low’ and ‘high’ [O/Fe] baselines are compared. This is a direct consequence of the considered systematic uncertainties (see Sect. 3.4 and the inset on the right hand side of Fig. 7).
(ii)
The differences between ⟨[O/Fe]_bin⟩ obtained in the lowest sSFR bin are ≈0.1 dex smaller than in the highest sSFR bins when extreme baselines are compared. This is not surprising, as there are no low sSFR data points in our sample for which Z_Fe was estimated with UV-spectra relying on SPS models for interpretation. Therefore, the lowest sSFR bin is not affected by Δ_SPS systematics, for which we assumed the average value of 0.1 dex.
(iii)
⟨[O/Fe]_bin⟩ found in the high sSFR bin on the ‘low [O/Fe]’ baseline is 0.3 dex below the average level of enrichment of the MW metal-poor stars < [O/Fe]_MW > ≈0.52 dex. Any common baseline choice where Z_O measurements are placed on the collisionally excited line scale lead to high sSFR ⟨[O/Fe]_bin⟩ lower than ⟨[O/Fe]_MW⟩. As we discuss further in 4.2, ⟨[O/Fe]_bin⟩ at high sSFR is not expected to fall below ⟨[O/Fe]_MW⟩. Therefore, Z_O assuming collisionally excited line abundance scale may underestimate the oxygen-based metallicity with respect to stellar measurements. If the above interpretation is correct, the systematic uncertainty on the absolute ⟨[O/Fe]_bin⟩ values presented in our paper is reduced by ADF = 0.24 dex.
(iv)
When only ‘intermediate [O/Fe]’ or ‘high [O/Fe]’ baselines are considered (as motivated above), the MW-based relation and the MW disc evolutionary track in the [O/Fe]–sSFR plane (see Sect. 3.2) are consistent with the observational [O/Fe] – sSFR relation inferred here from the properties of star-forming galaxies across redshifts (see Fig. 8 for the direct comparison).

Fig. 8.

Observational [O/Fe]–sSFR relation compared with a broad range of theoretical expectations. Data points (big circles) were shifted to a common intermediate [O/Fe] baseline with additional offset due to possible oxygen dust depletion (Δ_d) included. This baseline provides the closest match to [O/Fe] of metal-poor dwarf stars in the MW from Amarsi et al. (2019) on the high sSFR end (which we use as a lower limit for the expected [O/Fe]_CCSN). The average [O/Fe] found in three sSFR bins is shown in the background (see caption of Fig. 7 and Table 1). Small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. The grey vertical band indicates the range of sSFR in which we expect the turnover based on the literature SN Ia DTD (see Fig. 2). Dark coloured ranges show the [O/Fe]–sSFR relations calculated with Eq. (1) for different SN Ia DTD and parameter choices. Left panel: power-law DTD with slope α_Ia = −1.1 and different minimum SN Ia delay times τ_Ia; min. Right panel: exponential DTD for two different values of the τ_Ia parameter. The coloured ranges span between the relations calculated with C_Ia/CC = 0.74 (upper edges) and C_Ia/CC = 2.5 (bottom edges) – see text for the details. We also plot the relations followed by TNG100-1-like galaxies (brown line, left panel) and EAGLE-like galaxies (turquoise line, right panel) and the average MW evolutionary track reconstructed with disc stars assuming constant star formation history (thick orange line, see Sect. 3.2).

Point (ii) means that the slope of the [O/Fe]–sSFR relation is influenced by the systematic uncertainties related to the choice of SPS model. In particular, evolution between the bins is steeper when we shift all UV-spectra based Z_Fe to the BPASS scale (as in high [O/Fe] baseline) than if we use the S99 SPS scale (as in low and intermediate [O/Fe] baselines), because the former SPS models tend to lead to lower Z_Fe values (higher [O/Fe]) than the latter (see Table 1). Nonetheless, the slopes of the [O/Fe]–sSFR relation for different baseline choices are consistent within uncertainties (see Fig. B.4).

4.2. Expected level of [O/Fe] enrichment at high sSFR and the oxygen abundance scales

In the inset on the right hand side of Fig. 7 we compare ⟨[O/Fe]_bin⟩ found in the highest sSFR bin on different baselines with ⟨[O/Fe]_MW⟩ = 0.52 dex found for dwarf MW stars with [Fe/H]< − 2 and abundances derived in non-LTE analysis performed by Amarsi et al. (2019). As discussed in earlier sections, those stars follow the flat part of the Galactic [O/Fe]–[Fe/H] relation (see also Fig. B.2). This flattening is commonly interpreted as a consequence of the early Galaxy chemical evolution being dominated by CCSN (e.g. Matteucci & Greggio 1986; Wheeler et al. 1989; Kobayashi et al. 2020a). In this view, ⟨[O/Fe]_MW⟩ probes the same feature as ⟨[O/Fe]_bin⟩ in the high sSFR bin(s) (see Sect. 2). In principle, ⟨[O/Fe]_bin⟩ could be higher than ⟨[O/Fe]_MW⟩ because the sample of Amarsi et al. (2019) does not probe very low metallicities ([Fe/H] ≲ –3), where [O/Fe] could be influenced by explosions of the more massive and metal poor CCSN progenitors. Such CCSN can eject material with higher oxygen abundance (e.g. Nomoto et al. 2013). Given that the CCSN oxygen yields are predicted to considerably vary with the mass of CCSN progenitor, the plateau [O/Fe] value can also be affected by variations in the stellar IMF. IMF may become top-heavy in metal-poor and high SFR conditions (Bromm & Loeb 2003; Weidner & Kroupa 2005; Marks et al. 2012; Jeřábková et al. 2018). This would further increase the [O/Fe]_CCSN level, unless the excess massive low metallicity stars do not explode in CCSN, but rather collapse without any significant metal ejecta (Fryer 1999; Fryer et al. 2006; Sukhbold et al. 2016; Schneider et al. 2021). However, if such an environmental-dependence of the stellar explosion properties and IMF exists, there is no obvious reason for it to be significantly different in the early evolution of the MW (recorded in the properties of old, metal-poor stars) and in young galaxies included in our sample.

All common baseline choices where Z_O is placed on the collisionally excited line abundance scale lead to [O/Fe] in the high sSFR bin that is below ⟨[O/Fe]_MW⟩. The above mismatch argues against the use of this abundance scale in combination with stellar metallicity measurements (unless the average ADF = 0.24 dex correction is overestimated or Z_Fe values are overestimated for the high sSFR part of our galaxy sample). ⟨[O/Fe]_bin⟩ derived for the ‘intermediate [O/Fe] ’ baseline is also below ⟩[O/Fe]_MW⟩, but consistent with this estimate within 3-σ-equivalent percentiles. Including the systematic offset Δ_d = 0.1 dex associated with the oxygen dust depletion in all measurements on this baseline brings ⟨[O/Fe]_bin⟩ = 0.54 dex to near perfect agreement with ⟨[O/Fe]_MW⟩. We use this ‘intermediate + Δ_d’ baseline as a reference for further comparison with models.

To our knowledge, there is currently no identified source of significant systematic uncertainty in ⟨[O/Fe]⟩_MW. Stellar samples with available oxygen abundance estimates at [Fe/H] ≲ –2 are small and their oxygen estimates are based mostly on differential analysis of the OI777 nm multiplet in dwarf stars with respect to the Sun. Therefore, the methodologies used are much more uniform than in the case of extragalactic abundance measurements, which limits the (known) systematics. Comparison of independent analyses by different authors (Bensby et al. 2014; Zhao et al. 2016; Amarsi et al. 2019) using different approaches to account for non-LTE effects yields consistent [O/Fe] values at [Fe/H] < − 2. Furthermore, recent solar oxygen abundance measurements agree with each other within 0.03 dex when 3D non-LTE modelling is adopted (Lind & Amarsi 2024). Based on this, we conclude that the systematic uncertainty in < [O/Fe]> _MW is negligible compared to that in extragalactic measurements and cannot resolve the tension between the high sSFR ⟨[O/Fe]_bin⟩ derived for the ‘low [O/Fe]’ baseline and ⟨[O/Fe]⟩_MW.

5. Comparison with theoretical expectations

In Fig. 8 we compare the observational [O/Fe] – sSFR relation with a broad range of model relations. We indicate the minimum level of [O/Fe] enrichment expected at high sSFR based on MW metal-poor stars as discussed in Sect. 4.2 and bring the data to the ‘intermediate + Δ_d’ common baseline which allows to match this value. The grey vertical band roughly indicates the range of sSFR below which we expect the change of slope of the relation given the minimum time required to form a white dwarf (the right edge of the band) and the range of SN Ia DTD compared in Fig. 2. Current observations suggest that the possible turnover is located at log₁₀(sSFR [yr⁻¹]) > − 9 (τ_SF < 1 Gyr), which is broadly consistent with expectations, but does not constrain the models. We note that we independently find the same log₁₀(sSFR) > − 9 limit when considering old MW disc stars (Sect. 3.2) and star-forming properties of other galaxies (Sect. 4). We show the MW evolutionary track crudely inferred from MW disc stars assuming a constant star formation history (thick orange line in both panels in Fig. 8). As discussed in Sect. 3.2, other plausible star formation histories tend to shift the MW track leftwards in the [O/Fe]–sSFR diagram, but overall do not strongly affect the result. It can be seen that the MW-based relation is consistent with the current constraints inferred from the properties of other star-forming galaxies. This is astonishing, and suggests that by taking a similar astro-archeological approach and following a more careful analysis, one can obtain tight constraints on the overall [O/Fe]–sSFR relation characterising star-forming galaxies across cosmic time.

5.1. SN Ia delay times

The two panels of Fig. 8 show [O/Fe]–sSFR relations obtained with Eq. (1) for different SN Ia DTD and C_Ia/CC choices. In both cases f_Ia is normalised to unity when integrated over the Hubble time, that is, 1 = N_Ia0 $\int_{τ_{Ia, min}}^{τ_{H}}$ $\int_{\tau_{\rm Ia,min}}^{\tau_{\rm H}}$ (t′) dt′ and [O/Fe]_CCSN is fixed to the average [O/Fe] value found in the high sSFR data bin.

In the left panel, we use a power-law SN Ia DTD: f_Ia ∝ t^−α_Ia at t ≥ τ_Ia, min and zero at t < τ_Ia, min. We assume α_Ia = 1.1 (average between the slope derived by Maoz & Graur 2017 and used in TNG f_Ia). Steeper slopes were also reported (e.g. Heringer et al. 2019) but as long as α_Ia is close to unity, the exact choice of its value has a minor effect on the relation compared to other factors (see additional examples in the Appendix E). t⁻¹-like DTD is generically found in double-degenerate SN Ia progenitor scenarios (i.e. involving two WDs whose merger triggers the explosion, e.g. Iben 1984; Webbink 1984). In such scenarios the time until SN Ia explosion depends steeply on the separation of the progenitor binary, driven to merger via gravitational waves emission. Such a DTD is consistent with a variety of observational estimates (Maoz et al. 2014; Strolger et al. 2020). These observations mostly probe delay times of 1–10 Gyr, and the time at which SN Ia begin to significantly contribute to enrichment is not constrained. The possibility that a power-law DTD continues to shorter delay times cannot be ruled out, and short τ_Ia, min∼40 Myr are favoured if a t⁻¹-like SN Ia DTD is fitted to the cosmic SN Ia rate (Maoz & Graur 2017). However, double-degenerate SN Ia scenarios typically require at least a few 100 Myr to ∼1 Gyr after the formation of the most massive WDs to start producing SN Ia according to a power-law DTD and the earlier behaviour is uncertain (e.g. Maoz et al. 2014). In Fig. 8 we compare the relations for two minimum SN Ia delay times τ_Ia, min = 40 and 400 Myr (light and dark blue areas, respectively).

In the right panel, we use an exponential SN Ia DTD: f_Ia ∝ e^−t/τ_Ia at t > τ_Ia, min and zero t < τ_Ia, min. Strolger et al. (2020) consider both individual galaxies and cosmic SN Ia rates and star formation histories and show that such SN Ia DTD parametrisation is also consistent with observations. A more concentrated DTD resulting from the exponential form is expected in some single degenerate SN Ia formation scenarios (i.e. involving mass accretion onto the WD from a close non-degenerate companion star, e.g. Whelan & Iben 1973; Nomoto 1982). It can be seen that this leads to a steeper [O/Fe] decline in the intermediate sSFR range and flattening on the low sSFR side earlier than power-law-like DTD due to the scarcity of SN Ia with very long delay times. Again, we show the relations for two example characteristic timescales τ_Ia = 0.7 and 3 Gyr (light and dark green areas, respectively) and assume τ_Ia, min = 40 Myr. To satisfy the cosmic SN Ia rate constraints, assuming an exponential SN Ia DTD, long τ_Ia ∼ 2 Gyr are required (e.g. Schaye et al. 2015; Strolger et al. 2020). This leads to a turnover in the [O/Fe]–sSFR relation at distinctly lower sSFR than the power-law DTD with τ_Ia, min = 40 Myr used to fit the same cosmic SN Ia rate constraints. While we cannot rule out any of the discussed models with current data, further constraints on the turnover sSFR can help to distinguish between such scenarios.

Different SN Ia formation channels may operate in nature, leading to a more complex overall f_Ia than considered in this section (e.g. Greggio 2010; Nelemans et al. 2013; Maoz et al. 2014; Livio & Mazzali 2018; Rajamuthukumar et al. 2023). While this makes the interpretation in light of a particular SN Ia formation scenario challenging, with better constraints [O/Fe] – sSFR relation can help to infer valuable information about the general properties of the SN Ia population. In particular, as long as the iron mass ejected per SN Ia is high compared to that produced per CCSN: (i) the turnover point on the high sSFR side of the relation can be linked to the minimum timescale at which SN Ia start to significantly contribute to iron enrichment and (ii) the range of sSFR over which the relation shows steep evolution before it saturates on the low sSFR side carries information about the extent and importance of the long delay time tail of the SN Ia DTD. If the functional form of f_Ia is known (or inferred from other observations), then the evolution of the low sSFR part of the relation alone can shed light (i).

5.2. Iron yields

Each of the coloured areas shown in Fig. 8 spans between the relations calculated with $C_{Ia / CC} = \frac{m_{Fe}^{Ia}}{m_{Fe}^{CCSN}} \frac{N_{Ia 0}}{k_{CCSN}} = 0.74$ $C_{\mathrm{Ia/CC}} = \frac{m^{\mathrm{Ia}}_{Fe}}{m^{\mathrm{CCSN}}_{\mathrm{Fe}}} \frac{N_{\mathrm{Ia0}}}{k_{\mathrm{CCSN}}} = 0.74$ (upper edges) and C_Ia/CC = 2.5 (bottom edges). SN Ia are expected to eject most of the mass in iron-group elements, with the typical iron mass $m_{Fe}^{Ia} \approx 0.7 M_{⊙}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}\approx0.7\,{M}_{\odot}$ (Nomoto et al. 1997; Mazzali et al. 2007; Maoz et al. 2014; Kobayashi et al. 2020b) and the relative formation efficiency of CCSN to SN Ia is close to 10 (e.g. Madau & Dickinson 2014; Maoz & Graur 2017; Strolger et al. 2020). Both quantities appear known to within a factor of a few. The iron mass that is ejected per CCSN event is by far the most uncertain ingredient of C_Ia/CC. Observational estimates span a broad range (Müller et al. 2017; Anderson 2019; Rodríguez et al. 2021, 2023; Martinez et al. 2022) and indicate systematically higher iron masses produced by stripped-envelope supernovae ( $m_{Fe}^{CCSN} ≳ 0.07 M_{⊙}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}} \gtrsim0.07\,{M}_{\odot}$ , e.g. Anderson 2019; Afsariardchi et al. 2021; Rodríguez et al. 2023) than by normal, hydrogen-rich CCSN events (with the average $m_{Fe}^{CCSN} \sim 0.03 - 0.045 M_{⊙}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}\sim 0.03 {-} 0.045\,{M}_{\odot}$ , e.g. Rodríguez et al. 2021; Martinez et al. 2022). In this view, the average $m_{Fe}^{CCSN}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}$ depends on the relative mixture of different types of CCSN happening in the Universe. Predicted iron yields also vary significantly between the CCSN explosion models (e.g. Woosley & Heger 2007; Pejcha & Thompson 2015; Sukhbold et al. 2016; Curtis et al. 2019; Ebinger et al. 2020; Ertl et al. 2020; Schneider et al. 2021; Imasheva et al. 2023; Sawada & Suwa 2023). Assuming $m_{Fe}^{Ia} = 0.74 M_{⊙}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}=0.74\,{M}_{\odot}$ (i.e. nucleosynthesis yields of SNe Ia in the commonly used W7 model; Nomoto et al. 1997; Iwamoto et al. 1999) and $\frac{N_{Ia 0}}{k_{CCSN}} = 1 / 10$ $\frac{N_{\mathrm{Ia0}}}{k_{\mathrm{CCSN}}}=1/10$ , the considered C_Ia/CC values correspond to a broad range of $m_{Fe}^{CCSN} = 0.03 - 0.1 M_{⊙}$ $m^{\mathrm{CCSN}}_{\mathrm{Fe}}=0.03-0.1\,{M}_{\odot}$ . It can be seen that a full variety of presented model relations is broadly consistent with the current constraints.

The [O/Fe] value at which the relation saturates on the low sSFR side strongly depends on C_Ia/CC and can inform the relative iron production efficiency in SN Ia and CCSN. Constraining this requires extending the sample of galaxies with available iron abundances to log₁₀(sSFR)≲-10.5, i.e. accounting for MS MW-like galaxies at low redshifts.

6. Discussion and future prospects

Improving the constraints on the [O/Fe]–sSFR relation requires predominantly expanding the sample of galaxies with iron abundance determination and having a good handle on the related systematic uncertainties. Contrary to iron abundances, sSFR and Z_O are already known for large samples of star-forming galaxies. Those samples will only grow with the instruments like MOONS, expected to conduct a SDSS-size survey of galaxies at z∼1.5 and provide their Z_O measurements (Maiolino et al. 2020). Furthermore, with JWST ‘direct’ (collisional-line) gas-phase oxygen abundances can now be determined at z ≳ 3 (e.g. Curti et al. 2023; Nakajima et al. 2023). While oxygen abundance determinations suffer from significant systematic uncertainties, these are relatively well characterised in the literature (Kewley & Ellison 2008; Telford et al. 2016; Maiolino & Mannucci 2019; Kewley et al. 2019) compared to issues associated with iron abundance determinations and can be dealt with. Furthermore, we argue that the collisionally excited line oxygen abundance scale (conventionally used in ‘direct’ gas-phase oxygen abundance measurements) is inconsistent with stellar metallicity measurements. This allows to reduce the biggest source of systematic uncertainty in the absolute oxygen abundance values relevant for this study.

Currently, the sSFR range in which the relation shows the strongest evolution (and can be particularly constraining for the models) is probed by a single data point at log₁₀(sSFR) ≈ –9. This is partially due to the fact that galaxies with sSFR around this value are the most likely to be found at redshifts 0.5 ≲ z ≲ 2 (e.g. Popesso et al. 2023), where none of the currently available methods is suitable to measure Z_Fe (see Sect. 3.1). However, at least at log₁₀(sSFR) ≳ –9, the sample can be expected to grow with ongoing efforts to obtain rest-frame UV spectra of MS galaxies z ∼ 2.5–4 (where the rest-frame UV is conveniently shifted to optical). This regime is particularly important to pinpoint the high sSFR turnover of the [O/Fe]–sSFR relation, interesting as a potential probe of the poorly constrained short delay time end of the SN Ia DTD. However, we emphasise that the turnover point and the overall [O/Fe]–sSFR relation are not specifically sensitive to SN Ia DTD, but to SN Ia iron production DTD (which is an important distinction if SN Ia iron yields were to correlate with some intrinsic SN Ia progenitor properties and favour certain delay times). Z_Fe obtained for galaxies in the intermediate sSFR range relies on SPS models for the interpretation of the observed rest-frame UV spectra. As discussed in Sect. 3.1, different SPS models can lead to substantial differences in Z_Fe and their origin needs to be better understood. To this end, studies of local metal-poor galaxies are desirable, where more details in the UV spectra are available and can be compared with the models (e.g. Senchyna et al. 2022), and where ideally several methods can be used to infer metallicity to test their consistency.

Constraints are also lacking on the low log₁₀(sSFR) ≲ –10.5 side of the relation, occupied by low redshift MS galaxies with masses comparable to the MW. This regime is also important for differentiating between models, as discussed in the previous section. In principle, the low sSFR sample could be expanded with BSG/RSG based methods, provided that they can be adapted to target the iron-group element abundance instead of providing metallicity estimates relying on both iron-group and α-element lines. While it would be beneficial to obtain Z_Fe of such galaxies using the same method as applied for high redshift objects, this would require the use of space telescopes to access the UV emisson and even then obtaining tight constraints might not be feasible given their low SFR (i.e. they can be expected to be UV-faint).

Finally, the average [O/Fe] at which the relation flattens at log₁₀(sSFR)≳–7.6 is expected to reflect some cosmic average [O/Fe] enrichment from massive, low metallicity stars with no/negligible contribution from SN Ia. We argue in Sect. 4.2 that ⟨[O/Fe]_MW⟩ provides a lower limit on this value, which can be challenged with future observations. The scatter/prevalence of galaxies that are outliers in terms of [O/Fe] in this sSFR regime can in turn yield valuable constraints on the efficiency of formation of rare, massive-star related explosions predicted to eject material with [O/Fe] ratios significantly different than produced by regular CCSNe. In particular, pair instability supernovae (e.g. Heger & Woosley 2002; Takahashi et al. 2018) originating from massive (> a few 100 M_⊙) metal-poor progenitors exploding within just a few Myr after the star formation are predicted to eject material with [O/Fe] < 0. Similarly low [O/Fe] ratio is predicted in some of the hypernovae models (e.g. Grimmett et al. 2021). A signature massive pair instability supernova abundance pattern has recently been found in a MW halo star (Xing et al. 2023). Such explosions could potentially explain the surprisingly low [O/Fe] < 0 reported by Kojima et al. (2021) for two of their extremely metal poor local galaxies with log₁₀(sSFR)≳–7.6 (e.g. Isobe et al. 2022; Goswami et al. 2022).

In terms of its application to constraining models of the chemical evolution of galaxies, there are two main differences between the [O/Fe] – sSFR relation proposed in this paper and the commonly used abundance-abundance diagrams (e.g. [O/Fe] – [Fe/H]). The first difference lies in the type of data used to constrain the models. The abundance-abundance diagrams are typically based on the properties of individual old stars in the MW or its satellite dwarf galaxies (e.g. Matteucci et al. 2009; Schönrich & Binney 2009; Romano et al. 2010; Kobayashi et al. 2020b; Matteucci 2021; Kobayashi & Taylor 2023). In this paper, the constraints come from empirical properties of star-forming galaxies (see also Cullen et al. 2021; Kashino et al. 2022, who use extragalactic abundance measurements to compare with the models in the [O/Fe] – [Fe/H] diagram). These two approaches probe different environments: the latter can span a wide range of environments (and may be a more natural point of reference for models/simulations performed in a cosmological volume), while the former probes the history of a single galaxy.

The second difference is the choice of horizontal axis (sSFR or [Fe/H]). The use of sSFR instead of [Fe/H] appears to be more favourable for discussing the relative timescales of enrichment by different stellar sources than [Fe/H], as it is a more direct proxy for time. For example, in both cases the characteristic turnover point is sensitive to the minimum delay in the enhanced production of iron (interpreted as the minimum SN Ia delay). However, the low [Fe/H] turnover point in the [O/Fe]–[Fe/H] relation is also influenced by factors such as star formation efficiency or mass loading factor (Kashino et al. 2022). The high sSFR turnover in the [O/Fe] – sSFR plane appears to be insensitive to such factors (at least within the framework and examples from other studies used in this paper) and is determined by the relative timescales of oxygen and iron production.

7. Conclusions

To date, our knowledge of star-forming metallicity relies mostly on gas-phase oxygen abundances. This is not ideal because the main element responsible for the differences in the evolution and fate of stars formed with different metallicities is iron. Also, it is the varying abundance of iron that determines the strength of radiation-driven winds, feedback (mechanical and chemical), and ionising radiation input from the stellar population. This makes it the most critical element for properly describing and understanding the evolution and properties of star-forming galaxies, stars, stellar afterlives, and related transients. Oxygen and iron abundances are known to evolve on different timescales and observations of old stars reveal that their relative abundances can differ by a factor of ≳5 when compared to the solar ratio. This means that the former is not a good proxy for the latter. Furthermore, determining the star-forming iron abundances for large, representative samples of galaxies is likely to remain a challenge for the foreseeable future.

To remedy this situation, we investigate the [O/Fe]–sSFR relation, which is expected to be tightly adhered to by star-forming galaxies on theoretical grounds, as discussed in Sect. 2. Due to its apparent universality, this relation can provide a reasonable and simple way of translating the readily available oxygen abundances to iron abundances. We further explore this possibility and derive the iron-based metallicity-dependent cosmic star formation history in Paper II (Chruslinska et al, in prep.). In the present study, we present the first observational determination of the [O/Fe]–sSFR relation over a wide range of sSFR:

We compile a sample of star-forming galaxies with available iron abundances from the literature (Sect. 3.3 and Table E.1) and bring the data to a common baseline by correcting for the known systematic offsets related to Z_O and Z_Fe determinations.
The resulting relation shows a clear sign of evolution towards lower [O/Fe] with decreasing sSFR and a hint of flattening at log₁₀(sSFR) > − 9, consistent with theoretical expectations (Figs. 7 and 8).
We independently reconstruct the [O/Fe]–sSFR relation from old MW disc stars (Sect. 3.2). The MW relation is remarkably consistent with that inferred from the properties of star-forming galaxies, as long as the ‘direct’ oxygen abundances are placed on the recombination-line abundance scale.
The above conclusion argues against the use of collisionally excited line abundance scales in combination with stellar metallicity measurements (Sect. 4.2).
The agreement between the MW-based relation and the relation obtained by populating the [O/Fe]–sSFR plane with present-day properties of star-forming galaxies reinforces the idea that the relation can be used both (i) to follow the [O/Fe] evolution of regular star-forming galaxies as they age, and (ii) to deduce the typical star-forming [O/Fe] ratio of galaxies of a given sSFR.

We compare the [O/Fe]–sSFR relations resulting from the EAGLE and TNG cosmological simulations and show that the differences between them can be fully attributed to the differences in the assumed SN Ia delay-time distribution and the relative SN Ia and CCSN formation efficiency and metal yields (Sect. 2.5). Based on these findings, we come to the following conclusions:

The [O/Fe]–sSFR relation is driven by differences in the timescales (probed by sSFR) on which stellar sources enrich the interstellar medium with oxygen (prompt CCSNe) and iron (both CCSNe and delayed SNe Ia).
The main characteristics of the [O/Fe]–sSFR are determined by stellar evolution, interactions (setting the formation efficiency of the different types of supernova progenitors and the timescales on which they explode or collapse), core-collapse physics, and supernovae explosion properties (determining which stellar progenitors explode and the associated metal yields), and are not strongly influenced by large-scale processes (e.g. galaxy mergers, feedback).
With better constraints, the [O/Fe]–sSFR relation can shed light on the uncertain SN Ia delay-time distribution, CCSN metal yields, and the formation efficiency of rare explosions of the most massive, metal-poor stellar progenitors (Sect. 5).

In particular, the relation could help us to constrain the minimum delay following which SN Ia start to contribute significantly to iron enrichment, which is difficult to constrain with other observations and is strongly dependent on the SN Ia formation scenario. Improving the constraints on the [O/Fe]–sSFR relation requires that we expand the sample of galaxies with measured iron abundances and obtain better control of the systematic uncertainties. In particular, the origin of the differences between the iron abundances derived (directly and indirectly) from different parts of the rest-frame UV galaxy spectra (continuum, wind features, ionising part) and obtained using different spectral population synthesis models needs to be better understood.

¹

[O/Fe] = log₁₀(O/Fe) – log₁₀(O/Fe)_⊙ is the logarithm of the oxygen to iron abundance ratio relative to the reference solar abundance ratio of the two elements.

²

Matthee & Schaye (2018) fit a relation that separates the mass and SFR dependencies but the difference with respect to using only the sSFR is not significant. This is reflected in the similarity of the fitted M_* and SFR coefficients. The average EAGLE relation can effectively be described by [O/Fe] = 0.29 log₁₀(sSFR) + const.

³

However, the differences can be much larger. For instance, Cullen et al. (2021) obtain a ∼0.6 dex lower UV continuum based metallicity using BPASS models than when using Starburst99 models for their low mass stack.

⁴

Consequently, metallicities derived with methods sensitive to the ionising part of the UV (e.g. using HII region emission line rations as discussed later in this section) rather than the continuum can be expected to be lower when obtained with Starburst99 than with BPASS models (i.e. the opposite to what is found for the UV continuum).

⁵

Namely, we remove any object whose stellar parameter, metallicity, or [O/Fe] are flagged and select stars with S/N > 45, $χ_{s p}^{2} < 4$ $\chi^2_{sp} < 4$ , T_eff < 6200 K, σ(T_eff) < 150, −1 < [Fe/H]< 0.5, 3.5 < log₁₀g < 4.1, age > 1.75 Gyr, and σ(age)/age < 0.2.

⁶

For common IMF choices, sSFR is largely unaffected by this assumption because it affects M_* and SFR estimates in similar way.

⁷

For instance, SPS model and IMF assumptions are used in both common galaxy stellar mass determination method and UV-continuum/indirect iron abundance derivations.

⁸

But note that the Sextans A stellar mass appears particularly uncertain, with values used in the literature ranging from log(M_*/M_⊙) = 6.24 following Lee et al. (2006), log(M_*/M_⊙) = 7.38 in de los Reyes & Kennicutt (2019), up to log(M_*/M_⊙) = 8.14 estimated by Weisz et al. (2011). Using the latter would result in Sextans A sSFR comparable to that of the MW.

⁹

We note that the resulting 12+log₁₀(O/H) = 7.21 is on the high end of the 12+log₁₀(O/H) = 7.1-7.2 suggested by the most recent direct method metallicity estimates (Kehrig et al. 2016)

Acknowledgments

MCh is grateful for many insightful discussions on various aspects of this work, and would like to thank in particular to Allison Strom, Claudio Dalla Vecchia, Jorge Sánchez Almeida, Gijs Nelemans, Svea Hernandez, Sabyasachi Goswami, Valeriya Korol, Alexandre Vazdekis, Robert Grand, Andre Sieverding, Jakub Klencki, Søren Larsen and Scott Trager. TM acknowledges support by a Spinoza Grant from the Dutch Research Council (NWO). We thank the anonymous referee for their constructive report. Data and code availability: The data compiled from the literature (Table E.1) and the code underlying our analysis are available on GitHub at https://github.com/Mchruslinska/trading_oxygen_for_iron_I. Software: matplotlib (Hunter 2007), scipy (Virtanen et al. 2020), numpy (Harris et al. 2020), astropy (Astropy Collaboration 2013, 2018).

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Appendix A: Cosmological simulations example

In Table A.1 we summarise the choice of parameters of Equation 1 used to model the tracks of EAGLE-like and TNG-like MS galaxies in the [O/Fe] – sSFR plane shown in Figure 4. Table A.2 summarises the parameters of the SFMR used to describe the star formation histories of EAGLE-like and TNG-like MS galaxies. In case of TNG we use the fits from Donnari et al. (2019) up to redshift = 2 (Table 3 therein). To obtain the rough SFMR of the EAGLE galaxies and extend the TNG SFMR to redshift = 5 we use the SFR and M_* of simulated galaxies selected as described in Section 2.5 and perform least-square linear fit in log₁₀(SFR)-log₁₀(M_*) plane. We interpolate between the redshift bins. If needed, at higher redshifts we use the SFMR from redshift = 5.

Table A.1.

Parameters used to describe the EAGLE-like and TNG-like MS galaxies

Table A.2.

Parameters of the SFMR used to model SFH of mock EAGLE-like and TNG-like MS galaxies.

Appendix B: Observational results used in this study: further discussion

B.1. Old Milky Way stars

Figure B.2 shows the [O/Fe] – [Fe/H] relation for the sample of MW disc/halo stars from Amarsi et al. (2019). We highlight the stars used to determine the average < [O/Fe]_MW> value at the low metallicity [Fe/H]< -2 part of the relation. Table B.1 summarises the < [O/Fe]> of MW disc stars grouped in 14 age bins as discussed in Section 3.2.

Fig. B.1.

Same as Figure 6, but excluding data points with ‘indirect’ Fe or O determinations.

Fig. B.2.

[O/Fe] versus [Fe/H] of MW disc and halo dwarf stars from Amarsi et al. (2019). Blue points indicate stars which were used to estimate the [O/Fe]_CCSN shown in Figure 6. Their average < [O/Fe]_MW > = 0.52 dex is indicated by the thick black line. Thin grey lines span between 13 and 99.8 percentiles of the average ([O/Fe] = 0.48-0.56 dex). Amarsi et al. (2019) measure relative abundances with respect to the Sun and derive log₁₀(O/Fe)_⊙ = 1.179 dex. For consistency with the rest of the analysis, we convert those relative measurements to absolute abundances and place them on GS98 solar scale. The thin dashed lines show the solar values from Amarsi et al. (2019).

Table B.1.

Average [O/Fe] of MW disc stars in age bins

B.2. Present-day Milky Way

As discussed in 3.2, to obtain present-day [O/Fe] MW we combine the HII region-based oxygen abundance gradient obtained by Arellano-Córdova et al. (2020) and the iron abundance gradient determination from Galactic open clusters from Spina et al. (2022). We assume a present day MW SFR = 2±0.5 M_⊙/yr and stellar mass of M_∗ = 5 ± 1 × 10¹⁰ M_⊙Bland-Hawthorn & Gerhard (2016), Elia et al. (2022).

We caution that the adopted [Fe/H] may somewhat underestimate the star-forming iron abundance for two main reasons: i) it is based on metallicities of open clusters, whose ages span a broad range from a few Myr to ∼1 Gyr (and therefore, not only recently formed objects) and ii) current [Fe/H] determinations may be underestimated for the youngest objects. Puzzlingly, literature [Fe/H] abundance estimates of Galactic star-forming regions and open clusters with ages < 100 Myr (and especially < 10 Myr) are lower than those of the older ones (e.g. Spina et al. 2022, and references therein). Baratella et al. (2020) show that this anomalous behaviour might be attributed to issues with abundance analysis approaches. In particular, chromospheric and magnetic activity effects on line formation that are not accounted for in atmospheric models of dwarf stars (used in abundance estimates of young clusters) but expected to be particularly strong in young stars may lead to underestimated [Fe/H]. Baratella et al. (2020) propose a new approach to bypass those issues and find [Fe/H] = -0.01 to 0.06 dex for a sample of stars from 5 open clusters younger than 150 Myr and located at R_gal = 7.72 - 8.66 kpc. Using the [Fe/H] metallicity gradient from Spina et al. (2022), we obtain [Fe/H] = 0.018 dex at R_gal = 8 kpc. Therefore, there is no clear indication that our assumed value is underestimated.

B.3. Local star-forming galaxies

Figure 6 includes the present-day [O/Fe] and sSFR estimates for nearby star-forming dwarf galaxies: Small and Large Magellanic Clouds (SMC and LMC, respectively), Sextans A, NGC3109.

For the Magellanic Clouds we use the average direct method HII regions based Z_O/H reported by Domínguez-Guzmán et al. (2022). In contrast to big spirals, galaxies such as SMC and LMC are typically rather chemically homogeneous, i.e. there is little difference between the abundances estimated in their different regions (Domínguez-Guzmán et al. 2022). We use iron atmospheric abundance estimates from individual stars in NGC 330 (with the age of ∼40 Myr) for the SMC and from NGC 1850 (younger than ≲100 Myr) for the LMC derived by Song et al. (2021). Those are the youngest clusters that were included in their analysis. The adopted LMC iron abundance (12+log₁₀(Fe/H) = 7.19) is further supported by the recent analysis of red supergiants in NGC 1850 cluster by Sollima et al. (2022) and consistent with that derived from ∼100-200 Myr old Cepheids (Lemasle et al. 2017). We note that it is 0.13 dex lower than the commonly used OB-star based estimate from Rolleston et al. (2002), which brings the present-day LMC [O/Fe] ratio closer to the value expected given its global properties (e.g. Russell & Dopita 1992; Pagel & Tautvaisiene 1998). We use the global LMC and SMC SFR and M_* values from Skibba et al. (2012).

For Sextans A we adopt the average of the direct method HII region based oxygen abundance estimates from Magrini et al. (2005) and the average iron abundance determined from 3 A-type supergiant star UVES spectra by Kaufer et al. (2004). Their uncertainty estimates include systematic errors due to uncertainties in the stellar atmospheric parameters. We use the range spanning between the FUV and V-band SFR estimates from Hunter et al. (2010). and the stellar mass reported in Woo et al. (2008) to estimate its sSFR⁸. For NGC3109 we use the blue supergiant based metallicity derived mainly from Fe-group elements lines (and therefore suitable as current iron abundance probe) provided by Hosek (2014), direct method HII region based oxygen abundance from Peña et al. (2007) and the stellar mass and SFR from Woo et al. (2008).

B.4. High redshift star-forming galaxies

Steidel et al. (2016) estimate the average [O/Fe] for star-forming galaxies at z∼2.4 by using composite spectra of 30 MS objects. Photospheric and wind line features in the composite UV spectrum are fitted using both BPASS and Starburst99 models. Oxygen abundance is estimated with a number of methods (photoionization models, strong-line calibrations and the direct method including ADF=+0.24 dex offset to put the estimate on the recombination line scale). We adopt their final estimate of (O/Fe) = 4±1 (O/Fe)_⊙ as quoted in Figure 17 and the median sSFR given in Table 1 therein. Topping et al. (2020) extend the above sample to 62 galaxies. They construct two stacks based on the locations of their galaxies on the local BPT diagram. The UV continuum spectra were analysed with BPASS models to determine the iron abundance. The corresponding best fitting SPS model was used in the photoionization modelling to fit for oxygen abundances. Topping et al. (2020) also show [O/Fe] estimates for several individual galaxies with the highest SNR, but their SFR and M_* are not given. Therefore, we only show the estimates for the two stacks in Figure 6.

Cullen et al. (2021) obtain gas-phase and stellar metallicities for 4 star-forming galaxies and for two composite spectra at z∼3.4. Iron-based metallicities are determined from rest-frame UV spectra by fitting stellar-metallicity sensitive features with Starburst99 SPS models. The gas-phase oxygen abundances are determined using the empirical calibration from Bian et al. (2018), built on the local analogues of high-redshift galaxies with direct metallicity estimates. Contrary to Steidel et al. (2016) and Topping et al. (2020), Cullen et al. (2021) do not use the inferred iron abundance as constraints in the oxygen abundance determination.

Strom et al. (2018), Sanders et al. (2020), Strom et al. (2022) estimate [O/Fe] using only rest-frame oxygen optical emission lines as constraints (i.e. without any UV constraints). Strom et al. (2018) (further expanded in Strom et al. 2022) determine abundances of both elements by simultaneously varying the metallicity of the input SPS models and gas oxygen abundance in photoionisation modelling when fitting for the observed line ratios. In contrast, Sanders et al. (2020) first infer the oxygen abundance using direct method (including ADF=+0.24 dex offset), and use that as an input in the photoionisation modelling to infer the iron abundance. All of those estimates used BPASS SPS models. We only report median results from Strom et al. (2018, 2022), in Table E.1, as the sSFR for individual galaxies are not given by the authors.

B.5. (Very) metal poor local dwarf galaxies

Senchyna et al. (2022) provide direct method HII region oxygen abundances and UV-continuum based iron abundances for 6 galaxies. They use different SPS models than used in the remaining studies referenced in this paper (which employ either S99 or BPASS models) and refer to the paper in preparation by Charlot & Bruzual for their description. They compare the Z_Fe values obtained using C&B and S99 SPS models in table 7 therein. We show the differences in [O/Fe] resulting from the use of those two SPS models for their sample in Figure B.3. We report the [O/Fe] obtained with S99 SPS in Table E.1 for easier comparison with other results used in this paper. Senchyna et al. (2022) shift their derived [O/Fe] ratios by ADF=+0.24 dex to put them on the recombination line oxygen abundance scale and include additional correction of ∼+0.11 dex to account for oxygen dust depletion. We use the sSFR from Berg et al. (2016) for J082555 and J104457 (no errors were given), sSFR from Senchyna et al. (2019) for HS1442+4250 and sSFR from Senchyna et al. (2017) for SB2 and SB82. We do not find SFR/sSFR for J120202 and therefore, we do not include it in the analysis.

Fig. B.3.

Comparison of the [O/Fe] for the sample from Senchyna et al. (2022) where Z_Fe was derived with C&B SPS models (circles, as plotted in Figure 6) and S99 SPS models (diamonds, reported in Table E.1). We add a small offset in sSFR between the two estimates for easier comparison.

Fig. B.4.

Slope of the linear fit to the [O/Fe]–log₁₀(sSFR) relation for different choices of the baseline (colours) and including/excluding of the sample from Bresolin et al. (2016, 2022) at low sSFR (crosses/circles). We show the result obtained when fitting only the slope at log₁₀(sSFR) < − 7.6 (symbols with grey edges), at log₁₀(sSFR) < − 8.5 (symbols with blue edges) or when fitting the slope to the full sample (black edges). Error bars range from 16 to 84 percentiles of the fits, the symbol indicates the median.

The sample compiled by Kojima et al. (2021) was observed as part of the Extremely Metal-Poor Representatives Explored by the Subaru Survey (EMPRESS) (Kojima et al. 2020) and supplemented by earlier literature results. Their oxygen abundances have been derived with the direct method using HII region nebular oxygen lines. [Fe III]λ4658 line is also detected and the authors follow the method described in Izotov et al. (2006) to estimate the iron abundance. Kojima et al. (2021) note that the dust depletion is negligible in their metal poor sample. For the least massive object (J1142-0038) only the lower limit on the [O/Fe] could be determined.

For IZw 18 we use the literature average oxygen and iron abundances listed in Lebouteiller et al. (2013) (the last column of their Table 7) inferred from HII region observations ⁹. Lebouteiller et al. (2013) note that the dust content in IZw 18 is exceptionally low and dust depletion is expected to be insignificant. We therefore assume that its HII region-based abundance is a good measure of the iron content in the star-forming material. We use the SFR and M_* values from Zhou et al. (2021).

Kojima et al. (2021) include a 0.2 dex systematic error in their iron abundance estimate due to varying Fe²⁺ ionisation correction factors resulting from different models. We also include this systematic in the IZw18 iron abundance estimate, as it was obtained with the same method.

Appendix C: Potential impact of ignoring systematic uncertainties in sSFR

As discussed in Section 3.4, empirical sSFR determinations are subject to systematic uncertainties related to factors such as the choice of SFR tracer, IMF, applied dust corrections or SPS model. Given the large inhomogeneity of the sample collected and the plethora of tools used to derive both the SFR and stellar masses of these galaxies, properly accounting for sSFR systematics is a challenge in itself and beyond the scope of the present paper. Instead, for the currently limited sample used in our main analysis, we argue that we can largely ignore these effects.

Our main conclusions (Section 4, Fig. 7) could be affected if the sSFR systematics were to preferentially shift galaxies from the low sSFR bin to the intermediate/high sSFR bin(s) and/or vice versa (Fig. 7, Table 1). We consider the extreme scenario where the sSFR systematics for galaxies in the "low sSFR" (log₁₀(sSFR) < − 9) and "high sSFR" range (log₁₀(sSFR) > − 9) go in the opposite direction. Given that there are few galaxies with log₁₀(sSFR)≳-9 in our final sample, as long as the systematics are ≲0.5 dex, this would only force two objects in our sample to move across the two sSFR bins. In such a case the quoted < [O/Fe]_bin> values are consistent with those given in the text within the estimated 1-sigma equivalent percentiles. However, given the larger spread of [O/Fe] values in the respective bins, this would increase the uncertainty of < [O/Fe]_bin>. The offset between the low and high sSFR bins would no longer be larger than the area spanned by the 99.8 and 0.13 percentiles of < [O/Fe]_bin> (light coloured areas in Fig. 7), but still larger than the 16-84 percentile (dark coloured areas in Fig. 7). This only reinforces our conclusion that the turnover point of the relation is poorly constrained with the current data. Our conclusion that it lies at log₁₀(sSFR)≥-9 remains intact, as does the comparison with the MW-based constraints.

Appendix D: Including the low sSFR sample with BSG based metallicity estimates

Table D.1 summarises the average < [O/Fe]> values found in three sSFR bins when including the low sFSR sample from Bresolin et al. (2016, 2022) with BSG-based metallicities and assuming those metallicities probe Z_Fe. We note that the bin edges are different than in the main analysis (Section 4 and Table 1) and were selected to include possibly equal number of data points in each bin. Figure D.1 shows the [O/Fe]–ssSFR relation with the resulting bins and data shifted to a common ‘intermediate + Δ_d’ baseline (matching the expected high sSFR [O/Fe] level, see Section 4.2).

Fig. D.1.

Star-forming [O/Fe] – sSFR relation including the sample from Bresolin et al. (2016, 2022) with BSG-based metallicities, assuming they probe Z_Fe. Data points (big circles) were shifted to a common ‘intermediate+Δ_d’ [O/Fe] baseline. Inner colour of big circles indicates the stellar mass, outer colour indicates the bin to which the data point belongs. Values listed in the figure indicate median [O/Fe] in each of the log₁₀(sSFR) bins (see Table D.1 for the values found with different [O/Fe] baseline choices). Dark (light) area of each bin spans between 16-84 (0.13-99.87) percentiles of 10⁵ draws of the average [O/Fe]. Small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. Data with indirect O or Fe estimates are not shown. Thick horizontal lines indicate zero points for reference solar O and Fe abundance from Grevesse & Sauval (1998) (GS98) and Asplund et al. (2009).

Table D.1.

Average < [O/Fe]> values in three log₁₀(sSFR) bins, including the sample with BSG based Z_Fe from Bresolin et al. (2016, 2022).

Appendix E: Comparison with theoretical expectations: additional figures

Figure E.1 compares the observational [O/Fe]–sSFR relation with model relations calculated as described in Section 5 but for additional SN Ia DTD variations. In the left panel, we use a power-law DTD and vary the slope α_Ia. In the right panel, we show the relation for the analytical SN Ia DTD accounting for a mixed single-degenerate and double-degenerate progenitor SN Ia population (Greggio 2005, 2010), as used in Kashino et al. (2022).

Fig. E.1.

Observational [O/Fe]–sSFR relation compared with a range of model relations. Data points (big circles) were shifted to a common intermediate [O/Fe] baseline with additional offset due to possible oxygen dust depletion (Δ_d) included (see Figure 8 and Section 5). Dark coloured ranges show the [O/Fe]–sSFR relations calculated with 1 for different SN Ia DTD and parameter choices. Left panel: power-law DTD with the minimum SN Ia delay time τ_Ia; min = 100 Myr and different slopes α_Ia. Right panel: analytic DTD for mixed single degenerate and double degenerate SN Ia scenario from Greggio (2005, 2010), as used by Kashino et al. (2022). The coloured ranges span between the relations calculated with C_Ia/CC = 0.74 (upper edges) and C_Ia/CC = 2.5 (bottom edges) – see text for the details. We also plot the relations followed by TNG100-1-like galaxies (brown line, left panel) and the relation from Kashino et al. (2022) (black dotted line, right panel).

Table E.1.

Summary of the observational data used in this study.

All Tables

Table 1.

Binned [O/Fe]–sSFR relation for different baseline choices.

In the text

Table A.1.

Parameters used to describe the EAGLE-like and TNG-like MS galaxies

In the text

Table A.2.

Parameters of the SFMR used to model SFH of mock EAGLE-like and TNG-like MS galaxies.

In the text

Table B.1.

Average [O/Fe] of MW disc stars in age bins

In the text

Table D.1.

Average < [O/Fe]> values in three log₁₀(sSFR) bins, including the sample with BSG based Z_Fe from Bresolin et al. (2016, 2022).

In the text

Table E.1.

Summary of the observational data used in this study.

In the text

All Figures

Fig. 1.

Schematic illustration of the expected characteristics of the star-forming [O/Fe]–sSFR relation of galaxies. Young, high-redshift main sequence galaxies (with high sSFR) occupy the upper right part of the relation. Their chemical enrichment is dominated by prompt sources (CCSNe), which are expected to eject material with supersolar oxygen-to-iron abundance ratios. Below a certain sSFR (when the characteristic timescale τ_SF = 1/sSFR becomes comparable to the minimum SN Ia delay), SNe Ia begin to contribute significantly to the iron enrichment. As a result, old, low-redshift main sequence galaxies occupy the lower left part of the relation, with [O/Fe] approaching the solar ratio (orange dashed line). The exact shape of the relation depends on a number of uncertain factors (e.g. relative oxygen and iron yields, and rates and delays of different supernovae).

In the text

Fig. 2.

Cumulative distribution functions of the example SN Ia DTD. The distributions were normalised to unity when integrated over the Hubble time. Solid lines correspond to single power-law-shaped DTD: brown – TNG cosmological simulations, black – fitted to the observed SN Ia volumetric rate by Maoz & Graur (2017). Dashed lines correspond to the exponential DTD: thick turquoise line – EAGLE cosmological simulations, thin blue line – Galaxy chemical evolution model from Schönrich & Binney (2009) with DTD parameters tuned to reproduce observed oxygen abundances. The black dotted line corresponds to the DTD used by Kashino et al. (2022), which follows the theoretical analytic formulation by Greggio (2005, 2010) allowing for a mixed contribution of different proposed SN Ia progenitors. The intersection with the horizontal dashed line indicates the median of each DTD. The vertical dashed line at 40 Myr marks the evolutionary timescale of an 8 M_⊙ star (i.e. roughly the minimum time needed to form a white dwarf).

In the text

Fig. 3.

Star-forming [O/Fe] versus sSFR relation for simulated galaxies from the EAGLE cosmological simulations (turquoise contours) and TNG 100 cosmological simulations (brown contours). The contours enclose 50, 68, and 95 % of all central galaxies with log₁₀(M_*/M_⊙) = 9–10.5 at redshifts between 0 and 8. The solid turquoise line shows the fit to the relation in EAGLE from Matthee & Schaye (2018), while the dashed brown line shows our fit to the relation in TNG 100. The black dotted line shows the relation obtained by Kashino et al. (2022) for MS galaxies modeled within the gas-regulator framework.

In the text

Fig. 4.

Star-forming [O/Fe] – log₁₀(sSFR) relation for the simulated galaxies from the EAGLE cosmological simulations (turquoise contours), for the simulated galaxies from the TNG 100 cosmological simulations (brown contours), and those obtained by Kashino et al. (2022) (black dotted line). The contours enclose 50, 68 and 95 % of all central galaxies with log₁₀(M_*/M_⊙) = 9–10.5 at redshifts between 0 and 8. The thick solid lines show evolutionary tracks of MS galaxies along the relation calculated with Eq. (1) for different parameter choices. Squares/diamonds show the locations of galaxies of different masses (indicated by the symbol shading) at redshift 3.5/0. The tracks in panel a were calculated using the SFMR, DTD, $m_{Fe}^{Ia}$ $m^{\mathrm{Ia}}_{\mathrm{Fe}}$ , k_CCSN and N_Ia0 from the EAGLE (turquoise) or TNG (brown) simulations (see Appendix A). The remaining parameters are chosen to match the relation resulting from the EAGLE or TNG simulations, respectively. In panel b all tracks were caluclated with the same SFMR as in Kashino et al. (2022). In panel c we additionally change the DTD for turquoise tracks to the one used in the TNG simulations. In panel d we further change [O/Fe]_CCSN used to calculate the turquoise tracks to be the same as used to calculate the brown tracks.

In the text

Fig. 5.

MW-based star-forming [O/Fe] versus sSFR relation. The big data point corresponds to the present-day MW, where the light grey extension of the error bars indicates the systematic uncertainty (see text and Table E.1). Grey points: [O/Fe] of the MW disc MS turn-off stars from GALAH DR3 with sSFR estimated from stellar ages assuming constant MW disc star formation history. Contours enclose 50%, 68%, and 95 % of stars in the diagram. Black empty squares indicate the average [O/Fe] of those stars grouped in 14 age bins (see Table B.1). Orange curves show part of the MW evolutionary track in the diagram reconstructed using binned ages and average [O/Fe] for different assumptions about the disc star formation history (see text for the details). The horizontal hatched bar at [O/Fe] ≈ 0.52 dex shows the average abundance ratio of the MW thick disc/halo dwarf stars with [Fe/H] < −2 from Amarsi et al. (2019) (x-axis value is arbitrary).

In the text

Fig. 6.

Observational estimates of the star-forming [O/Fe] versus sSFR for the MW (estimated at R_gal = 8 kpc and at 1.5 × R_e effective radius), nearby dwarf galaxies (LMC, SMC, IZw 18, Sextans A, NGC 3109), local galaxies with blue supergiant-based metallicity estimates from Bresolin et al. (2016, 2022), extremely metal-poor dwarf galaxies from Senchyna et al. (2022), Kojima et al. (2021), Thuan et al. (2022), and Izotov et al. (2018), and high-redshift star-forming galaxies/stacks from Steidel et al. (2016), Cullen et al. (2021), and Topping et al. (2020). For the remaining high-redshift estimates (marked with ^* in the legend), either the iron or oxygen abundance was inferred indirectly. Light grey extensions of the error bars indicate known sources of systematic uncertainty in the abundance determination (see text and Table E.1). Small orange points show the MW disc stars and orange curves indicate part of the MW disc evolutionary track in the diagram (see Sect. 3.2 and Fig. 5). Horizontal hatched bar at [O/Fe] ≈ 0.52 dex indicates the average abundance ratio of the MW thick disc/halo dwarf stars with [Fe/H] < –2 from Amarsi et al. (2019) (x-axis value is arbitrary). Only the offsets due to different reference solar abundances choices were corrected in this figure. Horizontal lines indicate zero points for different reference solar O and Fe abundance choices. There is a 0.14 dex offset between the Grevesse & Sauval (1998) (GS98, orange dashed line) scale used here and the commonly used Asplund et al. (2009) solar scale (black dashed line).

In the text

Fig. 7.

Star-forming [O/Fe] versus sSFR relation. Left/right panel: Data points (big circles) were shifted to a common high/low [O/Fe] baseline. The inner colour of the large circles indicates the stellar mass, and the outer colour indicates the bin to which the data point belongs. Values listed in the figure indicate the median [O/Fe] in each of the three equally populated log₁₀(sSFR) bins. The dark (light) area of each bin spans between 16–84 (0.13–99.87) percentiles of 10⁵ draws of the average [O/Fe]. The small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. Data with indirect O or Fe estimates are not shown. Thick horizontal lines indicate zero points for reference solar O and Fe abundance from Grevesse & Sauval (1998) (GS98) and Asplund et al. (2009) (A+09). The absolute [O/Fe] values are uncertain but there is a clear evolution towards lower [O/Fe] with decreasing log₁₀(sSFR) and no apparent secondary dependence on log₁₀(M_*) within the current sample. On the right hand side of the figure we summarise the average < [O/Fe]_bin> values found in the highest sSFR bin for different choices of the common baseline described in Sect. 3.4. The differences are equal to the sum of the average systematic offsets between the baselines. The yellow horizontal bar on the right shows the average < [O/Fe]_MW> of metal-poor dwarf stars in the MW from Amarsi et al. (2019). Baselines where Z_O measurements are placed on the collisionally excited line scale give < [O/Fe]_bin> which are inconsistent with this value.

In the text

Fig. 8.

Observational [O/Fe]–sSFR relation compared with a broad range of theoretical expectations. Data points (big circles) were shifted to a common intermediate [O/Fe] baseline with additional offset due to possible oxygen dust depletion (Δ_d) included. This baseline provides the closest match to [O/Fe] of metal-poor dwarf stars in the MW from Amarsi et al. (2019) on the high sSFR end (which we use as a lower limit for the expected [O/Fe]_CCSN). The average [O/Fe] found in three sSFR bins is shown in the background (see caption of Fig. 7 and Table 1). Small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. The grey vertical band indicates the range of sSFR in which we expect the turnover based on the literature SN Ia DTD (see Fig. 2). Dark coloured ranges show the [O/Fe]–sSFR relations calculated with Eq. (1) for different SN Ia DTD and parameter choices. Left panel: power-law DTD with slope α_Ia = −1.1 and different minimum SN Ia delay times τ_Ia; min. Right panel: exponential DTD for two different values of the τ_Ia parameter. The coloured ranges span between the relations calculated with C_Ia/CC = 0.74 (upper edges) and C_Ia/CC = 2.5 (bottom edges) – see text for the details. We also plot the relations followed by TNG100-1-like galaxies (brown line, left panel) and EAGLE-like galaxies (turquoise line, right panel) and the average MW evolutionary track reconstructed with disc stars assuming constant star formation history (thick orange line, see Sect. 3.2).

In the text

	Fig. B.1. Same as Figure 6, but excluding data points with ‘indirect’ Fe or O determinations.
In the text

Fig. B.2.

[O/Fe] versus [Fe/H] of MW disc and halo dwarf stars from Amarsi et al. (2019). Blue points indicate stars which were used to estimate the [O/Fe]_CCSN shown in Figure 6. Their average < [O/Fe]_MW > = 0.52 dex is indicated by the thick black line. Thin grey lines span between 13 and 99.8 percentiles of the average ([O/Fe] = 0.48-0.56 dex). Amarsi et al. (2019) measure relative abundances with respect to the Sun and derive log₁₀(O/Fe)_⊙ = 1.179 dex. For consistency with the rest of the analysis, we convert those relative measurements to absolute abundances and place them on GS98 solar scale. The thin dashed lines show the solar values from Amarsi et al. (2019).

In the text

	Fig. B.3. Comparison of the [O/Fe] for the sample from Senchyna et al. (2022) where Z_Fe was derived with C&B SPS models (circles, as plotted in Figure 6) and S99 SPS models (diamonds, reported in Table E.1). We add a small offset in sSFR between the two estimates for easier comparison.
In the text

Fig. B.4.

Slope of the linear fit to the [O/Fe]–log₁₀(sSFR) relation for different choices of the baseline (colours) and including/excluding of the sample from Bresolin et al. (2016, 2022) at low sSFR (crosses/circles). We show the result obtained when fitting only the slope at log₁₀(sSFR) < − 7.6 (symbols with grey edges), at log₁₀(sSFR) < − 8.5 (symbols with blue edges) or when fitting the slope to the full sample (black edges). Error bars range from 16 to 84 percentiles of the fits, the symbol indicates the median.

In the text

Fig. D.1.

Star-forming [O/Fe] – sSFR relation including the sample from Bresolin et al. (2016, 2022) with BSG-based metallicities, assuming they probe Z_Fe. Data points (big circles) were shifted to a common ‘intermediate+Δ_d’ [O/Fe] baseline. Inner colour of big circles indicates the stellar mass, outer colour indicates the bin to which the data point belongs. Values listed in the figure indicate median [O/Fe] in each of the log₁₀(sSFR) bins (see Table D.1 for the values found with different [O/Fe] baseline choices). Dark (light) area of each bin spans between 16-84 (0.13-99.87) percentiles of 10⁵ draws of the average [O/Fe]. Small grey data points were not used in the analysis as it is not clear how to consistently correct them for systematic offsets. Data with indirect O or Fe estimates are not shown. Thick horizontal lines indicate zero points for reference solar O and Fe abundance from Grevesse & Sauval (1998) (GS98) and Asplund et al. (2009).

In the text

Fig. E.1.

Observational [O/Fe]–sSFR relation compared with a range of model relations. Data points (big circles) were shifted to a common intermediate [O/Fe] baseline with additional offset due to possible oxygen dust depletion (Δ_d) included (see Figure 8 and Section 5). Dark coloured ranges show the [O/Fe]–sSFR relations calculated with 1 for different SN Ia DTD and parameter choices. Left panel: power-law DTD with the minimum SN Ia delay time τ_Ia; min = 100 Myr and different slopes α_Ia. Right panel: analytic DTD for mixed single degenerate and double degenerate SN Ia scenario from Greggio (2005, 2010), as used by Kashino et al. (2022). The coloured ranges span between the relations calculated with C_Ia/CC = 0.74 (upper edges) and C_Ia/CC = 2.5 (bottom edges) – see text for the details. We also plot the relations followed by TNG100-1-like galaxies (brown line, left panel) and the relation from Kashino et al. (2022) (black dotted line, right panel).

In the text

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