On the variation in stellar alpha-enhancements of star-forming galaxies in the EAGLE simulation
MMNRAS , 1–17 (2021) Preprint 10 February 2021 Compiled using MNRAS L A TEX style file v3.0
On the variation in stellar alpha-enhancements of star-forminggalaxies in the EAGLE simulation
Andrea Gebek , ★ & Jorryt Matthee † Department of Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281-S9, B-9000 Gent, Belgium
10 February 2021
ABSTRACT
The ratio of 𝛼 -elements to iron in galaxies holds valuable information about the star-formationhistory since their enrichment occurs on different timescales. The fossil record of stars ingalaxies has mostly been excavated for passive galaxies, since the light of star-forming galax-ies is dominated by young stars which have much weaker atmospheric absorption features.Here we use the cosmological EAGLE simulation to investigate the origin of variations in 𝛼 -enhancement among star-forming galaxies at 𝑧 =
0. The definition of 𝛼 -enhancement ina composite stellar population is ambiguous. We elucidate two definitions - termed ‘mean’and ‘galactic’ 𝛼 -enhancement - in more detail. While a star-forming galaxy has a high ‘mean’ 𝛼 -enhancement when its stars formed rapidly, a galaxy with a large ‘galactic’ 𝛼 -enhancementgenerally had a delayed star formation history. We find that absorption-line strengths of Mgand Fe correlate with variations in 𝛼 -enhancement. These correlations are strongest for the‘galactic’ 𝛼 -enhancement. However, we show that these are mostly caused by other effectswhich are cross-correlated with 𝛼 -enhancement, such as variations in the light-weighted age.This severely complicates the retrieval of 𝛼 -enhancements in star-forming galaxies. The ambi-guity is not severe for passive galaxies and we confirm that spectral variations in these galaxiesare caused by measurable variations in 𝛼 -enhancements. We suggest that this more complexcoupling between 𝛼 -enhancement and star formation histories can guide the interpretation ofnew observations of star-forming galaxies. Key words: methods: numerical – galaxies: evolution – galaxies: abundances
Stars enrich the ambient interstellar medium (ISM) with metalsthrough stellar winds and supernovae (SN) explosions. Elementsformed in the 𝛼 -process (the 𝛼 -elements C, O, Ne, Mg, Si, S, Ar,and Ca) are predominantly produced by Type II SNe, which markthe endpoint of the stellar evolution of massive, short-lived stars.On the other hand, the enrichment in iron-peak elements (Fe, Cr,Co, Ni, Cu, Mn) receives a significant contribution from Type IaSNe (e.g. Tinsley 1979; Greggio & Renzini 1983; Wiersma et al.2009b). These occur in binaries when a white dwarf accretes acritical amount of material from its companion star. Since theseSNe explosions exhibit significantly different timescales, the ratioof 𝛼 -elements to iron-peak elements contains information about thestar-formation history (SFH) of a composite stellar population suchas a galaxy.It is well known that the delayed iron enrichment from SNe Ialeads to a declining 𝛼 -enhancement over cosmic time (e.g. Weinberget al. 2017). At the same time, the stellar metallicities of galaxies ★ E-mail: [email protected] † Zwicky Fellow. E-mail: [email protected] generally increase as each generation of stars returns a fraction oftheir mass as metals into gas in the ISM, which then partly fuelslater generations of stars. Therefore, the distribution functions ofstars in the [ 𝛼 /Fe]-[Fe/H]-plane may act as a chemical fossil recordof the star formation and chemical enrichment history of a galaxy(e.g. Mackereth et al. 2018).For simple stellar populations (SSPs) such as globular clusters,there is a wealth of evidence both from observations and simulationsthat the timescale of star formation and 𝛼 -enhancement are indeedcausally related (Puzia et al. 2005; Woodley et al. 2010; Hugheset al. 2020). In our own Milky Way, recent large spectroscopic cam-paigns have made it possible to map the distribution of individualstars in the [ 𝛼 /Fe]-[Fe/H]-plane (e.g. Hayden et al. 2015). This planeis bimodal and contains a high- and a low- 𝛼 -sequence (e.g. Ratcliffeet al. 2020; Vincenzo et al. 2021). These sequences are often asso-ciated with distinct structures which formed at different times andwhich share orbital parameters (e.g. Freeman & Bland-Hawthorn2002; Venn et al. 2004; Naidu et al. 2020; Spitoni et al. 2021) andare therefore used to obtain a detailed picture of the history of ourGalaxy.Extending such studies to distant galaxies is challenging. Mea-surements of stellar 𝛼 -enhancement in integrated spectra have so © a r X i v : . [ a s t r o - ph . GA ] F e b Gebek & Matthee far mainly been limited to passive galaxies out to a redshift of 𝑧 ≈ 𝛼 -enhancement on a combinationof Lick indices, or in the case of Conroy et al. (2014) full spec-tral fitting. In a pioneering study of passive galaxies, Thomas et al.(2005) used a chemical evolution model to relate 𝛼 -enhancement tothe FWHM Δ 𝑡 of a gaussian-shaped star-formation history follow-ing [ 𝛼 / Fe ] ≈ / − / ( Δ 𝑡 ) . Subsequently, de La Rosa et al.(2011) found an empirical relation between the timescale of theSFH and galactic 𝛼 -enhancement, as predicted by chemical evolu-tion models. Multiple studies measured the 𝛼 -enhancement of sam-ples of passive galaxies, where a notable trend with galactic stellarmass was found: Alpha-enhanced galaxies tend to be more massive,consistent with the idea of ‘galactic downsizing’ (massive galaxiestend to form their stars earlier and more rapidly). This trend, startingat 𝑀 ∗ ≈ . 𝑀 (cid:12) , has been reproduced in the EAGLE simulation(Segers et al. 2016). These authors attribute the rapid quenching ofmassive galaxies to the feedback of active galactic nuclei (AGN).It is of interest to use measurements of 𝛼 -enhancements toconstrain the star formation histories of star-forming galaxies onrelatively long time-scales. Such measurements would serve as in-teresting cross-checks for recent model-based (e.g. Pacifici et al.2013, 2016) or non-parametric (e.g. Iyer et al. 2019; Leja et al.2019a) inferences of SFHs which are crucial for obtaining reliablestellar masses (e.g. Leja et al. 2019b). They may also help extend-ing the dynamic range of observations of the power spectrum ofthe time-variability of star formation histories (e.g. Tacchella et al.2020). However, measurements of 𝛼 -enhancement for star-forminggalaxies are much more challenging than those for passive galaxiesas the atmospheres of the young stars that dominate the spectraof such galaxies have much weaker absorption features comparedto the stars in passive galaxies (Walcher et al. 2009; Conroy 2013).Gallazzi et al. (2020) however recently presented first measurementsof 𝛼 -enhancement in the star-forming galaxy population in the localUniverse. Furthermore, resolved observations of local star-forminggalaxies are also starting to report measurements of 𝛼 -enhancementin star-forming galaxies (e.g. Pinna et al. 2019; Neumann et al. 2020;Domínguez Sánchez et al. 2020). A detailed investigation in the rela-tion between stellar 𝛼 -enhancement and the star formation historiesof star-forming galaxies is therefore timely.Besides the observational challenges, the interpretation of ob-served 𝛼 -enhancements in star-forming galaxies is not trivial. Mostobservational studies of 𝛼 -enhancement in integrated galaxy spectratreat the galaxies as simple stellar populations. For passive galax-ies, this is justifiable by the fact that the (light-weighted) spectrumof an old stellar population that formed in a narrow and rapid starformation history resembles a stellar population with a single age.As we show in this work, this simplification can not be applied tostar-forming galaxies which tend to have a longer and slower starformation history.For composite stellar populations one can investigate variousdefinitions of 𝛼 -enhancement. One definition is the average of theratios of 𝛼 -elements to iron in individual stars or SSPs (‘mean’ 𝛼 -enhancement), but one can also define the ratio of the average 𝛼 -element-abundance to the average iron abundance integrated overthe full galaxy (‘galactic’ 𝛼 -enhancement). As we will show, thefirst definition of 𝛼 -enhancement is basically the average positionof stars on the [ 𝛼 /Fe]-[Fe/H]-plane along the 𝛼 /Fe axis, while thesecond definition weights the individual 𝛼 -enhancements by theiron abundance. Therefore, it is crucial to understand the origin ofboth 𝛼 -enhancements in order to link results on resolved stars in the Milky Way into a more complete extra-galactic and cosmologicalcontext.In this paper, we use the cosmological hydrodynamical EA-GLE simulation (Schaye et al. 2015) to investigate the origin ofthese 𝛼 -enhancements in terms of galactic star formation historiesand chemical evolution. We aim to identify the properties that drivegalactic 𝛼 -enhancement in the context of star-forming galaxies, andrestrict ourselves to the stellar 𝛼 -enhancement (instead of the gas-phase 𝛼 -enhancement). We summarize the relevant aspects of theEAGLE simulation and our galaxy sample in § 2, and present twodistinct definitions of 𝛼 -enhancement in § 3. We relate these 𝛼 -enhancements to galactic star-formation histories in § 4 and discusshow variations in these 𝛼 -enhancements affect the integrated spec-tral energy distributions in § 5. We investigate 𝛼 -enhancement inpassive galaxies and compare these results to the ones obtained forstar-forming galaxies in § 6, discuss future improvements in § 7 andsummarise our work in § 8.The EAGLE simulation used throughout this work is basedon a standard Λ CDM-universe with the cosmological parametersfrom the 2013
Planck mission (Planck Collaboration et al. 2014).Furthermore, we use 13.798 Gyr for the age of the universe basedon the 2015
Planck results (Planck Collaboration et al. 2016). Weuse the same set of solar abundances as in Wiersma et al. (2009b),with the following mass fractions: 𝑋 H (cid:12) = . 𝑋 M (cid:12) = . 𝑋 O (cid:12) = . × − , 𝑋 Fe (cid:12) = . × − , 𝑋 Mg (cid:12) = . × − , with 𝑋 M (cid:12) denoting the total metal mass fraction of the sun. We study galaxies that have been simulated in the cosmologicalhydrodynamical EAGLE simulation suite (Schaye et al. 2015; Crainet al. 2015). Here we briefly describe the main code and its subgridphysics, with emphasis on the chemical enrichment scheme (§ 2.2).We also specify the sample that we selected in our study and howthis compares to the total sample of galaxies at 𝑧 = EAGLE is run using a heavily modified version of the 𝑁 -bodysmoothed particle hydrodynamics (SPH) code gadget3, last de-scribed by Springel (2005). For this work we use the largest ref-erence simulation Ref-L0100N1504 to which we refer as ‘EAGLEsimulation’. This simulation has a box size of 100 cMpc and con-tains 2 × baryonic & dark matter particles. The resolution ofthe baryonic particles is chosen to marginally resolve the Jeans scalein the warm ISM (Schaye et al. 2015). Haloes are identified using afriends-of-friends algorithm (Davis et al. 1985) for the dark matterparticles. Subsequently, the subfind algorithm (Springel et al. 2001;Dolag et al. 2009) finds substructures bound by saddle points in thedensity distribution. These gravitationally bound subhaloes are thenidentified as galaxies. Properties of the baryonic & dark matter par-ticles (The EAGLE team 2017), and of the galaxies (McAlpine et al.2016), are stored in 29 snapshots between redshift 20 and 0.The baryonic particles, which occur in different phases (gas,stars, black holes) have masses of the order ∼ 𝑀 (cid:12) for the refer-ence model we are using. Relevant processes which are not resolvedby the simulation are implemented as subgrid physics. Radiativecooling is calculated using the 11 most important elements forthe cooling function: H, He, C, N, O, Ne, Mg, Si, S, Ca, and Fe(Wiersma et al. 2009a). Hydrogen is reionized instantaneously at MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs M * [M ]10 s S F R [ y r ] [O/Fe] mean M * [M ]10 s S F R [ y r ] [O/Fe] gal Figure 1.
Relation between specific star formation rate and stellar mass for galaxies in the EAGLE simulation at 𝑧 =
0. Galaxies are color-coded by two differentdefinitions of 𝛼 -enhancement, by [ O / Fe ] mean in the left panel and by [ O / Fe ] gal in the right panel. The 𝛼 -enhancements are calculated on a logarithmic100 × 𝑀 ∗ ) galactic 𝛼 -enhancements for each cell. The range of the colorbar is limited to better visualizethe trends. The galaxies on the diagonal sequence in the bottom-left are devoid of star forming gas and formally have a zero SFR. We display them with aconstant SFR=10 − M (cid:12) yr − for visualisation purposes. Dash-dotted black lines show the mass and sSFR cuts we use to select the galaxy sample (§ 2.3). Thesolid black lines indicate the running median sSFR of star-forming galaxies (the galactic main sequence), the dashed lines show the interquartile range. Sincethere are only few very massive galaxies in the EAGLE simulation, we stop the calculation of the median sSFR and the interquartile range at 𝑀 ∗ = . 𝑀 (cid:12) as the curves become dominated by individual galaxies. 𝑧 = . . − 𝑀 (cid:12) .Star formation feeds energy back into the ISM, through both stel-lar winds and core-collapse supernovae. This feedback is thermaland implemented stochastically to minimise numerical losses (DallaVecchia & Schaye 2012). In EAGLE, feedback from supermassiveblack holes contributes to the quenching of star formation in mas-sive galaxies (Booth & Schaye 2009). The parameters associatedwith these feedback processes are chosen such that the simulationsimultaneously reproduces 𝑧 ∼ Since the 𝛼 -enhancement is determined by the chemical enrich-ment prescription within EAGLE, we describe the simulated pro-cesses here. A general enrichment scheme within SPH-codes isdescribed in Wiersma et al. (2009b), which is also used for theEAGLE simulation. Chemical enrichment happens via three differ-ent channels: Asymptotic giant branch stars (AGB-stars), Type Ia supernovae and Type II (core-collapse) supernovae including thestellar winds from their progenitors. The nucleosynthetic yield forintermediate-mass AGB-stars are taken from Marigo (2001), forSNe Ia from Thielemann et al. (2003), and for mass loss and SNeII in high-mass stars (up to 100 𝑀 (cid:12) ) from Portinari et al. (1998).These (metallicity-dependent) yields, together with the mass- andmetallicity-dependent lifetimes from Portinari et al. (1998), definethe ejected mass of a SSP at each timestep. Nine elements are trackedindividually in the chemical enrichment scheme of EAGLE: H, He,C, N, O, Ne, Mg, Si & Fe . The simulation also tracks the totalmetal mass, using 𝑌 𝑍 = −( 𝑌 H + 𝑌 He ) for the yield of the metals.The yields of hydrogen and helium are negative since destructiondominates over production in the nucleosynthesis process. Specifi-cally relevant for this work is the implementation of the delay timedistribution of SN Ia. As described in Schaye et al. (2015) the SNIa rate of a single star particle follows an exponential decay. Thenormalisation and e-folding time of 2 Gyr are chosen to reproducethe observed evolution of the cosmic SN Ia rate.EAGLE uses abundances smoothed by the SPH-kernel(smoothed abundances) for the calculation of cooling rates, stel-lar lifetimes and yields. Compared to the standard ‘particle abun-dances’, smoothed abundances have the advantage of being moreconsistent with the SPH-formalism, furthermore they counterthe lack of metal mixing which is inherent to SPH-simulations(Wiersma et al. 2009b). Following Matthee & Schaye (2018) weuse smoothed abundances throughout this work. For the calculation of the radiative cooling rates, Ca and S are addition-ally taken into account. Within EAGLE, the abundances of Ca and S areproportionally set to the Si abundance.MNRAS000
0. Galaxies are color-coded by two differentdefinitions of 𝛼 -enhancement, by [ O / Fe ] mean in the left panel and by [ O / Fe ] gal in the right panel. The 𝛼 -enhancements are calculated on a logarithmic100 × 𝑀 ∗ ) galactic 𝛼 -enhancements for each cell. The range of the colorbar is limited to better visualizethe trends. The galaxies on the diagonal sequence in the bottom-left are devoid of star forming gas and formally have a zero SFR. We display them with aconstant SFR=10 − M (cid:12) yr − for visualisation purposes. Dash-dotted black lines show the mass and sSFR cuts we use to select the galaxy sample (§ 2.3). Thesolid black lines indicate the running median sSFR of star-forming galaxies (the galactic main sequence), the dashed lines show the interquartile range. Sincethere are only few very massive galaxies in the EAGLE simulation, we stop the calculation of the median sSFR and the interquartile range at 𝑀 ∗ = . 𝑀 (cid:12) as the curves become dominated by individual galaxies. 𝑧 = . . − 𝑀 (cid:12) .Star formation feeds energy back into the ISM, through both stel-lar winds and core-collapse supernovae. This feedback is thermaland implemented stochastically to minimise numerical losses (DallaVecchia & Schaye 2012). In EAGLE, feedback from supermassiveblack holes contributes to the quenching of star formation in mas-sive galaxies (Booth & Schaye 2009). The parameters associatedwith these feedback processes are chosen such that the simulationsimultaneously reproduces 𝑧 ∼ Since the 𝛼 -enhancement is determined by the chemical enrich-ment prescription within EAGLE, we describe the simulated pro-cesses here. A general enrichment scheme within SPH-codes isdescribed in Wiersma et al. (2009b), which is also used for theEAGLE simulation. Chemical enrichment happens via three differ-ent channels: Asymptotic giant branch stars (AGB-stars), Type Ia supernovae and Type II (core-collapse) supernovae including thestellar winds from their progenitors. The nucleosynthetic yield forintermediate-mass AGB-stars are taken from Marigo (2001), forSNe Ia from Thielemann et al. (2003), and for mass loss and SNeII in high-mass stars (up to 100 𝑀 (cid:12) ) from Portinari et al. (1998).These (metallicity-dependent) yields, together with the mass- andmetallicity-dependent lifetimes from Portinari et al. (1998), definethe ejected mass of a SSP at each timestep. Nine elements are trackedindividually in the chemical enrichment scheme of EAGLE: H, He,C, N, O, Ne, Mg, Si & Fe . The simulation also tracks the totalmetal mass, using 𝑌 𝑍 = −( 𝑌 H + 𝑌 He ) for the yield of the metals.The yields of hydrogen and helium are negative since destructiondominates over production in the nucleosynthesis process. Specifi-cally relevant for this work is the implementation of the delay timedistribution of SN Ia. As described in Schaye et al. (2015) the SNIa rate of a single star particle follows an exponential decay. Thenormalisation and e-folding time of 2 Gyr are chosen to reproducethe observed evolution of the cosmic SN Ia rate.EAGLE uses abundances smoothed by the SPH-kernel(smoothed abundances) for the calculation of cooling rates, stel-lar lifetimes and yields. Compared to the standard ‘particle abun-dances’, smoothed abundances have the advantage of being moreconsistent with the SPH-formalism, furthermore they counterthe lack of metal mixing which is inherent to SPH-simulations(Wiersma et al. 2009b). Following Matthee & Schaye (2018) weuse smoothed abundances throughout this work. For the calculation of the radiative cooling rates, Ca and S are addition-ally taken into account. Within EAGLE, the abundances of Ca and S areproportionally set to the Si abundance.MNRAS000 , 1–17 (2021)
Gebek & Matthee
Table 1.
Summary of the properties of the simulated galaxies in the EAGLEsimulation at 𝑧 = Gal
Star-Forming 𝑀 ∗ = ( − ) × M (cid:12) , sSFR > − yr − 𝑀 ∗ > × M (cid:12) , SFR = (cid:12) yr − , centralgalaxy 27 We note that the simulations we analyse are all assuming a con-stant Chabrier initial mass function (IMF). In principle, variationsin 𝛼 -enhancements could also trace variations of the IMF betweendifferent star-forming regions (as for example implemented in Bar-ber et al. 2019). Such variations could be relatively independent ofvariations in star formation histories. For example, a top-heavy IMFwill lead to a higher fraction of Type II SNe compared to Type IaSN, and thus a higher 𝛼 -enhancement (Fontanot et al. 2017). Wetherefore caution that IMF variations may complicate the applica-bility of our results to the observed Universe in case IMF variationsare occurring. The RefL0100N1504-simulation consists of 40312 galaxies at red-shift zero with stellar masses ranging from 𝑀 ∗ ≈ − × M (cid:12) .The distribution of these galaxies in the stellar mass-sSFR-plane (thegalactic main sequence) is shown in Figure 1. To minimise resolu-tion effects we do not include low-mass galaxies in our sample asthese are resolved by less than 100 star particles. In the simulation,the most massive galaxies tend to be dominated by 𝛼 -enhanced starsand are typically quenched or about to (see Figure 1). Therefore,their star formation histories may have been significantly affected byAGN feedback (e.g. Segers et al. 2016; Matthee & Schaye 2019). Tominimise the mass dependence of 𝛼 -enhancement and to reduce theimpact of AGN feedback we focus on galaxies in an intermediatemass range and select galaxies within 𝑀 ∗ = ( − ) × M (cid:12) ,leading to a sample of 1949 galaxies. However, we note that Figure 1illustrates that, for star-forming galaxies, there are little variations in 𝛼 -enhancement as a function of mass, particularly once galaxies thatare experiencing AGN feedback are ignored. We investigate star-forming galaxies in the current study, imposing sSFR > − yr − (1455 galaxies). These cuts are illustrated in Figure 1. We remarkthat this sample contains some rejuvenated galaxies which havebeen quiescent for a long time, but experienced a recent burst ofstar formation and hence fulfill our star formation criterion. Sincethe fraction of rejuvenated galaxies is less than one percent in oursample we do not expect any significant impact on our results.We also define a sample of massive, passive galaxies in theRefL0100N1504-simulation. This sample is chosen to allow com-parisons between our methodology and some well-known results forthe 𝛼 -enhancement of early-type galaxies. As quenching occurs at (cid:38) M (cid:12) , we choose galaxies with 𝑀 ∗ > × M (cid:12) . To ensurethat our sample consists of early-type galaxies we only select cen-tral galaxies (which have a subgroup number of zero in the EAGLEgalaxy catalogue) that are devoid of star-forming gas. This passivesample consists of 27 galaxies, the attributes of both samples aresummarised in Table 1.Furthermore, for calculations involving metal abundances weneglect a few star particles with peculiar abundances. Some particles(predominantly old ones) have very low or even zero-valued metalmass fractions, occurring both for individual abundances (such asthe iron mass fraction) or the total metal mass fraction. Althoughthis is a rare effect among the star particles it introduces numerical errors, especially when calculating ratios of mass fractions (like the 𝛼 -enhancement of a single star particle). In essence, this complica-tion arises due to the poorly understood formation of the first stars(Population III), where it is well known that they can be extremelymetal-poor with [Fe/H] ∗ < − . For our star-forming sample of 1455 galaxies, ≈ .
50 % of all stars have a total metal mass fraction below this cut.The oxygen or iron mass fraction of ≈ .
76 % stars is below ourimposed cut.
Since oxygen dominates the mass budget of the 𝛼 -elements, we useoxygen as a proxy for the 𝛼 -elements as done in other studies ofthe 𝛼 -enhancement in EAGLE (e.g. Segers et al. 2016). We remarkthat while the gas-phase oxygen abundance can be measured reliablyfrom nebular emission lines, the stellar oxygen abundance is difficultto retrieve due to the lack of strong oxygen absorption lines in stellaratmospheres. Hence, some authors opt to use magnesium as a proxyfor the 𝛼 -elements. We verified that our results do not change whenusing magnesium instead of oxygen.In order to obtain a census picture of the 𝛼 -enhancements of allthe stars (i.e. star particles representing SSPs) in the galaxies in ourstar-forming sample, we show the relation between their oxygen-to-iron ratio and age and their distribution in the 𝛼 -enhancement-metallicity-plane in Figure 2. This figure displays some of the well-known relations of the 𝛼 -enhancement of SSPs with age and metal-licity. The left panel shows that after the onset of star formation,[O/Fe] of newborn stars quickly decreases until 𝑡 ≈ . − . < [ Fe / H ] < − .
5, the stars areconstantly 𝛼 -enhanced, while for higher metallicities [O/Fe] bendsover and starts to decrease. Both for very low ( [ Fe / H ] < − . [ Fe / H ] > − . 𝛼 -enhancement is ap-parently driven by a depletion in iron and not by an enhancementin oxygen. Several studies find a similar distribution of stars in themetallicity- 𝛼 -enhancement-plane using chemical evolution models(e.g. Matteucci & Brocato 1990; Andrews et al. 2017) or cosmolog-ical simulations (e.g. Mackereth et al. 2018; Agertz et al. 2020). Onthe other hand, surveys of stars in the Milky Way such as APOGEE(Majewski et al. 2017) find a bimodal distribution in this plane (e.g.Fuhrmann 1998; Lian et al. 2020b; Lian et al. 2020a). This can beattributed to an irregular and atypical star formation history of ourGalaxy (e.g. Mackereth et al. 2018; Evans et al. 2020). The low-metallicity stars are still taken into account when computing andfitting star-formation histories. We adopt the following convention for stellar abundance ratios: [A/B] = log ( 𝑋 A / 𝑋 B ) − log ( 𝑋 A (cid:12) / 𝑋 B (cid:12) ) , where 𝑋 𝑗 denotes the abundance (stellarmass fraction) of element 𝑗 . MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs t [Gyr]1.00.50.00.51.01.52.0 [ O / F e ] [ O / F e ] l o g ( m a ss f r a c t i o n ) l o g ( m a ss f r a c t i o n ) Figure 2.
Distribution of the current masses of star particles within our sample of star-forming galaxies with 𝑀 ∗ = ( − ) × M (cid:12) (see § 2.3), in terms ofstellar age, metallicity, and 𝛼 -enhancement (linearly discretised to a 100 ×
100 grid). 𝑡 denotes cosmic time, [O/Fe] (and equivalently [Fe/H]) the logarithmicratio of the oxygen to iron mass fractions (normalised to the solar value). The solid black lines indicate the running median stellar 𝛼 -enhancement, the dashedlines show the interquartile range (both weighted by current stellar masses). For individual stars or simple stellar populations, the 𝛼 -enhancement is well defined as a simple abundance ratio. However,for a composite stellar population various definitions are possi-ble. Here we present two meaningful definitions of the integratedmass-weighted 𝛼 -enhancement of a galaxy that we will investigatethroughout the paper. The first definition is essentially the average 𝛼 -enhancement of the SSPs, a relevant quantity to inform chemicalevolution models used for instance by Thomas et al. (2005). Fur-thermore, retrieval codes which find a linear combination of SSPs(with varying 𝛼 -enhancements) to fit an integrated galaxy SED likepPXF (Cappellari & Emsellem 2004) measure this quantity (Pinnaet al. 2019). We term this quantity ‘mean 𝛼 -enhancement’ (§ 3.1).On the other hand, earlier analyses of 𝛼 -enhancement withinEAGLE (Segers et al. 2016; Matthee & Schaye 2018; Mackerethet al. 2018; Hughes et al. 2020) consider the total mass of oxygenlocked up in stars, divided by the total iron mass. Since this quan-tity corresponds to the ratio of the galactic oxygen and iron massfractions, we term this quantity ‘galactic 𝛼 -enhancement’ (§ 3.2).When measuring [ 𝛼 /Fe] from a ratio of absorption lines as is typi-cally done (e.g. Gallazzi et al. 2020), we naively expect the measuredvalue to correspond to the galactic 𝛼 -enhancement. This is due tothe measured absorption line ratio corresponding to a ratio of lineswhich have first been integrated separately over the entire galaxy,comparable to the galactic 𝛼 -enhancement where the oxygen andiron abundances are integrated separately over the galaxy and thentheir ratio is taken. The first definition of the 𝛼 -enhancement of a galaxy that we con-sider is the (mass-weighted) average ratio of the stellar oxygen-to-iron abundances of the individual star particles: [ O / Fe ] mean = log (cid:32) (cid:205) 𝑖 𝑚 𝑖 × 𝑋 O 𝑖 / 𝑋 Fe 𝑖 𝑀 ∗ (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) = log (cid:32)(cid:28) 𝑋 O 𝑋 Fe (cid:29) 𝑚 (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) , (1)where 𝑋 𝑗𝑖 ( 𝑋 𝑗 (cid:12) ) denotes the abundance of element 𝑗 in starparticle 𝑖 (in the sun). We abbreviate averages with weights 𝑦 by (cid:104) 𝑥 (cid:105) 𝑦 . 𝑚 𝑖 is the current mass of star particle 𝑖 such that 𝑀 ∗ = (cid:205) 𝑖 𝑚 𝑖 where the sum runs over all star particles in a particular galaxy.Note that one could also calculate the 𝛼 -enhancement of galax-ies by swapping the operational order of logarithm and averaging.This definition is nearly equivalent to Definition 1, but using theweighted geometric mean of the stellar oxygen-to-iron ratios (in-stead of the arithmetic one). Since the oxygen-to-iron ratios vary byless than an order of magnitude for the majority of the star parti-cles, the arithmetic and the geometric mean track each other quitewell. We find a Pearson correlation coefficient of 𝜌 = .
87 whencomparing these two definitions for our star-forming galaxy sam-ple. 𝛼 -enhancement calculated using the geometric mean is offsetto smaller values compared to [O/Fe] mean by ≈ .
05 dex, which isexpected due to the geometric mean yielding an average smaller orequal the arithmetic mean. We focus on the analysis of [O/Fe] mean for the present work since this quantity is readily comparable toanother definition of 𝛼 -enhancement of galaxies, presented in thefollowing subsection. MNRAS000
05 dex, which isexpected due to the geometric mean yielding an average smaller orequal the arithmetic mean. We focus on the analysis of [O/Fe] mean for the present work since this quantity is readily comparable toanother definition of 𝛼 -enhancement of galaxies, presented in thefollowing subsection. MNRAS000 , 1–17 (2021)
Gebek & Matthee
The second definition of the 𝛼 -enhancement is the ratio of the totaloxygen (as a proxy for the 𝛼 elements) mass locked up in stars,divided by the total iron mass locked up in stars in a galaxy: [ O / Fe ] gal = log (cid:32) 𝑋 O ∗ 𝑋 Fe ∗ (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) , (2)where 𝑋 𝑗 ∗ is the galactic mass fraction in element 𝑗 , i.e. 𝑋 𝑗 ∗ = (cid:205) 𝑖 ( 𝑚 𝑖 × 𝑋 𝑗𝑖 )/ 𝑀 ∗ . We rewrite Eqn. 2 using a similar averaging overall star particles as in Eqn. 1: [ O / Fe ] gal = log (cid:32) (cid:10) 𝑋 O (cid:11) 𝑚 (cid:10) 𝑋 Fe (cid:11) 𝑚 (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) . (3)Due to our usage of smoothed abundances for the star particlesand our cut on low-metallicity star particles (see § 2.3), [O/Fe] gal calculated using the EAGLE subhalo catalogue (Eqn. 2) or the starparticles (Eqn. 3) do not coincide perfectly. We find small deviationsfrom a one-to-one relation, with a Pearson’s correlation coefficientof 𝜌 = .
991 for our star-forming galaxy sample. For the remainderof this paper, we will use [O/Fe] gal as defined in Eqn. 3 using theEAGLE star particle catalogue, since this definition incorporatesan averaging procedure which will make it easier to compare ourdefinitions of ‘mean’ and ‘galactic’ 𝛼 -enhancement.For a SSP (or a CSP where all stars exhibit the same oxygen-to-iron ratio), [O/Fe] mean and [O/Fe] gal must coincide. Since thesimulated galaxies consist of star particles with varying oxygen-to-iron ratios, we naively expect a strong, positive correlation between[O/Fe] mean and [O/Fe] gal . We show a comparison of these two def-initions of 𝛼 -enhancement for our star-forming and passive galaxysamples in Figure 3. We find that the 𝛼 -enhancements of the pas-sive sample indeed correlate quite well with a Pearson correlationcoefficient of 𝜌 = .
75. This positive correlation among passivegalaxies extends to lower masses, a sample of 494 galaxies with 𝑀 ∗ = ( − ) × M (cid:12) and sSFR < − yr − is distributed simi-larly as the sample of 27 massive, passive centrals. On the other hand[O/Fe] mean and [O/Fe] gal are uncorrelated for the star-forming sam-ple ( 𝜌 = − . 𝛼 -enhancements for star-forming galaxies: For [O/Fe] gal (cid:47) . gal (cid:39) .
25 the values start to correlate strongly and followthe trend of the passive population, probably due to the rejuvenatedgalaxies.We also note that [O/Fe] mean is significantly larger than[O/Fe] gal , on average the shift is ≈ .
15 dex. This can be under-stood in terms of the ‘metallicity-weighting’ of [O/Fe] gal , revealedby rewriting the ratio of the averaged abundances: (cid:10) 𝑋 O (cid:11) 𝑚 (cid:10) 𝑋 Fe (cid:11) 𝑚 = (cid:205) 𝑖 𝑋 O 𝑖 𝑚 𝑖 (cid:205) 𝑖 𝑋 Fe 𝑖 𝑚 𝑖 = (cid:205) 𝑖 𝑋 O 𝑖 / 𝑋 Fe 𝑖 × 𝑋 Fe 𝑖 𝑚 𝑖 (cid:205) 𝑖 𝑋 Fe 𝑖 𝑚 𝑖 = (cid:28) 𝑋 O 𝑋 Fe (cid:29) 𝑚 Fe . (4)Here 𝑚 Fe = 𝑋 Fe × 𝑚 denotes the current iron mass in the starparticles. Combining Eqns. 3 and 4 leads to [ O / Fe ] gal = log (cid:32)(cid:28) 𝑋 O 𝑋 Fe (cid:29) 𝑚 Fe (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) . (5)Hence, [O/Fe] mean and [O/Fe] gal describe the same quantity,the stellar oxygen-to-iron ratio, but averaged (weighted) by different mean [ O / F e ] g a l Star-FormingPassivePassive (low-mass)
Figure 3.
Alpha-enhancements of EAGLE galaxies at 𝑧 =
0, for the star-forming (blue circles) and passive (red circles) galaxy samples (Table 1). Asample of 494 galaxies in the same mass range as the primary star-formingsample but with sSFR < − yr − is shown as ‘Passive (low-mass)’ (redtriangles). The running medians (solid lines) and quartiles (dashed lines)for the star-forming and the low-mass passive samples are also shown.For optimal visualisation we exclude 19 galaxies with particularly large [ O / Fe ] mean and/or [ O / Fe ] gal in this figure. functions. Note that [O/Fe] mean uses the intuitive mass-weighting ofthe stars, while [O/Fe] gal is weighted by the stellar iron mass. Sinceiron-rich stars are comparatively young, and young stars are sup-pressed in 𝛼 -elements (Figure 2), [O/Fe] gal is dominated by youngstars and systematically lower than [O/Fe] mean . We remark thatthe range of 𝛼 -enhancements spanned by the star-forming galaxiesin our sample is rather small: The two- 𝜎 -interval for [O/Fe] mean ranges from 0 . − .
36 ( ≈ .
07 dex), the one for [O/Fe] gal onlyfrom 0 . − .
26 ( ≈ .
11 dex).
In this section we focus on the connection between the two def-initions of 𝛼 -enhancement and the star formation history. Due tothe different time-scales associated to the enrichment of 𝛼 elementsand iron, a connection between 𝛼 -enhancement and SFH is ex-pected (e.g. Thomas et al. 2005; de La Rosa et al. 2011). However,we have seen that the two 𝛼 -enhancements anti-correlate slightlyfor star-forming galaxies, suggesting that the single interpretationof 𝛼 -enhancement as a tracer for the rapidness of the SFH is over-simplistic.Starting from our definitions of 𝛼 -enhancement, we can expandon Eqn. 1 and reveal a twofold dependency of [O/Fe] mean on theSFH: [ O / Fe ] mean = log (cid:32) 𝑀 ∗ ∫ (cid:16) 𝑋 O ∗ 𝑋 Fe ∗ (cid:17) ( 𝑡 ) d 𝑀 ∗ d 𝑡 d 𝑡 (cid:33) − log (cid:32) 𝑋 O (cid:12) 𝑋 Fe (cid:12) (cid:33) . (6) MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs t [Gyr]0.000.250.500.751.001.251.501.752.00 S F R [ M y r ] [O/Fe] mean t [Gyr]0.000.250.500.751.001.251.501.752.00 S F R [ M y r ] [O/Fe] gal Mean0.304679101318 % C h a n g e % C h a n g e Figure 4.
SFHs of star-forming EAGLE galaxies, with 𝑡 denoting cosmic time. The mean SFH is calculated as the average SFR of all star-forming galaxiesin the sample in each time bin of 0.2 Gyr. For the other curves, the galaxies are split into eight equally-large subsets, sorted by [O/Fe] mean or [O/Fe] gal . Weshow the average SFR for each of these subsets. The color scale indicates the level of 𝛼 -enhancement of each subset relative to the subset with the lowest value(which is 0.30 for [O/Fe] mean and 0.16 for [O/Fe] gal ) in percent. There is significantly more scatter in [O/Fe] gal compared to [O/Fe] mean . Here, d 𝑀 ∗ / d 𝑡 denotes the current stellar mass formed and as-sembled between 𝑡 and 𝑡 + d 𝑡 as function of cosmic time 𝑡 . Thisquantity closely resembles the definition of the star-formation his-tory , and equals the actual galactic SFH when neglecting stellarmass loss. The other term in the integral of Eqn. 6 is the evolvingstellar oxygen-to-iron ratio, which itself depends on the past SFH.Hence, the SFH affects [O/Fe] mean both directly (as ‘weighting’function d 𝑀 ∗ / d 𝑡 ) and indirectly (via 𝑋 O ∗ / 𝑋 Fe ∗ ( 𝑡 ) ).Mathematically, [O/Fe] mean is fully determined by the stellaroxygen-to-iron ratio and the current mass formed per unit time (bothfunctions of cosmic time 𝑡 ). For [O/Fe] gal we need the current iron mass formed per unit time to weigh the stellar oxygen-to-iron ratio,i.e. d 𝑀 Fe ∗ d 𝑡 . Hence, with a set of three functions of time one cancalculate both [O/Fe] mean and [O/Fe] gal . Note that this basis set is not unique, but to facilitate the physical interpretation of thesefunctions we analyse the following three time-dependent quantitiesin § 4.1 and 4.2: SFR ( 𝑡 ) , 𝑋 O / 𝑋 Fe ( 𝑡 ) , and 𝑋 Fe ( 𝑡 ) . Our analysisconsists of grouping galaxies by their 𝛼 -enhancement, and thencalculating the average evolution of these three quantities withineach group. We calculate SFHs using a similar procedure as Sparre et al. (2015).The star particles of a particular galaxy are binned into age binsof 0.2 Gyr. Then, we sum the initial masses of all star particlesformed within the individual age bins. This sum, divided by 0.2 Gyr,yields the SFR as a function of time. As noted by Diemer et al.(2017), this extraction of the SFR means that we do not differbetween stars formed in situ (within the galaxy in question, which The star-formation history is defined as the function SFR ( 𝑡 ) , which is the initial mass formed per unit time. we would for example do when following the merger trees of thesimulated galaxies) or ex situ (in a smaller galaxy that mergedwithin the time interval). We proceed by grouping the galaxies intoeight equally-large subsets, sorted by [O/Fe] mean or [O/Fe] gal , andcalculate average SFHs for each of the subsets. These average SFHsare shown in Figure 4, which also displays the average SFH for theentire star-forming sample of 1455 galaxies as a black line in bothpanels.Remarkably, the SFH of the highest [O/Fe] mean bin coincidesrather well with the SFH of the bin with the lowest [O/Fe] gal . TheseSFHs peak early and have rapid star-formation over a comparativelysmall time-interval. Such rapid SFHs are expected to have a high 𝛼 -enhancement (e.g. Thomas et al. 2005), since the bulk of the starsformed early from an ISM which is not yet iron-enriched by SNeIa (see also Figure 2). We emphasize that while [O/Fe] mean followsthis theoretical picture, [O/Fe] gal behaves exactly in the oppositeway. This at first sight puzzling behaviour can be explained whentaking the chemical evolution into account, which we shall discussin § 4.2.Figure 4 also shows that at the low-[O/Fe] mean -end the dif-ferences in the late SFHs become smaller, indicating a saturationof the effect that SFH parameters correlate with 𝛼 -enhancement.This means that it is mostly early star formation that determines[O/Fe] mean . Contrarily, for [O/Fe] gal we find significant differencesboth at early and late times. The continuous ordering of the SFHsindicates a monotonic correlation between the shape of the SFH andthe 𝛼 -enhancements. Furthermore, we notice that the average SFHshave a log-normal shape, as is found in other studies for simulatedgalaxies (e.g. Diemer et al. 2017). We fit log-normal functions tothe SFHs of the individual galaxies in our sample in § 4.3. MNRAS000
SFHs of star-forming EAGLE galaxies, with 𝑡 denoting cosmic time. The mean SFH is calculated as the average SFR of all star-forming galaxiesin the sample in each time bin of 0.2 Gyr. For the other curves, the galaxies are split into eight equally-large subsets, sorted by [O/Fe] mean or [O/Fe] gal . Weshow the average SFR for each of these subsets. The color scale indicates the level of 𝛼 -enhancement of each subset relative to the subset with the lowest value(which is 0.30 for [O/Fe] mean and 0.16 for [O/Fe] gal ) in percent. There is significantly more scatter in [O/Fe] gal compared to [O/Fe] mean . Here, d 𝑀 ∗ / d 𝑡 denotes the current stellar mass formed and as-sembled between 𝑡 and 𝑡 + d 𝑡 as function of cosmic time 𝑡 . Thisquantity closely resembles the definition of the star-formation his-tory , and equals the actual galactic SFH when neglecting stellarmass loss. The other term in the integral of Eqn. 6 is the evolvingstellar oxygen-to-iron ratio, which itself depends on the past SFH.Hence, the SFH affects [O/Fe] mean both directly (as ‘weighting’function d 𝑀 ∗ / d 𝑡 ) and indirectly (via 𝑋 O ∗ / 𝑋 Fe ∗ ( 𝑡 ) ).Mathematically, [O/Fe] mean is fully determined by the stellaroxygen-to-iron ratio and the current mass formed per unit time (bothfunctions of cosmic time 𝑡 ). For [O/Fe] gal we need the current iron mass formed per unit time to weigh the stellar oxygen-to-iron ratio,i.e. d 𝑀 Fe ∗ d 𝑡 . Hence, with a set of three functions of time one cancalculate both [O/Fe] mean and [O/Fe] gal . Note that this basis set is not unique, but to facilitate the physical interpretation of thesefunctions we analyse the following three time-dependent quantitiesin § 4.1 and 4.2: SFR ( 𝑡 ) , 𝑋 O / 𝑋 Fe ( 𝑡 ) , and 𝑋 Fe ( 𝑡 ) . Our analysisconsists of grouping galaxies by their 𝛼 -enhancement, and thencalculating the average evolution of these three quantities withineach group. We calculate SFHs using a similar procedure as Sparre et al. (2015).The star particles of a particular galaxy are binned into age binsof 0.2 Gyr. Then, we sum the initial masses of all star particlesformed within the individual age bins. This sum, divided by 0.2 Gyr,yields the SFR as a function of time. As noted by Diemer et al.(2017), this extraction of the SFR means that we do not differbetween stars formed in situ (within the galaxy in question, which The star-formation history is defined as the function SFR ( 𝑡 ) , which is the initial mass formed per unit time. we would for example do when following the merger trees of thesimulated galaxies) or ex situ (in a smaller galaxy that mergedwithin the time interval). We proceed by grouping the galaxies intoeight equally-large subsets, sorted by [O/Fe] mean or [O/Fe] gal , andcalculate average SFHs for each of the subsets. These average SFHsare shown in Figure 4, which also displays the average SFH for theentire star-forming sample of 1455 galaxies as a black line in bothpanels.Remarkably, the SFH of the highest [O/Fe] mean bin coincidesrather well with the SFH of the bin with the lowest [O/Fe] gal . TheseSFHs peak early and have rapid star-formation over a comparativelysmall time-interval. Such rapid SFHs are expected to have a high 𝛼 -enhancement (e.g. Thomas et al. 2005), since the bulk of the starsformed early from an ISM which is not yet iron-enriched by SNeIa (see also Figure 2). We emphasize that while [O/Fe] mean followsthis theoretical picture, [O/Fe] gal behaves exactly in the oppositeway. This at first sight puzzling behaviour can be explained whentaking the chemical evolution into account, which we shall discussin § 4.2.Figure 4 also shows that at the low-[O/Fe] mean -end the dif-ferences in the late SFHs become smaller, indicating a saturationof the effect that SFH parameters correlate with 𝛼 -enhancement.This means that it is mostly early star formation that determines[O/Fe] mean . Contrarily, for [O/Fe] gal we find significant differencesboth at early and late times. The continuous ordering of the SFHsindicates a monotonic correlation between the shape of the SFH andthe 𝛼 -enhancements. Furthermore, we notice that the average SFHshave a log-normal shape, as is found in other studies for simulatedgalaxies (e.g. Diemer et al. 2017). We fit log-normal functions tothe SFHs of the individual galaxies in our sample in § 4.3. MNRAS000 , 1–17 (2021)
Gebek & Matthee t [Gyr]1510 X O / X F e [ X O / X F e ] [O/Fe] mean t [Gyr]1510 X O / X F e [ X O / X F e ] [O/Fe] gal t [Gyr]10 X F e [ X F e ] t [Gyr]10 X F e [ X F e ] Figure 5.
Chemical evolution of star-forming EAGLE galaxies, equivalent color-coding as in Figure 4. The mean 𝑋 O / 𝑋 Fe and 𝑋 Fe (black curves) are averagedover all galaxies in the sample in each time bin of 0.2 Gyr. For the other curves, the galaxies are split into eight equally-sized subsets, sorted by [ O / Fe ] mean or [ O / Fe ] gal . We show the average 𝑋 Fe and 𝑋 O / 𝑋 Fe for each of these subsets. We analyse the galactic oxygen-to-iron ratio and the iron abundanceas a function of time. Similar as for the SFHs, we bin the starparticles into age bins of 0.2 Gyr, and then compute (cid:104) 𝑋 O / 𝑋 Fe (cid:105) 𝑚 and (cid:104) 𝑋 Fe (cid:105) 𝑚 for each age bin. The results for galaxies grouped by their 𝛼 -enhancements are shown in Figure 5. Differences between the curvesarise mostly at late times. For both definitions of 𝛼 -enhancement, theoxygen-to-iron ratios imitate the SFR at late times: a high SFR todayleads to a high 𝑋 O ∗ / 𝑋 Fe ∗ today and vice versa. This is a consequenceof the correlation between SFH and chemical enrichment: Galaxieswith an early-peaked SFH have their ISM enriched in iron suchthat stars that form at late times have a small oxygen-to-iron ratio.Comparing the upper panels with the lower panels in Figure 5, wefind that the curves appear to be mirrored. This behaviour indicatesthat star particles with a small (large) oxygen-to-iron ratio have thisvalue mostly due to a large (small) iron abundance. As expected, theiron abundance is a strongly increasing function of time (more thantwo orders of magnitude over the age of the universe), and galaxieswith delayed star-formation (late-peaked SFHs) have smaller ironabundances throughout.With these two functions - SFR and 𝑋 O / 𝑋 Fe - we can explainhow a galaxy ends up with a certain mean 𝛼 -enhancement today. Galaxies with high [O/Fe] mean have an early-peaked SFH, such that[O/Fe] mean is dominated by old stars. Since these older stars havecomparatively large oxygen-to-iron ratios, the galaxy ends up with alarge value of [O/Fe] mean . Note that these galaxies have a subnormaloxygen-to-iron ratio at late times (Figure 5), but this does not affectthe galactic [O/Fe] mean significantly as these galaxies consist ofonly few young stars (Figure 4). Galaxies with a low [O/Fe] mean have a subnormal star formation activity at early ( 𝑡 < mean do not haveexcessive star formation today, at least not to the degree as thehigh-[O/Fe] gal -galaxies (Figure 4).To explain how a galaxy ends up with a certain galactic 𝛼 -enhancement we need to invoke yet another function: The stellariron abundance, 𝑋 Fe , as a function of time. While 𝑋 Fe ( 𝑡 ) does notaffect [O/Fe] mean directly, it does enter the averaging process forthe calculation of the galactic 𝛼 -enhancement [O/Fe] gal . Metal-richstar particles receive significantly more weight than metal-poor onesfor the computation of the galactic 𝛼 -enhancement. This effect isstrong enough to approximately reverse the behaviour of galaxieswhen sorted by their [O/Fe] gal (compared to when they are sortedby [O/Fe] mean ). For galaxies to achieve a large value of [O/Fe] gal , MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs t [Gyr]0.00.20.40.60.81.0 d M * / d t [ M y r ] [O/Fe] mean t [Gyr]0.00.20.40.60.8 d M F e * / d t [ M F e y r ] [O/Fe] gal Figure 6.
Star-formation histories as in Figure 4, but with the actual weighting functions used for [O/Fe] mean ( current galactic mass formed per unit time, leftpanel) and [O/Fe] gal (current galactic iron mass formed per unit time, right panel). The galaxies are split into eight equally-sized subsets according to their[O/Fe] mean and [O/Fe] gal , respectively. We show the average weighting functions within each of these subsets, the black lines indicate the mean tracks of theentire star-forming galaxy sample. The color-coding coincides with the one of Figure 4. it is more ‘efficient’ to have late-peaked, extended SFHs (Figure 4).This leads to a subnormal amount of old, 𝛼 -enhanced stars, butthese are negligible within the averaging process of the galactic 𝛼 -enhancement. The late-peaked SFH ensures that younger stars(formed after 𝑡 = gal , are 𝛼 -enhanced compared to other curves at the same age (Figure 5).Vice versa, galaxies with a small value of [O/Fe] gal have early-peaked SFHs and build a lot of iron early on, such that younger starsformed from the iron-rich ISM have comparatively low oxygen-to-iron ratios.For completeness we also show the actual weighting functionsused for mean (d 𝑀 ∗ / d 𝑡 ) and galactic (d 𝑀 Fe ∗ / d 𝑡 ) 𝛼 -enhancement inFigure 6. These functions directly give the 𝛼 -enhancements of thegalaxies when connected with the evolving oxygen-to-iron ratios(upper panels of Figure 5). The left panel of Figure 6 shows the cur-rent galactic mass formed per unit time, for groups of galaxies splitby [O/Fe] mean . The tracks closely resemble the actual star-formationhistories (left panel of Figure 4), scaled down by approximately fortypercent which corresponds to the integrated mass loss of an SSP(Wiersma et al. 2009b). This scaling is essentially uniform through-out cosmic history except for the most recent Gyr. Accordingly, theright panel of Figure 6 shows the current galactic iron mass formedper unit time, for groups of galaxies split by [O/Fe] gal . The tracks areessentially a convolution of the SFHs (right panel in Figure 4), theiron abundance histories (lower right panel in Figure 5), and the SSPmass loss effects. These tracks show quantitatively that younger starsare dominant for setting [O/Fe] gal , opposed to [O/Fe] mean which ismostly set by older stars. In order to explore the apparent relation between SFHs and the 𝛼 -enhancements of galaxies (Figure 4) in a quantitative way and on thelevel of individual galaxies, we parametrise galactic SFHs and in-vestigate the relation between their fitted parameters and [O/Fe] mean and [O/Fe] gal . Following Gladders et al. (2013) and Diemer et al. (2017) we describe SFHs of individual galaxies by log-normal func-tions, given by the following expression:SFR ( 𝑡 ) = 𝐴 √ 𝜋𝜏 × 𝑡 exp (cid:32) − (cid:0) ln ( 𝑡 ) − 𝑇 (cid:1) 𝜏 (cid:33) , (7)where 𝐴 , 𝑇 and 𝜏 are free parameters (the latter two haveunits of Gyr). For readability we refrain from inserting unit factorssuch as ln ( 𝑡 / ) into the equations in this section, and remarkthat we measure times always in Gyr and star-formation rates in 𝑀 (cid:12) yr − . We use the open-source lmfit package for python toexecute least-squares minimisations with the built-in Levenberg-Marquardt-algorithm, fitting Eqn. 7 to the simulated SFHs. Thesimulated SFHs are calculated as described in § 4.1 and age binswithout any star-formation are ignored by the fitting routine. Dueto the discrete nature and implementation of star-formation in thesimulation our calculated SFHs contain Poisson noise. FollowingMatthee & Schaye (2019) we calculate the associated error as 𝜎 ( 𝑡 ) = SFR ( 𝑡 )/√ 𝑁 , where 𝑁 is the number of star particles formed in aparticular age bin. Hence, the fitting routine effectively correspondsto a minimization of the following quantity: 𝜒 = ∑︁ 𝑡 = 𝑡 𝑖 (cid:16) SFR sim ( 𝑡 ) − SFR fit ( 𝑡 ) 𝜎 ( 𝑡 ) (cid:17) , (8)where the sum runs over all age bins (excluding bins withoutstar-formation activity). Following Diemer et al. (2017), we replace 𝑇 and 𝜏 with the more convenient peak time of the SFH ( 𝑡 peak ,Eqn. 9) and FWHM ( 𝜎 SFR , Eqn. 10): 𝑡 peak = exp (cid:0) 𝑇 − 𝜏 (cid:1) . (9) 𝜎 SFR = 𝑡 peak sinh (cid:0)√︁ ( ) 𝜏 (cid:1) . (10) MNRAS000
Star-formation histories as in Figure 4, but with the actual weighting functions used for [O/Fe] mean ( current galactic mass formed per unit time, leftpanel) and [O/Fe] gal (current galactic iron mass formed per unit time, right panel). The galaxies are split into eight equally-sized subsets according to their[O/Fe] mean and [O/Fe] gal , respectively. We show the average weighting functions within each of these subsets, the black lines indicate the mean tracks of theentire star-forming galaxy sample. The color-coding coincides with the one of Figure 4. it is more ‘efficient’ to have late-peaked, extended SFHs (Figure 4).This leads to a subnormal amount of old, 𝛼 -enhanced stars, butthese are negligible within the averaging process of the galactic 𝛼 -enhancement. The late-peaked SFH ensures that younger stars(formed after 𝑡 = gal , are 𝛼 -enhanced compared to other curves at the same age (Figure 5).Vice versa, galaxies with a small value of [O/Fe] gal have early-peaked SFHs and build a lot of iron early on, such that younger starsformed from the iron-rich ISM have comparatively low oxygen-to-iron ratios.For completeness we also show the actual weighting functionsused for mean (d 𝑀 ∗ / d 𝑡 ) and galactic (d 𝑀 Fe ∗ / d 𝑡 ) 𝛼 -enhancement inFigure 6. These functions directly give the 𝛼 -enhancements of thegalaxies when connected with the evolving oxygen-to-iron ratios(upper panels of Figure 5). The left panel of Figure 6 shows the cur-rent galactic mass formed per unit time, for groups of galaxies splitby [O/Fe] mean . The tracks closely resemble the actual star-formationhistories (left panel of Figure 4), scaled down by approximately fortypercent which corresponds to the integrated mass loss of an SSP(Wiersma et al. 2009b). This scaling is essentially uniform through-out cosmic history except for the most recent Gyr. Accordingly, theright panel of Figure 6 shows the current galactic iron mass formedper unit time, for groups of galaxies split by [O/Fe] gal . The tracks areessentially a convolution of the SFHs (right panel in Figure 4), theiron abundance histories (lower right panel in Figure 5), and the SSPmass loss effects. These tracks show quantitatively that younger starsare dominant for setting [O/Fe] gal , opposed to [O/Fe] mean which ismostly set by older stars. In order to explore the apparent relation between SFHs and the 𝛼 -enhancements of galaxies (Figure 4) in a quantitative way and on thelevel of individual galaxies, we parametrise galactic SFHs and in-vestigate the relation between their fitted parameters and [O/Fe] mean and [O/Fe] gal . Following Gladders et al. (2013) and Diemer et al. (2017) we describe SFHs of individual galaxies by log-normal func-tions, given by the following expression:SFR ( 𝑡 ) = 𝐴 √ 𝜋𝜏 × 𝑡 exp (cid:32) − (cid:0) ln ( 𝑡 ) − 𝑇 (cid:1) 𝜏 (cid:33) , (7)where 𝐴 , 𝑇 and 𝜏 are free parameters (the latter two haveunits of Gyr). For readability we refrain from inserting unit factorssuch as ln ( 𝑡 / ) into the equations in this section, and remarkthat we measure times always in Gyr and star-formation rates in 𝑀 (cid:12) yr − . We use the open-source lmfit package for python toexecute least-squares minimisations with the built-in Levenberg-Marquardt-algorithm, fitting Eqn. 7 to the simulated SFHs. Thesimulated SFHs are calculated as described in § 4.1 and age binswithout any star-formation are ignored by the fitting routine. Dueto the discrete nature and implementation of star-formation in thesimulation our calculated SFHs contain Poisson noise. FollowingMatthee & Schaye (2019) we calculate the associated error as 𝜎 ( 𝑡 ) = SFR ( 𝑡 )/√ 𝑁 , where 𝑁 is the number of star particles formed in aparticular age bin. Hence, the fitting routine effectively correspondsto a minimization of the following quantity: 𝜒 = ∑︁ 𝑡 = 𝑡 𝑖 (cid:16) SFR sim ( 𝑡 ) − SFR fit ( 𝑡 ) 𝜎 ( 𝑡 ) (cid:17) , (8)where the sum runs over all age bins (excluding bins withoutstar-formation activity). Following Diemer et al. (2017), we replace 𝑇 and 𝜏 with the more convenient peak time of the SFH ( 𝑡 peak ,Eqn. 9) and FWHM ( 𝜎 SFR , Eqn. 10): 𝑡 peak = exp (cid:0) 𝑇 − 𝜏 (cid:1) . (9) 𝜎 SFR = 𝑡 peak sinh (cid:0)√︁ ( ) 𝜏 (cid:1) . (10) MNRAS000 , 1–17 (2021) Gebek & Matthee t [Gyr]0.00.51.01.52.0 S F R [ M y r ] A =15.0 t peak =4.2 Gyr SFH =10.2 GyrGalaxy A (ID 12148340)0 2 4 6 8 10 12 t [Gyr]0.00.51.01.52.0 S F R [ M y r ] A =9.5 t peak =5.4 Gyr SFH =6.0 GyrGalaxy B (ID 2111838)0 2 4 6 8 10 12 t [Gyr]0.00.51.01.52.0 S F R [ M y r ] A =61.9 t peak =11.6 Gyr SFH =46.4 GyrGalaxy C (ID 10537185)FitNo PenaltyNo Errors M / t Figure 7.
Comparison of the fitted SFHs (black curves) for three star-forminggalaxies spanning a large range in 𝑡 peak and 𝜎 SFR . The SFR(t) of simulatedgalaxies are indicated as red points with the corresponding Poissonian errorbars. For comparison we also show the best-fitting log-normal SFHs withoutusing the penalty terms (dash-dotted yellow curves) and without weighingthe star-formation rates with Poisson noise (dashed blue curves). The fittedparameters which are written in the panels correspond to the regular fittingprocedure (black curves).
As noted by Diemer et al. (2017), a small fraction of galax-ies have rising SFHs today, leading to poorly conditioned log-normal fits with unphysically large values of 𝑡 peak and 𝜎 SFR .To address this effect we introduce a penalty term by multiply-ing the residuals with 1 + . (cid:0) log ( 𝑡 peak ) − log ( . ) (cid:1) if 𝑡 peak > . 𝜎 SFR >
20 Gyr we have a similar penaltyterm: 1 + . (cid:0) log ( 𝜎 SFR ) − log (
20 Gyr ) (cid:1) . Although some of the fitted peak times and SFH widths are significantly affected, thefit quality barely changes due to these penalty terms. 91 galaxies(out of the total star-forming sample of 1455 objects) have their 𝜒 (Eqn. 8) enlarged by more than one percent, 31 galaxies by morethan ten percent, and no galaxy experiences a change in 𝜒 largerthan sixty percent.Figure 7 shows fitted SFHs (black curves) for three galaxiesspanning a wide range in the 𝑡 peak - 𝜎 SFR -parameter space (thesegalaxies are marked in Figure 8). The unique galaxy IDs from theEAGLE galaxy catalogue are given in the headers. We illustratethe effect of the penalty terms through the yellow dash-dotted fits,which were calculated without multiplying the penalty terms. Onlythe SFH in the lowest panel exhibits visible differences betweenthe two SFHs. This is a galaxy with a SFH that increases up tothe present day leading to large values of 𝑡 peak and 𝜎 SFR (evenfor the regular fit invoking the penalty terms). We also show fitswithout using the Poisson noise 𝜎 ( 𝑡 ) (dashed blue curves), thesefits lie almost always slightly above the regular ones. This is becausethese fits are dominated by bins with large star-formation rates. Fora single age bin with a certain SFR, assume that the fitted star-formation rate deviates by a factor of 𝜅 . Without accounting forPoisson noise, we then have for this bin 𝜒 𝑖 = ( SFR − 𝜅 · SFR ) = ( − 𝜅 ) SFR ∝ SFR . Hence, bins with a comparatively large SFRreact more sensibly to (multiplicative) deviations of the fitted SFH.This scaling is weakened when invoking the Poisson noise, where 𝜒 𝑖 = ( SFR − 𝜅 · SFR ) /( SFR /√ 𝑁 ) ∝ SFR /√ SFR ∝ SFR.The regular fits using Poisson noise are still dominated by binswith large SFRs, but to a lesser extent compared to fitting routineswithout assigning errors.The parameter space that galaxy SFHs span in terms of 𝑡 peak and 𝜎 SFR is shown in Figure 8. We omit the normalisation 𝐴 in thisdiscussion as we did not find any relation between stellar mass and 𝛼 -enhancement for the galaxies in our star-forming sample with itsnarrow mass range. As Diemer et al. (2017) found using the cosmo-logical Illustris simulation, 𝑡 peak and 𝜎 SFR correlate approximatelylinearly in log-log space: log ( 𝜎 SFR ) = . ( 𝑡 peak ) − . ( 𝜎 SFR ) = .
17 log ( 𝑡 peak ) + .
12 (red line in Figure 8). Wenote that for our log-normal parameter distribution the power lawseems to be shallower at early times and becomes steeper for in-creasing 𝑡 peak , unlike in Diemer et al. (2017). Differences couldarise due to different galaxy samples (Diemer et al. 2017 considerall galaxies with 𝑀 ∗ ≥ 𝑀 (cid:12) ), different SFHs in EAGLE and Illustris (see Iyer et al. 2020 for an in-depth discussion on the differ-ences in SFHs of various cosmological and semi-analytical models)or varying fitting routines (Diemer et al. 2017 fit the cumulative SFHwith an integrated log-normal function, furthermore these authorsdo not assign Poisson noise).With the results from the SFH fitting routine we can investigatehow individual SFHs correlate with the 𝛼 -enhancements of thegalaxies, shown as color-coding in Figure 8. We make the followingobservations: • Galaxies with high [O/Fe] mean have small SFH widths, and -as subdominant effect - early peak times. • Galaxies with a low low-[O/Fe] mean are broadly located at thehigh- 𝑡 peak , high- 𝜎 SFR region. • Galaxies with high [O/Fe] gal have late peak times and - assubdominant effect - small SFH widths. • Galaxies with small [O/Fe] gal have early peak times and - assubdominant effect - small SFH widths.
MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs t peak [Gyr]510203040506070 S F R [ G y r ] [O/Fe] mean Diemer+2017This work 5 10 15 20 t peak [Gyr]510203040506070 S F R [ G y r ] C BA [O/Fe] gal
Figure 8.
Correlation of fitted SFH parameters with [O/Fe] mean and [O/Fe] gal . The range of the colorbar is limited and two rejuvenated galaxies with verysmall 𝑡 peak are excluded from the figure for optimal visualisation. The best-fitting power laws for the 𝑡 peak - 𝜎 SFR -relation from Diemer et al. (2017) (blue line)and this work (red line) are also shown. Furthermore, the individual galaxies investigated in Figure 7 are marked in the right panel.
Noting the first and the last point of this list, this explains whythe tracks of the high-[O/Fe] mean -galaxies and the low-[O/Fe] gal -ones closely resemble each other in Figure 4. In the following, weargue how these observed correlations between the SFH parame-ters, 𝜎 SFR and 𝑡 peak , and our two definitions of 𝛼 -enhancements ofgalaxies emerge.For [O/Fe] mean , small SFH widths correspond to 𝛼 -enhancedgalaxies, in line with many studies that explain the high 𝛼 -enhancement of passive galaxies through a fast and rapid SFH (e.g.Thomas et al. 2005; Arrigoni et al. 2010; Segers et al. 2016). Theparameter 𝑡 peak plays a subdominant role. Small peak times lead tomore stars forming from 𝛼 -enhanced gas, but galaxies with large 𝑡 peak can quickly enhance the oxygen-to-iron ratio in the ISM bya burst of star formation (i.e. small 𝜎 SFR ) and then form stars outof this 𝛼 -enhanced gas. Reverting this reasoning to explain howa galaxy has low [O/Fe] mean is apparently not straightforward, asthe correlation fades for larger 𝜎 SFR and 𝑡 peak . This weakeningof the correlation of SFHs and [O/Fe] mean for lower values of 𝛼 -enhancement is also visible in Figure 4, where the low-[O/Fe] mean -tracks are only weakly separated. We argue that this behaviour isdue to 𝜎 SFR being the dominant driver of mean 𝛼 -enhancement,and while a large 𝜎 SFR leads to stronger iron enrichment of theISM, the distributed star formation inevitably means that more starsare formed at early times when the ISM is very 𝛼 -enhanced. Thesetwo effects oppose each other such that the correlation fades at thelow-[O/Fe] mean -end. Crucially, the reasoning that 𝜎 SFR has two op-posing effects on [O/Fe] mean only applies to large peak times, elsewe would not observe any correlation at the high-[O/Fe] mean -end.This is because for small peak times, an extended SFH does not leadto more stars being formed at early times simply because there is aboundary at 𝑡 = gal correlatesmostly with 𝑡 peak and is only weakly dependent on the width ofthe star formation history. As remarked in § 4, the galactic 𝛼 -enhancement is dominated by younger stars, and hence to obtain a large [O/Fe] gal the galaxy must form as little iron as possible suchthat the younger stars are not too 𝛼 -suppressed. The peak time ismuch more important than the width of the SFH in terms of the totalsynthesized iron until today, with larger peak times correspondingto less iron and higher galactic 𝛼 -enhancement. A second-order ef-fect is that, once the peak time is already large, a small 𝜎 SFR furtherreduces the iron buildup and enhances [O/Fe] gal . Correspondingly,to obtain a small galactic 𝛼 -enhancement, the galaxy needs to syn-thesize as much iron as early as possible, which is achieved viasmall peak times and (as second-order effect) small SFH widths.This reasoning accounts for all features in Figure 8.We also note that the right panel in Figure 8 explains why atfixed mass, the galactic 𝛼 -enhancement correlates with sSFR (seeFigure 1 and Matthee & Schaye 2018). Compared to other galaxieswith the same mass, galaxies with a high sSFR at 𝑧 = 𝛼 -enhancement. Here we investigate the impact of variations in 𝛼 -enhancements onthe integrated galaxy spectra of star-forming galaxies. While the 𝛼 -enhancement of passive galaxies has been measured routinely, thecorresponding measurements for star-forming galaxies are relativelyunexplored territory. This is because the relevant spectral absorptionfeatures are typically much weaker in galaxies with younger stellarpopulations compared to passive galaxies (e.g. Conroy et al. 2014).Recently, spatially resolved spectroscopy (e.g. Neumann et al.2020) has allowed measurements of 𝛼 -enhancement in (parts of)relatively nearby star-forming galaxies. Moreover, Gallazzi et al.(2020) presented measurements of 𝛼 -enhancement in SDSS fibrespectra of the centers of star-forming galaxies. However, it is unclear MNRAS000
Noting the first and the last point of this list, this explains whythe tracks of the high-[O/Fe] mean -galaxies and the low-[O/Fe] gal -ones closely resemble each other in Figure 4. In the following, weargue how these observed correlations between the SFH parame-ters, 𝜎 SFR and 𝑡 peak , and our two definitions of 𝛼 -enhancements ofgalaxies emerge.For [O/Fe] mean , small SFH widths correspond to 𝛼 -enhancedgalaxies, in line with many studies that explain the high 𝛼 -enhancement of passive galaxies through a fast and rapid SFH (e.g.Thomas et al. 2005; Arrigoni et al. 2010; Segers et al. 2016). Theparameter 𝑡 peak plays a subdominant role. Small peak times lead tomore stars forming from 𝛼 -enhanced gas, but galaxies with large 𝑡 peak can quickly enhance the oxygen-to-iron ratio in the ISM bya burst of star formation (i.e. small 𝜎 SFR ) and then form stars outof this 𝛼 -enhanced gas. Reverting this reasoning to explain howa galaxy has low [O/Fe] mean is apparently not straightforward, asthe correlation fades for larger 𝜎 SFR and 𝑡 peak . This weakeningof the correlation of SFHs and [O/Fe] mean for lower values of 𝛼 -enhancement is also visible in Figure 4, where the low-[O/Fe] mean -tracks are only weakly separated. We argue that this behaviour isdue to 𝜎 SFR being the dominant driver of mean 𝛼 -enhancement,and while a large 𝜎 SFR leads to stronger iron enrichment of theISM, the distributed star formation inevitably means that more starsare formed at early times when the ISM is very 𝛼 -enhanced. Thesetwo effects oppose each other such that the correlation fades at thelow-[O/Fe] mean -end. Crucially, the reasoning that 𝜎 SFR has two op-posing effects on [O/Fe] mean only applies to large peak times, elsewe would not observe any correlation at the high-[O/Fe] mean -end.This is because for small peak times, an extended SFH does not leadto more stars being formed at early times simply because there is aboundary at 𝑡 = gal correlatesmostly with 𝑡 peak and is only weakly dependent on the width ofthe star formation history. As remarked in § 4, the galactic 𝛼 -enhancement is dominated by younger stars, and hence to obtain a large [O/Fe] gal the galaxy must form as little iron as possible suchthat the younger stars are not too 𝛼 -suppressed. The peak time ismuch more important than the width of the SFH in terms of the totalsynthesized iron until today, with larger peak times correspondingto less iron and higher galactic 𝛼 -enhancement. A second-order ef-fect is that, once the peak time is already large, a small 𝜎 SFR furtherreduces the iron buildup and enhances [O/Fe] gal . Correspondingly,to obtain a small galactic 𝛼 -enhancement, the galaxy needs to syn-thesize as much iron as early as possible, which is achieved viasmall peak times and (as second-order effect) small SFH widths.This reasoning accounts for all features in Figure 8.We also note that the right panel in Figure 8 explains why atfixed mass, the galactic 𝛼 -enhancement correlates with sSFR (seeFigure 1 and Matthee & Schaye 2018). Compared to other galaxieswith the same mass, galaxies with a high sSFR at 𝑧 = 𝛼 -enhancement. Here we investigate the impact of variations in 𝛼 -enhancements onthe integrated galaxy spectra of star-forming galaxies. While the 𝛼 -enhancement of passive galaxies has been measured routinely, thecorresponding measurements for star-forming galaxies are relativelyunexplored territory. This is because the relevant spectral absorptionfeatures are typically much weaker in galaxies with younger stellarpopulations compared to passive galaxies (e.g. Conroy et al. 2014).Recently, spatially resolved spectroscopy (e.g. Neumann et al.2020) has allowed measurements of 𝛼 -enhancement in (parts of)relatively nearby star-forming galaxies. Moreover, Gallazzi et al.(2020) presented measurements of 𝛼 -enhancement in SDSS fibrespectra of the centers of star-forming galaxies. However, it is unclear MNRAS000 , 1–17 (2021) Gebek & Matthee whether the methodology (i.e. calibrations of combinations of Lickindices) that has been used for passive galaxies can be appliedto star-forming galaxies. In this section we therefore explore thecharacter and strength of the expected spectral signatures dependingon [O/Fe] mean and [O/Fe] gal . As a simple approach to model SEDs of EAGLE galaxies, we usethe MILES SSP models (Vazdekis et al. 2015) which cover thewavelength range 3525-7500 Å (with a spectral resolution of 0.9 Å)to model the SEDs of the star particles in the simulated galax-ies. MILES is an empirical library containing self-consistent 𝛼 -enhanced models for the BaSTI isochrones which take the impactof [ 𝛼 /Fe] on the isochrones into account. We use a Chabrier IMF(Chabrier 2003) throughout for consistency with EAGLE. We inter-polate the age, metallicity and 𝛼 -enhancement of the star particles(with initial masses M star = M (cid:12) ) in the simulated galaxies tothe MILES parameter grid which spans ages from 0.03 to 14 Gyr(53 values), metallicities from -2.27 to 0.4 (12 values) and two val-ues of 𝛼 -enhancement (0 and +0.4). Unfortunately, there are onlyvery few self-consistent SSP libraries with an extended range of 𝛼 -enhancements. While having only two possible 𝛼 -enhancementsfor the SSP models is not optimal, the global 𝛼 -enhancements ofthe galaxies (i.e. [O/Fe] mean and [O/Fe] gal ) are still captured sincewe average over > 𝛼 -enhancements we normalise all SEDs by their integratedluminosity over the wavelength region of the magnesium and ironfeatures between ( − ) Å. 𝑏 , Fe5270 and Fe5335 The relative strengths of the Mg 𝑏 , Fe5270 and Fe5335 Lick indicesare known to be sensitive to variations in [ 𝛼 /Fe] (e.g. McQuitty et al.1994; Trager et al. 1998). Recently, Gonçalves et al. (2020) indeedshowed that these features lie in the wavelength region that is mostoptimal for measuring [ 𝛼 /Fe] in integrated spectra. Hence, for thisshort discussion, we focus on the wavelength region encompassingthese features.For the analysis of how [O/Fe] mean and [O/Fe] gal leave imprintson the SEDs, we bin the galaxies in our sample into eight subsetsordered by 𝛼 -enhancement (as done in § 4.1). We calculate medianSEDs for each of these subsets and divide these by the median SEDof our entire galaxy sample. This therefore shows the change in theSED as one varies the 𝛼 -enhancement. The result of this calculationis shown in Figure 9, with the same color-coding as in Figure 4. Itis clear that variations in [ 𝛼 /Fe], despite that these variations aresmall, can be seen in the integrated spectra of star-forming galax-ies. Comparing the two definitions of 𝛼 -enhancement, we see thatthe changes in the SEDs with increasing [ 𝛼 /Fe] behave oppositely,similar to the behaviour of the variations in their SFHs shown inFigure 4. The differences are larger for variations in [O/Fe] gal be-cause we have seen that the galactic 𝛼 -enhancement is impactedrelatively more by younger stars which dominate the SED. Table 2.
Pearson-r correlation coefficients between the Mg 𝑏 /(cid:104) Fe (cid:105) index andproperties of the stellar populations in our sample of star-forming galaxies.We investigate both mass-weighted (MW) and light-weighted (LW) quanti-ties and show the results for the regular synthetic SEDs where variations inthe stellar 𝛼 /Fe are accounted for and for the synthetic SEDs where [ 𝛼 /Fe]is fixed to the solar value.SED type Weighting Age Z [O/Fe] mean [O/Fe] gal Regular MW 0.42 0.34 0.40 -0.15LW 0.74 0.3 0.54 -0.50Fixed [ 𝛼 /Fe] MW 0.73 0.71 0.19 -0.61LW 0.92 0.64 0.15 -0.84 We notice that the Mg 𝑏 , Fe5270 and Fe5335 lines clearly varywith varying 𝛼 -enhancement, with variations of ≈ mean and [O/Fe] gal , respectively). These variations aretherefore second-order effects (as the strengths of the absorptionlines are on the order of 20 %), but they are observable when thesignal-to-noise ratio of spectra is >
30 per resolution element of 2.5Å (which is the resolution of the MILES spectra that we use).To address whether the observed variations in the spectra aredue to variations in the 𝛼 -enhancements of stellar atmospheres, weperform the following test. We create alternative synthetic SEDs ofthe simulated galaxies where we fix the [ 𝛼 /Fe] of the star particles tothe solar value, instead of using the actual value. Then, we repeat theanalysis and show the relative changes in the SEDs when varyingthe mean and the galactic 𝛼 -enhancement. The results are shown inFigure 10. For visualisation purposes we only show the normalisedSEDs of the high and low extremes of the 𝛼 -enhancement distri-butions. The dot-dashed (fixed [ 𝛼 /Fe]) and solid (varying [ 𝛼 /Fe])lines are basically indistinguishable with differences on the (cid:46) . 𝛼 /Fe] are not caused by them, butrather trace underlying correlations between the absorption linesand the stellar age and metallicity distributions. 𝑏 /(cid:104) Fe (cid:105) In integrated galaxy spectra the measurement of 𝛼 -enhancementhas often been based on Mg 𝑏 /(cid:104) Fe (cid:105) (e.g. Gallazzi et al. 2020),where (cid:104) Fe (cid:105) = . ( Fe5270 + Fe5335 ) . We explore how well thisindex correlates with [O/Fe] mean , [O/Fe] gal and other propertiesof the stellar populations in simulated galaxies. In addition to themass-weighted quantities we have been using so far we also showthe correlation coefficients for the corresponding light-weightedquantities, such that for instance the stellar masses in Eqns. 1 and 3are replaced by stellar luminosities (integrated over the MILESwavelength range of 3525-7500 Å). We explore both the regularSEDs and the SEDs calculated with 𝛼 /Fe fixed to the solar value.The results are listed in Table 2.From Table 2 it is clear that, for our sample of star-forminggalaxies, Mg 𝑏 /(cid:104) Fe (cid:105) varies mostly with the light-weighted age of thestellar populations. The index is not strongly correlated with mass-weighted 𝛼 -enhancements, but there is a mild correlation with thelight-weighted 𝛼 -enhancements. These correlations are however notindependent of the light-weighted age. Indeed, Figure 11 shows thatthere is no evidence for variations in Mg 𝑏 /(cid:104) Fe (cid:105) that correlate withvariations in the 𝛼 -enhancement and are independent of variationsin the light-weighted age. This demonstrates that the variations in MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs Å ]0.960.981.001.021.04 S E D [O/Fe] mean Å ]0.960.981.001.021.04 S E D [O/Fe] gal Figure 9.
The impact of variations in 𝛼 -enhancements in the median spectra of star-forming galaxies. The left panel shows variations in [O/Fe] mean and theright panel shows variations in [O/Fe] gal . Each line shows the spectrum of an 𝛼 -enhancement bin (equivalent color-coding as in Figure 4, red being the mostenhanced and blue the least) relative to the median spectrum of all star-forming galaxies. Shown is the wavelength region containing the Mg b (around 5170 Å)and the Fe5270 and Fe5335 features. Å ]0.970.980.991.001.011.021.031.04 S E D [O/Fe] mean Low, RegularLow, Fixed 5150 5200 5250 5300 5350[ Å ]0.970.980.991.001.011.021.031.04 S E D [O/Fe] gal High, RegularHigh, Fixed
Figure 10.
Median SEDs (as in Figure 9) of the two subsets with the highest (red) and lowest (blue) 𝛼 -enhancements for [O/Fe] mean (left) and [O/Fe] gal (right),respectively. The solid lines show the synthetic SEDs taking the actual [ 𝛼 /Fe] of the star particles into account, while the dash-dotted lines show the syntheticSEDs assigning all star particles a fixed solar 𝛼 -enhancement. Mg 𝑏 /(cid:104) Fe (cid:105) in our simulated spectra are mostly due to variations inage. We can learn more about this result by looking at the correla-tions between Mg 𝑏 /(cid:104) Fe (cid:105) and the properties in the SEDs computedwith fixed [ 𝛼 /Fe]. The correlation coefficients are now even strongerwith age, metallicity and the 𝛼 -enhancements. This implies that thespectral variations induced by differences in the [ 𝛼 /Fe] abundancesin the stellar atmospheres are somewhat in the opposite directioncompared to the (much larger) spectral variations due to age andmetallicity.We stress that these results do not necessarily mean that mea-surements of the Mg 𝑏 /(cid:104) Fe (cid:105) index are always measuring age varia- tions instead of 𝛼 /Fe variations – it depends of the actual amount ofvariation in [ 𝛼 /Fe]. Besides the correlation coefficients between theMg 𝑏 /(cid:104) Fe (cid:105) index and the properties listed in Table 2, we find thatthe average value (i.e. the normalisation) of Mg 𝑏 /(cid:104) Fe (cid:105) is higherby ≈ + .
15 in the regular SEDs compared to the SEDs that areconstructed with solar [ 𝛼 /Fe]. On average, the difference betweenthe solar [ 𝛼 /Fe] and the actual [ 𝛼 /Fe] are +0.2 and +0.3 dex for thegalactic and mean 𝛼 -enhancement, respectively. This means thatvariations in [ 𝛼 /Fe] that are on the order > . 𝑏 /(cid:104) Fe (cid:105) and can thus be measured(e.g. Gallazzi et al. 2020). However, the variations of [ 𝛼 /Fe] amongthe simulated star-forming galaxies in our study are much smaller MNRAS000
15 in the regular SEDs compared to the SEDs that areconstructed with solar [ 𝛼 /Fe]. On average, the difference betweenthe solar [ 𝛼 /Fe] and the actual [ 𝛼 /Fe] are +0.2 and +0.3 dex for thegalactic and mean 𝛼 -enhancement, respectively. This means thatvariations in [ 𝛼 /Fe] that are on the order > . 𝑏 /(cid:104) Fe (cid:105) and can thus be measured(e.g. Gallazzi et al. 2020). However, the variations of [ 𝛼 /Fe] amongthe simulated star-forming galaxies in our study are much smaller MNRAS000 , 1–17 (2021) Gebek & Matthee LW [Gyr]0.500.550.600.650.70 M g b / F e [ O / F e ] L W m e a n Figure 11.
The correlation between the Mg 𝑏 /(cid:104) Fe (cid:105) index and the light-weighted age in the sample of star-forming galaxies using synthetic spectrathat take variations in [ 𝛼 /Fe] into account. The colour-coding shows thelight-weighted [O/Fe] mean and shows that there are no significant variationsin the spectral index that correlate with [O/Fe] mean at fixed age. ( 𝜎 ≈ .
03 dex). In this regime, we thus conclude that the changes inMg 𝑏 /(cid:104) Fe (cid:105) are particularly due to variations in the age distribution.Therefore, this implies a systematic lower limit of the degree ofvariations in [ 𝛼 /Fe] of ≈ . 𝛼 /Fe] (e.g. Robotham et al. 2020) are notheavily affected by this assumption for star-forming galaxies. We have seen that while variations in 𝛼 /Fe are correlated withvariations in the observed spectra of star-forming galaxies, thesemostly trace differences in the age and metallicity distributions ofstars. As comparison and discussion, here we also perform severalparts of our analysis for central passive galaxies with masses above 𝑀 ∗ = × M (cid:12) which are devoid of star formation. We repeat the calculation of the synthetic spectra for subsets ofgalaxies split by 𝛼 -enhancement for this passive sample, and showthe result in Figure 12. Although the contrast in the absorptionfeatures is still just ≈ 𝛼 -enhancements appears more feasi-ble. Due to the positive correlation between the mean and galactic 𝛼 -enhancement for passive galaxies (see Figure 3), the spectralvariations in both panels coincide. Unlike the synthetic spectra ofstar-foming galaxies, we notice that the absorption features frommagnesium and iron lines are now anti-correlated in the expectedway, with 𝛼 -enhanced galaxies having comparatively large magne-sium and weak iron lines, respectively. Mg 𝑏 /(cid:104) Fe (cid:105) and galaxy properties We investigate the correlations between the Mg 𝑏 /(cid:104) Fe (cid:105) index andvarious galactic properties for the sample of passive galaxies. The Table 3.
Pearson-r correlation coefficients between the Mg 𝑏 /(cid:104) Fe (cid:105) indexand properties of the stellar populations in our sample of passive galaxies(see Table 1).SED type Weighting Age Z [O/Fe] mean [O/Fe] gal Regular MW 0.40 0.52 0.43 0.75LW 0.50 0.40 0.51 0.85Fixed [ 𝛼 /Fe] MW 0.19 0.89 -0.02 0.11LW 0.26 0.89 0.06 0.25 index varies from 0.70 to 0.89 for the 27 galaxies in this sample,to be compared to a range from 0.48 to 0.72 for the galaxies inthe star-forming sample. The Pearson-r coefficients for the corre-lations of Mg 𝑏 /(cid:104) Fe (cid:105) with various galactic properties are listed inTable 3. In stark contrast to the star-forming sample, the passivesample has a moderately (strong) correlation between [O/Fe] mean ([O/Fe] gal ) and Mg 𝑏 /(cid:104) Fe (cid:105) which vanishes when calculating thesynthetic SEDs with a fixed [ 𝛼 /Fe] for the stellar atmospheres. Thisdemonstrates that the observed variations in the index are indeeddue to variations in the [ 𝛼 /Fe] distribution of stars and not due toconfounding variables such as stellar age. It is interesting to notethat the index correlates most strongly with [O/Fe] gal , which wehave shown that can be interpreted as the the metallicity-averaged[ 𝛼 /Fe] of the galaxy. For passive galaxies, a wealth of studies have described the con-nection between star-formation histories and 𝛼 -enhancement. In apioneering study, Thomas et al. (2005) quantitatively describe thisconnection as [ 𝛼 / Fe ] ≈ / − / Δ 𝑡 , where [ 𝛼 / Fe ] is the 𝑉 -band luminosity-weighted mean 𝛼 -enhancement (see their sec-tion 6.1) and Δ 𝑡 corresponds to the FWHM of a SFH characterisedby a Gaussian. Figure 8 displays a very similar relation, where the 𝛼 -enhancements of galaxies are plotted in the 𝑡 peak - 𝜎 SFR -plane.Here we fit the following linear relation of SFH parameters to thelight-weighted [O/Fe]
LWmean and [O/Fe]
LWgal : [ O / Fe ] LWmean / gal = 𝑎 log 𝑡 peak + 𝑏 log 𝜎 SFR + 𝑐, (11)where the SFH parameters are measured in Gyr. We use the python lmfit package to find the free parameters 𝑎 , 𝑏 and 𝑐 andtheir uncertainties in Eqn. 11. The resulting parameters for both thestar-forming and the passive sample are listed in Table 4. The resultsfor the relation between SFH parameters and 𝛼 -enhancements areconsistent with those presented in Figures 4 and 8 for the star-forming sample. We remark that the linear approximation of Eqn. 11is a poor description for the mean 𝛼 -enhancement of this sample.For the mean 𝛼 -enhancement of the passive sample, whichis the quantity closest to the one used by Thomas et al. (2005),we find 𝜎 SFR6 a slope of 𝑏 = − .
20 which is very comparable to1 /
6. We therefore confirm the canonical result that variations in 𝛼 /Fe correlate with the compactness of the star formation history.Additionally, we find a 𝑡 peak slope of 𝑎 = − .
19, indicating that Technically, Thomas et al. (2005) use a slightly different quantity than theone defined in Eqn. 1 as they swap the operational order of averaging andlogarithm. We remark that 𝜎 SFR is defined as the FWHM of a log-normal SFH, andhence comparable to the FWHM Δ 𝑡 of a Gaussian SFH used by Thomaset al. (2005). MNRAS , 1–17 (2021) lpha-Enhancement in simulated SFGs Å ]0.960.981.001.021.04 S E D [O/Fe] mean Å ]0.960.981.001.021.04 S E D [O/Fe] gal Figure 12.
Same as Figure 9, but for the passive sample (see Table 1). The left panel shows variations in [O/Fe] mean and the right panel shows variations in[O/Fe] gal . Each line shows the spectrum of an 𝛼 -enhancement bin (equivalent color-coding as in Figure 4, red being the most enhanced and blue the least)relative to the median spectrum of all passive galaxies. Shown is the wavelength region containing the Mg b (around 5170 Å) and the Fe5270 and Fe5335features. Table 4.
Best-fitting parameters to predict light-weighted mean and galactic 𝛼 -enhancement from SFH parameters (Eqn. 11) for the samples of star-forming galaxies and passive galaxies. 𝑎 and 𝑏 denote the correlations with 𝑡 peak and 𝜎 SFR , 𝑐 is the normalisation.Quantity 𝑎 𝑏 𝑐 Star-forming[O/Fe]
LWmean . ± . − . ± .
004 0 . ± . LWgal . ± .
008 0 . ± . − . ± . LWmean − . ± . − . ± .
04 0 . ± . LWgal . ± . − . ± .
07 0 . ± . early-peaked SFHs additionally lead to large mean 𝛼 -enhancementsfor passive galaxies.For [O/Fe] gal , we find a strong negative correlation with 𝜎 SFR ( 𝑏 = − . 𝑡 peak is not significant. Aswe have seen that the Mg 𝑏 /(cid:104) Fe (cid:105) index most strongly correlates with[O/Fe] gal , this result therefore confirms that the observed spectralvariations in passive galaxies are mostly sensitive to variations in 𝛼 /Fe that are caused by different widths of the star formation historyand not necessarily the peak time. Here we discuss the limitations of our paper and further directionsin which our understanding of variations in 𝛼 -enhancements can beimproved.On the simulation side, there are several limitations to ourstudy. First, our results rely on a single hydrodynamical simulationwith a sub-grid model for stellar yields and the delay time distribu-tion of Type Ia supernovae (Wiersma et al. 2009b). Therefore ourresults could quantitatively change somewhat in case any of thesemodels can be improved. To first order, we expect small effects.Different yields would only change the normalisation of 𝛼 /Fe and a different delay time distribution may lead to a slightly differentrelation between age, 𝑍 and 𝛼 /Fe. Second, the IMF is assumed tobe fixed. In case the IMF would vary, the relative amounts of TypeII to Type Ia SNe could change, impacting the 𝛼 -enhancement (e.g.Barber et al. 2019). Such variations could be quite complicated, asIMF variations may be (indirectly) correlated with the SFH. Thiscould be addressed in a future study.On the analysis side, we note that we have only parametrised thestar formation history, and not the chemical evolution history. Onewould expect that the chemical evolution is tied to the star formationhistory (see for instance a model that is used in the ProSpect SEDgenerator code; Robotham et al. 2020). However, we note that such aconnection may not be straightforward because chemical evolutionhistory is also influenced by metal-enriched gas in- and outflows.These on themselves could be correlated with the SFH in a complexway. A parametrised connection between the SFH and chemicalenrichment is appealing particularly as it could be used as prior forfitting of observed spectra.In this paper we only focused on the 𝛼 -enhancements of thefull simulated galaxy (i.e. subhalo). It could be interesting to studyspatial gradients in 𝛼 -enhancement as they will yield informationon the way galaxies build-up. In particular it will be interesting tofocus on the bulges of star-forming galaxies, as it will likely beeasier to observe 𝛼 -variations there than in the spiral arms.Finally, in the future the synthetic SEDs can be improved in var-ious ways. Improved libraries with a finer grid in 𝛼 /Fe ratios wouldbe welcomed. It is possible that short-term burstiness of the SFHsis underestimated due to the resolution of the EAGLE simulation(e.g. Iyer et al. 2020). This could result in an underestimate of thecontribution of the flat-continuum spectra from youngest stars to theintegrated spectra and therefore result in overestimated absorptionline strengths. Furthermore the effects of relative dust attenuationof young and old stars could be investigated. MNRAS000
07 0 . ± . early-peaked SFHs additionally lead to large mean 𝛼 -enhancementsfor passive galaxies.For [O/Fe] gal , we find a strong negative correlation with 𝜎 SFR ( 𝑏 = − . 𝑡 peak is not significant. Aswe have seen that the Mg 𝑏 /(cid:104) Fe (cid:105) index most strongly correlates with[O/Fe] gal , this result therefore confirms that the observed spectralvariations in passive galaxies are mostly sensitive to variations in 𝛼 /Fe that are caused by different widths of the star formation historyand not necessarily the peak time. Here we discuss the limitations of our paper and further directionsin which our understanding of variations in 𝛼 -enhancements can beimproved.On the simulation side, there are several limitations to ourstudy. First, our results rely on a single hydrodynamical simulationwith a sub-grid model for stellar yields and the delay time distribu-tion of Type Ia supernovae (Wiersma et al. 2009b). Therefore ourresults could quantitatively change somewhat in case any of thesemodels can be improved. To first order, we expect small effects.Different yields would only change the normalisation of 𝛼 /Fe and a different delay time distribution may lead to a slightly differentrelation between age, 𝑍 and 𝛼 /Fe. Second, the IMF is assumed tobe fixed. In case the IMF would vary, the relative amounts of TypeII to Type Ia SNe could change, impacting the 𝛼 -enhancement (e.g.Barber et al. 2019). Such variations could be quite complicated, asIMF variations may be (indirectly) correlated with the SFH. Thiscould be addressed in a future study.On the analysis side, we note that we have only parametrised thestar formation history, and not the chemical evolution history. Onewould expect that the chemical evolution is tied to the star formationhistory (see for instance a model that is used in the ProSpect SEDgenerator code; Robotham et al. 2020). However, we note that such aconnection may not be straightforward because chemical evolutionhistory is also influenced by metal-enriched gas in- and outflows.These on themselves could be correlated with the SFH in a complexway. A parametrised connection between the SFH and chemicalenrichment is appealing particularly as it could be used as prior forfitting of observed spectra.In this paper we only focused on the 𝛼 -enhancements of thefull simulated galaxy (i.e. subhalo). It could be interesting to studyspatial gradients in 𝛼 -enhancement as they will yield informationon the way galaxies build-up. In particular it will be interesting tofocus on the bulges of star-forming galaxies, as it will likely beeasier to observe 𝛼 -variations there than in the spiral arms.Finally, in the future the synthetic SEDs can be improved in var-ious ways. Improved libraries with a finer grid in 𝛼 /Fe ratios wouldbe welcomed. It is possible that short-term burstiness of the SFHsis underestimated due to the resolution of the EAGLE simulation(e.g. Iyer et al. 2020). This could result in an underestimate of thecontribution of the flat-continuum spectra from youngest stars to theintegrated spectra and therefore result in overestimated absorptionline strengths. Furthermore the effects of relative dust attenuationof young and old stars could be investigated. MNRAS000 , 1–17 (2021) Gebek & Matthee
In this paper we investigated the origin of variations in stellar 𝛼 -enhancements of star-forming galaxies in the EAGLE simulationin the present-day Universe. Oxygen is used as a proxy for the 𝛼 -abundance throughout our paper. We investigated two distinct defi-nitions of 𝛼 -enhancement, their connection to the star formation andchemical enrichment histories and their impact on integrated syn-thetic spectra. We discussed our results in the context of interpretingobserved spectra and compared our results to the previously studied 𝛼 -enhancement variations in passive galaxies. The following pointssummarize our main findings: • The stellar 𝛼 -enhancement of a star-forming galaxy is notuniquely defined. We present two definitions of 𝛼 -enhancement:mean 𝛼 -enhancement [O/Fe] mean (the mass-weighted averageoxygen-to-iron ratio, Eqn. 1) and galactic 𝛼 -enhancement [O/Fe] gal (the ratio of the galactic oxygen abundance to the galactic ironabundance, Eqn. 2). Both definitions of 𝛼 -enhancement of galaxiescorrespond to the same quantity, the stellar oxygen-to-iron ratio,but they are weighted differently. For [O/Fe] mean , each star (or SSP)is weighted by its current mass, while for [O/Fe] gal , each star isweighted by its current iron mass. • Applying these two definitions to a mass-limited sample(5 × M (cid:12) < 𝑀 ∗ < M (cid:12) ) of star-forming galaxies fromthe EAGLE simulation, we find that [O/Fe] mean and [O/Fe] gal are slightly anti-correlated (Figure 3). For a high-mass sample( 𝑀 ∗ > × M (cid:12) ) of passive central galaxies, the two defini-tions correlate strongly. • We find, in accordance with previous studies targeting the 𝛼 -enhancement of passive galaxies, that star formation historiesare crucial in determining the 𝛼 -enhancements of the star-forminggalaxies. When splitting the star-forming galaxies according to their[O/Fe] mean or [O/Fe] gal , we discover a distinct trend such that agalaxy with a high-[O/Fe] mean and/or a low-[O/Fe] gal has an earlyand rapid star formation history and vice versa (Figure 4). • The reversed dependence of the two definitions of 𝛼 -enhancement on the SFH can be explained when taking both thegalactic chemical evolution (Figure 5) and the different weight-ing functions (Figure 6) into account. [O/Fe] mean follows the well-known trend of passive galaxies such that early-peaked, compactSFHs lead to a high 𝛼 -enhancement. However, the iron-weightingfor [O/Fe] gal leads to young stars dominating this quantity. Hence,to acquire a large galactic 𝛼 -enhancement, it is more ‘efficient’ todelay star formation in order to boost the oxygen-to-iron ratio of theyoungest stars instead of having a very rapid SFH. • By fitting individual star-formation histories with log-normalfunctions, we explore the correlation of the 𝛼 -enhancements ofstar-forming galaxies with SFHs at the level of individual galaxies.Interestingly, [O/Fe] mean is mostly correlated with the width of thestar-formation history 𝜎 SFR , while [O/Fe] gal is mostly correlatedwith the peak time 𝑡 peak (Figure 8). For [O/Fe] mean , the correlationfades at the low-[O/Fe] mean -end. • We investigate the impact of 𝛼 /Fe variations on synthetic inte-grated spectra by mapping the star particles in simulated galaxies toSSP models with different levels of 𝛼 -enhancement and metallicityfrom MILES. We show that variations in well-known absorptionlines as Mg 𝑏 , Fe5270 and Fe5335 correlate with variations in 𝛼 -enhancements (Figure 9). However, the spectral differences can beattributed to variations in the age distribution of the star particles,and they are not due to [ 𝛼 /Fe] variations of the stellar atmospheresthemselves (Figure 11). This is because, for the dynamic range of[ 𝛼 /Fe] variations in our simulated star-forming galaxies, spectra are not significantly affected. If star-forming galaxies have larger, > . 𝛼 -enhancements they may have anobservable imprint on Mg 𝑏 /(cid:104) Fe (cid:105) that is independent of the SFH. • Finally, as a comparison, we perform a similar analysis forsimulated passive galaxies (§6). We confirm earlier results thatvariations in 𝛼 -enhancements in these galaxies correlate with thecompactness of the star-formation history and that these variationscause spectral variations of, for example, the Mg 𝑏 /(cid:104) Fe (cid:105) index.This work shows that the star formation histories of star-forming galaxies determine their 𝛼 -enhancements, similar as pas-sive galaxies. However, results for the 𝛼 -enhancement of passivegalaxies cannot be extended to star-forming galaxies in a straight-forward fashion. We stress that both for observational and theoreticalstudies of 𝛼 -enhancement in the context of star-forming galaxies,[ 𝛼 /Fe] should be carefully defined. Furthermore, while measure-ments of [ 𝛼 /Fe] from the integrated light of star-forming galaxiesare difficult when relying on magnesium and iron Lick indices, theymight be possible in spectra with very high signal-to-noise ratio andadvanced retrieval methods.With respect to resolved measurements of age, metallicity and 𝛼 -enhancement simultaneously in stars in very local galaxies, ourresults imply that both the width and the peak time of the SFHcan be retrieved by weighting the individual 𝛼 -enhancements dif-ferently. Ultimately variations in SFHs can be related to variationsin dark matter accretion histories on long time-scales, and thereforefuture measurements of the variation of 𝛼 -enhancements amongstar-forming galaxies can provide unique information on the growthof structure on the longest time-scales. ACKNOWLEDGEMENTS
Topcat (Taylor2013) and the programming language
Python , including the numpy (van der Walt et al. 2011), matplotlib (Hunter 2007) and scipy (Virtanen et al. 2020) packages.
DATA AVAILABILITY
All simulation data used in this work is accessible through the web-site of the EAGLE project (http://icc.dur.ac.uk/Eagle/). The galaxycatalogues are described by McAlpine et al. (2016) and the particledata by The EAGLE team (2017).
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