Abundance scaling in stars, nebulae and galaxies
David C. Nicholls, Ralph S. Sutherland, Michael A. Dopita, Lisa J. Kewley, Brent A. Groves
AAbundance scaling in stars, nebulae and galaxies
David C. Nicholls , Ralph S. Sutherland , Michael A. Dopita , Lisa J. Kewley , & Brent A.Groves , [email protected] Abstract
We present a new basis for scaling abundances with total metallicity in neb-ular photoionisation models, based on extensive Milky Way stellar abundancedata, to replace the uniform scaling normally used in the analysis of H ii regions.Our goal is to provide a single scaling method and local abundance referencestandard for use in nebular modelling and its key inputs, the stellar atmosphereand evolutionary track models. We introduce a parametric enrichment factor, ζ ,to describe how atomic abundances scale with total abundance, and which al-lows for a simple conversion between scales based on different reference elements(usually oxygen or iron) . The models and parametric description provide a morephysically realistic approach than simple uniform abundance scaling. With ap-propriate parameters, the methods described here may be applied to H ii regionsin the Milky Way, large and dwarf galaxies in the local universe, Active GalacticNuclei (AGNs), and to star forming regions at high redshift. Subject headings:
ISM: abundances – stars: abundances – Sun: abundances – galaxies: abun-dancesAccepted by MNRAS 11 Dec 2016
1. Introduction
Photoionisation modelling provides a powerful tool for understanding the physics of H ii regions andother ionised nebulae. Its aim is to solve the radiative transfer equations and associated physics as theionising radiation from the central star cluster traverses the gas. The goal is to predict the emission spectraarising from the ionised nebula, as a basis for interpreting observations, allowing us to determine the physicalconditions and chemical abundances in the nebula. Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT, Aus-tralia a r X i v : . [ a s t r o - ph . GA ] D ec There are a number of problems in developing reliable photoionisation models. First, a full knowledgeof the atomic data for elements involved in the processes is critical. This has improved a great deal in recentyears through resources such as the CHIANTI Database (Dere et al. 1997; Landi et al. 2013), but there arestill gaps in our knowledge. However, the situation is likely to improve with time, and our current knowledgeis sufficient to construct physically realistic photoionisation models of nebulae.Second, our ability to synthesise accurately the spectrum of the source of the ionising radiation is farfrom complete. In H ii regions, this involves the estimation of the emission spectrum of the stars at theheart of the region. This depends on three factors: reliable models of stellar atmospheres ranging from hotO-stars to cool dwarfs; the evolutionary tracks of the stars as they age, for the lifetime of the ionised region,typically 10 to 20 Myr; and effective synthesis of the total spectrum from ensembles of stellar populations.Worse, some of the commonly used stellar atmosphere model sets cover only sparsely (if at all) thehotter stars that dominate the excitation of H ii regions. The stellar evolutionary tracks generally are notwell matched to the modelled main sequence stars, and use different metallicity standards, in part becausethese standards have been based on solar abundance references that have changed with time.Population synthesis models combine the stellar models and evolutionary tracks, but cannot generatephysically realistic results without consistent input data. If we hope to build physically realistic photoionisa-tion models, we need a single metallicity standard for future work on stellar atmosphere models, evolutionarytrack models and nebular models, to put them on the same footing. The lack of a consistent abundance scaleintroduces errors into nebular photoionisation models and makes the works of different authors difficult tocompare.Third, abundance scaling of elements at metallicities lower than the reference standard has been wellexplored in stars, but in the nebular modelling community only the simplest uniform scaling assumptions, orarbitrary adjustments to these, appear to have been used. Stellar astronomers have known for a long time,for example, that iron abundances relative to α -element abundances have changed both over time and withthe galactic environment since the formation of the earliest stars (e.g., Wyse & Gilmore 1993). Consequently,photoionisation models for nebulae with different metallicities need to take this variation into account, andin general this has not been done.Fourth, the extent of element depletion into dust in H ii regions and in different galactic environmentsis poorly known. It is possible to measure dust composition in the interstellar medium through absorption ofstarlight, but this does not tell us much about the nature of the dust in the giant molecular clouds from whichH ii regions form, nor how the dust is destroyed by the ionising radiation in nebulae. Dust depletion canbe measured, for example for refractory elements, by comparing nebular abundances with the photosphereabundances of the central stars (where available). A third approach, using photoionisation models, allows usto estimate dust depletion through comparison of models and observations. This paper addresses the secondand third of these problems, and outlines how we propose to tackle the fourth.We adopt a standard, present-day scale, extended from the cosmic abundance standard developed byNieva & Przybilla (2012), based on the observed metallicities of 29 main-sequence B-stars in local galacticregion, augmented with data from other recent sources for elements which are of minor importance in nebularand stellar modelling. This is a local, present-day scale, rather than the conventional solar scale(s), wherethe abundance values include minor evolutionary effects overlaid on a scale deriving from the proto-solarnebula from 5 Gyr ago, and uncertainties with the origin of the proto-solar nebula. To avoid confusion withthe Universe at large, we refer to the extended scale, together with the associated scaling behaviour , as the “Galactic Concordance”. We suggest that this reference standard and scaling system be used for consistencyin stellar atmosphere modelling, stellar evolutionary tracks and nebular models.We examine stellar metallicity data assembled over the past two decades, from Milky Way observationsand nearby dwarf galaxies, to derive a model for the way individual element abundances scale with totalnebular metallicity. We suggest this should replace the simple linear scaling used in models to date. Usingpiece-wise linear fits to the stellar abundance data, we show that abundances expressed in the iron-basedstellar metallicity scale can be readily converted to the oxygen-based nebular metallicity scale, and vice-versa.We use the stellar data available to derive general rules for the nebular scaling of the important nebularelements as a function of total nebular oxygen metallicity.Finally we suggest approaches to estimate nebular dust depletion, including comparison of nebular pho-toionisation models with the observed emission line data from simply-structured (and thus reliably modelled)H ii regions.
2. The need for a consistent standard abundance set and a realistic scalingmodel2.1. The problem of inconsistency
Full radiative transfer nebular modelling requires inputs from a number of sources. Among these,an accurate estimate of the central star cluster excitation spectrum is critical to to production of realisticnebular models. This requires detailed stellar atmosphere and stellar evolutionary track models. Theseare convolved through a spectrum synthesis application which takes the raw stellar spectra and tracks, andbuilds a composite spectrum based on estimates of the ionising cluster initial mass function and the clusterevolution with time.To generate a realistic cluster spectrum, grids of stellar models are needed, and the spectral paths takenby the stars as they evolve. There is a dearth of such models. A major concern is that what models thereare are based on abundance standards from different eras. For example, the WMBasic atmosphere models(Pauldrach et al. 2012, and earlier papers) are based on the Anders & Grevesse (1989) solar photosphericstandard abundances whereas the Geneva evolutionary track models (Ekstr¨om et al. 2012, and other papersin this sequence) are based on solar photospheric abundances from Asplund et al. (2005). The oxygenabundance differs between these sources by 0.27 dex and the iron abundance by 0.22 dex. Such differencescast doubt on the reliability of combining the track and atmosphere data as inputs to population synthesisapplications.In order to generate plausible nebular models, it is important that the stellar atmospheres and evo-lutionary tracks be computed using a common abundance standard. In addition, the manner in whichthe abundances scale relative to each other is critical for modelling atmospheres, tracks and nebulae atmetallicities less than the reference standard (e.g., “solar”).
We use the
Mappings photoionisation modelling code (Dopita et al. 2013) to generate nebular strongline ratio grids for the ionisation parameter log(Q) vs. oxygen metallicity, the inadequacy of simple uniformabundance scaling (i.e., the same ratio for all elements) is apparent. Uniform scaling is incapable of explainingthe observations. Conversely the simple non-uniform scaling model we describe below does a very good jobof matching observational data. Figure 1 demonstrates this.While the geometry adopted for an H ii region model plays a key role in the predicted emission lineoutputs, we find that a plane parallel geometry provides a computationally tractable result that matchesobservations well. In this example, we assume constant pressure conditions with log(P/k) = 6.0, where P isthe pressure and k is the Boltzmann constant. We adopt the WMBasic stellar atmosphere models (Sternberget al. 2003), the Geneva evolutionary tracks for rotating stars (Ekstr¨om et al. 2012), and use Starburst99with a Salpeter IMF (Leitherer et al. 2014) and continuous stellar evolution sampled at 5 Myr. For atomicabundances we use the Galactic Concordance scale, described in detail below.Figure 1 (left panel) shows the strong line ratios log[O iii ] /H α plotted vs. log([N ii ] /[O ii ] ),using the non-uniform scaling described below and standard GC abundances (red), and the same metallicitystandard but with uniform scaling (black). The grey points are data from the Sloan Survey Data Release 7(Abazajian et al. 2009). They show that uniform scaling is not capable of reproducing the observed data,while non-uniform scaling fits the observations well. (The vertical spray of SDSS points arises from activegalactic nuclei, not modelled here). Other strong line ratios also show discrepancies between models andobservations when uniform scaling is used..The choice of a “standard” abundance reference does not play a major role in explaining the observa-tional data. Figure 1 (right panel) shows the same grids using three “standard” abundance sets with uniformscaling. None of them can explain the observational data. It is useful to explore what differences occur in metallicity and ionisation parameter, log(Q), usingdifferent abundance references. The grids in Figure 1 (right panel) provide a guide to these differences. Foruniform abundance scaling, we can estimate the effects of using different abundance reference sets (black,Galactic Concordance (this work); green Anders & Grevesse (1989) and blue Asplund et al. (2009). Themetallicity differences for this combination of line ratios vary between 0 and 0.15 at low metallicity andbetween 0 and 1.4 for metallicities > < The ionisation parameter, Q, is the velocity of the ionisation front that the radiation field can drivethrough through medium. It is the ionising photon flux in photons cm − s − divided by the neutral hydrogennumber density in cm − , and an indicator of the physical conditions at the inner edge of the photoionisedzone in an H ii region. -2.0 -1.0 0.0-3.0-2.0-1.00.01.0 log([NII] /[OII]+) l og ( [ O III] / H β ) log(Q)=6.56.757.07.257.58.5 GC non-uniformGC uniformSDSS
Z=0.050.2 0.5 1.0 3.0 -2.0 -1.0 0.0
GC non-uniformGC uniformAGSS09 uniformAG89 uniform
Fig. 1.— An illustration of the importance of non-uniform scaling in nebular mod-elling. The left panel shows grid plots for the strong line ratios log[O iii ] /H α vs.log([N ii ] /[O ii ] ), showing the ionisation parameter log(Q) (left to right) vs.metallicity Z relative the the standard value (near vertical lines), using the non-uniformscaling and standard abundances proposed in this paper (red), and the same metallicitystandard and scaled values but with uniform scaling (black). The grey points are data forobjects where O iii abundance reference.
3. Abundance scaling3.1. The “solar standard”
The choice of a standard metallicity scale plays an important role in nebular stellar atmosphere andevolutionary track models. In the past the only detailed reference values have been the solar abundances.This has advantages because the abundances of many elements have been accurately measured in the solarphotosphere. But it has significant shortcomings: some elements (for example, F, Cl, Ne and Ar) have notbeen directly detected, or only marginally detected, in the solar atmosphere; some elements (for example, Heand Li) have been processed in the sun during its evolution and photospheric abundances do not necessarilyreflect bulk or proto-solar values; and some elements that are crucial for nebular physics (i.e., oxygen) aredifficult to measure in the solar spectrum (see discussion in Asplund et al. 2009). As a result, measuredsolar abundance values for some elements have differed considerably over the past 40 years. They alsogenerate three “standard” abundance sets: photospheric, bulk and proto-solar nebular. The published solarabundance estimates are listed in Appendix Table 3. Of major concern is that the measured solar oxygenabundance value has varied by a factor of 1.9, iron by 1.7, nitrogen by 1.9, and carbon by 2.1. Further,solar photospheric values differ from the calculated bulk and proto-solar values. Different workers have useddifferent standards for comparison. In general, the latest solar values have been used, but this can lead toconfusion when comparing data from earlier works based on previous solar standards.
The solar standard reference (or any alternative standard) should, ideally, specify the relative abun-dances for local, present day values. This presents a further problem for the solar values, as they derivefrom proto-solar nebula values from ∼ ii regions, justifying a careful examination of what we may be able to determine aboutthe actual scaling behaviour. See section 2 above.The problems arise due to the rate at which the heavier elements have been formed in stars since earlyepochs. Different enrichment processes occur for the elements that are most important to the heating/coolingbalance in H ii regions, so it is important to improve our estimates of actual scaling behaviour, insofar asthis can be determined.We also strike a definition problem: stellar abundances are measured relative to iron as the reference, whereas nebular abundances are measured relative to oxygen. The ratios of these two reference elementshave varied considerably with time: oxygen is principally produced in core-collapse supernovae (SN), whereasiron is principally produced in detonation SN. Core-collapse SN began enriching the primordial interstellargas very early in the history of the Universe, but detonation SN have a delayed onset. So iron is relativelyscarce early and increases rapidly after the delayed onset of detonation SN. Nitrogen is more complicatedstill: it is produced in both type of SN, but also in evolved stars, for example on the AGB branch and inhot young WN stars—some of these processes are prompt and some delayed, and some dependent on totalmetallicity and stellar mass.Helium presents further problems. It is the second most common element in the Universe and isimportant in the nebular heating and cooling balance, especially at low total metallicities. It was createdin the Big Bang and is being created continuously in stars, therefore its abundance has increased in theinterstellar medium (ISM) from the primordial value to the present day value. We have no detailed dataon the historical rate of production of helium, but it is no doubt determined by the overall history of starformation, so, in the absence of better data, we assume a linear behaviour with oxygen metallicity. Thecalculation of helium abundance at different total metallicities depends on our estimate of the primordialvalue, itself prone to revision. Before attempting to calibrate the way abundances scale with total metallicity, we need an abundancereference standard set. As noted above, inconsistencies in stellar atmosphere and evolutionary track modelscan arise whenever a new standard solar abundance set is published. For this reason we adopt the “CosmicAbundance Standard” proposed by (Nieva & Przybilla 2012, hereafter, NP12), based on local B stars as thestandard for the present day and the local region of the Milky Way, extended for completeness to includeelements not present in NP12.The suitability of the local B star abundances as a standard reference scale has been discussed in detailby NP12. Although the values derived from local B stars have uncertainties similar to the solar values,and are also potentially subject to revision if a more extensive stellar population is used, our reasons forproposing this set as a reference standard are: B star photospheric abundances measure the bulk abundancesof the nebulae in which they recently formed; they formed locally in the Milky Way; and they provide anensemble average over 29 stars, rather than depending on a single star (the sun) which may or may not betypical of current local abundances.The NP12 list includes the eight most important nebular elements, He, C, N, O, Ne, Mg, Si, and Fe.We augment this set for completeness with the best estimates of abundances for elements not included in theNP12 list, for example from the most recent solar (Grevesse et al. 2015; Scott et al. 2015b) and meteoriticabundances (Scott et al. 2015a,b; Grevesse et al. 2015; Lodders et al. 2009). This approach has been used inall previous solar reference lists. However, these other elements are less important in the physics of nebularprocesses. Although the values we suggest are not arbitrary, other sources could be chosen. We discuss thereasons for adopting the particular values in detail below.The “Galactic Concordance” scale is given in Table 1. It is encouraging to note that the local B starabundance for oxygen (12+log(O/H)=8.76) is closer to the estimated primordial solar abundance (8.73) fromAsplund et al. (2009) than to the often used solar photospheric abundance (8.69). The Galactic Concordance scale also includes scaling behaviour, as we now discuss.
Through long usage, the “Z” symbol specifies metallicity (that is, the combined mass fraction of allelements heavier than He) and Z is the solar reference metallicity. Using the terminology “Z/Z ” as themeasurement of metallicity relative to solar metallicity is ambiguous. The ambiguity arises from the factthat whereas Z is strictly defined as the total abundance of elements heavier than helium (specified in theX(H)+Y(He)+Z = 1 mass fraction relationship), it has come to be loosely used in nebular analysis to meanthe abundance of oxygen. While oxygen makes the dominant contribution to total Z, the two values are notidentical.An alternative “solar-independent scaling factor” is desirable, to avoid this ambiguity. In order toput abundance scaling on a more systematic basis, we propose a scaling parameter, ζ . The scaling originstandard fiducial point, ζ = 1 (log ζ = 0), is based on the mean values of local region B stars from Nieva& Przybilla (2012), and therefore refers to the present day chemical abundances in the local region of theMilky Way.We also need to specify, with ζ , the element used as the scale reference. We could use any elementor group of elements as the basis for scaling. The obvious choices are iron (used in the stellar abundancescale) or oxygen (employed in nebular physics), or the total metallicity, Z. We refer to these as ζ F e , ζ O and ζ Z , respectively. In practice, Fe and O are the most useful and the most widely used. While these scalingfactors are different, we will show that they can be readily converted one to the other, using observed scalingbehaviour derived from the stellar spectra (section 4). For H ii regions, the measured spread of metallicity ranges over 1 / (cid:46) Z/Z (cid:46)
2, with most beingfound at
Z/Zo > .
1. Stellar metallicities (measured on the [Fe/H] scale) span a wider range, between ∼ − and ∼ ii regions at low abundances, since there is very littleobservational material on nebular Fe abundances, and we have little knowledge on how depletion onto dustaffects the gas-phase abundance of Fe. This is especially true at low metallicities.To deal with this problem, we can draw on the extensive information from stellar spectra as a guide torelative abundances of many elements at low metallicities, (see, for example, Gonz´alez Hern´andez et al. 2013).If we use data for main sequence stars, before their atmospheres have evolved due to local nucleosynthesisand dredge-up, we have useful information on the abundances in the H ii regions in which they formed,spanning a far greater range of total metallicity than possible from nebular data.Major benefits of this approach are in the wide metallicity range available and the ability to avoidabundance uncertainties due to dust depletion. Minor problems include the different, Fe-based, scaling usedin stellar measurements, and the difficulty of measuring the abundances of some elements, notably oxygen.As we will show, the choice of scaling reference element is not a problem using the ζ parameter, and sufficientstellar spectra are available to provide an accurate idea of how the available stellar data for oxygen scales Z X 12+log(X/H) Source1 H 12.000 -2 He 10.990 13 Li 3.278 24 Be 1.320 25 B 2.807 26 C 8.423 37 N 7.790 48 O 8.760 19 F 4.440 210 Ne 8.090 111 Na 6.210 512 Mg 7.560 113 Al 6.430 514 Si 7.500 115 P 5.410 516 S 7.120 517 Cl 5.250 218 Ar 6.400 519 K 5.040 520 Ca 6.320 521 Sc 3.160 522 Ti 4.930 523 V 3.890 524 Cr 5.620 525 Mn 5.420 526 Fe 7.520 127 Co 4.930 528 Ni 6.200 529 Cu 4.180 530 Zn 4.560 5Source Reference1 Nieva & Przybilla (2012)2 Lodders et al. (2009)3 fit to O and Fe4 fit to N/O vs O curve5 Scott et al. (2015a,b),Grevesse et al. (2015)
10 – with iron.In the following section, we explore the stellar data available for 6 elements that play a key role incontrolling the nebular emission line spectrum (O, Ne, Mg, Al, Si, S), and also Ca. We present simplepiece-wise linear fits to the abundances derived from the spectral data for these elements. We fit carbonusing the iron scale so that it is consistent with the observed log(C/O) curves vs log(O/H) from Nieva &Przybilla (2012). For nitrogen a fit is obtained from stellar abundance log(N/O) values plotted vs stellaroxygen abundance, and similarly for Cl. From nebular measurements, we assume that the α -process elementsNe and Ar scale with O directly. Stellar data for elements of minor nebular importance are treated similarlyin Appendix A (Na, P, K, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn).It is worth stressing that our purpose is not to model exactly how the abundances scale with iron,because of the intrinsic variation between individual stars and stellar populations even within the MilkyWay, but to gain an overview of the trends where they are apparent, and to use these to build improvedmodels for scaling nebular abundances.
4. Abundance scaling in stellar data4.1. Stellar data sources
The study of the scaling of stellar abundance ratios has a long history. It was reviewed by Wheeleret al. (1989), using the stellar data available at the time. Since then, far more stellar data have becomeavailable, in terms of the stellar populations, the range of metallicities and the elements measured. For overtwo decades, much effort has been put into conducting surveys of stellar spectra (see, for example Mayoret al. 2003; Magrini et al. 2014). In particular, work searching for evidence of extra-solar planets (see, e.g.,Gonz´alez Hern´andez et al. 2013) has yielded an extensive collection of high quality stellar spectra. Theseprovide direct measurements of how element abundances evolve with increasing total metallicity.Some of these studies have been targeted at the derivation of abundances of specific elements, othershave been directed at ranges of elements such as the iron-peak or the α -elements. Some investigate dwarf F,G and K stars in the solar neighbourhood, others concentrate on stars in the thin disk, thick disk and halo.The stellar data references used here are listed in Table 4 and with each abundance plot (Figures 2 - 6 and10- 13). The stellar populations observed in these references are given in Table 5. Taken as a whole, theyprovide an extensive database from which to explore abundance scaling over a wide range of metallicities.We use data from these sources to develop models for the nebular scaling relations between each element.In nebular modelling, the abundant elements which determine both the ionisation and thermal struc-tures of nebulae, and hence the emission line spectra, are H, He, C, N, O, Ne, Mg, Si, Ar, and Fe. However,as the critical inputs to any nebular model include stellar atmospheres and evolutionary paths, we considerhere all the elements up to Zn. Further, by including less abundant elements such as Ni and Cl, we makepossible comparisons of observed line fluxes and model predictions, thereby allowing us to calibrate themodel settings, and, ideally, estimate dust depletions.The ease of measuring iron in stellar spectra makes it the natural choice for comparing with otherelements. We therefore present the abundances of the elements considered here as a fraction of iron, vs iron,i.e., [X/Fe] vs. [Fe/H] (Equation 1). Although it would be possible to plot [X/O] vs [O/H] from the stellar
11 – spectra, the number of stars with recorded oxygen is significantly less than those with iron measured in thespectrum, and the oxygen data is noisier than the iron data. Consequently we obtain fits to the abundancedata for [Fe/H] scaling, and then invert them to oxygen as the scaling base, using the relation between [O/Fe]and [Fe/H].
Before looking at the stellar data element by element, a few general points are worth noting. • A comparison of stellar abundance measurements using iron as the reference scale and the oxygen-scaled nebular measurements requires us to convert between the two scales. To do this we can observehow stellar oxygen abundance varies with stellar iron abundance, and use this to convert the observedstellar abundance scaling of the other elements between the iron and oxygen scales. The conversionis not a linear process, as different elements are synthesised at different rates during stellar evolution.This analysis is given in detail in the next section. • In general, the scaling of α -elements with iron (log scale) in Milky Way stars is approximately constantfor [Fe/H] > -2.5 until the Type Ia supernovae begin to emerge, and then falls with increasing ironabundance starting at a well defined break point at [Fe/H] ∼ -1.0 (see the discussion in Wyse &Gilmore 1993, especially their Figure 1). The initial abundance ratio of oxygen to iron is determinedby the massive star IMF, and the break point is determined by the star formation rate. There isevidence that the massive star IMF is largely invariant (see, for example, Wyse 1998; Kordopatiset al. 2015). Thus the stellar abundance scaling relations (Figures 1 to 13 below) remain largelyconstant for stars in the Milky Way. This may be a useful starting point for other large galaxieswith similar evolutionary histories to the Milky Way, but may not be the case for smaller galaxies, ormassive active starburst galaxies. • Stellar spectra analyses over the past decade (e.g., Bensby et al. 2005) provide evidence that differentstellar populations in the thin disk, the thick disk, the bulge and the halo of the Milky Way havesomewhat different star formation histories and can therefore be distinguished in abundance plots.As we wish to derive simple abundance scaling models as a guide to abundance scaling in nebulae, webase our models on ensemble average fits to the stellar scaling, rather than using single populations,although in most cases, the sampled populations are dominated by Milky Way thick disk stars. Weprovide a list of the sources used for each element, and the populations studied, in Table 4. We listthe populations studied in these sources in Table 5.
Oxygen is the most abundant element in H ii regions after H and He, and plays a dominant role in thephysical processes. However, it is not an easy element to measure in stellar spectra, due to the weaknessof the absorption lines, especially at low metallicity, and, in some cases, interference from adjacent nickellines. As a consequence, there is significant scatter in the computed abundance values. The manner in whichabundances are calculated is also critical: ignoring non-Local Thermodynamic Equilibrium (NLTE) effectscan introduce errors of ∼
12 – / H] = log(Fe / H) star − log(Fe / H) reference (1)and [O / Fe] = log(O / Fe) star − log(O / Fe) reference . (2)Each data set has been converted to the Galactic Concordance scale (see previous section). The redlines are adopted fits to the observations, discussed below. They are close to the least-square fits to the data(see left panel, Figure 1 ), but the scatter in the stellar data due to the different measured populations andintrinsic measurement and modelling uncertainties, make least-square fitting of little value.In the reported stellar abundance data, there is increasing scatter below [Fe/H] ∼ -2.5. Some of thisis due to measurement noise, and some is due to different methods used to derive the metallicity (LTE orNLTE, 1D or 3D). However, some scatter imay also be caused by intrinsic stochasticity in the abundanceratio, indicating stars that formed in regions where the elements in the ISM had not been uniformly enrichedby sufficiently many core-collapse supernovae to generate a uniform abundance pattern (Wyse 1998). It isalso possible that some scatter is due to the local influence of different types of core-collapse supernovae.More recent data for metal-poor stars from the thick disk from the RAVE survey (Figure 2, Ruchti et al.2011, dark green points, Mg and Si) show a tighter spread than for the oxygen data between [Fe/H] = -2.8and -1.0. To avoid uncertainty in deriving generic fits to the trends, we only attempt fits above [Fe/H] =-2.5. For -2.5 < [Fe/H] < -1.0, there is a region where [O/Fe] appears approximately constant but withwide scatter. This is the zone where the enrichment by core-collapse supernovae has generated an ISMwith approximately constant composition, and also where the element abundances are sufficient to reducemeasurement uncertainty.The next feature occurs at [Fe/H] = -1.0, where there is a breakpoint, followed by clear downwardtrend in [O/Fe] as Type 1a (detonation, or low-mass) supernovae commence enriching the ISM with largeamounts of iron. The scatter in this region is likely due to the intrinsic diversity of stellar populations andindividual evolutionary paths.At some point, a further constant plateau at a lower value of [O/Fe] may be reached, when the enrich-ment balance of core-collapse and detonation supernovae again achieve a constant abundance ratio, assuminga continuing supply of interstellar gas. The stellar data do not show if, or exactly where this second break-point occurs, so, for the purposes of analysis we have set it at [Fe/H] = +0.5, corresponding to ∼
13 – the current reference iron abundance. It does not seem likely that the enrichment of iron relative to otherelements will continue indefinitely. There is some evidence consistent with this assumption in the α -elementresults presented by Casagrande et al. (2011, in particular, their figure 19).A further point to note is that there appears to be a sharp upper limit, ∼ +0.6, to the [Fe/H] valuesobserved. The reason for this may be that no stars have yet formed above this iron abundance to enrichthe ISM. It is the subject of a current research program (M. Asplund, 2016, pers. comm.). The equivalentwidths of iron absorption lines are also difficult to measure at high metallicity against a stellar continuumeroded by numerous fine absorption lines. Figure 2 (middle and right panels) shows the logarithmic abundance plots for the α -elements magnesiumand silicon, both of which exhibit the same behaviour as oxygen, repeated in this figure for comparison. It isclear that the upper breakpoint is very similar for each α -element, at [Fe/H] ∼ -1.0 for the Milky Way starsanalysed. This is consistent with the idea that for [Fe/H] < -1.0, the abundance patterns are established bynumerous core-collapse supernovae. Above that value, in each case, detonation supernovae commence theiron enrichment process. Other similar published data, e.g., Bensby et al. (2005, their Figure 8) show thesame behaviour, but have not been included in the diagrams for clarity. The data for Ca, S and Al in Figure 3 follow oxygen, magnesium and silicon, as expected for elementsgenerated by the alpha process. In the aluminium plot, the offset and scatter at low [Fe/H] may be theresult of stellar model deficiencies in the older data, and so have not been included in the line fit.
Carbon and nitrogen in nebulae present a problem when scaled to metallicities higher or lower than thestandard baseline. Vila Costas & Edmunds (1993, figure 4) showed that the nebular scaling of nitrogen withoxygen can be explained by a combination of primary nitrogen (a constant fraction of oxygen with increasingoxygen abundance) and secondary nitrogen (a linearly increasing fraction of oxygen with increasing oxygen inlog space). The primary abundances originate from enrichment by core-collapse supernovae in the native gascloud from which the H ii region formed, and the secondary abundances arise from delayed nucleosynthesisthrough hot-bottom burning and dredge-up in intermediate mass stars as they evolve.The existence of primary nitrogen has been questioned for stellar spectra (Asplund 2005), but thenebular data consistently appear to follow the primary/secondary trend (see Vila Costas & Edmunds (1993);
14 – -2.0 -1.0 0.00.00.51.0 [ X / F e ] O 6300O 7770 adopted fit ___least squares fit ----- Ξ = 0.50 O -2.0 -1.0 0.0 Ξ = 0.4 Si -2.0 -1.0 0.0[Fe/H] Ξ = 0.40 Mg Fig. 2.— Scaling of O, Mg, Si vs. Fe from stellar spectra. Left panel: Oxygen scaling asa function of [Fe/H] from Amarsi et al. (2015), the most carefully and consistently reducedstellar oxygen data available. The adopted piece-wise linear fit is shown as a red line, andthe standard (GC) metallicity (fiducial point) as a yellow circle. The dashed orange line is apiece-wise least-squares fit to the data, and differs from the adopted fit by far less than theintrinsic scatter of the stellar data. The parameter Ξ is defined in Equation 5 and specifiesthe low metallicity plateau value. Note that, in this and subsequent figures, while the trendlines drawn extend to [Fe/H] < -2.5, we only use values > -2.0 in our nebular fits. Mid- andright panels show the stellar data for Mg and Si. Sources: (Amarsi et al. 2015, O, blue andblack points) (Ruchti et al. 2011, Mg, Si, dark green), (Adibekyan et al. 2012, Mg, Si, grey),(Gonz´alez Hern´andez et al. 2013, Mg, Si, orange), (Bensby et al. 2014, Mg, Si, blue discs),(Hinkel et al. 2014, Mg, Si, purple), (Howes et al. 2015, Mg, Si, red circles) (Cayrel et al.2004, Si, blue circles) 15 – Dopita et al. (2000); Groves et al. (2004); Dopita et al. (2013), and Izotov & Thuan (1999)), so we acceptthis model as a useful description of the scaling behaviour of nitrogen. The observed dispersion in the valuesof log(N/O), especially at low metallicity, are discussed in Gavil´an et al. (2006). Clearly, this spread makesspecifying a single description problematic, but we use the fit described here, noting that it should be treatedas a starting point for modelling, rather than being prescriptive.Figure 4 presents plots of log(C/O) and log(N/O) vs. 12+log(O/H), showing the complex scalingbehaviour due to primary and secondary sources. (We use the 12+log(O/H) scale, rather than [O/H],following the nebular physics convention). The left panel of that figure shows stellar carbon data fromGustafsson et al. (1999) (squares, galactic disk solar type dwarfs), Spite et al. (2005) (diamonds, halo metal-poor unmixed giants), Fabbian et al. (2009) (crosses, halo solar type dwarfs and subgiants), and Nieva &Przybilla (2012) (blue circles, B stars in the local region). The nitrogen data are also consistent with thatfrom Moll´a et al. (2006); Gavil´an et al. (2006). Likewise, the fits and data from Gavil´an et al. (2005) areconsistent with the carbon data presented here.For carbon, the data from Akerman et al. (2004) and Nissen et al. (2014) were not used in the fit,as information on computation methods used (solar standard, N/LTE) was not clear, but the data fromthose sources suggests they are consistent with the fit. The scaling we assume for carbon depends on stellarobservations with consequent caveats on their reliability. It is well established that some very early starsare rich in carbon while being very metal poor (carbon enhanced metal poor, or CEMP) (e.g. Norris et al.2013). Thus the fit for carbon scaling can at best be an average. The observed scaling can be fit with thepiecewise linear method as a function of [Fe/H], used for the α -elements, well within the scatter of the data,so we use this method for simplicity. The best fit is achieved for a fiducial value of 12+log(C/H) = 8.42,rather than the B star value of 8.33. The latter value was similar to the previous B star value reported bythose authors, and somewhat lower than solar photospheric or bulk value, as discussed by Asplund et al.(2009). The fiducial value we propose is closer to previous solar and meteoritic values (see Table 3), but thismay require revision in the light of better data and more accurate analysis methods.The right panel shows the equivalent data for nitrogen, from Spite et al. (2005) (diamonds, halo metal-poor unmixed giants), Fabbian et al. (2009) (crosses, halo solar type dwarfs and subgiants), Nieva & Przybilla(2012) (local B stars, blue dots) and nebular data from Blue Compact Galaxies from Izotov & Thuan (1999)who state that there is little evidence for dust in these objects, and, by implication, that there is little oxygenor nitrogen depletion into dust.The determination of N is doubly difficult. Primary and secondary source behaviours that dependon individual galaxy star formation histories and particular populations, mean that the onset of secondarybehaviour will vary from case to case, making a single function unlikely to match any given object. A furthercomplication is the difficulty in estimating nitrogen abundance spectroscopically in metal poor stars, whereNLTE and 3D effects need to be taken into account. Any abundance scale used in nebular modelling, basedon N or N/O ratios, is somewhat uncertain. Consequently, the fit we propose here only applies to bulkwell-mixed nebular abundances for the Milky Way. A check on this fit is available from the Blue CompactDwarf galaxy nebular data in Figure 4 from Izotov & Thuan (1999) (orange discs). Although limited by thenature of the objects to a restricted metallicity range, the fit suggests that this curve provides a satisfactorydescription of the nebular abundance behaviour.The stellar data for carbon and nitrogen span a range from 12+log(O/H) ∼ ∼
16 –
We fit a simple expression combining the primary and secondary sources to the stellar data,log(
X/O ) = log (cid:104) a + 10 [log(O / H)+b] (cid:105) (3)where X = N or C, using χ -square minimisation to obtain a best-fit analytic curves. The fits to the stellardata are shown in Figure 4 (red lines), with primary and secondary fits (black-dashed lines). For carbon,a = -0.8, b = 2.72, and for nitrogen a = -1.732, b = 2.19. The nitrogen data show a greater scatter thanfor carbon, due to the intrinsic variation in nitrogen. However, the fit provides a means for scaling nitrogenabundance based on known physics. The fit of the nebular points (orange dots) suggests the curve is likelyto be a considerable improvement on simple linear scaling. The observed behaviour of nitrogen was fittedanalytically by Groves et al. (2004) for AGNs, who derived a relation similar to Equation 3. Helium was created through nucleosynthesis during the Big Bang, and is still being created continuouslyby stars. Thus, the abundance of helium began at the primordial value and has increased steadily sincethen. In the absence of a detailed knowledge of the historical star formation rate in our galaxy, we assumea linear rate of increase with oxygen abundance. (Both oxygen and helium abundances increase due toearly core-collapse supernovae, whereas the main increase in iron abundance has a delayed onset, as notedearlier). There have been numerous attempts to estimate primordial He. We adopt the primordial abundancefrom WMAP measurements (Olive & Skillman 2004; Cyburt et al. 2008) corresponding to a mass fractionY primordial = 0.2486 ± ± ii regions and may be affected by stellar evolutionary processes. Whenexamining the helium content of enriched populations in globular clusters, Portinari et al. (2010) adopt thevalue for Y primordial = 0.240 ± ζ for oxygen, i.e., ζ O , we can express theabundance of helium as: log(He / H) = − . . × ζ O /ζ O (0)] (4)In the absence of better data, following Pagel et al. (1992), we assume a simple linear relationship. Itshould be noted, however, that the same formalism can be used for any other primordial and present-dayhelium abundances, and if data is available to suggest a non-linear relationship with oxygen abundance, thiscan also be accommodated.
17 – -2.0 -1.0 0.00.000.501.00 Ξ = 0.35 Ca [ X / F e ] -2.0 -1.0 0.0[Fe/H] Ξ = 0.40 S -2.0 -1.0 0.0 Ξ = 0.40 Al Fig. 3.— Scaling of Ca, S, Al vs. Fe from stellar spectra. Sources: (Ruchti et al. 2011,Ca, dark green), (Adibekyan et al. 2012, Ca, yellow), (Howes et al. 2015, Ca, red circles),(Cayrel et al. 2004, Ca, blue circles), (Hinkel et al. 2014, Ca, Al, purple), (Bensby et al.2014, Ca, Al, blue), (Gonz´alez Hern´andez et al. 2013, Ca, S, Al, orange), (Caffau et al. 2005,2011b, S, black, red), (Spite et al. 2011, S, magenta), (Edvardsson et al. 1993, Al, yellow),(Andrievsky et al. 2010, Al, grey), (Cayrel et al. 2004, Al, red) l og ( C / O ) C l og ( N / O ) primarysecondary N secondary primary Fig. 4.— Scaling of C and N. C: sources: (Gustafsson et al. 1999, orange squares), (Akermanet al. 2004, blue circles), (Fabbian et al. 2009, green ’x’), (Spite et al. 2005, black diamonds),(Nieva & Przybilla 2012, blue discs), (Nissen et al. 2014, yellow discs) N: sources: (Izotov& Thuan 1999, orange discs), (Israelian et al. 2004, green ’+’), (Spite et al. 2005, blackdiamonds), (Nieva & Przybilla 2012, blue discs) 18 –
The noble gases neon and argon are not normally detected in the solar spectrum, so we need to seekother ways of determining how they scale. The Neon abundance has been measured in B star atmospheresby Morel & Butler (2008) and Nieva & Przybilla (2012), who propose values of 7.97 ± ± ii regions, and as α -elements, we can useoxygen scaling with iron as a guide. Figure 5 presents plots of log(Ne/O) and log(Ar/O) vs 12+log(O/H)taken from several nebular sources. The red circles indicate the galactic concordance fiducial values. Notethat these indicate the total abundances, whereas the nebular data only record the gas phase abundances,making no allowance for the dust depletion, which is likely to be variable and is not well known. It isunlikely that any neon or argon is depleted into dust, as indicated by the very low abundances in chondriticmeteorites (Lodders 2003; Lodders et al. 2009). In Figure 5, error bars have been included to illustrate thatconstant linear fits are warranted in both cases. Because the nebular data do not allow for dust depletion,the total (dust and gas phase) oxygen is greater than the plotted nebular points indicate, and one wouldexpect the GC origin points to be below the linear fits. The GC fiducial value for neon from the B star data(Nieva & Przybilla 2012) is above the fit line, whereas dust depletion of oxygen would suggest it should bebelow. The sizes of the error bars do not allow us to draw any conclusion, so for consistency we have retainedthe B star value. For argon we have adopted the most recent solar value (see Table 3). Both values mayneed to be adjusted in the light of planned modelling of particular H ii regions in the Magellanic Clouds, thesubject of forthcoming papers. Solar photospheric abundances of chlorine can only be measured (indirectly) in sunspots from the HClabundances (Asplund et al. 2009, and references therein). The solar values for chlorine from Asplund et al.(2009) date back with minor variations to sunspot measurements, ca. 1970.However, gas-phase abundances of chlorine have been measured from high resolution nebular spectra(e.g., Garc´ıa-Rojas & Esteban 2007). Recently, Esteban et al. (2015) presented revised values for nebularchlorine as it scales with oxygen in Milky Way H ii regions. Figure 6 shows log(Cl/O) vs 12+log(O/H)from Milky Way H ii regions (Esteban et al. 2015) and from extra-galactic H ii regions (Izotov & Thuan2004; Izotov et al. 2006). The horizontal dashed lines show the scaling for solar photosphere data fromAsplund et al. (2009, AGS09, black dashed line) and meteoritic data from Lodders et al. (2009, LPG09,blue dashed line), assuming chlorine scales with oxygen. The nebular abundances have not been correctedto total abundance (gas-phase plus dust), because dust depletion for oxygen and chlorine are variable andnot well known.Chlorine is likely to be depleted into moderately volatile compounds (Lodders 2003), and can reactefficiently with neutral hydrogen to form H+Cl compounds (Balashev et al. 2015; Moomey et al. 2012), soit is likely that it will be somewhat depleted in H ii regions. Thus the nebular data cannot be used to definea generic value for chlorine abundance, but they do suggest a better fit to the meteoritic data than the solarphotospheric data (Figure 6), although Lodders (2003) notes that chlorine in meteorites is variable. For
19 – these reasons, in the Galactic Concordance we adopt the meteoritic values for chlorine from Lodders et al.(2009).Although they are not prominent, emission lines of chlorine [Cl ii ] and [Cl iii ] are observed in low noiseH ii region spectra. Chlorine does not play a significant role in the thermal balance of nebulae, but chlorinelines, where observed in nebulae, can be a useful density diagnostic and the reference abundance may warrantrevision when better data is available. Some stellar data is available for Z > > >
0. We have not attempted to model this behaviour for two reasons. Most important is that noneof these elements plays a major role in nebular thermal balances. Second, if the reality of the upturn isconfirmed with more extensive data, it will be possible to accommodate it using the ∆ parameter describedby Equation 8, below.
Apart from the 12 elements considered above, there are others that are of minor importance in theenergy balance in H ii regions and other emission nebulae, but may be important in modelling stellar at-mospheres and evolutionary tracks. The adopted reference abundances for the remaining 18 elements to Znand their sources are given in Table 1. The stellar data and scaling fits for these elements are in AppendixA.
5. The nebular scaling function5.1. General approach
The extensive stellar data demonstrate that different populations of stars in the Milky Way (and othergalaxies) are present that differ somewhat in their scaling behaviour with [Fe]. The objective of this work isto propose a series of linear fits to the bulk MW stellar trends as a first order approximation, rather thanto attempt different fits for specific populations. The latter is possible, but for the primary purpose of thiswork. Piece-wise linear fits to the bulk trends are appropriate to describe the scaling relations.
20 – l og ( A r / O ) l og ( N e / O ) ( ga s pha s e ) ArNeNeNe
Fig. 5.— Scaling of Ne and Ar vs. oxygen from nebular spectra (the red circles indicate theGC fiducial values). Sources: (van Zee et al. 1998, squares), (Izotov & Thuan 1999, circles),(van Zee & Haynes 2006, diamonds), (Berg et al. 2013, filled squares) l og ( C l / O ) ( ga s pha s e ) AGS09LPG09 Cl Fig. 6.— Nebular chlorine vs oxygen: the dashed lines are from Asplund et al. (2009)(AGS09, black line, solar) and Lodders et al. (2009) (LPG09, blue line, meteoritic). Thecircles are gas-phase Milky Way nebular data from Esteban et al. (2015). The dots are fromgas-phase nebular data from Izotov & Thuan (2004) (blue, Blue Compact Galaxies) andIzotov et al. (2006) (black, metal poor emission line galaxies). 21 –
To model this behaviour, we adopt simple piece-wise linear fits, as shown by the red lines in the stellardata plots. For the bulk trends, these need only be fit by eye, as a χ -square or least-squares fit is notwarranted for our purposes, and the statistical variability of the data points may not be Gaussian, renderingsuch fits inappropriate. However, Figure 2 (left panel) shows a least squares fit, which is close to the adoptedfit and well within the scatter of the data. While the real behaviour could exhibit curved breakpoints, theintrinsic scatter in the data (and the measurement uncertainties, not shown for clarity) do not warrant amore complex model. This model has the additional benefit of computational simplicity. The standard (GC)metallicity (which we refer to subsequently as the “fiducial point”) is marked with a yellow circle in Figure2 and subsequent plots. The piecewise linear fit for oxygen may be expressed as: [O / Fe] = +0 . , − . < [Fe / H] < − . , = − . × [Fe / H] , − . < [Fe / H] < . , = − . , [Fe / H] > . . (5) The initial 0.5 factor is characteristic of the initial O/Fe yield in massive early stars. Similar factorsapply to other α -elements, but with different values. We call this factor Ξ and as the scaling is relativeto iron, we append the Fe suffix: Ξ F e . For oxygen on the iron scale the factor is Ξ
F e (O), for magnesium,Ξ
F e (Mg), etc.As the α -elements, to a good approximation, share the same break points, Equation 5 can be generalisedto describe iron-based scaling for any element X with the same breakpoints: [X / Fe] = +Ξ
F e (X) , − . < [Fe / H] < − . , = − Ξ F e (X) × [Fe / H] , − . < [Fe / H] < . , = − Ξ F e (X) × . , [Fe / H] > . . (6) Below [Fe/H] =-2.5 the stellar data are too sparse to warrant a fit. Our aim here is to establish generalfits as the basis for improved abundance scaling in photoionisation models, recognising that the detailedabundance behaviour may be somewhat more complex, and/or variable. The intrinsic spread of the data inall the graphs provides an estimate of the errors in the Ξ parameters derived for each element, approximately ± In section 2.4 we introduced the scaling parameter ζ (referred to the chosen scaling base element,usually iron or oxygen), and the Galactic Concordance reference abundance set. To describe the scaling ofindividual elements, taking into account their different scaling behaviours, we use a general expression toseparate the specific behaviour of each element from the fiducial value and the scaling parameter.
22 –
We introduce the parameter ∆ (dex) to describe individual element behaviours. ∆ encompasses theevolutionary details, i.e., the way the abundance of an element scales with ζ in the scaling base chosen, forexample, Fe: log(X / H) = log(X / H) + ∆ Fe (X) + log ζ Fe (7)where the zero suffix refers to the fiducial value for the element X. For simple scaling, ∆ = 0. For piecewiselinear iron-base scaling, such as the α -elements exhibit (Equation 6), with a low abundance ratio Ξ F e andabundance break points χ and χ (dex), ∆ F e for a given element X is a function of ζ F e , Ξ
F e , χ , and χ : ∆ F e (X , ζ Fe ) = Ξ F e ( X ) = const . , log ζ Fe < χ , = Ξ F e (X) χ × log ζ F e , χ < log ζ F e < χ , = Ξ F e (X) χ × χ = const . , log ζ Fe > χ . (8) The second part of the fit passes through [Fe/H] = 0 at log( ζ F e ) = 0. While it would be possible to fita more complex function, given the uncertainties in the data, a high order function for ∆ is not warranted.However, nitrogen is not well described by a simple piecewise linear fit, because of the complexities ofprimary and secondary enrichment (Figure 4, right panel, and Equation 4). This case illustrates how ∆ canbe generalised to more complex forms, using oxygen as the scaling base:∆ O (N , ζ O ) = log (cid:0) − . + 10 log ζ O − . (cid:1) (9)Equation 8 demonstrates an important aspect of abundance scaling. As Fe scales, for example, at lowFe/H values, oxygen is enhanced considerably:log(O / H) = log(O / H) O + ∆(O , ζ Fe ) + log ζ Fe (10)where ζ Fe is linear in Fe enrichment and ∆ = Ξ Fe (O), or ∼ +0.5 dex at low Fe/H. In other words, the wellknown enhancement of oxygen relative to iron at low metallicity is expressed explicitly. Using this system it is easy to convert from one ζ scale to another, for example, to use oxygen scaling,allowing iron to be depleted at low oxygen enrichments, we have:log ζ O = ∆( O, ζ Fe ) + log ζ Fe (11)where ∆ is the same function used for Fe scaling. The break points χ , have different values on the ζ O and ζ F e scales, but can be converted simply from one scale to the other.If a different scaling for element Y is required, the Ξ X of all elements (Z) are converted to Y simplyvia: Ξ Y ( Z ) = Ξ X ( Z ) − Ξ X ( Y ) (12)
23 –
Note Ξ( X ) X ≡
0, so Ξ( X ) Y = − Ξ( Y ) X and the break points (in dex) by: χ ( Y ) = χ ( X ) + Ξ X ( Y ) (13)and χ ( Y ) = χ ( Y ) × χ ( X ) /χ ( Y ) (14)and then the ζ Y and ∆ Y parameters for the new element are available. Figure 7 illustrates equations 7-14 graphically. The upper panel shows [X/Fe] vs log ζ Fe (blue lines,where X = Fe and O) and [X/O] vs log ζ O (black lines, where X = Fe and O). The shorter dashes indicatewhere the fit is not reliably based on stellar data, the longer dashes are the assumed behaviour, withoutstellar evidence. The lower panel presents similar data for magnesium, showing how the scaling changeswhen the scale base element is changed. Note that for the x-axes,log ζ O ≡ log( O/H ) − log( O/H ) fiducial ≡ [ O/H ] (15)and log ζ Fe ≡ log( F e/H ) − log( F e/H ) fiducial ≡ [ F e/H ] . (16)The grey shaded areas illustrate the different values of the break points between Fe and O.Figure 8 shows plots of [X/H] vs log( ζ Fe ) for iron, oxygen and magnesium (X) (upper panel), and [X/H]vs log( ζ Fe ). The behaviour of the different scalings is much easier to understand in Figure 7, and is why wehave used this approach in Figures 2-13 and 9. Table 2 summarises the scaling parameters for Milky Way stellar abundances for hydrogen to zinc, withthe low metallicity level Ξ and the break points χ and χ expressed in the Fe base scale, and also convertedto the oxygen base scale. The fiducial scale log( X/H ) is included from Table 1, less the 12 factor. Forthe α and α -like elements, Ξ F e and the two break points are derived from the observed stellar abundances.For iron-peak and iron-peak-like elements, Ξ
F e (X) = 0. Because of the scatter on the stellar values anddifferences between stellar populations, precise fitting of the model is not possible.For F, Cl, Ne and Ar, there are no extensive stellar abundance scaling data and we assume theirabundances scale with oxygen, so the Ξ
F e values are that of oxygen. The abundance data for Li, Be, Bare taken from meteoritic values and we have little information on how they scale. As they do not play amajor role in nebular physics, they can safely be ignored here. Carbon can be scaled equally well to ironwith a low value of Ξ
F e or to the primary/secondary curve fit, given the spread in the data, so the formerwas chosen for simplicity of computation. For nitrogen we have used the primary/secondary fit curve, scaledwith oxygen.The data in Table 2 are intended as a general guide to how typical Milky Way thick disk stellarabundances scale. Precision is not possible from the available data, and it is likely that for any element, no
24 – -3.0 -2.0 -1.0 0.0 1.0-0.50-0.250.000.250.50 log ζ Fe,O [ M g / F e ], [ M g / O ] fiducial χ χ Ξ Fe (Mg) Ξ O (Mg) χ χ ζ Fe )[Mg/O] vs log( ζ O ) -0.50-0.250.000.250.50 [ O / F e ], [ F e / O ] Ξ Fe (O) fiducial χ χ Ξ O (Fe) χ χ Ξ O (O) [O/Fe] vs log( ζ Fe )[Fe/O] vs log( ζ O ) Ξ Fe (Fe) Fig. 7.— Upper panel: Plots of [X/Fe] vs log ζ Fe (blue lines, X = Fe and O) and [X/O] vslog ζ O (black lines, X = Fe and O). Lower panel: Plots of [Mg/Fe] vs log ζ Fe and [Mg/O] vslog ζ O
25 – -3.0 -2.0 -1.0 0.0 1.0-3.0-2.0-1.00.01.0 log ζ Fe , log ζ O [ X / H ] fiducial [Mg/H] vs log ζ Fe [O/H] vs log ζ Fe [Fe/H] vs log ζ Fe -3.0-2.0-1.00.01.0 [ X / H ] fiducial [O/H] vs log ζ O [Fe/H] vs log ζ O [ M g / H ] vs l og ζ O Fig. 8.— Upper panel: Plots of [X/H] vs log ζ O for iron, oxygen and magnesium (X). Lowerpanel: vs log ζ Fe
26 –Table 2: Scaling parameters Ξ Fe and Ξ O for Milky Way stars, with upper and lower breakpoints. For nitrogen the behaviour is not well described by the piecewise linear fit model, buta value can be ascribed to Ξ and the primary/secondary scaling specified by the ∆ parameter(Equations 8 and 9). Carbon can be sufficiently well described by the piecewise linear fit anda single Ξ value. The elements H, He, Li, Be and B are not described by the Ξ parameter,because hydrogen is the reference element, we assume helium scales simply with ζ O andLi - B are not important in nebular analysis, as well as having very low abundance. Forconvenience the ’fiducial’ value of log(X/H) is repeated from Table 1, without the additionof 12. Z X Ξ Fe ( X ) Ξ O ( X ) log(X/H) upper break -1.0 -0.5 lower break
27 – one single value of Ξ applies to all stellar populations sampled. As noted, carbon also has a primary/secondarygrowth curve (Figure 4, left panel), but given the observational uncertainties, abundances can be sufficientlywell described by the piecewise linear fit and a single Ξ value. We use the scaling described by these “average”Ξ values as the basis for nebular scaling in the Milky Way and similar galaxies, to replace the simple scalingpreviously assumed.
An online web application has been implemented that allows all of the above scaling calculations to becomputed: http://miocene.anu.edu.au/mappings/abund . This paper provides the background necessaryto use that application.
All the stellar data considered so far have been derived from Milky Way stars. The spectra of individ-ual giant stars can also be measured for nearby galaxies, for example the Large Magellanic Cloud (LMC)(Pomp´eia et al. 2008; Van der Swaelmen et al. 2013) and the Sculptor Dwarf Elliptical galaxy (Tafelmeyeret al. 2010; Geisler et al. 2005; Kirby et al. 2009). Figure 9 shows the same data for [Mg/Fe] vs [Fe/H] asin Figure 2 but including data for the Sculptor Dwarf and the LMC bar and disk. The figure shows theSculptor Dwarf (red circles), the LMC (blue circles) and the Milky Way (grey circles). The Sculptor starsexhibit same behaviour as the Milky Way stars, but with a lower [Fe/H] breakpoint and steeper drop. Thisis to be expected, as there would have been fewer core-collapse supernovae in the Sculptor Dwarf before theType 1a supernovae started enriching iron, compared to the Milky Way. The LMC stars also exhibit a lowerbreak point than the Milky Way, due to lesser contributions to the metallicity from core-collapse supernovae,as suggested by Van der Swaelmen et al. (2013). The LMC appears to have two populations as some starshave abundance ratios similar to the Milky Way stars, while others appear to be intermediate between theMilky Way and Sculptor. The piecewise linear fit lines are chosen by eye to illustrate the trends. The scalingbehaviour in each galaxy is similar in form, suggesting a universal process, but one where the break pointand “zero point” depend on the galaxy, as described by Wyse & Gilmore (1993). Stars in the Fornax Dwarfbehave similarly to the Sculptor Dwarf (Tafelmeyer et al. 2010), but have been omitted for clarity.We can draw an important conclusion from this. While the piece-wise linear scaling of α -elements withFe appears to be a universal process, the break point depends on the star formation history (Wyse & Gilmore1993) and thus on the galaxy mass. Where the star formation history of larger galaxies is similar to that ofthe Milky Way, the abundance scaling for these galaxies can be assumed to follow the scaling fits derivedfor the Milky Way. However, Kudritzki et al. (2015) found three distinct groups of star forming galaxies inthe local region. Modelling these groups may require modification to the break points, but this must awaitobservations of appropriate stellar populations and their abundances. It is possible that careful fitting of theabundance behaviour of the different populations in the Milky Way may cast light on the variability of thefit parameters in other galaxies. Modelling the abundance behaviour of small dwarf galaxies is also likelyto require different scaling than for the larger spirals. Calibrating the break point to star formation historymight provide useful information.The data in Figure 9 do not allow us to decide whether there is a common value for the low-metallicity
28 – trend for the three objects in Figure 9. As the early enrichment is due to core-collapse supernovae, andit is possible that the massive star IMF is invariant (Wyse 1998; Kordopatis et al. 2015), once we have astatistically mixed ISM, the [Mg/Fe] to [Fe/H] ratio should be consistent between different galaxies at lowmetallicities. Clearly, more data is required to confirm this. In general, however, the scaling behaviour followsa similar pattern. Appropriate fits to the parameters that specify the trends (fiducial point, break point andlow metallicity trend level) will most probably describe the scaling in any galaxy. Better observational datais required to identify appropriate parameters.
6. Dust depletion in H ii regions The quantity and composition of dust in H ii regions is an ongoing question in nebular physics. Forexample, Henry (1993) found that large errors could be introduced into C, N and O abundance estimates inH ii regions due to dust depletion. It appears likely that the dust amount increases with total metallicity,due to the greater availability of refractory elements (see, for example, Galametz et al. 2011, Figure 1).Both the amount and composition of dust may vary significantly, due to inhomogeneities in the distributionof dust-forming elements in supernova remnants and AGB star enrichment embedded in H ii regions. Thisproblem is likely to be especially complex in measuring the abundances in active star forming regions andin high redshift galaxies, as discussed in Prochaska et al. (2003).There are a number of approaches that can be taken to estimate the level of dust depletion. First,direct measurements of absorption lines in the spectra of nearby stars can be used to measure the abundanceof dust, e.g., Jenkins (2009), who summarised and modelled a range of elements, and Savage & Sembach(1996) and, Sembach & Savage (1996), who investigated Milky Way gas and dust abundances in the warmneutral medium, in cold diffuse clouds, and in distant halo clouds. The nature of the dust in the ISM islikely to be different than in giant molecular clouds, and in ionised regions of these, but ISM measurementsmay be useful as a starting point for modelling depletions.Second, as explored by Esteban et al. (1998, 2004), comparing the observed abundances, especially ofO, Mg, Si and Fe, in the atmospheres of young stars associated with H ii regions, if they can be measured,with the observed abundances from nebular emission lines can give a useful measure of the depletion levels.In a third approach, starting with some degree of a priori knowledge of depletion ratios and amounts,we can explore the emission regions with photoionisation models, to see how well different dust depletionassumptions match the observations. To explore this idea, we have obtained high resolution, low noiseintegral field spectra of several H ii regions in the Milky Way, LMC and SMC where the geometries aresimple and therefore can be modelled with some accuracy, as the basis for comparing with models.None of these methods is ideal, so educated combinations of such methods may need to be used. Theabundance scaling relations presented here suggest a starting point for estimating dust depletions, based onthe availability of elements to form dust and augmented by estimates of relative depletions. Where datais available by comparison of central star cluster stellar abundances and apparent nebular abundances, thiscan provide an independent check on the accuracy of the modelling method.A detailed analysis of the effects of dust depletion is beyond the scope of the present work. At thispoint it is reasonable to suggest that more accurate scaling of abundances is likely to provide a better basisfor estimating dust depletions, providing better estimates of the total abundances in nebulae.
29 – -4.0 -3.0 -2.0 -1.0 0.0-0.50.00.51.01.5 [Fe/H] [ M g / F e ] Sculptor
LMCMW
Fig. 9.— [Mg/Fe] vs [Fe/H] for Milky Way (grey circles), LMC (blue circles) and the SculptorDwarf (red circles) (MW: Frebel 2010; Ruchti et al. 2011; Adibekyan et al. 2012; Gonz´alezHern´andez et al. 2013; Bensby et al. 2014; Hinkel et al. 2014), (LMC: Pomp´eia et al. 2008;Van der Swaelmen et al. 2013), (Scl dwarf: Geisler et al. 2005; Kirby et al. 2009; Tafelmeyeret al. 2010). A common value for the low-metallicity trend for the three objects is expectedfor an invariant massive star IMF (Wyse 1998). The different break points and gradients inthe three galaxies reflect their different rates of specific star formation and enrichment. Thefiducial point circles also differ for each object, all marked in yellow for visibility. 30 –
7. Implications for stellar population synthesis models
Stellar population synthesis models are an important component in the photoionisation modelling of H ii regions, as they provide a guide to the ionising radiation energising the nebulae. Perhaps the most widelyused in nebular modelling is Starburst99 (Leitherer et al. 1999; V´azquez & Leitherer 2005; Levesqueet al. 2012; Leitherer et al. 2014). This takes as its input model spectra of stellar atmospheres and stellarevolutionary tracks for a variety of stellar masses and metallicities. These models have evolved over thepast 30 years, and the population synthesis applications have adapted to the new inputs (Leitherer 2014).However, the atmosphere and evolutionary track models are not fully compatible, due in part because theywere created for different purposes. In particular, there is a problem with the standard abundances used.For example, the stellar atmosphere models from Pauldrach et al. (2001) and Sternberg et al. (2003) use thesolar abundance values from Anders & Grevesse (1989) or earlier, and iron-based scaling. The evolutionarytrack models (Ekstr¨om et al. 2012; Georgy et al. 2013, 2014, and references to older models therein) arebased on Anders & Grevesse (1989) and Asplund et al. (2009) solar values, and use metallicities that areoxygen scaled. Consequently, matching tracks to atmospheres to generate a synthetic stellar population isdifficult. As far as possible, when modelling nebular emission, consistent abundances between the tracks,atmospheres and the total nebular metallicities should be used. This restricts the metallicities available formodelling to values that have some basis in the input stellar models. The ability to “translate” between thedifferent solar scales and scaling base elements provided in this paper give us some confidence that we arematching nebular models to stellar atmospheres and evolutionary tracks as best we can.To reduce the problems arising from the shortcomings if current stellar atmosphere models, we aredeveloping a new grid of models of hot stars as inputs to population synthesis applications, using theCMFGEN code (Hillier 2012). We are also working with another group to develop evolutionary track modelsusing metallicity scales consistent with the stellar atmosphere models, using the MESA code (Choi et al.2016). This should allow us to avoid the current scale discrepancies in population synthesis calculations.
8. Commentary and Conclusion
The problem of ongoing changes in “solar” abundance values is a source of uncertainty in photoionisa-tion models. It is conventional in detailed physical models (Cloudy,
Mappings , etc) to use a set of stellaratmosphere models, sets of stellar evolutionary tracks, combined into a model excitation spectrum to ionisethe nebula using population synthesis applications.Even ignoring the deficiency of hot star models in the stellar atmosphere data, there is a lack ofconsistency between the solar metallicity scales used in stellar atmospheres and the evolutionary tracks.Fixing this inconsistency by developing stellar atmosphere models and evolutionary tracks using the samereference abundances and scaling behaviour will be an important step in improving the reliability of nebularmodels.To avoid these problems, we advocate a reference scale derived from a population of present day Bstars as a sensible standard. Nieva & Przybilla (2012) provide such a basis, for all the elements that playan important part in nebular physics. We have augmented the scale with elements of lesser important fromother scales, including the latest solar and the most carefully measured meteoritic scales. However, from theperspective of nebular modelling, this is far less important than setting a reliable scale for the key elements.
31 –
We present a new scaling parameter, ζ , to specify the metallicity, and to replace the usual Z/Z (cid:12) parameter. We derive new scaling relations from the stellar spectra to describe the way in which elementalabundances scales in ionised nebulae. A consequence of these relations is a simple method to convertbetween different elements as the base for scaling measurement—usually oxygen for nebular analysis andiron for stellar analysis. We provide a simple web-based application to allow easy calculation and conversionof abundances, based on this paper, available at http://miocene.anu.edu.au/mappings/abund .We are not suggesting the Galactic Concordance scale is the only one that can be used, just thatit is important to use a single scale for all the components involved in photoionisation models. The scaleconversion methods we propose can be used to convert between any scale the photoionisation modeller wishesto use, and the online application allows this in a convenient way.The abundance scaling presented here is independent of the photoionisation model used. In any pho-toionisation modelling system, many parameters interact, and it is difficult to separate out the effects of asingle parameter such as abundance scaling. For this reason we leave detailed evaluation to a subsequentpaper in this series that describes the latest revision of the Mappings photoionisation code.However, the effects of the new scaling can be significant, as illustrated in Figure 1. Most important isthe result of incorporating the primary and secondary nitrogen scaling. A problem with nebular models fora long time has been insufficient N + flux at higher metallicities. Simple proportional scaling is incapable ofproducing sufficient flux in the key 6548 and 6584˚A [N ii ] lines which are important in high redshift nebularobservations. The new non-linear scale appears to go a long way to remedying this problem, though moreexploratory work is needed. Clearly, nitrogen abundance is complex, as it can be generated in significantquantities early in Wolf-Rayet WN stars as well as later in AGB stars. Objects such as the Blue CompactDwarf galaxy, HS0837+4717 (Pustilnik et al. 2004; P´erez-Montero et al. 2011) have anomalously high nitrogenabundance at low oxygen abundance and must be modelled individually, rather than using a generic approach.Primary/secondary nitrogen scaling was modelled by Groves et al. (2004) in the context of AGNs, but ispresented here more generally, as part of the new scaling relations with the revised standard abundance scaleand fit parameters.The new scaling presented here suggests that iron abundance is increasingly enhanced for 12+log(O/H) > Acknowledgments
DCN and RSS thank Prof. Martin Asplund for helpful discussions and comments. DCN, MAD and LJKacknowledge the support of the Australian Research Council (ARC) through Discovery projects DP130103925and DP160103631. BG acknowledges the support of the Australian Research Council (ARC) as the recipientof a Future Fellowship (FT140101202).
32 –
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A. Minor nebular elements
While Fe plays an important role in nebular cooling, the other iron-peak elements are of minor impor-tance. Ni and Cl lines do appear in the spectra of H ii regions, but at very low flux. However, as we arearguing the need for common scaling in nebular, stellar atmosphere and stellar evolutionary track modelling,it is important to set out a basis for commonality in this work. In this appendix, for completeness, we presentstellar data for Li, Be, B, F, Na, P, K, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn. A.0.1. Lithium, Beryllium and Boron
These elements have very low abundances in stars and nebulae. Li is both produced and consumed instars, so determining its primordial value from stellar spectra is difficult. It has been depleted in the sunby a factor of ∼
150 compared to the meteoritic value (Asplund et al. 2009), and Be and B have non-stellarprimordial chemical evolution paths. Meteoritic values for Li, B and Be are acceptable as they are onlytrace elements. They play little role in nebular physics, so for the purposes of nebular modelling we assumethey scale with oxygen. Abundance values at the Galactic Concordance fiducial point are taken from themeteoritic [X/Si] values in Lodders et al. (2009), using 12+log(Si/H) = 7.533 derived from that paper as theconversion standard.
A.0.2. Fluorine
Solar photospheric abundance of fluorine can only be measured (indirectly) in sunspots from the HFabundances (Asplund et al. 2009, and references therein). The solar values for fluorine from Asplund et al.(2009) date back with minor variations to sunspot measurements, ca. 1970. As fluorine is not normallyobserved in nebulae, in the Galactic Concordance we adopt the meteoritic values for fluorine from Lodderset al. (2009). This decision is not critical for nebular physics purposes, as fluorine does not play a significantrole in the thermal balance of nebulae.
A.0.3. Potassium, Scandium and Titanium
The elements K, Sc and Ti (Figure 10) also follow the α -element trends. Titanium and Scandiumare sometimes included with the iron-peak elements, but its abundance shows a clear trend similar to the α -elements. In other words, scandium and titanium appear to be generated in significant amounts in core-collapse supernovae.This preprint was prepared with the AAS L A TEX macros v5.2.
37 –
A.0.4. Sodium, Phosphorus and Zinc
Figure 11 shows the behaviour of Na, P and Zn. The trends for these elements appear to be on theborderline between α -group scaling and iron-peak scaling. The data for phosphorous (Caffau et al. 2011b;Jacobson et al. 2014) are so sparse that it is not possible to distinguish between the two apparent conflictingtrends. Sodium appears to show a slight α -process trend below [Fe/H] = 0. However, the upward trendat higher [Fe/H], previously attributed in open clusters to the “Na/O anti-correlation” observed in someglobular clusters (Geisler et al. 2012; Bragaglia et al. 2012), may be an artefact of the spectral data analysisas noted by MacLean et al. (2015). A.0.5. Scaling iron-peak elements
Iron-peak elements are produced in the nuclear fusion sequence that generates iron, so, at first glance,the abundances of vanadium, chromium, manganese, iron, cobalt, nickel and copper may be expected toremain constant as a fraction of iron. This is in large part supported by the stellar abundance data (Figures12 and 13), down to metallicities of [Fe/H] ∼ -2.5.However, at low metallicities, other trends are apparent in some elements. Decreasing trends below[Fe/H] ∼ -1.0 have been identified for chromium and manganese (see, for example, Cayrel et al. 2004). Theabundances of chromium and manganese in Figure 13 show an apparent decrease, and the abundance ofcobalt (Figure 12) shows an apparent increase, at iron abundances [Fe/H] (cid:46) -2.5.Some of the manganese data for [Fe/H] > -2.0 may be an artefact of the spectral analysis, with NLTEeffects not being taken into account. In a sample of metal-poor stars, Bergemann & Gehren (2008) foundthat taking NLTE effects into account significantly increased the values obtained for [Mn/Fe], by up to0.7dex, especially for lower iron abundances. Their data are shown in Figure 13, middle panel, as bluecircles. Battistini & Bensby (2015) found the same effect. They calculated manganese abundances withand without NLTE effects, and the former follow the downward trend, whereas the data calculated takinginto account NLTE physics remain constant with decreasing [Fe/H] (green circles, Figure 13, middle panel).However, it is possible that the low Mn abundance trend at low [Fe] is real, as higher levels of Mn at [Fe] < -1 are not well explained by core-collapse supernova models (Seitenzahl et al. 2013). For nebular purposesthis uncertainty is not significant, as Mn abundance has little effect in H ii region physics.Similarly, for chromium, Bergemann & Cescutti (2010) found that neglecting NLTE effects in stellarmodelling led to an apparent fall in chromium abundance at low metallicities. As NLTE effects are importantin analysing the data (as in the case of Na: see MacLean et al. 2015), we reason that the abundances shouldscale directly with iron at least down to metallicities of [Fe/H] (cid:38) -2.0. Even if this is not the case, above[Fe/H] ∼ -2, the constant fit is acceptable to good.Below [Fe/H] ∼ -2.5 the trends may be real, and were first reported for very low metallicity stars byMcWilliam et al. (1995) and subsequently by Ryan et al. (1996); Norris et al. (2001); Cayrel et al. (2004)and Yong et al. (2013). For example, Norris et al. (1997) found that high ( > Z (cid:12) ) carbon abundances “arenot uncommon” for [Fe/H] < -2.5 and suggest that this may may arise from different classes of core-collapsesupernovae. It is possible that the disparate behaviour of other elements for [Fe/H] < -2.5, may have thesame origin. Because the purpose of the present work is to model metallicity behaviour for [Fe/H] > -2,these effects do not affect the models presented here.
38 – -2.0 -1.0 0.00.000.501.00 [ X / F e ] Ξ = 0.4 K -2.0 -1.0 0.0[Fe] Ξ = 0.25 Sc -2.0 -1.0 0.0 Ξ = 0.35 Ti Fig. 10.— Scaling of K, Sc, Ti vs. Fe from stellar spectra. Sources: (Zhang et al. 2006,K, orange), (Takeda et al. 2009, K, black), (Andrievsky et al. 2010, K, grey), (Cayrel et al.2004, K, Sc, Ti, blue circles), (Howes et al. 2015, K, Sc, Ti, red circles) (Adibekyan et al.2012, Sc, grey (thin disk), green (thick disk, halo)), (Gonz´alez Hern´andez et al. 2013, Sc,Ti, orange), (Ruchti et al. 2011, Ti, dark green), (Adibekyan et al. 2012, Ti, grey), (Bensbyet al. 2014, Ti, blue), (Hinkel et al. 2014, Ti, purple) -2.0 -1.0 0.00.000.501.00 [ X / F e ] Ξ = 0.20 Na -2.0 -1.0 0.0 Ξ = 0.20 Zn -2.0 -1.0 0.0[Fe] Ξ = 0.0 P Fig. 11.— Scaling of Na, P, Zn vs. Fe from stellar spectra. Sources: (Adibekyan et al.2012, Na, grey), (Gonz´alez Hern´andez et al. 2013, Na, Zn, orange), (Bensby et al. 2014, Na,Zn, blue), (Howes et al. 2015, Na, Zn, red circles), (Cayrel et al. 2004, Na, Zn, blue circles),(Caffau et al. 2011b, P, blue), (Jacobson et al. 2014, P, orange) 39 –
In the case of Cu, the data are lacking below [Fe/H] ∼ -0.4, but above that, they are constant, asshown in (Gonz´alez Hern´andez et al. 2013, Figure 2) which is an expanded plot of the data in Figure 13,right panel. When viewed at a larger scale for [Fe/H] > -1.0, in some cases there appear to be slight upwardtrends in the iron-peak elements. This is apparent in the data from Bensby et al. (2005, their Figure 8)Bensby et al. (2014, their Figure 16), for example, but is not present in the data from Gonz´alez Hern´andezet al. (2013). It is not clear whether this is a real effect, or a result of abundance measurement methods. Thesame trend appears in the sodium data (Figure 11, left panel), and, as noted above, MacLean et al. (2015)suggest this an artefact. Whatever the cause, it does not materially affect the fitting of a simple iron-peakconstant trend with increasing [Fe/H]. While iron is critically important, especially at higher metallicitiesbecause of its abundance and presence in refractory dust, the other iron-peak elements are much less so.For this reason, and the stellar abundance trends themselves, we are confident that assuming the iron-peakelements scale directly with iron is reasonable.In general we have not included data from Frebel (2010) as they derive from several older sources forwhich the data reduction is uncertain. The exception is vanadium, where the lower metallicity data is scarceand the halo and thick disk data from Adibekyan et al. (2012) has a large spread, in order to clarify thelikely behaviour at low metallicity. B. Additional tables
This appendix contains a compendium of the major published standard solar abundances from 1976 tothe present (Table 3) a list of the stellar abundance sources we have used to derive the scaling fits (Table 4)and the stellar populations used in the referenced studies (Table 5).
40 – -2.0 -1.0 0.00.00.51.0 [ X / F e ] Ξ = 0.0 V -2.0 -1.0 0.0 Ξ = 0.0 Ni -2.0 -1.0 0.0[Fe] Ξ = 0.0 Co Fig. 12.— Scaling of V, Co, Ni vs. Fe from stellar spectra. Sources: (Frebel 2010, V,black), (Adibekyan et al. 2012, V, Co, Ni, grey), (Gonz´alez Hern´andez et al. 2013, V, Co,Ni, orange), (Bensby et al. 2014, Ni, blue), (Howes et al. 2015, Co, Ni, red circles) (Cayrelet al. 2004, Co, blue circles) -2.0 -1.0 0.00.00.51.0 [ X / F e ] Ξ = 0.0 Cr -2.0 -1.0 0.0[Fe] Ξ = 0.0 Mn -2.00 -1.00 0.00 Ξ = 0.0 Cu Fig. 13.— Scaling of Cr, Mn, Cu vs. Fe from stellar spectra. Sources: (Adibekyan et al.2012, Cr, Mn, grey), (Gonz´alez Hern´andez et al. 2013, Cr, Mn, Cu orange), (Bensby et al.2014, Cr, blue), (Bergemann & Gehren 2008, Mn, red disks), (Battistini & Bensby 2015, Mn,green), (Howes et al. 2015, Cr, Mn, Cu, red circles) (Cayrel et al. 2004, Mn, blue circles).The trends to low values of [Cr/Fe] and [Mn/Fe] at low [Fe/H] may be real or artefacts, andare discussed in the text.
Table 3: Solar, meteoritic, and B-star abundance standards
Z Sym. GC SGA15 NP12 C11 A09 A09 LPG09 GAS07 AGS05 L03 GS98 AG89 AG89 AE82 A76Element proto. photos. photos. metor.1 H 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.002 He 10.99 . . . 10.99 . . . 10.98 10.93 10.93 10.93 10.93 10.90 10.93 10.99 10.99 10.90 10.933 Li 3.28 . . . . . . 1.03 . . . 1.05 3.28 1.05 1.05 3.28 1.10 1.16 3.31 3.34 0.704 Be 1.32 . . . . . . . . . . . . 1.38 1.32 1.38 1.38 1.41 1.40 1.15 1.42 1.46 1.105 B 2.81 . . . . . . . . . . . . 2.70 2.81 2.70 2.70 2.78 2.55 2.60 2.88 2.95 3.006 C 8.42 . . . 8.33 8.50 8.47 8.43 8.39 8.39 8.39 8.39 8.52 8.56 8.56 8.65 8.527 N 7.79 . . . 7.79 7.86 7.87 7.83 7.86 7.78 7.78 7.83 7.92 8.05 8.05 7.96 7.968 O 8.76 . . . 8.76 8.76 8.73 8.69 8.73 8.66 8.66 8.69 8.83 8.93 8.93 8.87 8.829 F 4.44 4.40 . . . . . . . . . 4.56 4.44 4.56 4.56 4.46 4.56 4.56 4.48 4.49 4.6010 Ne 8.09 8.09 . . . 7.97 7.93 8.05 7.84 7.80 7.87 8.08 8.09 8.09 8.11 7.9211 Na 6.21 6.21 . . . . . . . . . 6.24 6.29 6.17 6.17 6.30 6.33 6.33 6.31 6.32 6.2512 Mg 7.56 7.59 7.56 . . . 7.64 7.60 7.54 7.53 7.53 7.55 7.58 7.58 7.58 7.60 7.4213 Al 6.43 6.43 . . . . . . . . . 6.45 6.46 6.37 6.37 6.46 6.47 6.47 6.48 6.49 6.3914 Si 7.50 7.51 7.50 . . . 7.55 7.51 7.53 7.51 7.51 7.54 7.55 7.55 7.55 7.57 7.5215 P 5.41 5.41 . . . 5.46 . . . 5.41 5.45 5.36 5.36 5.46 5.45 5.45 5.57 5.58 5.5216 S 7.12 7.12 . . . 7.16 7.16 7.12 7.16 7.14 7.14 7.19 7.33 7.21 7.27 7.28 7.2017 Cl 5.25 . . . . . . . . . . . . 5.50 5.25 5.50 5.50 5.26 5.50 5.50 5.27 5.29 5.6018 Ar 6.40 6.40 . . . . . . 6.44 6.40 6.50 6.18 6.18 6.55 6.40 6.56 6.56 6.58 6.8019 K 5.04 5.04 . . . 5.11 . . . 5.03 5.11 5.08 5.08 5.11 5.12 5.12 5.13 5.14 4.9520 Ca 6.32 6.32 . . . . . . . . . 6.34 6.31 6.31 6.31 6.34 6.36 6.36 6.34 6.34 6.3021 Sc 3.16 3.16 . . . . . . . . . 3.15 3.07 3.17 3.05 3.07 3.17 3.10 3.09 3.09 3.2222 Ti 4.93 4.93 . . . . . . . . . 4.95 4.93 4.90 4.90 4.92 5.02 4.99 4.93 4.95 5.1323 V 3.89 3.89 . . . . . . . . . 3.93 3.99 4.00 4.00 4.00 4.00 4.00 4.02 4.04 4.4024 Cr 5.62 5.62 . . . . . . . . . 5.64 5.65 5.64 5.64 5.65 5.67 5.67 5.68 5.69 5.8525 Mn 5.42 5.42 . . . . . . . . . 5.43 5.50 5.39 5.39 5.50 5.39 5.39 5.53 5.54 5.4026 Fe 7.52 7.47 7.52 7.52 7.54 7.50 7.46 7.45 7.45 7.47 7.50 7.67 7.51 7.52 7.6027 Co 4.93 4.93 . . . . . . . . . 4.99 4.90 4.92 4.92 4.91 4.92 4.92 4.91 4.92 5.1028 Ni 6.20 6.20 . . . . . . . . . 6.22 6.22 6.23 6.23 6.22 6.25 6.25 6.25 6.26 6.3029 Cu 4.18 4.18 . . . . . . . . . 4.19 4.27 4.21 4.21 4.26 4.21 4.21 4.27 4.28 4.5030 Zn 4.56 4.56 . . . . . . . . . 4.56 4.65 4.60 4.60 4.63 4.60 4.60 4.65 4.67 4.20
Sources
GC: this workSGA15 solar photosphere: Scott et al. (2015a,b); Grevesse et al. (2015)NP12 B stars: Nieva & Przybilla (2012)C11 solar photosphere: Caffau et al. (2011a)A09: proto-solar and solar photosphere: Asplund et al. (2009)LPG09 meteoritic (and solar): Lodders et al. (2009)GAS07 solar photosphere: Grevesse et al. (2007)AGS05 solar photosphere: Asplund et al. (2005)L03 meteoritic (and solar): Lodders (2003)GS98 solar photosphere: Grevesse & Sauval (1998)AG89: solar photosphere and meteoritic: Anders & Grevesse (1989)AE82 solar photosphere: Anders & Ebihara (1982)A76 solar photosphere: Allen (1976)
Table 4: Stellar data sources
Element SourcesC Gustafsson et al. (1999); Akerman et al. (2004); Fabbian et al. (2009); Spite et al. (2005); Nieva & Przybilla(2012); Nissen et al. (2014)N Akerman et al. (2004); Spite et al. (2005); Nieva & Przybilla (2012)O Cayrel et al. (2004); Trevisan et al. (2011); Gonz´alez Hern´andez et al. (2013); Ram´ırez et al. (2013); Bensbyet al. (2014); Amarsi et al. (2015)Ne Nieva & Przybilla (2012)Na Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Bensby et al. (2014); Howes et al. (2015)Mg Ruchti et al. (2011); Trevisan et al. (2011); Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013);Bensby et al. (2014); Hinkel et al. (2014); Howes et al. (2015)Al Edvardsson et al. (1993); Cayrel et al. (2004); Andrievsky et al. (2010); Gonz´alez Hern´andez et al. (2013)Si Ruchti et al. (2011); Trevisan et al. (2011); Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013);Bensby et al. (2014); Hinkel et al. (2014); Howes et al. (2015)P Caffau et al. (2011b); Jacobson et al. (2014)S Spite et al. (2011); Gonz´alez Hern´andez et al. (2013)K Cayrel et al. (2004); Zhang et al. (2006); Takeda et al. (2009); Andrievsky et al. (2010); Howes et al. (2015)Ca Cayrel et al. (2004); Ruchti et al. (2011); Trevisan et al. (2011); Adibekyan et al. (2012); Gonz´alez Hern´andezet al. (2013); Bensby et al. (2014); Howes et al. (2015)Sc Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Howes et al. (2015)Ti Cayrel et al. (2004); Ruchti et al. (2011); Trevisan et al. (2011); Adibekyan et al. (2012); Gonz´alez Hern´andezet al. (2013); Bensby et al. (2014); Howes et al. (2015)V Frebel (2010); Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013)Cr Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Bensby et al. (2014); Howes et al. (2015)Mn Bergemann & Gehren (2008); Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Battistini & Bensby(2015); Howes et al. (2015)Co Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Howes et al. (2015)Ni Adibekyan et al. (2012); Gonz´alez Hern´andez et al. (2013); Bensby et al. (2014); Howes et al. (2015)Cu Gonz´alez Hern´andez et al. (2013)Zn Gonz´alez Hern´andez et al. (2013); Bensby et al. (2014); Howes et al. (2015)See following table for stellar population details43–