He abundances in disc galaxies -- I. Predictions from cosmological chemodynamical simulations
Fiorenzo Vincenzo, Andrea Miglio, Chiaki Kobayashi, J. Ted Mackereth, Josefina Montalban
AAstronomy & Astrophysics manuscript no. Vincenzo2019_AA c (cid:13)
ESO 2019July 25, 2019
He abundances in disc galaxies – I. Predictions from cosmologicalchemodynamical simulations
Fiorenzo Vincenzo , Andrea Miglio , Chiaki Kobayashi , J. Ted Mackereth , Josefina Montalban School of Physics and Astronomy, University of Birmingham, Edgbaston, B15 2TT, UKe-mail: [email protected] Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, UKJuly 25, 2019
ABSTRACT
We investigate how the stellar and gas-phase He abundances evolve as functions of time within simulated star-forming disc galaxieswith di ff erent star formation histories. We make use of a cosmological chemodynamical simulation for galaxy formation and evolution,which includes star formation, as well as energy and chemical enrichment feedback from asymptotic giant branch stars, core-collapsesupernovae, and Type Ia supernovae. The predicted relations between the He mass fraction, Y , and the metallicity, Z , in the interstellarmedium of our simulated disc galaxies depend on the past galaxy star formation history. In particular, dY / dZ is not constant andevolves as a function of time, depending on the specific chemical element that we choose to trace Z ; in particular, dY / dX O and dY / dX C increase as functions of time, whereas dY / dX N decreases. In the gas-phase, we find negative radial gradients of Y , due tothe inside-out growth of our simulated galaxy discs as a function of time; this gives rise to longer chemical enrichment time scalesin the outer galaxy regions, where we find lower average values for Y and Z . Finally, by means of chemical evolution models, in thegalactic bulge and inner disc, we predict steeper Y versus age relations at high Z than in the outer galaxy regions. We conclude that,for calibrating the assumed Y - Z relation in stellar models, C, N, and C + N are better proxies for the metallicity than O, because theyshow steeper and less scattered relations.
Key words. galaxies: abundances — galaxies: evolution — ISM: abundances — stars: abundances — hydrodynamics
1. Introduction
In order to study the star formation history (SFH) of our Galaxy,undestanding how He abundances are distributed in the stars andinterstellar medium (ISM) is fundamental for a precise estimateof stellar ages for di ff erent metallicity and star-formation enviro-ments (Iben 1968; Chiosi & Matteucci 1982; Fields 1996; Chi-appini et al. 2002; Jimenez et al. 2003; Romano et al. 2007). Stel-lar ages in our Galaxy are typically inferred either by fitting theobserved colour-magnitude diagram (CMD) with a set of stellarisochrones (e.g., Bensby et al. 2014), or by adding asteroseismicconstraints (Casagrande et al. 2016; Silva Aguirre & Serenelli2016; Miglio et al. 2017; Silva Aguirre et al. 2018). In both casesthe resulting age distributions rely on the assumptions and un-derlying physics of stellar models (Casagrande et al. 2007; Le-breton et al. 2014). One of the most important assumptions ofstellar models is given by the initial He content of the stars, andstellar models are usually calibrated by assuming a linear scalingrelation between the He mass fraction, Y (cid:63) = M He / M (cid:63) , and thestellar metallicity, Z (cid:63) (which may be obtained from absorptionlines in stellar spectra) (e.g., Pagel & Portinari 1998).Historically, helium abundances in the stars of our Galaxycould be directly measured only in the photospheres of O- andB-type stars (Struve 1928; Shipman & Strom 1970; Morel etal. 2006; Nieva & Przybilla 2012), because in the later spec-tral types there are no strong He absorption features for accuratespectroscopic analysis. Helium abundances in the ISM of galax-ies can be directly measured within Galactic and extragalacticHII regions, by making use of optical He recombination lines(e.g., HeI λ λ λ λ dY / dZ , ranging in the interval [1 . , . . Thismakes the best calibration for Y = Y ( Z , t ) to assume in stellarmodels highly uncertain, from both an observational and the- We address the readers to the following website hosted by the Uni-versity of Rochester for a referenced list of measured dY / dZ from dif-ferent sources in the literature, put together by Eric Mamajek: .Article number, page 1 of 13 a r X i v : . [ a s t r o - ph . GA ] J u l & A proofs: manuscript no. Vincenzo2019_AA
Fig. 1.
The predicted age distribution of the stellar populations in ourthree reference galaxies. The curves are such that the area below eachof them corresponds to the galaxy stellar mass at redshift z = Fig. 2. (a)
The average IMF-weighted stellar yields of He from massivestars as functions of the initial stellar metallicity, as predicted by thestellar models of Nomoto et al. (2013, black solid line) and Limongi& Chie ffi (2018) for di ff erent stellar rotational velocities; in particular,the blue, green, and orange lines correspond to the Limongi & Chie ffi (2018) stellar models with v rot =
0, 150, and 300 km s − , respectively. (b) The average IMF-weighted stellar yields of He from AGB stars asfunctions of the initial stellar metallicity, as predicted by the stellar mod-els of Karakas (2010, black solid line) and Ventura et al. (2013, bluesolid line). oretical point of view (Casagrande et al. 2007; Portinari et al.2010; Gennaro et al. 2010); this results – in turn – in a large un-certainty in the final estimate of stellar ages. In particular, theimpact of assumed dY / dZ may give rise to relative variations inthe measurement of stellar ages from asteroseismic analysis ashigh as ∼
40 per cent (Lebreton et al. 2014, Miglio et al., inprep.). Moreover, Nataf & Gould (2012) pointed out that theremay be critical issues in determining the ages of Galactic bulgestars if dY / dZ (cid:44) const (see also Renzini et al. 2018).It is therefore important to investigate how the He contentin the ISM and in the stars of galaxies depends on the metal- Fig. 3.
The predicted ejection rate of He from stellar populations of dif-ferent metallicities (di ff erent colours) by assuming the stellar yields ofNomoto et al. (2013). The gray shaded area corresponds to our pre-dictions when assuming the Limongi & Chie ffi (2018) set of stellaryields of rotating massive stars with di ff erent metallicities ([Fe / H] = − −
2, and − v rot =
0, 150,and 300 km s − ). The blue shaded horizontal region corresponds to thechemical enrichment of super-AGB stars which are not included in ourgalactic chemical evolution model. licity and SFH. In this paper, we present the first attempt tostudy how He is produced and then released by ageing stellarpopulations in galaxies, by making use of a state-of-the-art cos-mological chemodynamical simulation (Vincenzo & Kobayashi2018a,b).Our paper is structured as follows. In Section 2, we sum-marise the main characteristics of our cosmological hydrody-namical simulation. In Section 3, we describe how He is de-posited by ageing stellar populations of di ff erent metallicities inour simulation, trying to quantify the uncertainty due to di ff erentstellar yield assumptions by means of a one-zone chemical evo-lution model. In Section 4, we present the results of our study onHe in the ISM and in the stars of our simulated galaxies. Finally,in Section 5, we draw our conclusions.
2. The assumed cosmological simulation
In this paper we make use of the same cosmological hydrody-namical simulation code as described in detail in Kobayashi et al.(2007); Vincenzo & Kobayashi (2018a,b), which is based on theG adget -3 code (Springel 2005). Our simulation code includesstar formation activity with mass- and metallicity-dependentchemical and thermal energetic feedback from (i) stellar windsof dying asymptotic giant branch (AGB) and massive stars ofall masses and metallicities, (ii)
Type Ia Supernovae (SNe), (iii)
Type II SNe and hypernovae (HNe).We assume the same nucleosynthesis prescriptions as inKobayashi et al. (2011), modified to include failed SNe formasses m ≥
25 M (cid:12) and metallicities Z ≥ .
02 of the progenitormassive stars (see also Smartt 2009, Müller et al. 2016, Beasor& Davies 2018, Prantzos et al. 2018, Limongi & Chie ffi .
01 and 120 M (cid:12) .In our simulation, we evolve a cubic volume of the Λ -cold dark matter ( Λ CDM) Universe, with the cosmological pa-rameters being given by the nine-year Wilkinson Microwave
Article number, page 2 of 13. Vincenzo et al.: He abundances in chemodynamical simulations
Fig. 4.
In this figure, we explore the e ff ect of di ff erent nucleosynthesis yields for massive stars (panels a and c) and AGB stars (panels b and d) onthe predicted Y versus Z relation from a one-zone galaxy chemical evolution model with star formation e ffi ciency SFE = − , infall time scale τ = ffi (2018) for di ff erent stellar rotational velocities ( v v
150 and v
300 represent rotationalvelocity v =
0, 150, and 300 km s − , respectively). For AGB stars, we explore the stellar yields of Karakas (2010), adopted in our cosmologicalsimulations, and those of Ventura et al. (2013) (e.g., see Vincenzo et al. 2016). Anisotropy Probe (Hinshaw et al. 2013). We assume periodicboundary conditions and a box side (cid:96) U =
10 Mpc h − , in comov-ing units. We have a total number of gas and DM particles whichis N DM = N gas = , with the following mass resolutions: M DM ≈ . × h − M (cid:12) and M gas = . × h − M (cid:12) . Fi-nally, the gravitational softening length is (cid:15) gas ≈ . h − kpc, incomoving units. Our simulations gives a good agreement withthe observed cosmic SFR, mass-metallicity relations, and theN / O–O / H relation (Vincenzo & Kobayashi 2018b).
In this paper, we investigate how He abundances vary withinthree simulated disc galaxies, which we have selected out ofthe ten reference galaxies of Vincenzo & Kobayashi (2018b). Inparticular, our galaxy A corresponds to galaxy 3 of Vincenzo &Kobayashi (2018b), galaxy B to galaxy 6, and galaxy C to galaxy9. Nevertheless, our results for He would have been the same,had we selected other galaxies from Vincenzo & Kobayashi(2018b) . These galaxies ABC are di ff erent from the sample in Vincenzo &Kobayashi (2018a). In Fig. 1 we show the age distribution of the stellar popula-tions in galaxy A-C as predicted at the present time. The di ff er-ent curves in Fig. 1 are normalised such that the area below eachof them corresponds to the total galaxy stellar mass at redshift z =
0. By looking at the figure, it is clear that – from galaxyA to galaxy C – the SFH becomes more and more concentratedtowards later epochs of the cosmic time.In summary, our three reference galaxies at redshift z = (i) M (cid:63), A = . × M (cid:12) and M gas , A = . × M (cid:12) ; (ii) M (cid:63), B = . × M (cid:12) and M gas , B = . × M (cid:12) ; (iii) M (cid:63), C = . × M (cid:12) and M gas , C = . × M (cid:12) .
3. He nucleosynthesis in the simulation
Apart from the primordial nucleosynthesis, which accounts formost of the He in the Universe, He can be synthesised andreleased into the ISM of galaxies by all mass range of starswith m (cid:63) (cid:38) (cid:12) . The main source of uncertainty for the Henucleosynthesis in our cosmological simulation is given (i) bythe assumptions about stellar rotation and mass loss in massivestar models (see the review by Maeder 2009), and (ii) by thetreatment of overshooting, convective boundary conditions, hot- Article number, page 3 of 13 & A proofs: manuscript no. Vincenzo2019_AA
Fig. 5.
From left to right, the various columns correspond to each of our reference galaxy, from galaxy A to galaxy C, respectively. In the first row,at the top, we show how the gas-phase He mass fraction, Y gas , varies as a function of the gas-phase O mass fraction, X O,gas ; in the second row, weshow Y gas versus X C,gas ; in the third row, we show Y gas versus X N,gas ; in the fourth row, we show Y gas versus X C + N,gas ; finally, in the fifth row, at thebottom, we show our predictions for the radial profile of Y gas as a function of the galactocentric distance, d , with the colour coding representingthe O mass fraction. bottom burning, and e ffi ciency of the third dredge-up (mixingprocesses) in AGB stellar models (see the detailed discussionin Ventura et al. 2013; Renzini 2015; Karakas & Lugaro 2016;Karakas et al. 2018).In Fig. 2, we show how the average IMF-weighted stellaryields of He, (cid:104)P He (cid:105) , vary as functions of the initial stellar metal-licity, Z (cid:63) , by assuming some di ff erent stellar models for massiveand AGB stars. In particular, the quantity (cid:104)P He (cid:105) is computed asfollows: (cid:104)P He ( Z (cid:63) ) (cid:105) MS = (cid:90)
40 M (cid:12)
13 M (cid:12) dm IMF( m ) p He ( m , Z (cid:63) ) , (1)for massive stars, where p He ( m , Z (cid:63) ) represents the He stellaryields as functions of mass and metallicity, and (cid:104)P He ( Z (cid:63) ) (cid:105) AGB = (cid:90) (cid:12) . (cid:12) dm IMF( m ) p He ( m , Z (cid:63) ) , (2)for AGB stars.In Fig. 2(a), the average stellar yields of He from the mas-sive star models of Nomoto et al. (2013) – which do includemass loss and SN nucleosynthesis but not the e ff ect of rotation– are compared with the average yields of Limongi & Chie ffi (2018), which do include also the e ff ect of rotation. In particu-lar, the di ff erent curves in Fig. 2(a) for the Limongi & Chie ffi (2018) yields correspond to models with di ff erent stellar rota-tional velocities (v0, v150, and v300, which stand for v rot = − , respectively). At sub-solar metallicities,massive star models with higher and higher rotational velocitiesgive rise – on average – to smaller amounts of He; moreover, thestellar yields of He from rotating stellar models show a strongerdependence on metallicity than non-rotating massive star mod-els; as we will see in Section 3.2, these resulting di ff erences inthe stellar yields for massive stars give rise to a systematic un-certainty in the predictions of chemical evolution models.Finally, in Fig. 2(b), the average stellar yields of He fromthe AGB stellar models of Ventura et al. (2013) are comparedwith those of Karakas (2010), assumed in our cosmological sim-ulation. We find that the Karakas (2010) stellar yields of Hedecrease as functions of metallicity, and this makes the Ven-tura et al. (2013) stellar yields larger by a factor of ≈ ff er-ences between the two stellar models reside in the physics ofsuper-adiabatic convection and mixing (Karakas, Lattanzio &Pols 2002; Karakas & Lattanzio 2007), which a ff ect the finalstellar yields from AGB stars. Article number, page 4 of 13. Vincenzo et al.: He abundances in chemodynamical simulations
In order to understand how He is produced by the stars in oursimulation, in Fig. 3, we show how much He is deposited bysimple stellar populations (SSPs) of di ff erent metallicity, perunit time and per unit mass of the SSPs (namely, in units ofM (cid:12) Gyr − M − , where M SSP represents the initial mass of theSSP), by assuming the same stellar lifetimes and IMF as in ourcosmological simulation. We remark on the fact that each starparticle in our simulation is treated as a SSP (Kobayashi 2004).The contribution from massive stars and AGB stars to theHe chemical enrichment is highlighted in Fig. 3; in particular,we compare our results with the Nomoto et al. (2013) stellaryields for massive stars (coloured curves) with the stellar yieldsof Limongi & Chie ffi (2018, grey shaded area) for rotating mas-sive stars. There is a tendency such that more metal-rich AGBstars release slightly larger amounts of He into the ISM per unittime. Note that the gap in the figure around 30-50 Myr (blueshaded horizontal region) corresponds to stellar masses in therange between 8 and 10 M (cid:12) (even though this mass range is quiteuncertain), which are not included in most galactic chemical evo-lution models including ours. Nevertheless, super-AGB stars donot provide a significant contribution to the global chemical en-richment of galaxies (see, for example, Vangioni et al. 2018,Prantzos et al. 2018, and Kobayashi et al. in prep.).We provide a useful formalism to compute the He productionrate from a SSP of age t and metallicity Z , by firstly defining a partial yield per stellar generation as follows: (cid:104)Y He ( t , Z ) (cid:105) = (cid:90) m max m TO ( t , Z ) dm IMF( m ) p He ( m , Z ) , (3)where p He represents the stellar nucleosynthetic yield of Hefrom all the stars with mass m and metallicity Z in the SSP, asweighted with the assumed IMF, m max corresponds to the max-imum stellar mass which is formed in the SSP, and m TO ( t , Z )represents the turn-o ff mass (as computed from the inverse stel-lar lifetimes). The extremes of the integral in equation 3 encloseall the stars that, at the time t from the birth time of the SSP, havealready died, enriching the galaxy ISM with He.The production rate of He by a SSP with metallicity Z andage t can then be computed as follows: d P He ( t , Z ) dt = (cid:104)Y He ( t , Z ) (cid:105) − (cid:104)Y He ( t − dt , Z ) (cid:105) dt (4)which is the quantity shown on the y -axis of Fig. 3. Y-Z relation due to different sets of stellar yields
To understand the e ff ect of di ff erent stellar yield assumptionsfor massive stars and AGB stars on the Y versus Z relation ingalaxies, in Fig. 4 we show the predictions of di ff erent one-zone chemical evolution models, assuming a star formation ef-ficiency SFE = . − , infall time-scale τ inf = . M inf ≈ . × M (cid:12) , with primordial chemical composition. The ac-cretion of gas into the galaxy potential well follows the follow-ing law: I ( t ) ∝ e − t /τ inf . Finally, for the SFR, we assume a linearSchmidt-Kennicutt relation, namely SFR( t ) = SFE × M gas ( t ).In Fig. 4(a,c), we fix the stellar yields of AGB stars and varythe stellar yields of massive stars. In particular, in Fig. 4(a), we Fig. 6.
The predicted evolution of dY gas / dX O (top panel), dY gas / dX C (second panel), dY gas / dX N (third panel), dY gas / dX C + N (third panel), and dY gas / dZ (bottom panel) as a function of the look-back time. The blackcurve corresponds to galaxy A, the red curve to galaxy B, and the bluecurve to galaxy C. The values of dY gas / dX C,N,O, Z correspond to our best-fit values for the predicted Y gas - X C,N,O, Z relations in each galaxy, by as-suming a simple linear law at all times. We only show the evolution ofthe slopes for times when the galaxy stellar mass M (cid:63) > × M (cid:12) . fix the stellar yields of Karakas (2010) for AGB stars, whereas inFig. 4(c) we fix for AGB stars the stellar yields of Ventura et al.(2013). The stellar yields of massive stars that we explore in Fig. Article number, page 5 of 13 & A proofs: manuscript no. Vincenzo2019_AA
Fig. 7.
The redshift evolution of the gas-phase He / H-O / H abundancepattern in our three simulated disc galaxies. The blue points correspondto the predicted gas-phase abundances at redshift z =
0, orange pointsto z = .
5, green points to z =
1, and red points to z =
2. The black andgray triangles with error bars correspond to the observational data ofAver, Olive & Skillman (2015), for a sample of metal-poor HII regionswithin 16 emission-line galaxies in the Local Universe; the black trian-gles correspond to their qualifying sample, whereas the gray trianglesmark the abundances a ff ected by large systematic uncertainty. Finally,the magenta points with error bars correspond to the observational dataof Fernández et al. (2019). ffi (2018) for di ff erent rotational velocities ( v =
0, 150,and 300 km s − ) and iron abundances ([Fe / H] = − −
2, and − ff ectof varying the stellar yields of AGB stars, assuming the yieldsof Karakas (2010) and Ventura et al. (2013) for AGB stars. Inparticular, in Fig. 4(b), we fix the massive star yields of Limongi& Chie ffi (2018), whereas in Fig. 4(d) we fix those of Nomoto etal. (2013).We find that the uncertainty on the predicted Y versus Z re-lation due to di ff erent stellar yield assumptions for massive starsincreases as a function of metallicity, being ∆ Y MS (0 < Z < ∼ . ∼ . ∆ Y MS ( Z > . ∼ . ∆ Y AGB (0 < Z < ∼ . ∼ . Fig. 8.
The evolution of the average SFR-weighted He / H abundancesas functions of the gas fraction ( f gas = M gas / ( M gas + M (cid:63) )) within oursimulated disc galaxies. Blue points correspond to galaxy A, orangepoints to galaxy B, and green points to galaxy C. and ∆ Y AGB ( Z > . ∼ . dY / dZ due to di ff erent stellar yield assumptions forAGB stars, which can be as large as ≈ .
4. Results
In this Section we present the results of our analysis for the evo-lution of the He abundances in our simulated disc galaxies. InSection 4.1 we focus on the He abundances within the ISM, com-paring the predictions of our simulation with the observed Heabundances in metal-poor HII regions by Aver, Olive & Skill-man (2015); Fernández et al. (2019), whereas in Section 4.3 westudy the He content in the stellar populations. Finally, in Sec-tion 4.4 we compare the predictions of our simulation with Heabundance measurements in a Galactic open cluster (McKeeveret al. 2019), horizontal branch stars in Galactic globular clusters(Mucciarelli et al. 2014), RR Lyrae stars in the Galactic bulge(Marconi & Minniti 2018), and in a sample of B-type stars inour Galaxy (Morel et al. 2006; Nieva & Przybilla 2012).
The ISM abundances of He in our simulated galaxies are ex-plored in Fig. 5. From left to right, the three columns of pan-els in the figure represent our three reference galaxies, and –from top to bottom – we show our predictions for the follow-ing relations in the ISM of the simulated galaxies: (i) Y gas versus X O,gas , (ii) Y gas versus X C,gas , (iii) Y gas versus X N,gas , (iv) Y gas ver-sus X C + N,gas , and (v) Y gas versus galactocentric distance, where Y gas = M Y , gas / M gas represents the He mass fraction within eachgas particle in the galaxy, and X O,gas = M O , gas / M gas representsthe O mass fraction (similar relations stand also for C, N, andC + N).In the lower right of each panel in Fig. 5, we report our bestfits to the predicted Y - X O , Y - X C , Y - X N , and Y - X C + N relations inour three reference galaxies, by assuming a simple linear law.First of all, as we consider galaxies with SFHs concentrated to-wards later and later epochs (namely, by moving from galaxy Ato galaxy C), we note that the slopes of Y - X O and Y - X C dimin-ish, whereas the slope of Y - X N increases. Secondly, the spreadin Y - X C , N is much smaller than that in Y - X O . Article number, page 6 of 13. Vincenzo et al.: He abundances in chemodynamical simulations
Fig. 9.
The predicted gas-phase He / H-O / H abundance pattern at redshift z = The lower scatter in Y - X C , N is a consequence of the fact thatthe absolute abundances of C and N are much lower than thoseof O; in particular, we obtain the following approximate valuefor the relative abundance variations of i = C, N, O, and C + Nin our three simulated galaxies, for He abundances in the range[0 . , . σ X i ¯ X i ≈ .
15 (5)Our findings suggest that the calibration of the Y - Z relationfor stellar models should be carried out using nitrogen or carbonabundances; however, since C and N abundances at the stellarsurface may be strongly a ff ected by (extra)mixing (e.g., Iben &Renzini 1983; Shetrone et al. 2019), we suggest to use C + N,which is instead a conserved quantity at the stellar surface, asthe stars experience dredge-up episodes after they leave the mainsequence.We predict radial gradients of both Y and X O in the ISM ofour simulated galaxies (see the bottom panels of Fig. 5); in par-ticular, we find that the most central galaxy regions have higheraverage metallicites and also higher He abundances than the out-ermost regions. To reach those high ISM metallicities in thecentral regions, numerous generations of stars should have suc-ceeded each other polluting the ISM with metals and He, givingrise to very short chemical enrichment time-scales in the galaxycentre. In fact, we find that our simulated disc galaxies grow from the inside out (see also Vincenzo & Kobayashi 2018b),giving rise to chemical enrichment time scales which increaseas functions of the galactocentric distance, d ; this, in turn, deter-mines the predicted trend of Y and Z as functions of d .In Fig. 6 we show how our best-fit values for dY / dX O , dY / dX C , dY / dX N , dY / dX C + N , and dY / dZ in the ISM of our threereference galaxies evolve as functions of the look-back time,where Z represents the sum of the abundances of all 31 chem-ical elements contributing to metallicity, which are traced in oursimulation. We only show our predictions for the epochs whenthe total galaxy stellar mass is > × M (cid:12) , in order to have anenough number of resolution elements for each galaxy. It is clearfrom the figure that galaxies with di ff erent SFHs exhibit also dif-ferent temporal evolution of dY / dX C,N,O . Interestingly, the tem-poral evolution of dY / dX N shows an opposite trend with respectto that of dY / dX O , dY / dX C , and dY / dZ .On the one hand, we predict that dY / dX N diminishes as afunction of time; this is due to the fact that N is mostly producedas a secondary element, and its stellar yields steadily increasewith metallicity, whereas the He stellar yields have a weaker de-pendence on metallicity than those of N. This way, the variationin N between two consecutive time-steps is always larger thanthat of He, at any epoch of the galaxy evolution.On the other hand, dY / dX O increases with time, because – inthe declining phase of the galaxy SFH – the variation of He be-tween two consecutive time-steps is larger than that of O; this isdue to the large production of He from AGB stars of all massesand metallicities, which pollute the ISM over a large range ofdelay times from the star formation event. Finally, the evolu-tion of dY / dX C is weaker than that of dY / dX O and dY / dX N , be-cause He and C are stricly coupled from the point of view ofthe stellar nucleosynthesis. Interestingly, the evolution with timeof dY / dX C + N , as well as its dependence on the galaxy SFH isrelatively weak, varying from ∼ . . dY / dX O in Fig. 6 are consistentwith the He abundance measurements in extragalactic HII re-gions, which use O lines to estimate the ISM metallicity, finding dY / dX O ∼ . . dY / dZ are lower than those determined withindirect He abundance measurements in Galactic open clusters,which report dY / dZ ∼ . ff set between model and data for dY / dZ can be due tothe systematic uncertainty in the He nucleosynthesis from AGBstars. For example, by assuming the Ventura et al. (2013) stellaryields, there is a more pronounced He enrichment at high metal-licities from AGB stars, giving rise to steeper Y - Z relations (i.e.higher dY / dZ ) than those predicted with the Karakas (2010) stel-lar yields (see Fig. 4). Nevertheless, various studies in the pastestimated dY / dZ ∼ . dY / dZ , mostly because of the indirect meth-ods employed to determine the He content of the stars, whichare strongly dependent on the assumptions of stellar evolutionmodels (e.g., Portinari et al. 2010). In Fig. 7(a-c), we show the predicted redshift evolution of thegas-phase He / H versus O / H abundance pattern in our three sim-ulated disc galaxies. For comparison, we also show the He / Habundance measurements as determined in the HII regions of
Article number, page 7 of 13 & A proofs: manuscript no. Vincenzo2019_AA
Fig. 10.
The predicted He mass fraction in the stellar populations ofour three reference galaxies as a function of the stellar ages. The colourcoding corresponds to the O mass fraction in the stars. Each panel, fromtop to bottom, shows our predictions for each reference galaxy, fromgalaxy A to galaxy C, respectively.
Fig. 11.
The dispersion of the He abundances in the stellar populationsof our simulated disc galaxies, σ Y (cid:63) , by considering di ff erent metallicitybins, (cid:104) X O (cid:105) (cid:63) , with width 0 . a sample of 16 metal-poor dwarf irregular galaxies in the lo-cal Universe by Aver, Olive & Skillman (2015); the black trian-gles with error bars correspond to the final qualifying sample ofAver, Olive & Skillman (2015), whereas the grey triangles witherror bars correspond to their flagged HII region abundances,which are a ff ected by large systematic uncertainties. Finally, inthe same figure, we also show the He / H abundance measure-ments of Fernández et al. (2019, magenta triangles with errorbars) for a sample of young metal-poor HII regions (see alsoFernández et al. 2018, for more information about their galaxysample), which employed a Bayesian approach to fit the spectrain the abundance analysis determination.At fixed O / H abundances, we predict that He / H steadily in-creases as a function of time; such increase of He / H is fasteras we move towards higher metallicities, which typically corre-spond to the more central galaxy regions. This is due to the factthat the most central galaxy regions had the highest star forma-tion activity in the past, giving rise to an enhancement of the Heabundances in those regions at the present time. In fact, the SFRin our simulated disc galaxies propagates from the inside out
Fig. 12.
In this figure, we present a set of one-zone chemical evolu-tion models assuming the same IMF, stellar lifetimes and stellar nucle-osynthetic yields as in our cosmological hydrodynamical simulation. Inthe chemical evolution models, we assume a star formation e ffi ciencySFE = − , no galactic winds, and we vary the infall timescalefrom τ = . (see also Vincenzo & Kobayashi 2018b), being stronger at thebeginning in the galaxy central regions, and reaching on longertypical time scales the outer disc; this explains why fixed He / Habundances are reached at later times, if their corresponding O / Habundances are lower.We remark on the fact that the observed data in Fig. 7(a-c)correspond to abundances within di ff erent metal-poor emission-line galaxies, which are put all together in the figure, whereas oursimulation data correspond to abundance variations in the ISM ofa single disc galaxy. Nevertheless, the observations show muchmore scatter at low metallicity than our simulated disc galax-ies, which are characterised – in their low-metallicity outskirts –by very homogeneous He / H abundances, about ≈ .
08, approx-imately corresponding to the assumed primordial He / H ratio inthe simulation.The di ff erence in the scatter at low-metallicity between theobservations and our simulation may be due to the fact that, inthe outskirts of our simulated galaxies, we do not see strong starformation activity; on the other hand, in the observed galaxysamples of Aver, Olive & Skillman (2015) and Fernández et al.(2019), there are prominent H α lines, which are the signatureof ongoing star formation activity. These relatively high SFRs atlow metallicities may explain such variation in He / H in the ob-served data. Nevertheless, we remark on the fact that the mass-resolution of our simulation is about ≈ M (cid:12) for primordialgas particles; therefore, at low metallicity, the pollution of Hefrom a single star formation episode with low intensity wouldbe distributed to a large number of ∼ M (cid:12) surrounding gas Article number, page 8 of 13. Vincenzo et al.: He abundances in chemodynamical simulations
Fig. 13.
The predicted Y (cid:63) - X O ,(cid:63) (left panels) and Y (cid:63) - X N ,(cid:63) (right panels) in the stellar populations of our three reference galaxies (from top tobottom). The colour coding represents the [ α/ Fe] (cid:63) ratios of the stars.
Fig. 14.
The predicted [O / Fe] (cid:63) -[Fe / H] (cid:63) diagrams in the stellar popula-tions of our three reference simulated galaxies, with the colour codingrepresenting the He content, Y (cid:63) , of the stars. particles, all with primordial He / H ratio, giving rise to more ho-mogeneous abundances at low-metallicity. Finally, the observedscatter at low metallicity may be the signature of He enrichmentfrom rotating massive Wolf-Rayet stars (Kumari et al. 2018),which are not included in our cosmological simulation.To demonstrate that the gas fraction is one of the main pa-rameters driving the evolution of the average He abundances inour simulated disc galaxies, in Fig. 8, we show how the averageSFR-weighted He / H abundances in the ISM of our three simu-lated disc galaxies evolve as functions of the galaxy gas fraction,which is defined as f gas = M gas / ( M gas + M (cid:63) ). As the galaxyevolves, because of the continuous star-formation activity, f gas decreases as a function of time. At the same time, we predictthat the average He / H abundances in the gas-phase increase, be-ing He produced by a larger number of ageing stellar populationsin the galaxy. Finally, in Fig. 9, we show how the inclusion of failed SNea ff ects the predicted He / H versus O / H abundance patterns at red-shift z = / O versus O / H abundance pattern; in particular,we find that the inclusion of failed SNe increases the inhomo-geneity of the chemical abundance patterns, making also the finalgalaxies less metal-rich at the present time. The assumption offailed SNe changes the evolution of the metallicity as a functionof time, by shifting the stellar metallicity distribution functiontowards lower metallicities; this way, there is – on average – alarger production of He as a function of time (see also Fig. 2,which shows that AGB stars with higher metallicities eject – onaverage – lower amounts of He per unit time). Therefore, at fixedO / H abundances, the simulation with failed SNe predicts higherHe / H abundances in the galaxy ISM.
In Fig. 10 we investigate how the He abundances in the stars ofour simulated galaxies vary as functions of the stellar ages. Thecolour coding in the figure represents the metallicity of the starparticles, as traced by the O abundance.Our findings in Fig. 10 can be easily interpreted in light ofour previous results in Section 4.1. In particular, at any givengalacto-centric radius on the galaxy disc, stellar populations ofdi ff erent ages and metallicities cohabit, depending on how thepast star formation activity was distributed in space as a func-tion of time. Therefore, for a given age of the stars, there is adistribution of metallicities, which automatically translate into Y variations. At any given bin of stellar ages, the star particles withthe lowest metallicities were typically born in the galaxy outer-most regions, where – because of the inside-out growth of thegalaxy disc – the chemical enrichment time scales are typicallylong. This gives rise to low He abundances in the galaxy outer re-gions, close to Y ∼ .
24, which is approximately the primordialvalue.
Article number, page 9 of 13 & A proofs: manuscript no. Vincenzo2019_AA
Fig. 15.
In this figure, we compare our predicted Y (cid:63) versus [Fe / H] (cid:63) rela-tions in galaxy A-C (from top to bottom; light blue points) with the ob-served data of Mucciarelli et al. (2014, red squared) for blue horizontal-branch stars in the Galactic globular clusters M30 and NGC 6397, Mar-coni & Minniti (2018, magenta pentagon) for a sample of RR Lyraein the Galactic bulge, the He abundances in the Galactic open clusterNGC6791 from McKeever et al. (2019, blue circle), and the He abun-dances in a sample of B-type stars within the Solar neighbourhood fromNieva & Przybilla (2012, black star). The yellow star corresponds to theinitial He abundance of the Sun (Serenelli & Basu 2010), for which[Fe / H] is computed by assuming that the iron mass fraction scale withrespect to the total metallicity like in the solar photospheric chemicalcomposition as derived by Grevesse & Sauval (1998).
To understand the impact of di ff erent stellar ages on the pre-dicted He abundances, we divide the stellar populations in Fig.10 in di ff erent bins of metallicity, with width 0 . σ Y (cid:63) , as due to the variation of the stellar ages inthe bin. Our results are shown in Fig. 11. We find that the disper-sion of the He content due to di ff erent stellar ages increases asa function of metallicity, reaching values as high as ≈ .
007 forgalaxy A, which corresponds to ∼
12 per cent of the predictedglobal variation of Y within the galaxy.In Fig. 12, we present a set of one-zone chemical evolutionmodels (similar as those described in Section 3) assuming thesame IMF, stellar lifetimes and stellar nucleosynthetic yields asin our cosmological hydrodynamical simulation. In this set ofmodels, we assume a star formation e ffi ciency SFE = − ,no galactic winds, and we vary the infall time scale from τ = . Y versus age relation. In particular, in the context of the inside-outgrowth of galaxies, shorter infall time scales correspond to morecentral galaxy regions. In Fig. 12(a), the colour coding representsthe infall timescale, whereas in Fig. 12(b) the colour coding rep-resents the gas-phase metallicity.Since the assumed SFE in our chemical evolution modelswould only systematically shift the Y - Z and Y - age relationsalong the y -axis, making faster or slower the chemical enrich-ment as a function of time (if one increases or decreases the SFE, Fig. 16.
In this figure, we compare our predicted (He / H) (cid:63) versus[Fe / H] (cid:63) relations in galaxy A-C (from top to bottom; light blue points)with the observed data of Morel et al. (2006, black points with errorbars) for B-type stars. We also show the value of the typical He abun-dance in a sample of B-type stars within the Solar neighbourhood fromNieva & Przybilla (2012, black star). The yellow star corresponds to theinitial He abundance in the Sun (Serenelli & Basu 2010), where we scalethe Fe abundances with respect to the solar photospheric abundance ofFe from Grevesse & Sauval (1998). respectively), Fig. 12 demonstrates that the inside-out growth ofthe galaxy disc is the main e ff ect regulating the evolution of theHe abundances in galaxies. In particular, diminishing the infalltime scale (namely, moving towards inner galaxy regions) de-termines a faster chemical enrichment in the galaxy, giving riseto higher metallicities and He abundances, for a fixed age. Ourchemical evolution models, therefore, predict that the innermostgalaxy regions (e.g., bulge and inner disc) have steeper Y ver-sus age relations at high metallicities than the outermost galaxyregions.In Fig. 13 we investigate how Y (cid:63) - X O ,(cid:63) (left panels) and Y (cid:63) - X N ,(cid:63) (right panels) in the stars of our simulated galaxies dependon [ α/ Fe] (cid:63) (colour coding, where we assume O as a proxy forthe α -elements). There is a trend, according to which the high-[ α/ Fe] stars have flatter Y (cid:63) - X O ,(cid:63) and steeper Y (cid:63) - X N ,(cid:63) relationsthan the low-[ α/ Fe] stars, even though the predicted spread in Y (cid:63) - X O ,(cid:63) is larger than that in Y (cid:63) - X N ,(cid:63) . These predictions are con-sistent with our results on the temporal evolution of dY / dX O and dY / dX N in the ISM (see Fig. 6, top and bottom panels).Finally, since in Fig. 13 we show our predictions for the[O / Fe] (cid:63) ratios, we show that our simulation can produce rea-sonable results also for the classical [O / Fe] (cid:63) -[Fe / H] (cid:63) diagramin Fig. 14, where the colour-coding corresponds to the He con-tent of the stars, Y (cid:63) . Nevertheless, we caution the readers that Feand O are produced by Type Ia and core-collapse SNe, respec-tively, on very di ff erent typical time scales from the star forma-tion event. Article number, page 10 of 13. Vincenzo et al.: He abundances in chemodynamical simulations
In Fig. 15, we compare the predictions of our simulation for Y (cid:63) versus [Fe / H] (cid:63) in galaxy A-C with the observations. In particu-lar, we show the observed He abundances in the Galactic opencluster NGC 6791 (McKeever et al. 2019), in a sample of hor-izontal branch stars in M30 and NGC 6397 (Mucciarelli et al.2014), as well as in a sample of RR Lyrae in the Galactic bulge(Marconi & Minniti 2018). We also show the He abundances inin a sample of B-type stars within the Solar neighbourhood fromNieva & Przybilla (2012), and the initial He abundance of theSun from Serenelli & Basu (2010). Even though some of the ob-served data in Fig. 15 represent indirect measurements of He instars (apart from the stellar data of Nieva & Przybilla 2012; Muc-ciarelli et al. 2014), and we did not choose our simulated galax-ies to reproduce the observed He abundances in the MW, thepredicted trend of Y (cid:63) versus [Fe / H] (cid:63) qualitatively agrees withthe observed trend, even though our model predictions alwayslie below the observed MW data at high metallicities.Finally, in Fig. 16, we compare the predictions of our simula-tion for (He / H) (cid:63) versus [Fe / H] (cid:63) in galaxy A-C with the observedHe abundances in Galactic B-type stars, as measured by Morel etal. (2006). For reference we also show the value of the typical Heabundance of B-type stars (Nieva & Przybilla 2012) and the ini-tial He abundance of the Sun from Serenelli & Basu (2010). Theobserved data in Fig. 16 represent direct He abundance measure-ments in the stars, and we predict a much less scattered relationthan in the observed data, even though our predicted values for(He / H) (cid:63) are qualitatively consistent with observations.Galactic globular clusters are nowadays known to host mul-tiple stellar populations, which clearly show up both in their ob-served CMD (particularly when combining passbands with dif-ferent response to the molecule bands of OH, CN, CH, and NH;see, for example, Milone, et al. 2012) and in their light-elementchemical abundance patterns (see, for example, Gratton, Sneden& Carretta 2004; Prantzos & Charbonnel 2006; Gratton, Carretta& Bragaglia 2012; Milone, et al. 2013). The He content in thedi ff erent stellar populations of globular clusters can be inferredby means of precise isochrone-fitting analysis; in particular, starswith higher Y are more luminous and tend to have bluer colours,especially at high metallicities (Milone, et al. 2018). One of themost puzzling results in globular cluster studies is that their lat-est generations of stars have enhanced He abundances, whichcan be as high as Y ≈ . z = ≈ - 10 M (cid:12) , hence of the order of globular cluster mass.Our simulation cannot naturally predict any He spread withinthe star particles, because – by construction – the latter are sim-ple stellar populations, with fixed age and metallicity. Moreover,the appearance of multiple stellar populations in globular clus-ters would be a sub-resolution process in our simulation, thatcould be included only through some parametrisation, withoutemerging from the simulation itself, like – for example – ourpredicted He enhancement in the central, more dense galaxy re-gions, which is a natural outcome of the cosmological inside-outgrowth of the galaxy disc as a function of time. Therefore, in conclusion, if we suppose that our star particles represent globu-lar clusters, then our simulation can provide only an average Hecontent between all the underlying stellar populations.
5. Conclusions
In this paper, we have shown, for the first time, how He abun-dances in star-forming disc galaxies evolve as functions of time,chemical composition, and SFH in the context of cosmologicalchemodynamical simulations (Kobayashi et al. 2007; Vincenzo& Kobayashi 2018a,b). We believe that the results of our studywill be of high interest for a wide range of sub-disciplines instellar physics, in which the assumed calibration between Y and Z represents one of the major sources of systematic uncertainty,being largely unknown.Our main conclusions can be summarised as follows.1. The predicted Y - X C,N,O relations in galaxies depend on theirpast SFH (see Figures 5-6). In particular, young galaxieshave – on average – flatter Y - X C,O and steeper Y - X N relationsthan the old ones.2. We find that dY / dZ depends on the galaxy SFH and is notconstant as a function of time. Moreover, the temporal evo-lution of dY / dZ depends on the particular chemical elementwhich is used to trace Z
3. The predicted temporal evolution of dY / dX O in the ISM isopposite with respect to that of dY / dX N (see Fig. 6). Inparticular dY / dX O increases – on average – as a functionof time, whereas dY / dX N decreases, because N is mostlysynthesised as a secondary element, with its stellar yieldsstrongly increasing as functions of metallicity. Finally, wefind that dY / dX C weakly increases as a function of time, be-cause He and C are strictly coupled from a nucleosynthesispoint of view. Interestingly, Y - X C + N depends very weakly onthe galaxy SFH, having values in the range ≈ [6 . , . Y - X C and Y - X N relations are steeper and lessscattered than Y - X O (see Figures 5-6). This suggests to useC, N, or C + N as metallicity calibrators for stellar models,instead of the O abundances.5. Our predicted values for dY / dX O are fairly in agreement withthe observed relations in extragalactic HII regions (Izotovet al. 2007); however, our predicted values for dY / dZ arelower than those found with indirect He abundance measure-ments in large samples of stars in our Galaxy (Jimenez et al.2003; Casagrande et al. 2007; Portinari et al. 2010), as wellin Galactic open clusters (Brogaard et al. 2012). This is likelydue to the large uncertainty in the He nucleosynthesis fromAGB stars in our cosmological simulation; for example, byassuming the Ventura et al. (2013) stellar yields for AGBstars, we obtain a steeper Y - Z relation than that found withthe Karakas (2010) stellar yields, with a di ff erence in dY / dZ which can be as large as ≈ .
35. Nevertheless, the observed dY / dZ values in the stars still su ff ers from some uncertainty,because of the typical indirect methods employed to measureHe abundances, which depend on the assumptions of stellarmodels (e.g., Casagrande et al. 2007; Portinari et al. 2010).6. We predict radial gradients of Y in the ISM of our simulateddisc galaxies, according to which the central regions have –on average – higher Y and metallicities than the outermost re-gions (see Fig. 5). This is due to an inside-out growth of thestellar mass (and to an inside-out propagation of the star for-mation activity) in our simulated disc galaxies as a functionof time (see also Vincenzo & Kobayashi 2018b), the maine ff ect of which – from the point of view of chemical evolu-tion – is an increase of the typical chemical enrichment time Article number, page 11 of 13 & A proofs: manuscript no. Vincenzo2019_AA scale as a function of the galactocentric distance, giving riseto higher average Y and Z values in the centre.7. We find that, at fixed O / H, the predicted gas-phase He / Habundances increase as a function of time, with such increasebeing faster in the inner galaxy regions (see Fig. 7). We con-clude that this is an e ff ect of the inside-out growth of oursimulated disc galaxies as a function of time.8. By comparing our simulations with the observed He / H abun-dances in a sample of low-metallicity star-forming galaxiesfrom Aver, Olive & Skillman (2015); Fernández et al. (2019),we predict much more homogeneous gas-phase He / H abun-dances at low metallicities than in the observed data set (seeFig. 7). This may be due to the fact that the observed galaxysample are relatively metal-poor with ongoing star forma-tion activity at the present time, whereas the low-metallicityenvironments in our simulated disc galaxies at the presenttime correspond to the galaxy outer regions, where there isno sign of recent strong star formation activity. Nevertheless,we also discuss that this disagreement in the scatter may bedue to the limited resolution of our simulation, as well as tochemical enrichment from rotating massive Wolf-Rayet stars(Kumari et al. 2018), which are not included in our cosmo-logical simulation.9. For a fixed stellar metallicity bin, the variation of Y (cid:63) due todi ff erent stellar ages becomes more and more important athigher metallicities (see Fig. 11). Since the stars in the bulgeand in the inner disc of galaxies typically have the highestmetallicities, we expect that the impact of the stellar ageson the variation of the He abundances becomes more impor-tant in the inner galaxy regions; in particular, we find that,for the typical high metallicities of Galactic bulge stars, thevariation of Y (cid:63) contributed by di ff erent stellar ages can be ashigh as ∼
12 per cent with respect to the global variation of Y (cid:63) . On the other hand, in the galaxy disc, the metallicity isthe most important quantity determining the variation of Y (cid:63) in the galaxy. Nevertheless, the systematic uncertainty intro-duced by di ff erent stellar yield assumptions for AGB stars iscomparable to the spread that we find for Y (cid:63) at high metal-licity, which is of the order of ≈ . ff erentinfall time scales, we find that the innermost galactic regions(which are characterised by shorter infall time scales, accord-ing to the inside-out scenario) have steeper Y versus age re-lations at high metallicities than the outermost disc regions(see Fig. 12).11. The predicted Y (cid:63) - X O ,(cid:63) relation in the stars is very sensitiveto [ α/ Fe]. In particular, the high-[ α/ Fe] stars exhibit a flatteraverage relation than those with low [ α/ Fe]. An opposite butweaker trend is found for Y (cid:63) - X N ,(cid:63) , when considering starswith di ff erent [ α/ Fe] (see Fig. 13).12. Even though we did not choose our simulated disc galaxiesto reproduce the observed chemical abundances of He in ourGalaxy, the predicted trend of our simulations for Y (cid:63) versus[Fe / H] (cid:63) qualitatively agrees with observations. Acknowledgments
We thank an anonymous referee for many constructive com-ments, which greatly improved the quality and clarity of ourpaper. Moreover, we thank Emma Willett for many useful dis-cussions. FV, AM, JTM, and JM acknowledge support fromthe European Research Council Consolidator Grant fundingscheme (project ASTEROCHRONOMETRY, G.A. n. 772293). CK acknowledges funding from the United Kingdom Sci-ence and Technology Facility Council (STFC) through grantST / R000905 / / K00042X / / K00087X /
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