Chemical abundance ratios of galactic globular clusters from modelling integrated light spectroscopy
aa r X i v : . [ a s t r o - ph . C O ] N ov Mon. Not. R. Astron. Soc. , 1–13 (2010) Printed 27 September 2018 (MN L A TEX style file v2.2)
Chemical abundance ratios of galactic globular clusters frommodelling integrated light spectroscopy
Daniel Thomas, Jonas Johansson, Claudia Maraston
Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, UKSEPNET, South East Physics Network
Accepted ... Received 20 October 2010 ; in original form 14 July 2010
ABSTRACT
In a companion paper we present new, flux-calibrated stellar population models of Lickabsorption-line indices with variable element abundance ratios. The model includes a largevariety of individual element variations, which allows the derivation of the abundances forthe elements C, N, O, Mg, Ca, Ti, and Fe besides total metallicity and age. We use thismodel to obtain estimates of these quantities from integrated light spectroscopy of galacticglobular clusters. We show that the model fits to a number of indices improve considerablywhen various variable element ratios are considered. The ages we derive agree well with theliterature and are all consistent with the age of the universe within the measurement errors.There is a considerable scatter in the ages, though, and we overestimate the ages preferentiallyfor the metal-rich globular clusters. Our derived total metallicities agree generally very wellwith literature values on the Zinn & West (1984) scale once corrected for α -enhancement, inparticular for those cluster where the ages agree with the CMD ages. We tend to slightly un-derestimate the metallicity for those clusters where we overestimate the age, in line with theage-metallicity degeneracy. It turns out that the derivation of individual element abundanceratios is not reliable at an iron abundance [Fe / H] < − dex where line strengths becomeweaker, while the [ α/ Fe ] ratio is robust at all metallicities. The discussion of individual el-ement ratios focuses therefore on globular clusters with [Fe / H] > − dex. We find generalenhancement of light and α elements, as expected, with significant variations for some ele-ments. The elements O and Mg follow the same general enhancement with almost identicaldistributions of [O/Fe] and [Mg/Fe]. We obtain slightly lower [C/Fe] and very high [N/Fe] ra-tios, instead. This chemical anomaly, commonly attributed to self-enrichment, is well knownin globular clusters from individual stellar spectroscopy. It is the first time that this pattern isobtained also from the integrated light. The α elements follow a pattern such that the heavierelements Ca and Ti are less enhanced. More specifically, the [Ca/Fe] and [Ti/Fe] ratios arelower than [O/Fe] and [Mg/Fe] by about . dex. Most interestingly this trend of elementabundance with atomic number is also seen in recent determinations of element abundancesin globular cluster and field stars of the Milky Way. This suggests that Type Ia supernovaecontribute significantly to the enrichment of the heavier α elements as predicted by nucle-osynthesis calculations and galactic chemical evolution models. Key words: stars: abundances Galaxy: abundances globular clusters: general galaxies:formation galaxies: stellar content
The abundances of a large variety of chemical elements can be de-rived from high-resolution spectroscopy of individual stars in thefield and globular clusters of the Milky Way as well as nearby dwarfgalaxies in the Local Group (e.g., McWilliam 1997; Carretta et al.2005; Pritzl et al. 2005; Tolstoy et al. 2009; Bensby et al. 2010).This level of detail cannot be achieved for most galaxies and extra-galactic globular clusters, because the individual stars are not re-solved. Observations have to resort to integrated light spectroscopy, which is applicable to unresolved stellar populations. It allows us tostudy element abundances in distant galaxies and globular clusters,but is naturally more limited. Nearby globular clusters are the in-terface between these two extremes. They allow detailed chemicalanalyses from resolved stellar spectroscopy as well as the study oftheir integrated light. They are therefore vital for the calibration ofstellar population models and integrated light analyses.The Lick group have defined a set of 25 optical absorption-line indices (Burstein et al. 1984; Faber et al. 1985; Gorgas et al. c (cid:13) Thomas, Johansson, Maraston ˚A, which increases thesignal-to-noise ratios but complicates their use for the derivation ofindividual element abundances. The first stellar population mod-els of Lick absorption-line indices with variable element abun-dance ratios have been published by Thomas et al. (2003a, 2004,hereafter TMB/K models) based on the index response functionsby Tripicco & Bell (1995) and Korn et al. (2005). In a compan-ion paper (Thomas et al. 2010, hereafter Paper I) we have updatedthese models (hereafter TMJ models) that are now flux calibratedthanks to the use of the newly computed index calibrations byJohansson et al. (2010) based on the flux-calibrated stellar libraryMILES (S´anchez-Bl´azquez et al. 2006).The Korn et al. (2005) model atmosphere calculations provideindex response functions for the variation of the ten elements C, N,O, Mg, Na, Si, Ca, Ti, Fe, and Cr. Through additional features inthe same part of the spectrum and modifications of the index defi-nitions even more elements may be accessible (Serven et al. 2005;Lee et al. 2009). Here we focus on those elements that can be bestderived from the 25 Lick indices considered in the TMJ models.These are C, N, Mg, Ca, Ti, and Fe besides total metallicity Z/ H ,age, and α/ Fe ratio.We already used the Thomas et al. (2003a) code to deriveabundances of nitrogen and calcium for globular clusters and galax-ies. Through a simple approach in Thomas et al. (2003a) we couldshow that galactic globular clusters must be significantly enhancedin nitrogen at fixed carbon abundance in order to reproduce theobserved CN indices. In Thomas et al. (2003b) we derive calciumabundances of galaxies. Subsequent work has developed this fur-ther. Clemens et al. (2006) add C abundances in their study ofSDSS galaxies, and Kelson et al. (2006) derive N abundances ofdistant galaxies. Graves & Schiavon (2008) and Smith et al. (2009)present the first full analyses of the abundances of C, N, Mg, Ca,and Fe in galaxies. In this paper we conduct the next step byadding the element titanium and derive the element abundance ra-tios [C/Fe], [N/Fe], [O/Fe], [Mg/Fe], [Ca/Fe], and [Ti/Fe] for galac-tic globular clusters.The paper is organised as follows. In Section 2 we describethe globular cluster data used. In Section 3 we introduce the newTMJ model and outline our method to derive element ratios. Themain analysis is presented in Section 5. The results are discussedin Section 6, and the paper concludes with Section 7. Following our strategy for the TMB/K models, in Paper I we com-pare the model predictions with observational data of galactic glob-ular clusters, as the latter are the closest analogues of simple stel-lar populations in the real universe (Maraston et al. 2003). Key isthat independent estimates of ages, metallicities, and element abun-dance ratios are available for the globular clusters of the Milky Wayfrom deep photometry and high-resolution stellar spectroscopy.The globular cluster samples are from Puzia et al. (2002, here-after P02) and Schiavon et al. (2005, hereafter S05). Critical for theintegrated light spectroscopy is a representative sampling of the un-derlying stellar population (Renzini 1998; Maraston 1998). To en-sure this P02 obtained several spectra with slightly offset pointings. In general three long-slit spectra were taken for each of the tar-get clusters, and the observing pattern was optimized to obtain onespectrum of the nuclear region and spectra of adjacent fields. Ex-posure times were adjusted according to the surface brightness ofeach globular cluster to reach a statistically secure luminosity sam-pling of the underlying stellar population. S05, instead, obtainedeach observation by drifting the spectrograph slit across the corediameter of the cluster. The telescope was positioned so as to off-set the slit from the cluster center by one core radius. A suitabletrail rate was chosen to allow the slit to drift across the cluster corediameter during the typically 15 minute long exposure.We do not use the indices tabulated in P02 directly, becausethese measurements have been calibrated onto the Lick/IDS sys-tem by correcting for Lick offsets. S05 do not provide line indexmeasurements. Hence we measure line strengths of all 25 Lickabsorption-line indices for both samples directly on the globularcluster spectra using the definitions by Trager et al. (1998). Bothglobular cluster samples have been flux calibrated, so that no fur-ther offsets need to be applied for the comparison with the TMJmodels. We have smoothed the spectra to Lick spectral resolutionbefore the index measurement. Note that the spectral resolutions ofboth samples are below the resolution of the MILES library, so thatwe work with the TMJ models at Lick resolution.For the P02 sample we adopt the errors quoted in their paperusing the quadratic sum of the statistical (Poisson) error, the statisti-cal error derived from slit to slit variations, and the systematic errorintroduced through uncertainties in the radial velocity. This infor-mation is not directly available from S05. We therefore evaluatethe measurement errors in two steps. First we compute the Poissonerrors from the error spectra provided through Monte Carlo simu-lations. Then we scale these errors with the complete errors fromP02 from the overlapping globular clusters.We add the slit-to-slit error evaluated in P02 in order to ac-count for possible stellar population fluctuations that are not in-cluded in the statistical error. The observing strategies in both P02and S05 have been designed to minimise such an error. Still, this ef-fect may not negligible. The slit-to-slit variations overestimate thiseffect, as P02 have typically observed three slits per cluster. We re-gard the errors used in this study therefore as conservative estimate,and true errors are likely to be smaller.Finally, it should be noted that the S05 spectra are corruptaround 4546 and ˚A, so that the indices Fe4531 and Fe5015cannot be measured (S05). In case of multiple observations in S05we use the spectra with the highest signal-to-noise ratio.
In Paper I we present new stellar population models of Lickabsorption-line indices with variable element abundance ratios(TMJ). The model is an extension of the TMB/K model, whichis based on the evolutionary stellar population synthesis code ofMaraston (1998, 2005). For basic information on the model we re-fer the reader to Thomas et al. (2003a, 2004) and Paper I. Here weprovide a brief summary of the main features of our new models.
The key novelty compared to our previous models is that theTMJ model is flux-calibrated, hence not tied anymore to theLick/IDS system. This is because the new models are based onour calibrations of absorption-line indices with stellar parameters c (cid:13) , 1–13 hemical abundance ratios of galactic globular clusters (Johansson et al. 2010) derived from the flux-calibrated stellar li-brary MILES (S´anchez-Bl´azquez et al. 2006). The MILES libraryconsists of 985 stars selected to produce a sample with extensivestellar parameter coverage. Most importantly it has been carefullyflux-calibrated, making standard star-derived offsets unnecessary.A further new feature is that we provide model predictions forboth the original Lick ( ∼ ˚A) and the higher MILES ( ∼ . ˚A)spectral resolutions. Note that the latter appears to be comparableto the SDSS resolution, so that our new high-resolution models canbe applied to SDSS data without any corrections for instrumentalspectral resolution (see Paper I).As a further novelty we calculate statistical errors in the modelpredictions. The errors estimates are obtained from the uncertain-ties in the measurements of Lick index strengths and the stellarparameters of the library stars, hence do not include systematic er-rors. It turns out that the model errors are generally very small andwell below the observational errors around solar metallicity, butrise considerably toward the highest and lowest metallicities.The data release now provides models with two different stel-lar evolutionary tracks by Cassisi et al. (1997) as used in TMB/Kand additionally Padova (Girardi et al. 2000) at high metallicities.The model based on the Padova tracks is consistent with the modelusing Cassisi for the majority of indices. The cases of indicesfor which the discrepancy exceeds the model error significantlyare H β , CN , CN , and C . dex. A differen-tial element ratio bias at low metallicities is considered to accountof the fact that heavier α elements like Ca and Ti tend to be lessenhanced (see Section 6).The basic tests with globular cluster data following our strat-egy for the TMB/K model is presented in Paper I. The match to theglobular cluster data is satisfactory for the Balmer line indices H δ A , H γ A , and H γ F . A reasonably good match with globular cluster datais also seen for the α/ Fe sensitive, metallic indices G4300, Mg ,and Mg b and the Fe indices Fe4383, Fe4531, Fe5270, Fe5335,Fe5406. The models are well off, instead, for the indices CN , CN , Ca4227, C Mg . This is caused by the variationof further chemical elements beyond the α/ Fe ratio to which theseindices are sensitive, and the full analysis of these element abun-dance variations is subject of the present work. In the followingsection we describe how individual element ratios are derived fromthis set of absorption features. Fig. 1 shows the response of the 25 Lick indices to individual el-ement abundance changes for a Gyr, solar metallicity stellarpopulation. The fractional index change is calculated for an en-hancement of the respective element by a factor two normalised tothe typical observational measurement error for MILES stars fromJohansson et al. (2010). The scale on the y-axis is kept fixed forall elements, so that the figure allows us to identify easily thoseelements that are best traced by the current set of models. It canbe seen that the elements C, N, Na, Mg, Ca, Ti, and Fe are bestaccessible. The abundance of nitrogen is obtained from the CN indicesthat are also highly sensitive to C abundance. However, this de-generacy can be easily broken through other C sensitive indicessuch as C Mg . The Mg indices Mg , Mg , and Mg b are very sensitive to Mg abundance. Note, however, that all threeadditionally anti-correlate with Fe abundance (Trager et al. 2000;Thomas et al. 2003a). Ca can be measured well from Ca4227, ex-cept that this particular index is quite weak and requires good dataquality. Na abundance can be derived quite easily from NaD in prin-ciple. However, in practise this is problematic as the stellar compo-nent of this absorption feature is highly contaminated by interstellarabsorption, which makes this index useless and hence Na inaccessi-ble at least for globular clusters (Thomas et al. 2003a). Iron is wellsampled through the Fe indices.There are two among the Fe indices, however, that are alsosensitive to Ti abundance besides Fe. These are Fe4531 andFe5015. They offer the opportunity to estimate also Ti abundance.We will only use Fe4531, as Fe5015 is contaminated by a non-negligible Mg sensitivity besides Fe, which weakens its usefulnessfor Ti abundance determinations.The remaining three elements O, Si and Cr cannot easily bemeasured through the available indices. As discussed extensivelyin Thomas et al. (2003a), however, oxygen has a special role. Ois by far the most abundant metal and clearly dominates the massbudget of ’total metallicity’. Moreover, the α/ Fe ratio is actuallycharacterised by a depression in Fe abundance relative to all lightelements (not only the α elements), hence α/ Fe reflects the ratiobetween total metallicity to iron ratio rather than α element abun-dance to iron. As total metallicity is driven by oxygen abundance,the α/ Fe derived can be most adequately interpreted as O/Fe ratio.We therefore re-name the parameter α/ Fe to O/Fe under the as-sumption that this ratio provides an indirect measurement of oxy-gen abundance.Finally, iron abundance can be calculated through the follow-ing formula (Tantalo et al. 1998; Trager et al. 2000; Thomas et al.2003a). [Fe / H] = [
Z/H ] − .
93 [ α/ Fe] ≡ [ Z/H ] − .
93 [O / Fe]
A full description of the method we use to derive individual elementabundances and its application to SDSS galaxy data is presentedin a companion paper (Johansson et al, in preparation). Here weprovide a brief summary of the key aspects that are most relevantfor the present work. χ technique The derivation of the above set of element ratios is done in variousiterative steps by means of the χ code of Thomas et al. (2010).We generate a fine grid of model predictions for the parameterslog age, metallicity, and α/ Fe ratio with log steps of 0.1, 0.1, and . dex, respectively. Galactic globular cluster data generally arevery close to the 15 Gyr model (see Paper I), which is the high-est age for which we have stellar evolutionary track calculationsavailable. Therefore, we extrapolate the models logarithmically toa maximum age of Gyr for the initial set of templates, in or-der not to impose an upper age limit. Note that the index strengthsevolve very little as a function of age at these old ages, therefore c (cid:13) , 1–13 Thomas, Johansson, Maraston
Figure 1.
Response of the 25 Lick indices to individual element abundance changes for a Gyr, solar metallicity stellar population. The fractional indexchange is calculated for an enhancement of the respective element by a factor of two. The scale on the y-axis is error normalised. The plot range is kept fixedfor all elements, so that the figure allows us to identify easily those elements that are best traced by the current set of models. we do not expect this extrapolation to affect the derivation of indi-vidual element abundances significantly. As a sanity check we haveverified that the globular clusters with ages above Gyr are notbiased to particular element abundance ratios.The code computes the χ between model prediction and ob-served index value for all model templates summing over the n indices considered: χ = n X i =1 (cid:18) I obs i − I model i σ (cid:19) (1)The resulting χ distribution is then transformed into a probabilitydistribution. By means of the incomplete Γ function adopting thedegrees of freedom as ν = n indices − n para we compute the proba-bility Q that the chi-square should exceed a particular value χ bychance. This computed probability gives a quantitative measure forthe goodness-of-fit of the model. If Q is a very small probability,then the apparent discrepancies are unlikely to be chance fluctua-tions.The solution with the highest Q (i.e. lowest χ ) is chosen,and the - σ error is adopted from the FWHM of this probabilitydistribution. Different from Thomas et al. (2010) we discard badly calibratedindices from the start. In Paper I we find that the set of indicesthat appears to be best calibrated and most suited for the presentaims are the Balmer line indices H δ A , H γ A , and H γ F , the metallicindices CN , CN , Ca4227, G4300, C Mg , Mg , Mg b ,and the Fe indices Fe4383, Fe4531, Fe5270, Fe5335, and Fe5406.Then, similar to the approach of Graves & Schiavon (2008) we usedifferent sets of indices for different elements. We define a base set of indices including Mg b , the Balmer index H δ A , and the iron indices Fe4383, Fe5270, Fe5335, Fe5406. Firstwe determine the traditional light-averaged stellar population pa-rameters age, total metallicity, and α/ Fe ratio from this base set ofindices. Only indices that are sensitive to these three parameters areincluded in the base set. In the subsequent steps we add in turn par-ticular sets of indices that are sensitive to the element the abundanceof which we want to determine. In each step we re-run the χ fittingcode with a new set of models to derive the abundance of this ele-ment. This new set of models is a perturbation to the solution foundfor the base set. It is constructed by keeping the stellar populationparameters age, metallicity, and α/ Fe fixed and by modifying the c (cid:13) , 1–13 hemical abundance ratios of galactic globular clusters Figure 2.
Ages of galactic globular clusters derived from integrated light spectroscopy in comparison with literature data. Globular cluster spectra are takenfrom Puzia et al. (2002) and Schiavon et al. (2005). Literature ages from colour-magnitude isochrone fitting are adopted from Mar´ın-Franch et al. (2009).
Left-hand panel:
Grey symbols are the full sample, orange and blue symbols are metal-rich ( [ Z/ H] > − . dex) and metal-poor ( [ Z/ H] < − . dex)sub-samples, respectively. The dotted line marks the age of the universe as derived in Komatsu et al. (2010). Right-hand panel : Metallicity versus horizontalbranch morphology (horizontal branch ratio HBR adopted from Harris (1996)). The literature metallicities on the Zinn & West (1984) scale are taken from thecompilation by Harris (1996). The magenta symbols are those clusters for which we obtain ages larger than Gyr, while the cyan symbols are clusters forwhich our ages agree with the CMD ages within . dex. The dotted lines are the metallicity limits from the left-hand panel. Literature ages are generally wellreproduced. We tend to over-estimate ages for the most metal-rich globular clusters. Horizontal branch morphology only plays a minor role. element abundance of the element under consideration by ± dexin steps of . dex around the base value.A new best fit model is obtained from the resulting χ distri-bution. Then we move on to the next element. At the end of thesequence we re-determine the overall χ using all indices togetherand re-derive the base parameters age, metallicity, and α/ Fe for thenew set of element ratios. Then we go back to the second step anduse these new base parameters to derive individual element abun-dances. This outer loop is iterated until the final χ stops improvingby more than 1 per cent. The method converges relatively fast andwe generally require five steps at most to fulfil this criterion.In more detail, the sequence of elements is as follows. Thefirst element in the loop is carbon, for which we use the indices CN , CN , Ca4227, H γ A , H γ F , G4300, C Mg , and Mg on top of the base set. Next we drop these C-sensitive indices andproceed deriving N abundance, for which we use the N-sensitiveindices CN , CN , and Ca4227. Then we move on to Mg and Mg for Mg abundance, Ca4227 for Ca, and finally Fe4531 for theelement Ti. O abundance is indirectly inferred from the α/ Fe ratioby assuming that [O / Fe] ≡ [ α/ Fe] . (2)The typical errors for the parameters are . dex for logAge, . dex for [ Z/ H ], . dex for [ O / Fe ], and about . dexfor the other element ratios. It should be emphasised again thatthese are very conservative error estimates. From the χ fitting as described in Section 3 we obtain age, to-tal metallicity [ Z/ H ], iron abundance [ Fe / H ], the [ α/ Fe ] ratio,and the individual element abundance ratios [C/Fe], [N/Fe], [O/Fe],[Mg/Fe], [Ca/Fe], and [Ti/Fe] for a total of 52 globular clusters.We exclude the 47 Tucanae from our analysis, as age dating ofthis cluster from Balmer line indices is known to be problem-atic (Schiavon et al. 2002; Vazdekis et al. 2001). In this section we present the results and compare with literature data obtained fromcolour-magnitude (CMD) fitting (age) and high-resolution spec-troscopy of individual stars (metallicity and element abundance ra-tios). First we discuss the comparison of the derived ages with litera-ture data. CMD ages are taken from Mar´ın-Franch et al. (2009) andDe Angeli et al. (2005) where not available in Mar´ın-Franch et al.(2009). The overlap of the two samples contains 39 clusters.The age comparison is shown in the left-hand panel of Fig. 2,where we plot our derived ages as a function of the CMD ages.The grey symbols are the full sample, orange and blue are metal-rich and metal-poor sub-samples, respectively. The age derivationthrough the Lick indices works reasonably well. Almost half ofthe sample our globular cluster ages agree with Mar´ın-Franch et al.(2009) within . dex (18 out of 39), and three quarters (29) of theclusters agree within the (conservative) measurement errors. Mostimportantly, 35 clusters out of 52 (two thirds) are younger thanthe universe as derived by Komatsu et al. (2010, dotted line) froma combination of cosmic microwave background, supernova, andlarge-scale structure data, and the vast majority (45 out of 52) areconsistent with age of the universe within . dex. All but onecluster ages are consistent with the age of the universe within our(conservative) measurement errors.Generally, the ages from Lick indices agree well with theCMD ages, albeit with quite a large scatter. Note that Mendel et al.(2007) derived systematically larger ages with the TMB/K model The turnoff brightness, being the major indicator for the age of Note that we have not explicitly derived globular cluster ages inThomas et al. (2003a). with respect to CMD. The major difference isthat Mendel et al. (2007) adopted CMD ages from De Angeli et al. (2005)who derived systematically younger absolute ages than Mar´ın-Franch et al.(2009). It should be kept in mind, however, that the derivation of absolute c (cid:13) , 1–13 Thomas, Johansson, Maraston a stellar population, is highly sensitive to the distance of the ob-ject. As a consequence, only relative ages can be reliably measured(Ortolani et al. 1995; De Angeli et al. 2005; Mar´ın-Franch et al.2009).Still, it is interesting to investigate the reason for the exceed-ingly large ages of some clusters. Fig. 2 shows that the clusters forwhich we overestimate the ages with respect to the age of the uni-verse tend to be metal-rich with [ Z/ H] > − . dex (orange sym-bols). Most of the clusters whose ages agree well with the CMDages, instead, are metal-poor with [ Z/ H] < − . dex (blue sym-bols). To investigate this further, in the right-hand panel of Fig. 2we plot metallicity (on Zinn & West (1984) scale adopted fromMar´ın-Franch et al. (2009)) versus horizontal branch morphologyexpressed as horizontal branch ratio HBR adopted from Harris(1996). The magenta symbols are those clusters for which we ob-tain ages larger than Gyr, while the cyan symbols are clustersfor which our ages agree with the CMD ages within the measure-ment errors. It can be seen clearly that horizontal branch morphol-ogy only plays a minor role at a given metallicity. Metallicity is themain driver for the age discrepancy. To summarise, globular clusterages derived from absorption-line indices tend to be overestimatedfor the most metal-rich clusters around slightly sub-solar metallic-ity. This is a more general manifestation of the H β anomaly ofglobular cluster data noted by Poole et al. (2010), which may wellbe a ’Balmer anomaly’ rather than being restricted to H β . Note,however, that this pattern is more likely to be caused by problemsin the globular cluster data than the models, as galaxy data appearto be well matched instead (Kuntschner et al. 2010, Paper I). For the comparison of metallicity we adopt literature values fromMar´ın-Franch et al. (2009) on the Zinn & West (1984) scale. Theserepresent total metallicity [ Z/ H ] as Mar´ın-Franch et al. (2009)have corrected the iron measurement using the prescription ofSalaris et al. (1993). We therefore confront these literature valueswith our measurements of total metallicity [ Z/ H ] in Fig. 3. Themagenta symbols are those clusters for which we obtain ages largerthan Gyr, while the cyan symbols are clusters for which our agesagree with the CMD ages within . dex.Metallicities agree very well, with a tendency of slightly lowermetallicity estimates from the present work at low metallicities. Itcan further be seen from Fig. 3 that this match is particularly goodfor those clusters whose Lick index ages agree best with the CMDages (cyan symbols). For the clusters with the oldest Lick indexages (magenta symbols), instead, we tend to underestimate metal-licity by ∼ . dex This might in fact be an artefact produced bythe age-metallicity degeneracy, i.e. we tend to underestimate themetallicity of those globular clusters for which we overestimate theage. We now turn to discuss the individual abundances of the elementsC, N, O, Mg, Ca, and Ti relative to the abundance of Fe. Fig. 4presents the abundance ratios [ C / Fe ], [ N / Fe ], [ Mg / Fe ], [ Ca / Fe ],and [ Ti / Fe ] (coloured symbols) as functions of iron abundance[ Fe / H ] in comparison to [ O / Fe ] (grey symbols). the bottom panels globular cluster ages through CMDs carries its own problems as pointed outin both De Angeli et al. (2005) and Mar´ın-Franch et al. (2009). Figure 3.
Total metallicities [ Z/ H ] of galactic globular clusters derivedfrom integrated light spectroscopy in comparison with literature data. Glob-ular cluster spectra are taken from Puzia et al. (2002) and Schiavon et al.(2005). The literature metallicities on the Zinn & West (1984) scale andcorrected for α -enhancement are taken from Mar´ın-Franch et al. (2009).The magenta symbols are those clusters for which we obtain ages largerthan Gyr, while the cyan symbols are clusters for which our ages agreewith the CMD ages within . dex. Literature metallicities are well repro-duced. Metallicities are slightly underestimated for those clusters for whichwe overestimate the age. indicate the typical measurement error as a function of iron abun-dance.The element ratio [ O / Fe ], being equivalent to [ α/ Fe ] (seeequation 2), carries the smallest measurement error. This elementratio is well determined at all metallicities. The expected patternof super-solar [ α/ Fe ] with a slight decrease toward solar metal-licity is reproduced. The individual element abundance ratios, in-stead, have significantly larger errors. In all cases the typical er-rors increase with decreasing metallicity, and exceed ∼ . dex at [Fe / H] < − dex. In fact, the abundance pattern loses structure atsuch low iron abundance. This ought to be expected as the sensitiv-ity of the models to element ratio variations decreases dramaticallywith decreasing metallicity (e.g., Thomas et al. 2003a). Moreover,model errors become comparable to model variations for only mod-erate abundance ratio changes (see Paper I), which further hampersthe analysis. Hence abundance ratios cannot be reliably determined.At [Fe / H] > − dex, instead, our results reveal interesting abun-dance trends. Before discussing these abundance patterns in detail, we presentthe direct comparison of our results with the measurements ofPritzl et al. (2005), who have derived element abundance ratios ofa large sample of galactic globular clusters form individual stel-lar spectroscopy. Pritzl et al. (2005) have observed between oneand ten stars per cluster and derived the element ratios [ Mg / Fe ],[ Ca / Fe ], and [ Ti / Fe ]. The ratio [ α/ Fe ] is computed from the ge-ometrical mean of these three measurements. We have computedthe straight average when more than one star has been observed. Intotal, the Pritzl et al. (2005) sample has 18 clusters in common withthe present work.In Fig. 5 we plot the abundance ratios [Mg/Fe], [Ca/Fe],and [Ti/Fe] (coloured symbols) as derived in the present work c (cid:13) , 1–13 hemical abundance ratios of galactic globular clusters Figure 4.
Abundance ratios [C/Fe], [N/Fe], [Mg/Fe], [Ca/Fe], and [Ti/Fe] (coloured symbols) in comparison to the the [ O / Fe ] ratio (grey symbols) asfunctions of iron abundance [ Fe / H ] for galactic globular clusters. The globular cluster spectra are taken from Puzia et al. (2002) and Schiavon et al. (2005).The black dots are the element ratios of globular cluster stars from Pritzl et al. (2005). The bottoms panels show the 1- σ error on the element ratios with thedotted horizontal lines indicating an error of . dex. The typical abundance pattern of Milky Way field and globular cluster stars is well reproduced for[ O / Fe ]. The other element ratios have too large errors at low metallicities below [Fe / H] ∼ − dex, hence meaningful conclusions can only be drawn at [Fe / H] & − dex. Figure 5.
Abundance ratios [Mg/Fe], [Ca/Fe], and [Ti/Fe] (coloured sym-bols) of galactic globular clusters measured in this work from integratedlight spectroscopy in comparison with literature values from individual stel-lar spectroscopy by Pritzl et al. (2005). Black symbols show [ α/ Fe ] ratios.The error symbols indicate typical errors in both [ α/ Fe ] and [ Mg / Fe ]. Thesmall symbols are globular clusters with [Fe / H] < − dex, for which ele-ment ratios from integratd light spectroscopy are unreliable (see Fug. 4). from integrated light spectroscopy as functions of the measure-ments from Pritzl et al. (2005). Black symbols show [ α/ Fe ] ra-tios. The error symbols indicate typical errors in both [ α/ Fe ] and[ Mg / Fe ]. The small coloured symbols are globular clusters with [Fe / H] < − dex, for which individual element ratios from in-tegrated light spectroscopy are less reliable (see Fig. 4). There isa satisfactory agreement for [ α/ Fe ] at all metallicities, in agree- ment with the results of Mendel et al. (2007) obtained with theTMB/K models. [ Mg / Fe ] ratios are still in reasonable agreementat [Fe / H] > − dex. There is a hint for systematically lower[ Ca / Fe ] and [ Ti / Fe ] ratios in our work, instead. We present a fulldiscussion of this discrepancy in the following sections. In the following we compare the distributions of element ratiosfrom the integrated and stellar spectroscopy. We only consider clus-ters with [Fe / H] > − dex in our analysis leaving us with a sampleof 15 objects (out of 52). The reason is that element ratios cannotbe reliably determined at lower metallicities, because the relativesensitivity of the model predictions to element ratio changes is toosmall (see Fig. 4). Note also that we only can consider the P02 sam-ple for Ti (6 out of 12) as the Ti sensitive index Fe4531 cannot bemeasured for the S05 clusters.Fig. 6 shows the distributions of [C/Fe], [N/Fe], [Mg/Fe],[Ca/Fe], and [Ti/Fe] ratios (coloured histograms) in comparisonwith the distribution of the [O/Fe] ratio (grey histograms). Themedian values of these distribution are given in Table 1. The dis-tribution of [ O / Fe ] is reasonably tight with a median value of . dex as expected for Milky Way globular clusters. The other ofthe light α elements considered, [Mg/Fe], follows this distributionvery closely with a very similar median of . dex. The other lightelements, instead, deviate from this pattern. [C/Fe] and [Ca/Fe] ra-tios show similarly peaked distributions, but with different medianvalues. The element ratio [C/Fe] has a median slightly lower by ∼ . dex, while [Ca/Fe] peaks at significantly lower values witha median of . dex. A Kolmogorov-Smirnov test confirms thatthe distributions in [ O / Fe ] and [Ca/Fe] come from different under- c (cid:13) , 1–13 Thomas, Johansson, Maraston
Figure 6.
Distributions of [C/Fe], [N/Fe], [Mg/Fe], [Ca/Fe], and [Ti/Fe] ratios (coloured histograms) in comparison to the distribution of the [ O / Fe ] ratio(grey histogram) for galactic globular clusters. The globular cluster spectra are taken from Puzia et al. (2002) and Schiavon et al. (2005). Only clusters with [Fe / H] > − dex are considered (15 objects out of 52) as element ratios cannot be reliably determined at lower metallicities (see text). The dotted black lines(for [Mg/Fe], [Ca/Fe], [Ti/Fe] only) are the distributions of the element ratios of globular cluster stars from Pritzl et al. (2005). We find a general trend suchthat the heavier of the light elements (Ca and Ti) are less enhanced than O and Mg. N is strongly enhanced in a sub-population of clusters accompanied by aslight depression of [C/Fe] with respect to O and Mg. Table 1.
Median values of element ratio distributions (in dex).[O/Fe] [C/Fe] [N/Fe] [Mg/Fe] [Ca/Fe] [Ti/Fe]0.24 0.20 0.71 0.25 0.15 0.09 lying distributions at the > σ level. The distribution of [N/Fe] hasa pronounced peak at a significantly larger value of . dex. Thedistribution of [Ti/Fe] is somewhat scattered. Still, the data show aclear trend toward lower [Ti/Fe] ratios with a median of . dexin line with the neighbouring α element Ca.The significant enhancement of nitrogen together with theslight depression of carbon relative to the other light elementsis a well known abundance pattern in globular clusters observedin high-resolution spectroscopy studies of individual stars (e.g.,Norris et al. 1984; Carretta et al. 2005). This chemical anomaly iscommonly attributed to self-enrichment during the formation of thestar cluster (Ventura et al. 2009). Such N enhancement has beenquantified in Thomas et al. (2003a) for the first time for integratedlight observations of globular clusters, while the accompanying de-pression of C found in the present work is new. The [C/Fe] and[N/Fe] ratios derived here appear to be well consistent with themeasurements from Carretta et al. (2005).The next heavier of the light elements, Mg, follows the distri-bution of [O/Fe] closely. This ought to be expected as these el-ements are close in atomic number and created in very similarprocesses during supernova nucleosynthesis (Woosley & Weaver1995; Thielemann et al. 1996). However, the heavier α elementsCa and Ti deviate from this pattern. The typical [Ca/Fe] ratio issignificantly lower than the typical [O/Fe] and [Mg/Fe] ratios. The [ Ti / Fe ] ratio is less well determined, but the results suggest thatthis element continues this trend with even lower [ Ti / Fe ] ratios. The adjustment of individual element abundances helps to im-prove the fits to a number of indices. In Figs. 7 and 8 werevisit the calibration figure from Paper I for the model af-ter the full chemical analysis. We only show those indices thathave been used in the analysis, plotting index strengths as func-tions of [MgFe] ′ . Three models at Lick spectral resolution withan age of Gyr are shown for the metallicities [ Z/ H] = − . , − . , − . , . , . , . dex. Metallicity increasesfrom left to right. The solid lines are the final model for the av-erage of the individual element abundance ratios derived throughthe χ fit. The dotted and dashed lines are the base models with α/ Fe = 0 . dex and α/ Fe = 0 . dex for comparison. Thegrey shaded area along the model indicates the 1- σ error of themodel prediction. Galactic globular clusters from P02 and S05are filled and open squares, respectively. The typical errors in theglobular cluster index measurements are given the error symbolat the bottom of each panel. The small black dots are early-typegalaxies from the MOSES catalogue (MOrphologically SelectedEarly-type galaxies in SDSS Schawinski et al. 2007; Thomas et al.2010) drawn from the SDSS (Sloan Digital Sky Survey) data base(York et al. 2000) including only high signal-to-noise spectra with S/N > . c (cid:13) , 1–13 hemical abundance ratios of galactic globular clusters Figure 7.
Calibration of the line indices that are sensitive to light elements. Three models at Lick spectral resolution with an age of and the metallicities [ Z/ H] = − . , − . , − . , . , . , . dex are shown. The solid lines are the final model for the average of the individual element abundanceratios derived through the χ fit. The dotted and dashed lines are the base models with [ α/ Fe] = 0 . dex and [ α/ Fe] = 0 . dex. The grey shaded area alongthe model indicates the 1- σ error of the model prediction. Galactic globular clusters from Puzia et al. (2002) and Schiavon et al. (2005) are filled and opensquares, respectively. The typical errors in the globular cluster index measurements are given the error symbol at the bottom of each panel. The small blackdots are early-type galaxies from the MOSES catalogue (MOrphologically Selected Early-type galaxies in SDSS Schawinski et al. 2007; Thomas et al. 2010)drawn from the SDSS (Sloan Digital Sky Survey) data base (York et al. 2000) including only high signal-to-noise spectra with S/N > . Fig. 7 shows the indices that are sensitive to light element abun-dances, namely CN , CN , Ca4227, G4300, C Mg , Mg ,and Mg b . It can be seen from the top panels that the strengths ofthe CN indices are clearly underestimated in both solar-scaled and α/ Fe enhanced base models (dotted and dashed lines). As alreadydiscussed in Thomas et al. (2003a) a significant enhancement in Nis required to explain the high index strengths. At the same time, the indices G4300, and C Mg are slightly too strong inthe base models, which leads to a slight reduction of C abundancein the final best-fitting model.Another striking element abundance pattern that can be in-ferred from Fig. 7 directly is the abundance of Ca. The strength ofthe index Ca4227 is significantly over-predicted by the solar-scaledand α/ Fe enhanced base models. The model matches the globularcluster data very well, instead, when a depression of Ca abundanceis included. Finally, the indices Mg and Mg b (bottom panels) are c (cid:13) , 1–13 Thomas, Johansson, Maraston
Figure 8.
Calibration of the Fe and Balmer line indices. Three models at Lick spectral resolution with an age of and the metallicities [ Z/ H] = − . , − . , − . , . , . , . dex are shown. The solid lines are the final model for the average of the individual element abundance ratiosderived through the χ fit. The dotted and dashed lines are the base models with [ α/ Fe] = 0 . dex and [ α/ Fe] = 0 . dex. The grey shaded area alongthe model indicates the 1- σ error of the model prediction. Galactic globular clusters from Puzia et al. (2002) and Schiavon et al. (2005) are filled and opensquares, respectively. Note that the indices Fe4531 and Fe5015 cannot be measured for the Schiavon et al. (2005) sample. The typical errors in the globularcluster index measurements are given the error symbol at the bottom of each panel. The small black dots are early-type galaxies from the MOSES catalogue(MOrphologically Selected Early-type galaxies in SDSS Schawinski et al. 2007; Thomas et al. 2010) drawn from the SDSS (Sloan Digital Sky Survey) database (York et al. 2000) including only high signal-to-noise spectra with S/N > . well reproduced by the α/ Fe enhanced model (dashed line), andonly a negligible adjustment of Mg abundance is required to opti-mise the fit. Fig. 8 presents the Fe and Balmer line indices used in the fittingprocedure. The solar-scaled model (dotted lines) generally over- predicts the index strengths of the Fe indices, which is remediedthrough a depression of Fe abundance in the α/ Fe enhanced model(dashed lines). The index strength of Fe4531 is slightly re-adjustedthrough a depression of Ti abundance. The signal is very weak,though, and the determination of Ti abundance in this work mustin fact be considered tentative, in particular since only a handful ofclusters from P02 are available for the Ti abundance measurement.In general, the full chemical model only leads to minor corrections c (cid:13) , 1–13 hemical abundance ratios of galactic globular clusters of the Fe indices. The same is true for the Balmer line indices.Here the solar-scaled model under-predicts line strengths, whichis remedied by the enhancement of the α/ Fe ratio. Again, otherelements only have negligible impact on these indices. We have derived, for the first time, detailed chemical element abun-dance patterns of galactic globular clusters from integrated lightspectroscopy. The light elements O and Mg show the well-knownenhancement with respect to Fe, hence [O / Fe] ∼ [Mg / Fe] ∼ . dex. For C, N, and the heavier α elements Ca and Ti, how-ever, we detected interesting abundance anomalies. N is further en-hanced to very high [ N / Fe ] ratios, while C is slightly depressed.Ca exhibits significantly lower [ Ca / Fe ] ratios than O or Mg, a pat-tern that appears to be present also in [ Ti / Fe ]. These anomalieshave interesting consequences for supernova nucleosynthesis andthe chemical enrichment in the Milky Way.First we confront these results with the element ratios of indi-vidual stars in globular clusters as measured by Pritzl et al. (2005).These are shown by the dotted lines in Fig. 6 for [Mg/Fe], [Ca/Fe],and [Ti/Fe]. The distributions of the [Mg/Fe] ratios agree verywell. [Ca/Fe] and [Ti/Fe] ratios, instead, are somewhat higher inPritzl et al. (2005). The latter do suggest slightly lower enhance-ment of these elements, but not as pronounced as found here. Butour finding gets support from the study by Feltzing et al. (2009)who analyse six horizontal branch stars in the metal-rich galacticglobular cluster NGC 6352. As expected the cluster is enhanced inthe α -elements. But like in the present work Feltzing et al. (2009,see their Fig. 7) find a sequence of decreasing element ratios rela-tive to iron for increasing atomic numbers from Mg through Ca toTi. It should be expected that field stars show the same behavioursince globular cluster element abundances generally follow theones of the field stars in the galactic halo and discs (Pritzl et al.2005). In fact the trend reported here starts to crystallise out nowfrom recent high quality stellar spectroscopy of galactic field starsin bulge and disc. Bensby et al. (2010) analyse bulge and thick/thindisc stars and find [Ca/Fe] and [Ti/Fe] ratios to be lower than [O/Fe]and [Mg/Fe] ratios for all three populations.The implication is that some fraction of the abundance in theheavier α elements must come from Type Ia supernova explosions,while the lighter elements O and Mg remain to be enriched exclu-sively by Type II. The yields of the W7 model for Type Ia supernovaexplosions do indeed predict the production of traces of the heaviest α elements. As a consequence, galactic chemical evolution modelspredict lower [Ca/Fe] ratios for halo stars (Chiappini et al. 1997),which had not been confirmed from observational data so far. Theresults discussed here provide a new observational support for thispattern.This is critical for the chemical enrichment histories of galax-ies. It leads to the most natural explanation for the shallowslope of the [ Ca / Fe ]-galaxy mass relation of early-type galax-ies (Saglia et al. 2002; Thomas et al. 2003b; Cenarro et al. 2003;Michielsen et al. 2003). In this scenario, Ca is underabundant rela-tive to the lighter α elements in massive galaxies for the same rea-son as Fe is underabundant (see discussion in Thomas et al. 2003b).The short formation time-scales inhibit Type Ia supernovae to playa role in the chemical enrichment history of the stellar populationsin these galaxies, such that elements that are produced in Type Iasupernova are depleted in the stars. In fact chemical evolution mod- els of bulges and spheroids predict lower element abundances forthe heavier α elements, Ca in particular (Matteucci et al. 1999).This implies that also Ti would have to be underabundant in mas-sive galaxies. We investigate this issue in a companion paper (Jo-hansson et al, in preparation). Modelling integrated light spectroscopy of unresolved stellar pop-ulations allows us to study the detailed element abundances in dis-tant galaxies and globular clusters. In Paper I we present new, flux-calibrated stellar population models of Lick absorption-line indiceswith variable element abundance ratios (TMJ models). The newmodel includes a large variety of individual element variations,which allows the derivation of the abundances for the elements C,N, O, Mg, Ca, Ti, and Fe besides total metallicity and age. In thepresent paper we use this model to obtain estimates of these pa-rameters and element abundance ratios from integrated light spec-troscopy of galactic globular clusters.The globular cluster data is taken from Puzia et al. (2002) andSchiavon et al. (2005). We measure line strengths of all 25 Lickabsorption-line indices for both samples directly on the globularcluster spectra. Both globular cluster samples are flux calibrated,so that no further offsets need to be applied for the comparisonwith the TMJ models.We derive the element abundance ratios [ C / Fe ], [ N / Fe ],[ O / Fe ], [ Mg / Fe ], [ Ca / Fe ], [ Ti / Fe ] through an iterative χ fit-ting technique. First we determine the traditional light-averagedstellar population parameters age, total metallicity, and α/ Fe ratiofrom the indices Mg b , the Balmer index H δ A , and the iron indicesFe4383, Fe5270, Fe5335, and Fe5406. In the subsequent steps we add in turn particular sets of indices that are sensitive to the elementthe abundance of which we want to determine. The indices used are CN , CN , Ca4227, H γ A , H γ F , G4300, C Mg , and Mg for carbon, CN , CN , and Ca4227 for nitrogen, Mg and Mg for magnesium, Ca4227 for calcium, and Fe4531 for titanium. TheTi sensitivity of Fe4531 is relatively weak, hence the abundancederivations for this element are only tentative. The [ O / Fe ] ratiois indirectly inferred by assuming that [O / Fe] ≡ [ α/ Fe] . We showthat the model fits to these indices in globular clusters improve con-siderably through this full chemical analysis.The ages we derive agree well with the literature. In particularthe ages derived here are all consistent with the age of the universewithin the measurement errors. There is a considerable scatter inthe ages, though, and we overestimate the ages preferentially forthe metal-rich globular clusters, which appears to extend the previ-ously reported H β anomaly of globular clusters to the other Balmerindices. Our derived total metallicities agree generally very wellwith literature values on the Zinn & West (1984) scale once cor-rected for α -enhancement, in particular for those cluster where theages agree with the CMD ages. We tend to slightly underestimatethe metallicity for those clusters where we overestimate the age, inline with the age-metallicity degeneracy.It turns out that the derivation of individual element abundanceratios is highly unreliable at [Fe / H] < − dex, while the [ α/ Fe ]ratio is robust at all metallicities. The discussion of individual ele-ment ratios focuses therefore on globular clusters with iron abun-dances [Fe / H] > − dex. We find general enhancement of lightand α elements as expected with significant variations for some el-ements. The elements O and Mg follow the same general enhance-ment with almost identical distributions of [O/Fe] and [Mg/Fe]. c (cid:13) , 1–13 Thomas, Johansson, Maraston
We find slightly lower [C/Fe] and very high [N/Fe] ratios, instead.Hence N is significantly enhanced and C slightly depressed in glob-ular clusters with respect to the other light elements. This chemicalanomaly commonly attributed to self-enrichment is well known inglobular clusters from individual stellar spectroscopy, and it is thefirst time that this pattern is derived also from the integrated light.The α elements follow a pattern such that the elements withhigher atomic number, namely Ca and Ti, are less enhanced. Morespecifically, [Ca/Fe] ratios are lower than [O/Fe] and [Mg/Fe] byabout . dex. Ti continues this trend. We compare this result withrecent determinations of element abundances in globular clusterand field stars of the Milky Way. We come to the conclusion thatthis pattern is now universally found. It suggests that Type Ia su-pernovae contribute significantly to the enrichment of the heavier α ∼ thomasd. ACKNOWLEDGEMENTS
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