Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
AAstronomy & Astrophysics manuscript no. larsen c (cid:13)
ESO 2018May 14, 2018
Detailed abundances from integrated-light spectroscopy: MilkyWay globular clusters (cid:63)
S. S. Larsen , J. P. Brodie , and J. Strader Department of Astrophysics / IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlandse-mail: [email protected] UCO / Lick Observatory, University of California, Santa Cruz, CA 95064, USA Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USAReceived November 25, 2016; accepted February 21, 2017
ABSTRACT
Context.
Integrated-light spectroscopy at high spectral resolution is rapidly maturing as a powerful way to measure detailed chemicalabundances for extragalactic globular clusters (GCs).
Aims.
We test the performance of our analysis technique for integrated-light spectra by applying it to seven well-studied Galactic GCsthat span a wide range of metallicities.
Methods.
Integrated-light spectra were obtained by scanning the slit of the UVES spectrograph on the ESO
Very Large Telescope across the half-light diameters of the clusters. We modelled the spectra using resolved
Hubble Space Telescope colour-magnitudediagrams (CMDs), as well as theoretical isochrones, in combination with standard stellar atmosphere and spectral synthesis codes.The abundances of Fe, Na, Mg, Ca, Ti, Cr, and Ba were compared with literature data for individual stars in the clusters.
Results.
The typical di ff erences between iron abundances derived from our integrated-light spectra and those compiled from theliterature are less than ∼ . ff erence is found for one cluster (NGC 6752), and is most likely caused primarily bystochastic fluctuations in the numbers of bright red giants within the scanned area. As expected, the α -elements (Ca, Ti) are enhancedby about 0.3 dex compared to the Solar-scaled composition, while the [Cr / Fe] ratios are close to Solar. When using up-to-date linelists, our [Mg / Fe] ratios also agree well with literature data. Our [Na / Fe] ratios are, on average, 0.08–0.14 dex lower than averagevalues quoted in the literature, and our [Ba / Fe] ratios may be overestimated by 0.20–0.35 dex at the lowest metallicities. We find thatanalyses based on theoretical isochrones give very similar results to those based on resolved CMDs.
Conclusions.
Overall, the agreement between our integrated-light abundance measurements and the literature data is satisfactory.Refinements of the modelling procedure, such as corrections for stellar evolutionary and non-LTE e ff ects, might further reduce someof the remaining o ff sets. Key words. globular clusters: individual (NGC 104, NGC 362, NGC 6254, NGC 6388, NGC 6752, NGC 7078, NGC 7099) — stars:abundances — techniques: spectroscopic
1. Introduction
A typical globular cluster (GC) has an integrated absolute mag-nitude of M V ≈ − . ff use light. The latter approach, however, facesthe significant challenge of deconstructing a potentially complexmix of stellar populations with di ff erent ages, metallicities, andkinematics, a challenge which is much more easily overcomewith GCs. A particularly useful application of GCs is to use themas tracers of the (metal-poor) halos, which account for only asmall fraction of the total stellar mass (and luminosity) in most (cid:63) Based on observations collected at the European Organisation forAstronomical Research in the Southern Hemisphere under ESO pro-gramme(s) 095.B-0677(A). galaxies, but often have large numbers of GCs associated withthem. GCs have, indeed, been shown to trace coherent struc-tures in phase-space that are likely related to hierarchical galaxybuild-up (e.g. in the halos of M31 and M87; Mackey et al. 2010;Romanowsky et al. 2012). While photometry of the brightest in-dividual halo giants can currently be obtained out to distances of ∼
10 Mpc with the
Hubble Space Telescope (Harris et al. 2007;Peacock et al. 2015), and the
James Webb Space Telescope willsoon push the boundary even further, detailed spectroscopy ofindividual RGB stars at such distances will remain beyond thecapabilities even of future 30–40 m telescopes. Measurementsof ages and chemical composition for globular clusters thus holdgreat potential for studying the assembly histories of galaxies,especially when combined with other information such as kine-matics and spatial distributions of the GCs and / or resolved imag-ing of individual stars.The advent of e ffi cient multi-object spectrographs on 8–10m telescopes made it possible to carry out systematic spectro-scopic studies of extragalactic GCs as far away as the Virgo andFornax galaxy clusters (see review in Brodie & Strader 2006),although investigations of smaller samples started much earlier(e.g., van den Bergh 1969; Racine et al. 1978; Brodie & Huchra Article number, page 1 of 35 a r X i v : . [ a s t r o - ph . S R ] F e b & A proofs: manuscript no. larsen > ∼
10 Gyr) and enhanced inthe α -elements, with metallicities spanning a wide range from[Fe / H] ≈ − ∼ . ff erenceswere found for some elements (e.g., Mg, see below). Subse-quent comparisons involving larger samples (5–11) of Galac-tic GCs have found similar results (Sakari et al. 2013, 2014;Colucci et al. 2017). Integrated-light spectra have now also beenused to measure abundances for GCs in several external galax-ies, including the Large Magellanic Cloud, M31, and NGC 5128(Colucci et al. 2009, 2012, 2013, 2014; Sakari et al. 2015) andthe Fornax and Wolf-Lundmark-Melotte dwarf galaxies (Larsenet al. 2012, 2014, hereafter L12 and L14). These studies havefound abundance patterns that mostly match those seen in MilkyWay GCs and halo stars, with similar Fe-peak element abun-dances ([Cr / Fe] ≈
0, [Sc / Fe] slightly super-solar) and generallysuper-solar [ α/ Fe] ratios. However, potentially interesting dif-ferences have also emerged. Several of the above studies havefound Mg to be depleted with respect to other α -elements (suchas Ca and Ti), in some cases even reaching sub-solar values of[Mg / Fe] (Colucci et al. 2014). At the same time, [Na / Fe] iscommonly found to be elevated compared to the abundances ob-served in Galactic halo stars of similar metallicity (L14, Colucciet al. 2014; Sakari et al. 2015). These patterns are reminiscent ofthe Na / O and Mg / Al anti-correlations observed in Galactic GCs(Cohen 1978; Shetrone 1996; Sneden et al. 1997; Gratton et al.2004; Carretta et al. 2009b; Gratton et al. 2012), and may simplyreflect the prevalence of the “multiple populations” phenomenonalso in these extragalactic clusters.While [Na / Fe] spreads up to ∼ . / Fe] is usually quite small and very few stars reach sub-solar [Mg / Fe] values in most GCs (Car-retta et al. 2009b). It is therefore not clear that integrated-lightMg abundances are expected to be strongly a ff ected by the pres-ence of multiple populations (unless much larger Mg variationsare common in the extragalactic clusters studied so far). Thisraises the question whether the integrated-light Mg abundancesmay be subject to unknown systematic di ff erences compared toobservations of individual stars. Indeed, Colucci et al. (2017)found their integrated-light [Mg / Fe] ratios for eleven GalacticGCs to be about 0.3 dex lower on average compared to mea-surements of individual stars in the same clusters. On the otherhand, Sakari et al. (2013) found integrated-light [Mg / Fe] ratiosin good agreement with the average of literature data for individ-ual stars in five GCs. Clearly, obtaining a better understanding ofthese di ff erences would be desirable.Our technique for abundance analysis from integrated lightwas introduced in our study of the GCs in the Fornax dwarfgalaxy (L12). Compared to the techniques for integrated-lightabundance measurements that have been developed and testedby other groups (McWilliam & Bernstein 2008; Colucci et al.2012; Sakari et al. 2013), our approach is more heavily basedon spectral synthesis and full spectral fitting. For elements withmany lines (such as Fe, Ti, Ca) we generally obtain our abun-dance measurements by fitting relatively broad spectral rangesthat contain multiple features, rather than by measuring singlelines individually. In principle, we can fit for abundances of mul-tiple elements simultaneously, and the full spectral fitting ap-proach automatically accounts for line blending and hyperfinestructure (provided, of course, that adequate input line lists areused). Conceptually, as well as in its practical implementation,our approach thus di ff ers su ffi ciently from those of other groupsthat separate testing is warranted.In L12 we carried out a number of basic comparisons of ourintegrated-light abundance measurements for the GC Fornax 3with data for metal-poor stars in dwarf galaxies and in the clusteritself. However, a more stringent test is to compare abundancesderived from integrated-light observations with measurements ofindividual stars in well-studied Galactic globular clusters. Thisis particularly important at higher metallicities, where some as-pects of the analysis (e.g., line blending and continuum place-ment) become more challenging. In this paper we present newintegrated-light spectroscopy of seven Galactic GCs, selectedto span nearly two decades in metallicity from [Fe / H] ≈ − . / H] ≈ − .
2. Sample selection and observations
For the selection of our sample we used the list of clusters ob-served by Carretta et al. (2009b) as a starting point. It includes19 Galactic GCs, for which the abundances of several light ele-ments (including Na and Mg) were measured for individual starsin the clusters. As in our previous work, integrated-light spectrawere obtained with the UVES spectrograph (Dekker et al. 2000)on the ESO Very Large Telescope by scanning the slit acrossthe target clusters. According to the UVES Exposure Time Cal-culator, the exposure times required to obtain good integrated-light spectra (with signal-to-noise ratios of S / N > µ ≈
19 mag arcsec − . We therefore calculatedthe mean surface brightness within the half-light radius ( µ h ) for Article number, page 2 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table 1.
Basic data for the observed clusters
NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099 Ref V (mag) 3.95 6.40 6.60 6.72 5.40 6.20 7.19 1 r h (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) µ h (mag arcsec − ) 17.1 16.8 18.8 16.7 18.1 17.2 18.4 D (kpc) 4.7 8.6 5.0 9.9 4.0 10.3 8.1 1,4,5 E ( B − V ) (mag) 0.04 0.05 0.28 0.37 0.04 0.10 0.03 1 M V (mag) − . − . − . − . − . − . − . / H] − . − . − . − . − . − . − .
34 2,3Scan length 336 (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) T exp (s) 2 × × × × × × × M V (scan) − . − . − . − . − . − . − . V helio (km s − ) − . ± . . ± . . ± . . ± . − . ± . − . ± . − . ± . σ (km s − ) 11 . ± . . ± . . ± . . ± . . ± . . ± . . ± . Notes. V = apparent visual magnitude, r h = half-light radius, µ h = mean visual surface brightness within r h , D = distance. M V (scan) is the estimatedluminosity of the area covered by the scans, V helio is the heliocentric radial velocity derived from our observations, and σ is the line-of-sightvelocity dispersion. References. (1) Harris (1996), 2010 edition; (2) Carretta et al. (2009a); (3) Carretta et al. (2013); (4) Woodley et al. (2012); (5) van den Boschet al. (2006); (6) This work. See text for details. each cluster in the Carretta et al. (2009b) sample, using the ap-parent visual magnitudes and half-light radii from Harris (1996),and eliminated clusters with µ h >
19 mag arcsec − from the list.Among the remaining clusters, we selected two at the metal-poorend of the range (NGC 7078, NGC 7099), two at the metal-richend (NGC 104, NGC 6388), and two at intermediate metallic-ities (NGC 6254, NGC 6752). Among several back-up targets,we also included NGC 362 (Carretta et al. 2013).The clusters were observed on July 22 /
23 and July 23 / (cid:48)(cid:48) .
0, which yields a resolving powerof R ∼
40 000 over the wavelength range 4200 Å – 6200 Å.To sample the integrated light of the clusters we employed thesame basic drift-scan technique as in our previous observationsof the Fornax GCs, whereby the UVES slit was scanned acrossthe half-light diameter of the clusters during the exposures. Eachscience exposure was bracketed by two sky exposures with halfthe exposure time, which were co-added and used for sky sub-traction. Thin cirrus clouds were present throughout the run butdid not significantly a ff ect the observations, except towards theend of the second night. The seeing varied between 1 (cid:48)(cid:48) and 2 (cid:48)(cid:48) ,of little consequence for our observations.The large apparent sizes of Galactic GCs on the sky, com-bined with the relatively short UVES slit (10 (cid:48)(cid:48) ) pose specialchallenges for this type of observations. For a given total expo-sure time, the highest S / N ratio would be achieved by scanningonly the cluster cores, where the surface brightness is highest.However, this has to be balanced against other considerations.The stellar mass function might be a ff ected by mass segrega-tion in the cores, leading to possible systematic e ff ects in theintegrated light, and to minimise stochastic fluctuations in thenumber of bright RGB stars it is desirable to include the largestpossible fraction of the total cluster light. A further practical lim-itation is that the total area covered by the scans is given by theproduct of the exposure time, the slit length, and the di ff erentialtracking rate. For large, high surface brightness clusters (suchas NGC 104), where only relatively short exposures are neces-sary, a very large di ff erential tracking rate would be required inorder to cover a significant fraction of the cluster. Each observa-tion would then need to be split up into a large number of shortexposures, which would result in a substantially reduced observ- ing e ffi ciency and a more dominant contribution of detector readnoise. For these reasons, we did not use integrations shorter than20–30 min.Table 1 lists basic data for the seven clusters in our sam-ple, along with the exposure times and number of scans obtainedfor each cluster. In general, we scanned the clusters in both thenorth-south and east-west directions and for the lower surfacebrightness targets we obtained multiple parallel scans in each di-rection. In some cases, slight departures from our standard strat-egy were adopted: for NGC 6752, the large di ff erential trackingrate required for a scan across the full half-light diameter madeguide star acquisition problematic, so the scan length was re-duced by a factor of two. For NGC 7099, the exposure time hadto be reduced from the planned 4 × × / N. The north-south scansof NGC 7099 were a ff ected by the thickening cloud cover to-wards the end of the second night, but still proved useful. ForNGC 362, the available time only allowed for a single scan.The regions covered by the scans are indicated on Figure 1,which shows images of the clusters from the Digitized Sky Sur-vey . In Table 1 we also list the approximate integrated abso-lute magnitudes of the areas covered by the scans, M V (scan).These were estimated by selecting all stars from the ACS Sur-vey of Galactic Globular Clusters (ACSGCS; Sarajedini et al.2007) within the approximate areas covered by the scans andadding up the luminosities of these stars. The M V (scan) magni-tudes should only be treated as rough estimates as we have not at-tempted to correct the ACSGCS photometry for incompleteness,and there is some uncertainty in determining which stars exactlyfall within the scanned areas. Nevertheless, comparison of the M V (scan) values with the total integrated magnitudes shows thatour observations include between 8% (for NGC 104) and 25%(NGC 6254) of the integrated light, a significantly smaller frac-tion than would typically be included for extragalactic GCs (asis also evident from Fig. 1).
3. Data reduction
The initial processing of the data (following interpolation over afew bad columns with the fixpix task in
IRAF ) was done with
Article number, page 3 of 35 & A proofs: manuscript no. larsen
NGC 104 (47 Tuc) NGC 362NGC 6254 (M10) NGC 6388NGC 6752 NGC 7078 (M15)NGC 7099 (M30)
Fig. 1.
Digitized Sky Survey images of the globular clusters observedin this work. The regions covered by our drift-scan observations areindicated. The size of each panel is 10 (cid:48) × (cid:48) . version 5.5.7 of the UVES pipeline, executed within the Esorex environment. The pipeline processing involved bias subtraction,flat-fielding, and wavelength calibration. It also included merg-ing of the echelle orders to a single two-dimensional spectrumfor each of the two CCD detectors, with the UVES slit mappedonto 22 pixels in the spatial direction.The two sky exposures bracketing each science exposurewere median filtered in the spatial direction to eliminate cosmicray hits and were then co-added and subtracted from the scienceexposure. The 22 lines along the spatial direction were then ex- S / N p e r Å NGC 104NGC 362NGC 6254NGC 6388NGC 6752NGC 7078NGC 7099
Fig. 2.
Signal-to-noise (per Å) for the final reduced one-dimensionalintegrated-light spectra. tracted from each of the sky-subtracted 2-D spectra of a givencluster and co-added to a single one-dimensional spectrum, us-ing a custom-made programme that rejected bad pixels by meansof a sigma-clipping algorithm. The S / N ratios of the final spectrawere estimated based on the variance of the individual co-addedpixels at each wavelength sampling point.Fig. 2 shows the S / N ratio for each cluster as a function ofwavelength. The S / N ratios (per Å) range from 300–600 at theblue end to 650–1100 at the red end. The jump at 5200 Å occursbecause the blue and red parts of the spectra are recorded on twoseparate CCD detectors.
4. Analysis
Here we provide only a brief summary of our technique forabundance analysis from integrated-light spectra; the reader isreferred to L12 and L14 for more details. In essence, chemicalabundances are determined by fitting synthetic model spectra tothe observed spectra, iteratively adjusting the abundances of in-dividual elements until the best match to the data is obtained.The model spectra are computed by dividing the Hertzsprung-Russell diagrams (HRD) of the underlying stellar populationsinto a large number of bins (typically about 100), computing amodel atmosphere and a synthetic spectrum for each bin, andthen co-adding the spectra for each bin with appropriate weights(given by the number of stars in each bin). The model spectra arethen smoothed to match the resolution of the observed spectra, ascaling is applied, and the χ of the fit is evaluated.In our previous work we have used the ATLAS9 and
SYNTHE codes written by R. Kurucz to compute the model atmospheresand synthetic spectra (Kurucz 1970; Kurucz & Furenlid 1979;Kurucz & Avrett 1981; Kurucz 2005; Sbordone et al. 2004).However, these models are less suitable for the coolest giants,which are present in the more metal-rich clusters, and for starswith T e ff < MARCS atmospheres (Gustafs-son et al. 2008) and the
TurboSpectrum code (Alvarez & Plez1998; Plez 2012) to compute the synthetic spectra. This allowsfor spherical (rather than plane-parallel) symmetry of the atmo-
Article number, page 4 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters spheres. We downloaded the full grid of spherical model atmo-spheres from the
MARCS website and selected the closest modelfrom the grid for each bin of the HRD. Our reference abundancescale remains that of Grevesse & Sauval (1998).The input HRDs can be based on empirical data (e.g.,observed colour-magnitude diagrams, CMDs), on theoreticalisochrones, or on a combination of both. When using theo-retical isochrones, the stellar parameters (log g , T e ff , luminos-ity) can usually be taken directly from the isochrone tables, al-though assumptions need to be made about age and the appro-priate weights (e.g., one needs to assume a distribution of stellarmasses). When using empirical CMDs, stellar parameters canbe derived from photometry, once a set of transformations fromobservables to physical properties have been adopted. For ex-tragalactic GCs it is usually not feasible to obtain CMDs ofsu ffi cient depth to rely on a purely empirical modelling of theHRDs, although observations can still provide useful constraintson, e.g., horizontal branch morphology. In our study of the WLMGC, we found that purely isochrone-based modelling gave verysimilar results to models involving empirical CMDs (L14). Wewill revisit this point in more detail below. In this work we based the HRD modelling on photometry fromthe Advanced Camera for Surveys (ACS) on board the
HubbleSpace Telescope , obtained as part of the ACSGCS (Sarajediniet al. 2007; Anderson et al. 2008). Following the same proce-dure as in our previous work, the colour-magnitude diagramswere arranged into about 100 bins. For each bin, the median V − I colour and V magnitude were recorded, along with the numberof stars in the bin. Most of the bins were distributed along thered giant branch and main sequence (MS), but we also includedbins along the horizontal branch (HB) and the asymptotic giantbranch (AGB). For most clusters, the very tip of the RGB is rela-tively sparsely sampled and the brightest 10–20 RGB stars werethen included individually without any binning. In some clus-ters, sequences of blue stragglers (BS) were evident, but thesewere not included in our general modelling procedure. However,the e ff ect of including BS stars was investigated and found to bevery minor (Sec. 5.1.2).The photometry was corrected for foreground dust extinctionusing E ( B − V ) values from the 2010 edition of the Harris (1996)catalogue (Table 1). Most of the distances were also taken fromthat source. For NGC 104 we assumed D = . D = . ff erential reddening across the ACSfield of view (Busso et al. 2007), which is clearly noticeableas a “blurring” of the ACSGCS CMD. We did not attempt tocorrect the photometry for this e ff ect but expect that its conse-quences are relatively limited for our purpose, since we only usethe median colours and magnitudes in each CMD-bin. In addi- http://marcs.astro.uu.se M V NGC 104 NGC 3622024681012 M V NGC 6254 NGC 63882024681012 M V NGC 6752 0.0 0.5 1.0 1.5 2.0 2.5 3.0V-INGC 70780.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0V-I2024681012 M V NGC 7099
Fig. 3.
Binned colour-magnitude diagrams (black dots) and theoreti-cal isochrones (Dotter et al. 2007, red lines). The isochrones are thosecorresponding to the best-fitting metallicities in Table B.3 (see also Ta-ble 6). tion, NGC 6388 has a rather peculiar HB morphology for itsmetallicity, with an extended blue tail and a strongly sloped redstub. These features have been extensively discussed in the lit-erature and are not fully understood, but may be at least partlydue to variations in He abundance (Rich et al. 1997; Busso et al.2007; Bellini et al. 2013).For the brightest bins, including those along the HB, weightswere assigned simply by using the number of stars present inthese bins in the ACS CMDs. At fainter magnitudes ( M V > + Article number, page 5 of 35 & A proofs: manuscript no. larsen oretical LFs were normalised to give the same number of starsas the empirical CMDs at the bright end. The distribution ofstellar masses was assumed to follow the Salpeter (1955) law(d N / d M ∝ M − . ). The choice of mass function hardly a ff ectsthe LFs above the MS turn-o ff , since the post-MS phases con-tain stars spanning only a small range in (initial) mass and theLFs are therefore determined mainly by stellar evolution (i.e.,by how much time a star spends at a given location in the HRD).For stars with masses less than 0 . M (cid:12) –0 . M (cid:12) (corresponding to M V > ∼ + M V = + V -band light, but this is almostcertainly an overestimate of the actual contribution since eventhe initial slope of the MF was likely significantly shallower atthese low masses (Bastian et al. 2010). Following L12, we sim-ply leave out stars fainter than M V = +
9, noting that their e ff ecton the overall metallicities, as well as on individual abundanceratios, was found to be small ( < . M (cid:12) .The last step was to convert the photometry to physical pa-rameters. Again, we mostly followed the approach describedin L12, where temperatures and bolometric corrections werecomputed from the photometry, using transformations based onKurucz models (Castelli 1999). To calculate the surface gravi-ties, stellar masses were obtained by interpolation in the sameisochrones used for the theoretical LFs. For the most metal-richclusters in our sample (NGC 104 and NGC 6388), the coolestgiants fall outside the Castelli model grid and thus had to bedealt with separately. For these stars, we defined a colour- T e ff relation based on the colours and temperatures tabulated in theDartmouth isochrones, which use synthetic photometry based onPHOENIX model atmospheres (Hauschildt et al. 1999a,b). The spectral fits were carried out mostly as described in L12and L14. Radial velocity shifts and the appropriate broadeningof the model spectra required to match the observations weredetermined in an initial set of fits (using 200 Å spectral windowsbetween 4200 Å and 6200 Å) during which the overall scalingof all abundances was also allowed to vary. The iron abundanceswere then determined using the same 200 Å windows and forother elements we used smaller spectral windows around specificfeatures. In general, the spectral windows used were the same asin our previous work.The radial velocities (corrected to the heliocentric referenceframe) and velocity broadenings are included in Table 1. Theformal errors on the radial velocities (based on the bin-to-bindispersions) are 0.1–0.2 km s − , but this only reflects the un-certainties on the raw wavelength shifts required to match theobservations to the synthetic spectra. The mean di ff erence be-tween our radial velocities and those in the Harris catalogue is0.9 km s − with a standard deviation of 1.5 km s − . These dif-ferences exceed the formal errors on our measurements, as wellas the internal errors of 0.1–0.8 km s − quoted in the Harris cat-alogue, but according to the notes accompanying the cataloguethe true errors may be at least a factor of 2 higher. For our veloc-ities, an additional source of uncertainty comes from variationsin the internal UVES temperature of about ∼ ◦ C during the run(according to the image headers), which can introduce shifts of ∼ . − in the wavelength scale (D’Odorico et al. 2000). Wedo not explore these issues in further detail here, but note that theradial velocities in Table 1 are probably accurate to within ∼ − .For the velocity dispersions, the instrumental broadening,which corresponds to 3 km s − (L12) has been subtracted inquadrature. The errors, once again, reflect only the bin-to-bindispersions. We have not attempted to convert the velocity dis-persions to central or global values, nor has any correction beenmade for other e ff ects that may contribute to line broadeningsuch as stellar rotation and / or macroturbulence (Gray 1982; Car-ney et al. 2008). Nevertheless, our velocity dispersions generallyagree with those in the Harris catalogue within about 1 km s − ,although NGC 6752 deviates more significantly from the centralvelocity dispersion of σ = . ± . − in the Harris cat-alogue. However, recent studies have found larger velocity dis-persions for NGC 6752. Kimmig et al. (2015) find σ = . ± . − while Lardo et al. (2015) find σ = . − , the lat-ter value being identical to our integrated-light estimate. FromHST proper motions, Drukier et al. (2003) find an even higher σ =
12 km s − (which would, however, imply a very high mass-to-light ratio for a GC, M / L V ∼ M (cid:12) / L V , (cid:12) ).While the UVES pipeline reduction in principle accounts forthe blaze function, this does not work perfectly and a “wavy”structure on scales of 30–40 Å (corresponding to the wavelengthrange of the echelle orders) was still evident in the reduced spec-tra. We found that these variations in the continuum level (at thelevel of 1%–2%) could be removed by using a spline functionwhen scaling the observed spectra to match the models; for a200 Å range we found that typically 25 knots (i.e., correspond-ing to 26 spline segments) were required to adequately samplethe variations.Compared to our previous work, the modelling procedurewas modified in a few relatively minor ways. For the mod-elling of CN and CH, we replaced the older Kurucz line listsfor these molecules with the more recent line lists by Masseronet al. (2014) and Brooke et al. (2014), which are also used by TurboSpectrum . With the new molecular line lists, we foundthat C abundances of [C / Fe] ∼ − . / Fe] ∼ − . ff ect of using the new CH / CN linelists on other abundance ratios was negligible. We remind thereader that the interpretation of the carbon abundances in theintegrated-light spectra is not straight forward, due to signifi-cant e ff ects of extra mixing along the RGB (Gratton et al. 2000;Martell et al. 2008). For the atomic lines we continue using theline list of Castelli & Hubrig (2004, hereafter CH04) as ourmain source. We have included hyperfine splitting for some Mnand Sc lines from the line list at the Kurucz website. Hyper-fine splitting is already included in the CH04 list for Ba, but wehave adopted an oscillator strength of log g f = − .
15 insteadof log g f = − .
458 for the 4934 Å Ba ii line. The new valueis taken from the VALD database (Piskunov et al. 1995; Kupkaet al. 1999) and results in much better agreement with the Baabundances inferred from other lines. In addition, we have mod-ified the Ba isotopic ratios according to the r -process mixturein McWilliam (1998), which may be more appropriate for GCs(Straniero et al. 2014) than the default s -process dominated mix-ture in the CH04 list. This implies that a larger fraction of theBa is in the form of Ba and
Ba (in contrast to the
Ba-dominated s -process mixture) and hyperfine structure thus be-comes more important, leading to lower Ba abundances. Article number, page 6 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters F l u x ( n o r m a li s e d ) + o ff s e t F e I T i I F e I T i I F e II S c II T i I F e I F e I F e I F e I T i I F e I F e I F e I F e I F e I F e I F e I F e I T i II F e I F e I NGC 7078NGC 6254NGC 6388
Fig. 4.
Observed (black lines) and best-fitting model spectra (red lines) for three GCs spanning the full range of metallicities.
NGC 104 › [Fe/H] fi =-0.863, σ =0.049 NGC 362 › [Fe/H] fi =-1.076, σ =0.044 NGC 6254 › [Fe/H] fi =-1.481, σ =0.037 [ F e / H ] NGC 6388 › [Fe/H] fi =-0.506, σ =0.044 NGC 6752 › [Fe/H] fi =-1.883, σ =0.041 NGC 7078 › [Fe/H] fi =-2.388, σ =0.044 NGC 7099 › [Fe/H] fi =-2.396, σ =0.063 Fig. 5.
Iron abundance vs. wavelength. The horizontal dashed line ineach panel indicates the average [Fe / H] value (also given in the legend).
For stars fainter than the Sun ( M V > .
8) we assume a mi-croturbulent velocity of ξ = . − (Takeda et al. 2002). Forbrighter stars we adopt the same relation as in L12, i.e., ξ = − for 3 . < M V < . ξ = − for M V < − .
81, and lin- ear interpolation in ξ ( M V ) between M V = .
64 and M V = − . ξ = . − .Figure 4 shows example fits to the spectra of NGC 7078,NGC 6254, and NGC 6388, representing GCs of low, inter-mediate, and high metallicity, respectively. The increase in thestrength of the spectral features with increasing metallicity is ev-ident, and the fits are quite satisfactory over the full metallicityrange. In Fig. 5 we show the individual [Fe / H] values derivedfor each 200 Å bin as a function of wavelength. The dispersionaround the mean values is 0.04–0.06 dex and there are no obvi-ous trends with wavelength.Throughout this paper, we will refer to the analysis describedabove as the standard analysis . To assess the sensitivity of ourresults to the details of the analysis, we also carried out a numberof analyses where the standard analysis was modified in variousways.
As pointed out above, our integrated-light spectra only sample afraction of ∼ / N, they are still subject to stochastic fluctuations inthe number of stars in a given evolutionary stage that happen tofall within the slit scan areas. It is well-known that such stochas-tic fluctuations can lead to large random di ff erences between thecolours of star clusters with otherwise similar properties (age,metallicity, mass), although for clusters with GC-like masses thee ff ect becomes less dramatic for ages older than 10 –10 years(e.g. Girardi et al. 1995; Bruzual 2002; Piskunov et al. 2009;Fouesneau & Lançon 2010; Popescu & Hanson 2010; Silva-Villa& Larsen 2011).To test how much uncertainty stochastic sampling of theHRD introduces into our analysis, we carried out a set of Monte-Carlo simulations in which the same number of stars as thosepresent within the slit scan areas were sampled at random fromthe full ACSGCS CMDs. The corresponding random realisationsof the CMDs were then used to redetermine the abundances fromour spectra. For each cluster, we generated 50 random realisa- Article number, page 7 of 35 & A proofs: manuscript no. larsen
NGC 104 σ [Fe / H] =0.042 NGC 362 σ [Fe / H] =0.092 NGC 6254 σ [Fe / H] =0.058 N NGC 6388 σ [Fe / H] =0.020 NGC 6752 σ [Fe / H] =0.098 NGC 7078 σ [Fe / H] =0.049 NGC 7099 σ [Fe / H] =0.080 Fig. 6.
Distributions of Fe abundances for 50 random sub-samples of thecluster CMDs. Each subsample contains a similar number of stars to theareas covered by the slit scans. Vertical thin (red) lines: Fe abundancesbased on stars located approximately within the slit scan areas. Verticalthick (black) lines: Fe abundances based on all stars. tions of the CMD, and thus obtained 50 sets of abundance mea-surements.In Fig. 6 we show the distributions of [Fe / H] values derivedfrom the di ff erent stochastic realisations of the CMDs for eachcluster. The corresponding distributions for the main elementabundance ratios discussed in this paper are shown in Figs. 7 and8. In each of these figures we also indicate the values derived forthe full CMDs and for stars located within the estimated areasactually covered by the slit scans (see below). We see that thedispersion in the metallicity measurements varies considerablyfrom one cluster to another, and there is a strong inverse corre-lation with the luminosity of the sampled area. However, evenfor NGC 6752, which has the least luminous sampled area, thedispersion on the metallicity measurements does not exceed 0.1dex. For abundance ratios, the dispersions are generally smallerthan for the [Fe / H] determinations and exceed 0.05 dex onlyfor the [Ba / Fe] ratios of NGC 6752 and NGC 7099. This isbecause variations in the abundances derived for di ff erent ele-ments in the stochastic trials tend to correlate with each other,although there are exceptions. For example, the abundances ofMg correlate only weakly with those of Fe for the metal-richclusters (NGC 104, NGC 6388), so for NGC 104 the dispersionon [Mg / Fe] actually exceeds that on [Fe / H].
Table 2.
Oscillator strengths (log g f ) for Mg i lines from varioussources. λ Kurucz CH04 G2003 NIST VALD(Å) (1) (2) (3) (4,5)4352 − . − .
833 . . . − . − . − . − .
691 . . . − . − . − . − . − . − . − . − . − . − . − . − . a − . − . − . − . − . a − . − . − . − . − . a − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . Notes. ( a ) These lines (Mg b triplet) are not used in our analysis. References. (1) Castelli & Hubrig (2004); (2) Gratton et al. (2003b);(3) Kramida et al. (2013); (4) Piskunov et al. (1995); (5) Kupka et al.(1999)
In principle, the issue of stochasticity would be moot for our ob-servations if we knew exactly which regions of the clusters werecovered by the slit scans. We could then simply select the starsfrom the ACSGCS data that fall within those regions and usethem in the CMD modelling. In practice, however, it is still un-certain which stars contribute to the light. Stars near the edgeof the slit are not exactly “in” or “out”, but contribute by somefractional amount that depends on the seeing, guiding errors, etc.In addition, since each exposure started with the slit located atabout one half-light radius from the centre, and the telescopewas already drifting by the di ff erential tracking rate, this intro-duced a substantial uncertainty in the exact centring of the slitat the beginning of the exposure. When multiple parallel scanswere made, there may also be slight gaps or overlaps betweenthe scans.With these caveats in mind, we carried out an additional setof abundance determinations where only stars falling within theestimated slit scan areas were used for the CMD modelling. Incombination with the fully stochastic tests, the di ff erence be-tween this analysis and that based on the full CMDs should helpus quantify the uncertainties associated with sampling only partof the cluster light. The [Fe / H] values derived from these fits areindicated with the vertical thin red lines in Figs. 6-8.
In addition to our analysis based on the modified CH04 line list,we carried out a set of fits using the more recent atomic line listthat is available from the Kurucz web site (the version used herewas downloaded on 18 April 2016 and contains data updated on18 February 2016). The new Kurucz list includes 244719 atomiclines in the wavelength range from 4200 Å – 6200 Å, as com-pared to 69516 in the CH04 list. Part of this di ff erence is due tothe inclusion of hyperfine components for many of the odd- Z el-ements, such as Na, Mn, and Sc (as well as a large number of Vtransitions, although we do not measure these). The Kurucz listalso includes more lines for other elements, e.g. 30541 Fe linesin this wavelength range as compared to 12888 Fe lines in theCH04 list. Of course, the majority of these lines are too weak http://kurucz.harvard.edu Article number, page 8 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
NGC 104 σ [Na / Fe] =0.014 σ [Mg / Fe] =0.044 σ [Ba / Fe] =0.019
NGC 362 σ [Na / Fe] =0.027 σ [Mg / Fe] =0.031 σ [Ba / Fe] =0.041
NGC 6254 σ [Na / Fe] =0.030 σ [Mg / Fe] =0.026 σ [Ba / Fe] =0.032 N NGC 6388 σ [Na / Fe] =0.007 σ [Mg / Fe] =0.017 σ [Ba / Fe] =0.031
NGC 6752 σ [Na / Fe] =0.046 σ [Mg / Fe] =0.040 σ [Ba / Fe] =0.067
NGC 7078 σ [Na / Fe] =0.023 σ [Mg / Fe] =0.021 σ [Ba / Fe] =0.036
NGC 7099 σ [Na / Fe] =0.040 σ [Mg / Fe] =0.033 σ [Ba / Fe] =0.062
Fig. 7.
As Fig. 6, but for the [Na / Fe], [Mg / Fe], and [Ba / Fe] abundance ratios. in most stars to make a substantial di ff erence for the syntheticspectra.For many lines in common between the two lists, oscillatorstrengths have been updated. In particular, we call attention toMg, which has been found in our previous studies to be under-abundant compared to other α -elements (Ca, Ti). The log g f values for the Mg i lines according to various sources are sum-marised in Table 2. The CH04 and “Kurucz” columns give thelog g f values in the CH04 and Kurucz lists. The “G2003” col-umn gives the values according to Gratton et al. (2003b), whichwere used by Carretta et al. (2009b). The remaining two columnsgive the values listed in the NIST and VALD databases. We seethat the log g f values in the CH04 list di ff er by up to 0.25 dexfrom those in the other lists. We will return to the implicationsof these di ff erences for our abundance determinations below.We note that the Kurucz list does not include hyperfine struc-ture for Ba. We have added this information from the CH04 list,but kept the s -process dominated isotopic mixture. By compari-son with the r -process dominated mixture in our modified CH04list, this allows us to assess the sensitivity of the Ba abundancemeasurements to the assumed isotopic ratios. In more distant GCs, colour-magnitude diagrams may not al-ways be available, and one may need to rely on theoreticalisochrones for the analysis. To test how much this would changeour results, we carried out a set of fits based purely on theoreti-cal isochrones, again using the Dartmouth set. The metallicitiesof the isochrones were chosen to self-consistently match thosederived from the spectroscopy; this sometimes required a coupleof iterations to reach convergence. The isochrones were com- bined with the empirical CMDs for the horizontal branch (HB)and asymptotic giant branch (AGB), taken from ACSGCS.The appropriate scalings of the weights of the empirical datawere determined by requiring the isochrone-based CMDs andthe empirical ones to have the same number of RGB stars inthe range 1 < M V <
2. We assumed the same ages as for theluminosity functions (Sec. 4.2).The isochrones used for these fits are included in Fig. 3. Westress that these isochrones are not necessarily the same as thosethat would provide the best fits to the empirical CMDs. In somecases, it might be possible to improve the fits by adjusting thereddening and distance, but with the exception of NGC 6388(see below) we have not attempted to do so.
5. Results
The individual abundance measurements from the standard anal-ysis are listed in Tables A.1–A.7. For each spectral bin, we givethe best-fitting abundance of the corresponding element, alongwith the formal error from the χ minimisation. By comparisonwith Fig. 5, it is clear that the true uncertainties are larger thanthe random errors on the fits; the bin-to-bin dispersions on theFe abundances are 0.04–0.06 dex, whereas the formal errors aregenerally < .
01 dex. Comparing, for example, NGC 7078 andNGC 7099 (both of which have very similar overall metallici-ties), the variations in [Fe / H] with wavelength do indeed appearnon-random. Possible systematic e ff ects that could cause suchvariations include uncertainties in the atomic parameters of thelines, as well as in the continuum scaling procedure.Table 3 lists the weighted average of the individual abun-dance measurements for each cluster for the standard analysis.The weights w i are based on the random uncertainties in Ta-bles A.1–A.7, but we have added a “floor” of 0.01 dex in quadra- Article number, page 9 of 35 & A proofs: manuscript no. larsen
NGC 104 σ [Ca / Fe] =0.017 σ [Ti / Fe] =0.016 σ [Cr / Fe] =0.023
NGC 362 σ [Ca / Fe] =0.022 σ [Ti / Fe] =0.010 σ [Cr / Fe] =0.008
NGC 6254 σ [Ca / Fe] =0.015 σ [Ti / Fe] =0.011 σ [Cr / Fe] =0.018 N NGC 6388 σ [Ca / Fe] =0.011 σ [Ti / Fe] =0.016 σ [Cr / Fe] =0.017
NGC 6752 σ [Ca / Fe] =0.030 σ [Ti / Fe] =0.025 σ [Cr / Fe] =0.011
NGC 7078 σ [Ca / Fe] =0.019 σ [Ti / Fe] =0.011 σ [Cr / Fe] =0.007
NGC 7099 σ [Ca / Fe] =0.032 σ [Ti / Fe] =0.014 σ [Cr / Fe] =0.013
Fig. 8.
As Fig. 6, but for the [Ca / Fe], [Ti / Fe], and [Cr / Fe] abundance ratios.
Table 3.
Abundance measurements for the standard analysis.
NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099[Fe / H] − . − . − . − . − . − . − . w (N) 0 .
046 (9) 0 .
042 (9) 0 .
034 (9) 0 .
042 (9) 0 .
039 (9) 0 .
042 (9) 0 .
059 (9)[Na / Fe] 0 . − . − .
038 0 .
357 0 .
302 0 .
154 0 . w (N) 0 .
008 (2) 0 .
000 (2) 0 .
003 (2) 0 .
013 (2) 0 .
023 (2) . . . (1) 0 .
006 (2)[Mg / Fe] 0 .
442 0 .
149 0 .
378 0 .
108 0 .
391 0 .
177 0 . w (N) 0 .
095 (5) 0 .
088 (5) 0 .
067 (5) 0 .
092 (5) 0 .
130 (5) 0 .
126 (5) 0 .
144 (5)[Ca / Fe] 0 .
412 0 .
273 0 .
380 0 .
260 0 .
355 0 .
330 0 . w (N) 0 .
116 (7) 0 .
128 (8) 0 .
137 (8) 0 .
182 (7) 0 .
114 (8) 0 .
069 (8) 0 .
096 (8)[Sc / Fe] 0 .
219 0 .
117 0 .
130 0 .
118 0 .
120 0 .
221 0 . w (N) 0 .
178 (6) 0 .
098 (6) 0 .
068 (6) 0 .
190 (6) 0 .
067 (6) 0 .
107 (6) 0 .
099 (6)[Ti / Fe] 0 .
370 0 .
338 0 .
412 0 .
259 0 .
342 0 .
422 0 . w (N) 0 .
115 (8) 0 .
065 (9) 0 .
097 (9) 0 .
114 (8) 0 .
128 (8) 0 .
100 (9) 0 .
077 (9)[Cr / Fe] − . − .
026 0 . − . − . − . − . w (N) 0 .
135 (6) 0 .
083 (6) 0 .
411 (6) 0 .
220 (6) 0 .
070 (6) 0 .
067 (6) 0 .
125 (6)[Mn / Fe] − . − . − . − . − . − . − . w (N) 0 .
087 (2) 0 .
005 (2) 0 .
127 (2) 0 .
149 (2) 0 .
055 (2) 0 .
094 (2) 0 .
026 (2)[Ba / Fe] 0 .
155 0 .
330 0 .
413 0 .
200 0 .
182 0 .
436 0 . w (N) 0 .
078 (4) 0 .
051 (4) 0 .
087 (4) 0 .
252 (4) 0 .
109 (4) 0 .
053 (4) 0 .
171 (4)
Notes.
For each abundance ratio, the second line lists the weighted r.m.s. and the number of individual measurements in parentheses. ture to avoid having bins with very small formal uncertaintiesbecome too dominant. Hence, the weights were computed as w i = (cid:16) σ i + (0 .
01 dex) (cid:17) − (1)As in L14, we also list the bin-to-bin r.m.s., again weighted usingEq. (1):rms w = (cid:32) (cid:80) w i ( x i − (cid:104) x (cid:105) ) (cid:80) w i (cid:33) / (2) The numbers in parentheses after rms w give the number of indi-vidual fits for each entry, N .Simple propagation of the formal errors on the individualmeasurements will likely underestimate the uncertainties on themean values in Table 3. Taking the rms w as indicative of thetrue uncertainties on the individual measurements, we insteadestimate the uncertainties on the mean values as σ = rms w / √ N − Article number, page 10 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table 4.
Literature metallicities.
Cluster [Fe / H] Ref.NGC 104 − . ± .
003 1 (G) − . ± .
016 1 (U) − . ± .
01 2 − .
62 3 − . ± .
08 4 − . ± .
01 5NGC 362 − . ± .
004 6 (G) − . ± .
014 6 (U) − .
33 7 − . ± .
09 8NGC 6254 − . ± .
004 1 (G) − . ± .
016 1 (U) − .
52 3 − . ± .
06 4NGC 6388 − . ± .
013 1 (G) − . ± .
014 1 (U) − . ± .
15 4 − . / − .
58 9 − . ± .
02 8NGC 6752 − . ± .
004 1 (G) − . ± .
014 1 (U) − . ± .
01 10 − .
54 3 − . ± .
16 4NGC 7078 − . ± .
007 1 (G) − . ± .
016 1 (U) − .
38 3 − . ± .
14 4NGC 7099 − . ± .
006 1 (G) − . ± .
015 1 (U) − .
31 3
Notes.
For Carretta et al. (2009a) we list the [Fe / H] values derived fromtheir GIRAFFE (G) and UVES (U) observations.
References. (1) Carretta et al. (2009a); (2) Koch & McWilliam (2008);(3) Pritzl et al. (2005); (4) Roediger et al. (2014); (5) Lapenna et al.(2014); (6) Carretta et al. (2013); (7) Pritzl et al. (2005); (8) Worley &Cottrell (2010); (9) Wallerstein et al. (2007); (10) Yong et al. (2008);
Whenever we refer to uncertainties on the mean abundance ra-tios, these will have been calculated using Eq. (3). The equiva-lents of Table 3, but for the modified analysis methods, are in-cluded as Tables B.1–B.3 in the appendix.
We first compare our measurements of the iron abundances withdata from the literature. We have not attempted to carry out acomplete literature search for abundance measurements of allthe clusters in our sample, but rely on three main sources: theVLT / FLAMES survey by Carretta et al. (2009a), for which weinclude both the UVES and GIRAFFE iron abundances, and thecompilations by Pritzl et al. (2005) and Roediger et al. (2014).The iron abundances from these studies, as well as a few oth-ers, are summarised in Table 4. The di ff erences between di ff er-ent studies often exceed the formal random uncertainties on themeasurements, which are usually small ( ∼ .
01 dex). For theRoediger et al. (2014) compilation, the quoted uncertainties rep-resent the variation among the di ff erent studies in the compila-tion. Note that the overlap with Pritzl et al. (2005) and Roediger [ F e / H ] ( I n t e g r . ) NGC 6388NGC 362NGC 6254 NGC 6752 NGC 104NGC 7078NGC 7099
Fig. 9.
Integrated-light iron abundances versus literature values. Thehorizontal bars represent the range of [Fe / H] values quoted in the liter-ature (Table 4). Black bars indicate the values derived from our standardanalysis and red bars are for the stars within the slit scan areas. The blue(dashed) line is the 1:1 relation, not a fit. et al. (2014) is only partial, with NGC 6388 missing from theformer and NGC 362 and NGC 7099 from the latter.In Figure 9 we plot our integrated-light iron abundancemeasurements against the literature values. The horizontal bars(black for the standard analysis, red for stars in the slit scan ar-eas) represent the range of values quoted by the literature sourcesand the dashed line shows the 1:1 relation. From this figure, andby comparing Tables 3 and 4, we see that our integrated-lightiron abundances generally agree well with the literature values.NGC 6752 is the most conspicuous outlier in the standard analy-sis, but moves closer to the 1:1 line when the stars in the slit scanareas are used. Comparing with Figure 6, we see that this clusteralso has the largest spread in the iron abundances derived fromthe random CMD realisations. This suggests that stochastic fluc-tuations, caused by the limited coverage of the Galactic GCs byour scans, may indeed be an important contributor to the scatteraround the 1:1 line Fig. 9.Next, we discuss the comparison with individual clusters inmore detail.
According to the literature, as well as our measurements, themost metal-rich cluster in our sample is NGC 6388. Carrettaet al. (2009a) find [Fe / H] = − .
41 (GIRAFFE) or [Fe / H] = − .
44 (UVES). Wallerstein et al. (2007) found a metallicity aslow as [Fe / H] = − .
79 when using spectroscopically deter-mined surface gravities, but noted that these surface gravitiesseemed too low for the locations of the stars in the CMDs.When using photometrically inferred surface gravities, Waller-stein et al. (2007) instead found [Fe / H] = − . ± .
03, which iscloser to other recent determinations. Our integrated-light mea-surement of [Fe / H] = − . ± .
015 from the standard analysisthus falls well within the range found by studies of individualstars. We note that while NGC 6388 has a somewhat higher ironabundance than NGC 104, it is probably less α -enhanced (e.g. Article number, page 11 of 35 & A proofs: manuscript no. larsen M V NGC 6388 (D=9.9 kpc)NGC 104T=13 Gyr, [Fe/H]=-0.9T=13 Gyr, [Fe/H]=-0.6
Fig. 10.
Binned colour-magnitude diagrams of NGC 6388 andNGC 104.
Wallerstein et al. 2007) so the total metallicities of the two clus-ters may not be very di ff erent.NGC 6388 is quite massive and compact, and the uncer-tainty on our integrated-light analysis that arises from stochas-tic CMD sampling is small, with σ [Fe / H] = .
020 dex (Fig. 6).A more significant source of uncertainty for this cluster may liein the modelling of the colour-magnitude diagram. In Fig. 10we show the binned CMD of NGC 6388 together with that ofNGC 104. We also include theoretical isochrones for metallic-ities of [Fe / H] = − . / H] = − . α/ Fe] =+ .
2. Isochrones with [Fe / H] = − . / H] = − . α/ Fe] = + . / H] = − . α/ Fe] = + .
2, or [Fe / H] = − . α/ Fe] = + .
4) thanthe values quoted in the literature for these clusters, and do notreach the coolest parts of the RGB (although some of the cooleststars might be asymptotic giant branch stars). For NGC 6388,neither isochrone fits the MS.Considering only the RGB, we can get a better match be-tween the two clusters if the assumed distance of NGC 6388 isincreased. For a distance of D = . ff set remains forthe MS. This larger distance is also in better agreement with thedynamical distance estimate of 10 . + . − . kpc by Watkins et al.(2015). The e ff ect of a larger distance on the integrated-lightabundances is, in any case, quite modest: it leads to a decreaseof 0.13 dex in the surface gravities, and the iron abundance thendecreases by 0.03 dex. Thus, irrespective of the assumed dis-tance, the integrated-light analysis based on the observed CMDof NGC 6388 gives an iron abundance in good agreement withthat derived from measurements of individual stars. If we alsoallow the reddening to vary, it may be possible to find combina-tions of metallicity, age, alpha-enhancement, distance, and red-dening that allow acceptable fits to both CMDs. Such an exercise F l u x ( n o r m a li s e d ) NGC 6254NGC 6752
Fig. 11.
Spectra of NGC 6254 and NGC 6752. The di ff erence in thestrengths of the spectral features in the two integrated-light spectra isevident, despite their similar metallicities according to measurementsof individual stars. is beyond the scope of this work, but in Sec. 5.3 we will brieflyconsider the e ff ect of changing E ( B − V ) for NGC 6388.For NGC 104 our standard analysis yields [Fe / H] = − . ± . / H] = − . / H] = − .
75 (based on102 Fe i lines) with an estimated systematic error of 0.045 dex. Alower iron abundance of [Fe / H] = − . ± .
01 has recently beenmeasured by Lapenna et al. (2014) for 11 individual RGB stars,di ff ering only slightly from that derived here. It is interesting tonote that Lapenna et al. (2014) found a significantly lower metal-licity of [Fe / H] = − .
94 from AGB stars when using only Fe i lines, whereas measurements of Fe ii lines in the AGB stars gavean iron abundance similar to that measured for the RGB stars,[Fe ii / H] = − . ± .
01. While the reason for this di ff erenceremains unclear, discrepancies between Fe abundances derivedfrom Fe i and Fe ii lines have been observed in other clusters,e.g. M22 (Mucciarelli et al. 2015). In our integrated-light analy-sis we do not treat Fe i and Fe ii lines separately, and it is possiblethat our abundances for NGC 104 are a ff ected at some level bythe anomalous behaviour of the AGB stars. However, in theiranalysis of NGC 104, McWilliam & Bernstein (2008) found nosignificant di ff erence between the iron abundances based on Fe i lines (quoted above) and Fe ii lines ([Fe ii / H] = − .
72, based on 7lines with a dispersion of 0.15 dex).Our iron abundance for NGC 362, [Fe / H] = − . ± . / H] = − .
17. However, the dis-persion in the stochastic trials is relatively large for this cluster( σ [Fe / H] = .
092 dex) and the full range of Fe abundances en-countered in the 50 stochastic trials goes from [Fe / H] = − . / H] = − .
91. When using stars within the slit scan areato model the CMD we get [Fe / H] = − .
29. Thus, within theuncertainties introduced by stochastic sampling, our metallicitydetermination for NGC 362 is in agreement with most of thevalues quoted in the literature.
Article number, page 12 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Most literature sources agree that these two clusters have verysimilar metallicities, with [Fe / H] values in the range − . − .
52 for NGC 6254 and between − .
63 and − .
53 forNGC 6752 (Table 4). In spite of this, our integrated-light ironabundances for the two clusters di ff er by more than 0.4 dex, adi ff erence that appears far too large to be explained simply bymeasurement uncertainties.For NGC 6254, our standard analysis gives [Fe / H] = − . ± . − .
62 to − .
35 in[Fe / H], suggesting that the small di ff erence with respect to theliterature may well be caused by stochastic fluctuations. Indeed,the analysis based on stars in the estimated slit scan area gives[Fe / H] = − .
58, in excellent agreement with the literature val-ues.NGC 6752, on the other hand, is the most outlying of theclusters in our sample with an integrated-light iron abundanceof [Fe / H] = − . ± .
014 from the standard analysis, whichis about 0.3 dex lower than that found by other studies. A directcomparison of our spectra of NGC 6254 and NGC 6752 (Fig. 11)shows that the spectral features are indeed substantially weakerin the spectrum of NGC 6752. From this we conclude that thedi ff erence in the derived metallicities stems from a real di ff er-ence in our integrated-light spectra of the two clusters, and notfrom some failure of the fitting / modelling procedure. NGC 6752is the cluster in our sample for which the scanned area has thelowest luminosity, and it is therefore expected that the e ff ectsof stochastic CMD sampling manifest themselves more stronglyin this cluster. Fig. 6 shows that the dispersion in [Fe / H] forthe stochastic trials is indeed the largest among the clusters inour sample ( σ [Fe / H] = . ff erence between ourintegrated-light iron abundance and the literature is still about 3 σ [Fe / H] . By using only stars in the estimated slit scan area we get[Fe / H] = − .
73, which reduces (but does not entirely eliminate)the discrepancy with respect to the literature measurements. Thehighest iron abundance reached in the 50 stochastic realisationsof the CMD is [Fe / H] = − .
69, still not quite reaching the liter-ature values, although even higher values might conceivably bereached if more trials were carried out.A number of other uncertainties in our modelling procedurehave been considered in our previous papers (L12, L14). Theseinclude the adopted microturbulent velocities, luminosity func-tions, colour- T e ff transformations and extinction corrections. Un-certainties in the treatment of each of these quantities may addup to an uncertainty of ∼ . ff ect our re-sults, we carried out an extra set of fits in which three extra binswere introduced along the BS sequence in the slit scan CMD ofNGC 6752. The BSs were treated in the same way as the otherstars, i.e., their gravities and temperatures were estimated fromthe location in the CMD, and they were assumed to have thesame composition as other stars in the cluster. From these fits wefound the e ff ect of including the BSs to be relatively minor, withthe iron abundance increasing by ∼ .
03 dex to [Fe / H] = − . / H] in their analysis. This still leaves a di ff erence of ∼ . NGC 7078 (M15) and NGC 7099 (M30) are among the mostmetal-poor GCs in our Galaxy. Most recent studies find ironabundances in the range [Fe / H] = − . − . / H] = − . − . / H] = − .
39 forNGC 7078 and [Fe / H] = − .
40 for NGC 7099, in very goodagreement with the literature values. The scatter in the stochas-tic CMD realisations is σ [Fe / H] = .
049 and σ [Fe / H] = . / H] = − .
40 for bothclusters). NGC 7078 has also been studied in integrated light bySakari et al. (2013), who found [Fe / H] = − . ± .
03 (from Fe i lines) and [Fe / H] = − . ± .
10 (from one Fe ii line), which isagain in good agreement with our measurements. We next turn to the element abundance ratios. In the contextof globular clusters, the light elements (C, N, Na, O, Mg, Al)are of special interest because of the star-to-star variations inthe abundances of these elements and their relation to the phe-nomenon of multiple stellar populations in GCs (e.g. Grattonet al. 2012). In our spectra, we can measure sodium (via theNa i lines at 5683 / / / / i and Ca i lines, thee ff ect of which is exacerbated by the high velocity dispersionof NGC 6388. As such, these lines represent an interesting testof our full spectral fitting approach. As can be appreciated fromTables A.1-A.7, the agreement between the sodium abundancesinferred from the two sets of lines is, in fact, remarkably good,with a mean di ff erence of only 0.02 dex and an r.m.s. dispersionof 0.02 dex. For NGC 7078, the 6154 / / Fe] < + .
22 (one sigma; not included inTable A.6), which is consistent with the measurement based onthe 5683 / Article number, page 13 of 35 & A proofs: manuscript no. larsen F l u x ( n o r m a li s e d ) + o ff s e t N i I N a I S c II F e I N a I F l u x ( n o r m a li s e d ) + o ff s e t F e I N a I S i I C a I F e I N a I C a I C a I F e I C a I Fig. 12.
Spectral fits to the sodium doublets at 5683 / / In Fig. 13 we compare our integrated-light measurementsof sodium and magnesium with the results for individual starsfrom Carretta et al. (2009b). The clusters are ordered accord-ing to their metallicities, increasing from left to right. For eachcluster, we show the average of the logarithmic abundances forthe individual stars (filled black markers) as well as the abun-dances averaged on a linear scale (open markers). The full rangeof [Na / Fe] and [Mg / Fe] ratios measured for individual stars areindicated by the vertical black lines. We also indicate the aver-age literature values from Roediger et al. (2014) where available(‘x’-markers).We see that, in general, the integrated-light [Na / Fe] valuesfall within the range determined from individual stars by Carrettaet al. (2009b). At the lowest metallicities the sodium lines still lieon the linear part of the curve-of-growth for a typical GC giant,so in this regime we may expect the integrated-light abundancesto most closely reflect the linear average of individual stellarabundances (i.e., the open markers). At higher metallicities thesodium lines begin to saturate, and the integrated-light measure-ments may then yield abundances that are closer to the logarith- [ N a / F e ] C2009 (log avg)C2009 (lin avg) R2014IL N G C N G C N G C N G C N G C N G C N G C [ M g / F e ] C2009 (log avg)C2009 (lin avg) R2014IL
Fig. 13.
Comparison of our integrated-light [Na / Fe] and [Mg / Fe] abun-dance ratios with measurements of individual stars from Carretta et al.(2009b, C2009) and Roediger et al. (2014, R2014). Slight o ff sets to theright and left have been applied to our integrated-light data points andthose of Roediger et al. (2014) for clarity. N G C N G C N G C N G C N G C N G C N G C [ M g / F e ] C2009R2014IL (G2003 log gf ) Fig. 14.
As the bottom panel of Fig. 13, but using log g f values for Mg i lines from Gratton et al. (2003b) and basing the modelling of other lineson the Kurucz line list. mic average abundances of individual stars. The actual relationswill be more complicated as the lines will be on di ff erent partsof the curve-of-growth for di ff erent stars in the cluster. Regard-less of which average is considered, there is a tendency for ourintegrated-light measurements to yield slightly lower [Na / Fe]ratios than the average of the individual stars. From Table B.1-B.5, we see that the sodium abundances are not very sensitiveto the details of the analysis; if we model the CMDs using stars
Article number, page 14 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters within the slit scan areas the [Na / Fe] ratios generally changeby less than 0.05 dex, and the same is true if we use theoreticalisochrones instead of the empirical CMDs.We note that the Na abundance measurements from Carrettaet al. (2009b) have been corrected for non-LTE e ff ects, whereasno such correction has been attempted for our integrated-lightmeasurements. These corrections depend on the surface temper-ature and gravity of the stars, but for cool giants the correctionstend to be positive (Gratton et al. 1999) and might thus accountfor part of the o ff set. A full investigation of this issue is beyondthe scope of this work and will be left for a future paper.The lower panel in Fig. 13 shows that the [Mg / Fe] valuesderived from our integrated-light spectra are all super-solar. Thisis also the conclusion reached from the observations of individ-ual stars in the clusters, and is not unexpected for old stellarpopulations such as GCs. There is, nonetheless, again a notice-able o ff set between the [Mg / Fe] ratios derived from our stan-dard analysis and those of Carretta et al. (2009b). The latter find[Mg / Fe] ratios as high as ∼ + . / Fe] = .
18 to 0.44. The mean di ff erence betweenour [Mg / Fe] ratios and those of Carretta et al. (2009b) is about0.15 dex. The picture remains the same if we base our modellingon stars within the slit scan areas or on theoretical isochrones.However, we recall that the log g f values for several of the Mglines in the Castelli & Hubrig (2004) line list di ff er significantlyfrom those listed by other sources (Table 2). For our observa-tions, the lines at 4703 Å and 5528 Å tend to have the smallesterrors and thus carry the most weight in the average values. Forthese two lines, the log g f values in the CH04 list are about 0.07dex and 0.15 dex higher than those listed by most of the othersources, and our average Mg abundances increase by about 0.07dex when the Kurucz line list is used instead. The log g f valuesin the list of Gratton et al. (2003b), on which Carretta et al. basedtheir analysis, are lower still. If we derive Mg abundances fromthe three lines that we have in common with G2003 (4703 Å,5528 Å, 5711 Å) and use their log g f values, while otherwise fol-lowing the standard analysis, then the mean di ff erence betweenour [Mg / Fe] ratios and those of Carretta et al. (2009b) is reducedto − .
07 dex (with an r.m.s. of 0.06 dex). If we use the G2003log g f values together with the Kurucz line list, the di ff erence isreduced further to − .
04 dex (Fig. 14). (But we note that onlythe 5711 Å line is in common with Carretta et al. (2009b), whoalso used redder lines (near 6319 Å) that are not included in ouranalysis.).In any case, di ff erences at the level of 0.1 dex are not uncom-mon when comparing measurements of individual stars from dif-ferent studies, and other studies have found lower [Mg / Fe] ratiosfor some clusters than those quoted by Carretta et al. (2009b).For example, Carretta et al. (2009b) find a mean [Mg / Fe] =+ .
52 for NGC 104 (with a star-to-star r.m.s. of 0.03 dex),whereas Koch & McWilliam (2008) find [Mg / Fe] = + .
46 (withan r.m.s. of 0.05 dex) and Thygesen et al. (2014) find a median[Mg / Fe] = + .
44 for the same cluster. For NGC 7078, Sne-den et al. (1997) found an average (cid:104) [Mg / Fe] (cid:105) = + . ± . / Fe] = + .
45 (with an r.m.s. of 0.19 dexfor 13 stars) from Carretta et al. (2009b). In a recent study, Diaset al. (2016) find average [Mg / Fe] values close to ∼ + . g f values doesnot exist for the Na lines, where all the line lists contain essen- [Fe/H] [ B a / F e ] ILGCs (P2005)MW stars (V2004) [ C r / F e ] ILGCs (R2014)MW stars (I2013) [ T i / F e ] ILGCs (R2014)MW stars (V2004) [ C a / F e ] ILGCs (R2014)MW stars (V2004)
Fig. 15.
Comparison of our integrated-light [Ca / Fe], [Ti / Fe], [Cr / Fe],and [Ba / Fe] abundance ratios with data for individual Milky Way stars(V2014, I2013: Venn et al. 2004; Ishigaki et al. 2013) and literature datafor globular clusters (P2005, R2014: Pritzl et al. 2005; Roediger et al.2014). tially identical values. However, Fig. 13 shows that small di ff er-ences between literature averages and Carretta et al. (2009b) arepresent also for [Na / Fe].
Apart from the abundances of sodium and magnesium discussedabove, there is no homogeneous source of abundance measure-ments that we can use as a reference for a detailed one-to-onecomparison with our integrated-light abundances. Instead, wecompare the general trends of elemental abundance ratios as afunction of metallicity with data for individual Milky Way stars(Venn et al. 2004; Ishigaki et al. 2013) and the compilations ofGC data (Pritzl et al. 2005; Roediger et al. 2014). The result ofthis comparison is shown in Fig. 15 for elements that we have incommon with the GC compilations: Ca, Ti, Cr, and Ba. It shouldbe noted that the stars in the sample of Ishigaki et al. (2013)belong primarily to the thick disc and halo components of theMilky Way, whereas the Venn et al. (2004) sample also includesthin disc stars. Hence, di ff erences in the abundance patterns ofGCs and field stars may be expected, especially at higher metal-licities. Article number, page 15 of 35 & A proofs: manuscript no. larsen
Overall, our integrated-light abundances agree well with theliterature compilations for GCs, as well as with the abundancemeasurements for individual stars. At metallicities of [Fe / H] ≈− . ff erent sequences followed by the GCs andGalactic (disc) stars become apparent. We find the α -elements(Ca, Ti) to be enhanced at about 0.3 dex relative to Solar-scaled abundances, with formal (unweighted) mean values of (cid:104) [Ca / Fe] (cid:105) = + .
33 and (cid:104) [Ti / Fe] (cid:105) = + .
36. The r.m.s. disper-sions are 0.05 dex for both elements. The mean values changeonly slightly if the Kurucz line list is used, with the mean Caabundance increasing to (cid:104) [Ca / Fe] (cid:105) = + .
34 and with Ti re-maining unchanged at (cid:104) [Ti / Fe] (cid:105) = + .
36. Some of the scatter isprobably real; in particular, other studies have found the metal-rich cluster NGC 6388 to be less α -enhanced than a typical GC,with Roediger et al. (2014) quoting mean values of [Ca / Fe] = . ± .
13 and [Ti / Fe] = + . ± .
19 (the original sources be-ing Carretta et al. (2007) and Wallerstein et al. (2007)). Our Tiabundance for this cluster ([Ti / Fe] = + . ± .
04) agrees wellwith the literature average, although our Ca abundance measure-ment ([Ca / Fe] = + . ± .
08) is not as depleted as suggested bythe literature compilation. In fact, it matches the Ti abundance,as observed in other GCs.Cr belongs to the group of Fe-peak elements, and both MilkyWay field stars (Ishigaki et al. 2013) and GC literature data in-dicate a mean [Cr / Fe] ratio close to zero over a wide metallicityrange. This is confirmed by our integrated-light abundances, forwhich the standard analysis yields (cid:104) [Cr / Fe] (cid:105) = − .
06 with a dis-persion of 0.09 dex. The analysis based on the Kurucz line listgives (cid:104) [Cr / Fe] (cid:105) = − .
04, with a slightly larger dispersion (0.10dex). The other two iron-peak elements that we measure (Sc,Mn) are not included in the literature compilations for GCs, butour slightly super-solar Sc abundance ratios ([Sc / Fe] = . − . / Fe] ratios are generally negative,decreasing from [Mn / Fe] ≈ − . / Fe] ≈ − . − . ff ects; Bat-tistini & Bensby (2015) find an essentially flat behaviour with[Mn / Fe] ≈ / H] > ∼ − . / Fe] ratios also appear consistent with the general trends seenfor Milky Way GCs. Since the compilation by Pritzl et al. (2005)was published, a number of more recent determinations of Baabundances have appeared for several of the clusters in our sam-ple. These are summarised in Table 5, which also includes theintegrated-light measurements from Colucci et al. (2017) andSakari et al. (2014) for the clusters that we have in common. Formost clusters, our [Ba / Fe] ratios agree fairly well with the liter-ature data for individual stars, but for the most metal-poor clus-ters (NGC 7078, NGC 7099) we find higher [Ba / Fe] ratios thanthose quoted in the literature (although the data for NGC 7099are based on just a single star). The integrated-light Ba abun-dances measured by Sakari et al. (2014), on the other hand, arelower than our values as well as those by the other literaturesources for both NGC 104 and NGC 7078.NGC 7078 is one of a few GCs that are known to exhibita substantial star-to-star spread in Ba abundance, and the valueof [Ba / Fe] = + . ± .
02 for Sobeck et al. (2011) in Table 5is the weighted mean of their measurements for nine individ-ual stars. Sneden et al. (2000) found a mean Ba / Ca ratio of
Table 5.
Barium abundances. [Ba / Fe] Ref.NGC 104 + . ± .
24 1 + . ± .
09 2 + . ± .
12 (SG) 3 + . ± .
12 (TO) 3 + . ± .
11 (IL) 4 − . ± .
08 (IL) 5 + . ± .
05 Our analysisNGC 362 + . ± .
02 6 + . ± .
30 7 + . ± .
22 8 + . ± .
07 (IL) 4 + . ± .
03 Our analysisNGC 6254 + . ± .
09 9 + . ± .
05 Our analysisNGC 6388 + . ± .
21 7 + . ± .
10 10 + . ± .
07 11 + . ± .
10 (IL) 4 + . ± .
15 Our analysisNGC 6752 + . ± .
11 12 + . ± .
06 (IL) 4 + . ± .
06 Our analysisNGC 7078 + . ± .
02 13 − . ± .
06 (IL) 5 + . ± .
03 Our analysisNGC 7099 − . ± .
11 14 + . ± .
10 Our analysis
Notes. (IL) refers to integrated-light measurements, whereas (SG) and(TO) indicate measurements for sub-giants and turn-o ff stars. References. (1) Thygesen et al. (2014); (2) Worley et al. (2010);(3) James et al. (2004b); (4) Colucci et al. (2017); (5) Sakari et al.(2014); (6) Carretta et al. (2013); (7) Worley & Cottrell (2010);(8) Shetrone & Keane (2000); (9) Mishenina et al. (2003); (10) Carrettaet al. (2007); (11) Wallerstein et al. (2007); (12) James et al. (2004a);(13) Sobeck et al. (2011); (14) Shetrone et al. (2003) [Ba / Ca] = − . / Fe] ∼ . / Fe] = . / Fe] = + . ± . s -process dominated mixture, the [Ba / Fe] ratios increase by about0.06 dex for NGC 104, by 0.09 dex for NGC 362, and by0.03 dex for NGC 6388. The [Ba / Eu] ratios in these three clus-ters tend to be close to the Solar value (Carretta et al. 2007;Wallerstein et al. 2007; Worley & Cottrell 2010; Thygesen et al.2014), which suggests an s -process dominated origin of theheavy elements in these clusters, although other authors havefound evidence of an r -process dominated mixture in NGC 104(Cordero et al. 2014). Even if we adopt the s -process mix-ture for these clusters, our [Ba / Fe] ratios still agree well withthe literature (apart from the very high [Ba / Fe] ratio found forNGC 6388 by Worley & Cottrell 2010). In the low-metallicitycluster NGC 7078, the [Ba / Eu] ratio is about − . r -process dominated origin. Article number, page 16 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table 6. Di ff erences between CMD-based and isochrone-based abundances. NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099 t iso (Gyr) 11 11 13 13 13 13 13[Fe / H] iso − . − . − . − . − . − . − . α / Fe] iso + . + . + . + . + . + . + . ∆ i − c [Fe / H] − . − . − . − .
204 0 . − .
029 0 . ∆ i − c [Na / Fe] 0 .
004 0 .
028 0 .
050 0 . − .
015 0 . − . ∆ i − c [Mg / Fe] − .
005 0 . − .
008 0 . − .
022 0 . − . ∆ i − c [Ca / Fe] − . − . − . − .
054 0 . − . − . ∆ i − c [Sc / Fe] 0 .
011 0 .
019 0 . − . − .
080 0 . − . ∆ i − c [Ti / Fe] − . − . − . − . − . − . − . ∆ i − c [Cr / Fe] − . − . − . − .
022 0 .
013 0 .
001 0 . ∆ i − c [Mn / Fe] 0 . − .
002 0 .
011 0 .
023 0 .
013 0 . − . ∆ i − c [Ba / Fe] 0 .
023 0 . − . − . − .
032 0 . − . Notes.
The first three lines give the parameters of the isochrones (from Dotter et al. 2007) used in the modelling of the integrated-light spectra. [ F e / H ] ( I n t e g . ) NGC 6388NGC 362NGC 6254 NGC 6752 NGC 104NGC 7099NGC 7078
Fig. 16.
Integrated-light iron abundances for isochrone-based analysisversus versus literature values. Symbols are the same as in Fig. 9.
Fig. 16 shows the isochrone-based metallicities as a functionof the literature values and in Table 6 we list the di ff erencesbetween the isochrone-based and CMD-based abundances foreach cluster. (Equivalent di ff erence tables for the other modifiedanalysis techniques are in Tables B.4-B.5). In terms of overallmetallicities, the largest di ff erence between CMD- and isochronebased results occurs for NGC 6388, for which the isochrone-based metallicity is about 0.2 dex lower than that based on theCMD. The isochrone-based metallicity remains within the rangequoted in the literature, albeit towards the lower-metallicity end.Relatively large shifts are also seen for NGC 362 ( − .
09 dex)and NGC 6254 ( − .
14 dex), but for both clusters the isochrone-based metallicities remain close to those found by literature stud-ies for individual stars. For the most part, the changes to individ-ual abundance ratios are small, typically less than about 0.05dex, even for NGC 6388.For NGC 362, the RGB of the [Fe / H] = − . ff set noticeably towards the red compared to the empiricalCMD (Fig. 3). There is a hint that this cluster may be slightly less α -enhanced than most of the others (with the exception ofNGC 6388) and an isochrone with [ α/ Fe] = + . + .
4) would indeed provide a better match to the observed RGB.The e ff ect of using the less α -enhanced isochrone is very small,however, with the iron abundance changing by just − .
01 dex to[Fe / H] = − . E ( B − V ) ≈ .
31 (and simultaneously increasing the distancemodulus by ∼ .
20 mag). This would also lead to a decrease inthe e ff ective temperatures of the cluster stars, in turn causing adecrease in the metallicity obtained from the CMD-based anal-ysis, and better agreement with the isochrone-based result (butthen giving a somewhat lower metallicity than most recent liter-ature estimates). However, such a low reddening would be welloutside the range of E ( B − V ) values found by other studies. Inaddition to the E ( B − V ) = .
37 given in the Harris catalogue,Pritzl et al. (2002) find E ( B − V ) = .
40 (from RR Lyrae stars)and quote E ( B − V ) between 0.35 and 0.41 from other sources.The NED gives E ( B − V ) = .
355 (Schlafly & Finkbeiner 2011)or E ( B − V ) = .
386 (Schlegel et al. 1998). A more detailed anal-ysis of the NGC 6388 CMD in order to constrain the reddening,distance, and other parameters appears worthwhile, but for thepresent work we note that reconciling the ACSGCS CMD withthe Dartmouth isochrones remains problematic.We have chosen to base our analysis on the Dartmouthisochrones, since these are available for the full range of compo-sitions needed here. Other commonly used grids include PAR-SEC (Bressan et al. 2012) and BaSTI (Pietrinferni et al. 2009),as well as the recent MIST models (MESA Isochrones and Stel-lar Tracks; Choi et al. 2016; Dotter 2016). MIST has a morecomplete coverage of stellar evolutionary phases than the Dart-mouth models (it also includes the HB and AGB), and wouldtherefore in principle not require us to supplement the modelisochrones with empirical data for the post-RGB phases. How-ever, these models are currently only available for solar-scaledchemical composition. We nevertheless carried out a few testsusing the MIST isochrones. At low metallicities we found verysimilar results to those obtained from our standard analysis,with [Fe / H] = − .
39 for NGC 7078 and [Fe / H] = − .
37 forNGC 7099 and very similar abundance ratios to those presentedin this paper. At the metal-rich end, the situation is more com-plicated. Using the MIST isochrones by themselves, we tended
Article number, page 17 of 35 & A proofs: manuscript no. larsen to get lower metallicities than from the other methods adopted inthis paper ([Fe / H] = − .
94 for NGC 104 and [Fe / H] = − . ffi culties reproducing the observed luminosity func-tions of AGB stars in the Magellanic Clouds. Additionally, theselate phases may be a ff ected by the anomalous properties of stel-lar populations in GCs. If, instead, we only used the MISTisochrones up to the tip of the RGB and combined them withempirical HB and AGB data, then we found [Fe / H] = − . / H] = − .
65 for NGC 6388, slightly higher than the valuebased on the Dartmouth isochrone. Given the mismatch betweenthe composition of the MIST isochrones and that of the GCs, itwould be premature to draw strong conclusions from this com-parison, but we note that the results appear to be very robust atthe metal-poor end, whereas somewhat larger model dependen-cies may exist in the more metal-rich regime.
6. Discussion
Our main aim in this paper has been to assess how reliably thechemical composition of globular clusters can be determinedfrom spectroscopy of their integrated light. The fundamental as-sumption underlying the work presented here is that the “best”way of doing so is to compare with measurements of individualstars in the clusters. While this is probably a reasonable assump-tion, it should be kept in mind that even high-dispersion spec-troscopy of individual stars has associated systematic uncertain-ties at the level of ∼ ffi culty of establishing what the “right an-swer” is, integrated-light observations of Galactic globular clus-ters face the di ffi culty that the clusters have large angular sizeson the sky. As we have seen, this means that uncertainties dueto stochastic fluctuations in the numbers of stars sampled withinthe observed area can be dominant. This problem will usually beless acute in observations of extragalactic GCs, and our stochas-tic sampling experiments indicate that the stochastically induced(one-sigma) uncertainty on overall metallicities is less than 0.1dex even for clusters as faint as M V ∼ − . ff ect onmost abundance ratios will be even smaller. Of course, largerdeviations may still occur in cases that happen to be a ff ected byparticularly “unlucky” realisations of the HRD. Accurate abun-dance analysis is thus expected to be possible for clusters wellbelow the turn-over of the GC luminosity function in a typicalgalaxy, so that the majority of the GC population in a givengalaxy will generally be amenable to such integrated-light analy-sis. Studies that target significantly fainter (or younger) clustersshould, however, pay close attention to the uncertainties intro-duced by stochastic sampling of the HRD. To some extent, suchuncertainties may be alleviated if independent information aboutthe CMD is available, for example via resolved imaging. Indeed,we find that di ff erences between our integrated-light abundancesand literature values tend to decrease when only stars locatedwithin the scanned parts of the GCs are included. An alterna-tive approach, suggested by Colucci et al. (2011), is to generatelarge numbers of random CMD realisations and search for thosethat simultaneously reproduce the spectroscopic and photomet-ric properties (e.g., integrated colours) of the clusters. At anyrate, we note that abundance ratios are generally less sensitive tothese e ff ects. Table 7.
Mean di ff erences of our abundance measurements with respectto other studies. C2009 P2005 R2014(1) (2) (3) ∆ [Na / Fe] − .
14 (0.08) . . . − .
08 (0.11) ∆ [Mg / Fe] std − .
15 (0.07) − .
01 (0.19) − .
07 (0.08) ∆ [Mg / Fe]
Kur − .
08 (0.08) 0.06 (0.18) 0 .
00 (0.09) ∆ [Ca / Fe] . . . 0.06 (0.09) 0.12 (0.10) ∆ [Cr / Fe] . . . . . . 0.01 (0.09) ∆ [Ti / Fe] . . . 0.10 (0.07) 0.08 (0.08) ∆ [Ba / Fe] . . . 0.15 (0.17) . . .
Notes.
The di ff erences are in the sense (integrated light) - (literature).The numbers in parentheses are the r.m.s. of the di ff erences. References. (1) Carretta et al. (2009b); (2) Pritzl et al. (2005);(3) Roediger et al. (2014)
In modelling the integrated light of the seven globular clus-ters in our sample, we found that an approach based on empiricalinformation about the colour-magnitude diagrams of the clus-ters (from HST / ACS photometry) yields results that are of com-parable accuracy to modelling based on theoretical isochrones.This was also found by McWilliam & Bernstein (2008) forNGC 104. This is encouraging for applications of this techniqueto more distant systems, where resolved photometry may notbe available. One potentially outstanding issue is how to selectthe proper isochrone for the modelling. The metallicity and α -enhancement can be chosen to self-consistently match the val-ues of these quantities derived from the spectroscopy (possiblyrequiring some iteration), but this leaves the age and (to some ex-tent) the horizontal branch morphology as free parameters. How-ever, moderate uncertainties on the age have only a relatively mi-nor e ff ect on the abundances. In L14 we found that the di ff erencebetween using a 13 Gyr and an 8 Gyr isochrone changed [Fe / H]by less than 0.1 dex for the GC in the WLM galaxy, which has[Fe / H] ≈ −
2. Again, element abundance ratios were even lessa ff ected, by 0.05 dex or less. Similarly, McWilliam & Bernstein(2008) found that the metallicity of NGC 104 was basically in-sensitive to the choice of isochrone for ages between 10 and 15Gyr. Such age di ff erences may be constrained, for example, viaBalmer line strengths measured on low-resolution spectra (e.g.Cenarro et al. 2007; Caldwell et al. 2011). Even younger ageswould have a more noticeable e ff ect on the abundances, but alsoon other properties such as colours and mass-to-light ratios, withthe latter decreasing by a factor of about 2.6 from 13 Gyr to 4Gyr for constant metallicity (according to simple stellar popu-lation models calculated via the PARSEC website ). The mass-to-light ratios could be constrained via velocity dispersion mea-surements that are typically obtained as a free by-product of thespectroscopic analysis.The comparison of our integrated-light abundance ratio mea-surements with literature data for individual stars is summarisedin Table 7. Although we find good overall agreement with the lit-erature data, small systematic o ff sets remain. Our [Na / Fe] ratiosare, on average about 0.14 dex lower than those reported by Car-retta et al. (2009b), and they are about 0.08 dex lower than theaverage of the literature values in the compilation of Roedigeret al. (2014) (but note that Roediger et al. (2014) also includethe work of Carretta et al. (2009b) as one of their sources.).When using up-to-date oscillator strengths, our [Mg / Fe] ratiosare 0.08 dex lower on average than those found by Carretta et al. http://stev.oapd.inaf.it/cgi-bin/cmd Article number, page 18 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table 8.
Abundances of light elements for the four clusters in common between our study and those of Sakari et al. (2013) and Colucci et al.(2017).
NGC 104 NGC 362 NGC 6388 NGC 6752 NGC 7078[Na / Fe] C2009 (rms) 0.53 (0.15) 0.19 (0.19) 0.59 (0.16) 0.33 (0.27) 0.20 (0.25)Colucci et al. (2017) 0 . ± . − . ± . − . ± .
36 0 . ± .
07 . . .Sakari et al. (2013) 0 . ± .
12 . . . . . . . . . 0 . ± . − .
05 0.36 0.30 0.15[Mg / Fe] C2009 (rms) 0.52 (0.03) 0.33 (0.04) 0.21 (0.07) 0.50 (0.05) 0.45 (0.19)Colucci et al. (2017) 0 . ± .
08 0 . ± . − . ± .
10 0 . ± .
07 . . .Sakari et al. (2013) 0 . ± .
14 . . . . . . . . . − . ± . Notes.
For convenience we repeat our abundance measurements from Table 3 (standard analysis) and B.2 (Kurucz line list). For Carretta et al.(2009b) we include the rms dispersions as given in their Table 10. (Note that the data for NGC 362 are from Carretta et al. 2013). (2009b), but part of this o ff set may be attributed to the slightlydi ff erent log g f values used by Carretta et al. (Sec. 5.2.1). Fur-thermore, when comparing with the literature compilations theo ff sets largely vanish. Our average [Mg / Fe] ratios (for the Ku-rucz line list) are actually slightly higher (by 0.06 dex) than thoselisted by Pritzl et al. (2005), and the average di ff erence with re-spect to those in Roediger et al. (2014) is less than 0.01 dex.For the reasons given at the beginning of this section, ourmain focus in this paper has been on comparing our integrated-light measurements with data for individual stars. However, itis worth discussing how our measurements compare with thoseobtained from other integrated-light analyses, in particular withregards to the light elements. In Table 8 we compare our mea-surements of Na and Mg with the work of Colucci et al. (2017)and Sakari et al. (2013). For the four clusters in common withColucci et al. (2017), our [Na / Fe] and [Mg / Fe] ratios are on av-erage 0.24 dex (r.m.s. 0.20 dex) and 0.26 dex (r.m.s. 0.08 dex)higher (when using our Mg abundances based on the Kurucz linelist). The overall di ff erences, as well as the spread, exceed theuncertainties due to stochastic fluctuations by a substantial mar-gin. Colucci et al. (2017) consider several e ff ects that may causesystematic errors in their Mg abundances, such as the choice ofdamping constants, mismatch in the dwarf-to-giant ratios in theCMDs, or non-LTE e ff ects, but conclude that none of them canfully explain their low [Mg / Fe] ratios. Our [Na / Fe] and [Mg / Fe]ratios for NGC 104 are in excellent agreement with those foundby Sakari et al. (2013), while the measurements of Sakari et al.for NGC 7078 di ff er more substantially from both ours and thoseof Carretta et al. (2009b). Sakari et al. suggest that their Mg andNa abundances may be a ff ected by intra-cluster abundance vari-ations, but it should also be noted that their measurements of Mgand Na in NGC 7078 are based on only a single line each, withlarge uncertainties (Mg i i / Fe]ratios found by Sakari et al. (2013), suggest that the inherentuncertainties in measuring Mg abundances from integrated lightare comparable to those for other elements.The normal [Mg / Fe] ratios found here are in contrast to thelow [Mg / Fe] ratios that have been reported from integrated-lightobservations of some extragalactic GCs (L12, L14, Colucci et al.2009, 2014). If these very low (in some cases significantly sub-solar) [Mg / Fe] ratios are caused by internal Mg abundance vari-ations, then these clusters must have a much more extensiveMg / Al anti-correlation than those typical of Galactic GCs, withlarge numbers of very Mg-depleted stars. Of the clusters ob-served here, the largest internal spread in Mg abundance is found in NGC 7078, but we still measure a significantly super-solarMg / Fe abundance ratio for this cluster ([Mg / Fe] = + . ± . ff ects might play a role, and in this context it may beworth noting that the most extreme Mg spread among GalacticGCs is found in the remote cluster NGC 2419 (Cohen & Kirby2012).For Ca, Ti, and Cr our average abundance ratios lie within 0.1dex of those quoted in the literature compilations for individualstars. Our average abundances of Ca and Ti are also very simi-lar to those measured in integrated light for five GCs by Sakariet al. (2014), who find (cid:104) [Ca / Fe] (cid:105) = + .
33 (r.m.s. 0.06 dex) and (cid:104) [Ti / Fe] (cid:105) = + .
34 (r.m.s. 0.04 dex). Colucci et al. (2017) findslightly lower mean values of (cid:104) [Ca / Fe] (cid:105) = + .
24 (r.m.s. 0.09dex) and (cid:104) [Ti / Fe] (cid:105) = + .
21 (r.m.s. 0.16 dex) for the 12 GCsin their sample. Since we do not measure Ti i and Ti ii sepa-rately, we have used the average of the Ti i and Ti ii abundancesmeasured by Sakari et al. and Colucci et al. in this comparison.While the Ti i and Ti ii abundance measurements can di ff er sig-nificantly for some individual clusters, the mean di ff erences areonly (cid:104) [Ti i / Fe] (cid:105)−(cid:104) [Ti ii / Fe] (cid:105) = − . ± .
06 dex (for Sakari et al.study) and (cid:104) [Ti i / Fe] (cid:105) − (cid:104) [Ti ii / Fe] (cid:105) = + . ± .
04 dex (Colucciet al.), i.e., only marginally significant and with opposite signs.Using the average values in the comparison thus appears jus-tified. While a detailed comparison is somewhat hampered bythe limited overlap between the di ff erent samples, di ff erences of ∼ ff erences are in the samesense as the o ff sets in Table 7.For Ba, the average di ff erence between our measurementsand the literature data is slightly larger (0.15 dex) but we havenoted that this average may hide a trend with metallicity, withour [Ba / Fe] ratios being about 0.2–0.4 dex higher than the litera-ture values for the two most metal-poor clusters, NGC 7078 andNGC 7099. In addition to the isotopic mixture, it may again benecessary to consider the role of non-LTE e ff ects here. In theiranalysis of giants in NGC 104, Thygesen et al. (2014) found thatNLTE corrections could reach up to ∼ + . − . Article number, page 19 of 35 & A proofs: manuscript no. larsen consistent with the trends observed here, although detailed mod-elling of non-LTE e ff ects on the integrated light will be requiredin order to make more quantitative statements.In summary, we conclude that it is indeed possible to mea-sure chemical abundances reliably (to within ∼ . ff ects, which can be important for some elements.These have so far not been incorporated in our analysis, butmight account for some of the remaining systematic di ff erenceswith respect to studies of individual stars (e.g., for Na and Ba).When aiming for better than ∼ . ff ects such as atomic di ff usion, whichcan cause systematic variations in the surface abundances at thelevel of 0.1–0.2 dex as a function of evolutionary stage (Kornet al. 2007; Nordlander et al. 2012; Husser et al. 2016).
7. Summary and conclusions
We have presented integrated-light spectroscopic observationsof seven Galactic globular clusters. From these observations, wehave measured the abundances of several chemical elements andcompared with results for individual stars in the clusters com-piled from the literature. Our main findings are as follows: – The iron abundances generally agree well (within ∼ – A significant outlier is NGC 6752, for which we find a dif-ference of about 0.3 dex between our integrated-light ironabundance and literature values. We attribute this to the dif-ficulty of obtaining a good integrated-light spectrum of thisvery extended and relatively low surface brightness cluster,noting that the total luminosity sampled by the integrated-light spectrum ( M V = − .
4) is significantly lower for thiscluster than for other clusters in our sample. Indeed, if were-derive the abundances based on a CMD containing onlythose stars estimated to be contained within the slit scan area,the discrepancy is reduced to 0.10–0.15 dex. – Comparing our [Na / Fe] and [Mg / Fe] ratios with those foundby Carretta et al. (2009b) for individual stars, we find bothabundance ratios to be lower (by about 0.15 dex) than the av-erage values in the Carretta work. For [Na / Fe] we have notidentified a clear cause of this di ff erence, but we suggest thatthe role of non-LTE e ff ects on integrated-light abundancesmay be worth investigating. For [Mg / Fe], most of the di ff er-ence is attributable to the di ff erent line lists used in the dif-ferent studies. When we use Mg i oscillator strengths fromthe same source as Carretta et al. (2009b), the mean di ff er-ence with respect to Carretta’s work is only 0.04–0.07 dex(although this may be somewhat fortuitous, considering thelimited overlap in the actual lines used). When comparingwith Mg abundances from other literature sources, there isessentially no systematic di ff erence with respect to our mea-surements, and our [Na / Fe] ratios are only ∼ .
08 dex lowerthan the literature average. – The α -element abundance ratios show the usual enhance-ment compared to the Solar-scaled abundance patterns ( (cid:104) [Ca / Fe] (cid:105) = + . (cid:104) [Ti / Fe] (cid:105) = + . (cid:104) [Cr / Fe] (cid:105) = − . / Fe] and [Mn / Fe] ratios similar to thoseseen in Milky Way stars. – When comparing our [Ba / Fe] measurements with recent lit-erature data, we find good agreement at the metal-rich end,whereas we find higher [Ba / Fe] ratios at low metallicitiescompared to measurements of individual stars.The overall agreement between published abundance mea-surements for individual stars in the clusters and our integrated-light measurements is, of course, encouraging, as is the relativeinsensitivity of the results to the exact approach used in mod-elling the Hertzsprung-Russell diagrams of the clusters. Thisadds confidence to the metallicities and chemical abundancesderived for metal-poor GCs in our previous work on the Fornaxand WLM dwarf galaxies. While a number of consistency checkswere already carried out in those papers, the analysis presentedhere demonstrates that we can also extend such work into themore metal-rich regime.For the majority of elements that we have compared here,our abundance ratios agree well with those derived from obser-vations of individual stars. Abundances of Mg agree well withthose of other studies, once we adopt the most recent line lists,but the Mg abundances in our previous papers may be under-estimated by ∼ . ff ects andstellar evolutionary e ff ects (such as atomic di ff usion) may reducethe remaining systematic o ff sets for Na and Ba.With current 8–10 m telescopes it remains challenging topush this type of analysis significantly beyond the Local Groupfor old GCs, although it has been applied to GCs as far away asthe M81 group (L14) and NGC 5128 (Colucci et al. 2013), atdistances of ∼ / N spectra for clustersfainter than V =
21 in a few hours of integration time, which willbe suitable for detailed abundance measurements such as thosecarried out in this paper. Combined with the multiplexing capa-bility that is foreseen for ELT spectrographs (e.g. MOSAIC onthe European ELT; Hammer et al. 2016), this will allow e ffi cientobservations of more than a thousand GCs in NGC 5128 (Wood-ley et al. 2010; Harris et al. 2012; Taylor et al. 2016), well overa hundred clusters in galaxies such as the “Sombrero” (Spitleret al. 2006), and the brightest GCs in galaxies as far away asthe Virgo and Fornax clusters. At the same time, adaptive opticsassisted imaging with ELTs will provide photometry of individ-ual stars at similar distances (Deep et al. 2011). This combina-tion of detailed chemistry from GCs and resolved imaging ofdi ff use stellar populations will provide essential constraints onthe assembly- and chemical enrichment histories of galaxies in arepresentative volume of the Universe. Acknowledgements.
We thank the referee, Charli M. Sakari, for a prompt andhelpful report. This research has made use of the NASA / IPAC ExtragalacticDatabase (NED) which is operated by the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under contract with the National Aeronautics and SpaceAdministration. This work has made use of the VALD database, operated at Up-psala University, the Institute of Astronomy RAS in Moscow, and the Universityof Vienna. This research has made use of NASA’s Astrophysics Data SystemBibliographic Services. The Digitized Sky Surveys were produced at the SpaceTelescope Science Institute under U.S. Government grant NAG W-2166. The im-ages of these surveys are based on photographic data obtained using the OschinSchmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. Theplates were processed into the present compressed digital form with the permis-sion of these institutions. JB acknowledges support by NSF grant AST-1518294
Article number, page 20 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters and HST grant GO-13295.001-A. JS acknowledges support by NSF grant AST-1514763 and a Packard Fellowship.
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Article number, page 22 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Appendix A: Individual abundance measurementsAppendix B: Abundance measurements formodified procedures
Article number, page 23 of 35 & A proofs: manuscript no. larsen
Table A.1.
Individual abundance measurements for NGC 104 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
794 0.0024400.0–4600.0 − .
804 0.0014600.0–4800.0 − .
835 0.0034800.0–5000.0 − .
845 0.0015000.0–5150.0 − .
885 0.0015250.0–5400.0 − .
915 0.0025400.0–5600.0 − .
943 0.0035600.0–5800.0 − .
885 0.0026000.0–6200.0 − .
862 0.003[Na / Fe]5677.0–5695.0 + .
412 0.0106149.0–6166.0 + .
429 0.007[Mg / Fe]4347.0–4357.0 + .
289 0.0214565.0–4576.0 + .
289 0.0094700.0–4707.0 + .
481 0.0115523.0–5531.5 + .
439 0.0055705.0–5715.0 + .
538 0.002[Ca / Fe]4222.0–4232.0 + .
420 0.0074280.0–4320.0 + .
488 0.0094420.0–4460.0 + .
408 0.0044575.0–4591.0 + .
408 0.0055259.0–5268.0 + .
650 0.0115580.0–5610.0 + .
378 0.0116100.0–6175.0 + .
199 0.007[Sc / Fe]4290.0–4330.0 + .
501 0.0154350.0–4440.0 + .
338 0.0104665.0–4675.0 − .
070 0.0305026.0–5036.0 + .
060 0.0205521.0–5531.0 + .
130 0.0215638.0–5690.0 + .
079 0.011[Ti / Fe]4292.0–4320.0 + .
550 0.0024386.0–4420.0 + .
489 0.0024440.0–4474.0 + .
330 0.0014532.0–4574.0 + .
360 0.0024587.0–4593.0 − .
010 0.0264650.0–4715.0 + .
259 0.0014750.0–4850.0 + .
259 0.0014980.0–5045.0 + .
399 0.002[Cr / Fe]4250.0–4292.0 + .
030 0.0024350.0–4400.0 − .
109 0.0124520.0–4660.0 + .
030 0.0035235.0–5330.0 − .
011 0.0035342.0–5351.0 − .
340 0.0085407.0–5413.0 − .
290 0.027[Mn / Fe]4750.0–4790.0 − .
160 0.0116010.0–6030.0 − .
340 0.015[Ba / Fe]4551.0–4560.0 + .
102 0.0104929.0–4939.0 + .
134 0.0165849.0–5859.0 + .
348 0.0266135.0–6145.0 + .
181 0.021
Article number, page 24 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table A.2.
Individual abundance measurements for NGC 362 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
081 0.0054400.0–4600.0 − .
061 0.0104600.0–4800.0 − .
081 0.0114800.0–5000.0 − .
102 0.0065000.0–5150.0 − .
092 0.0065250.0–5400.0 − .
002 0.0055400.0–5600.0 − .
131 0.0055600.0–5800.0 − .
121 0.0106000.0–6200.0 − .
012 0.006[Na / Fe]5677.0–5695.0 − .
045 0.0156149.0–6166.0 − .
045 0.030[Mg / Fe]4347.0–4357.0 − .
095 0.0304565.0–4576.0 + .
196 0.0204700.0–4707.0 + .
196 0.0205523.0–5531.5 + .
135 0.0165705.0–5715.0 + .
205 0.021[Ca / Fe]4222.0–4232.0 + .
196 0.0114280.0–4320.0 + .
345 0.0114420.0–4460.0 + .
325 0.0054575.0–4591.0 + .
164 0.0154873.0–4883.0 + .
814 0.0455259.0–5268.0 + .
514 0.0165580.0–5610.0 + .
276 0.0166100.0–6175.0 + .
135 0.006[Sc / Fe]4290.0–4330.0 + .
276 0.0164350.0–4440.0 + .
154 0.0164665.0–4675.0 − .
005 0.0415026.0–5036.0 + .
055 0.0305521.0–5531.0 − .
016 0.0305638.0–5690.0 + .
055 0.011[Ti / Fe]4292.0–4320.0 + .
445 0.0114386.0–4420.0 + .
435 0.0114440.0–4474.0 + .
295 0.0114532.0–4574.0 + .
325 0.0054587.0–4593.0 + .
526 0.0364650.0–4715.0 + .
266 0.0114750.0–4850.0 + .
295 0.0054980.0–5045.0 + .
335 0.0055152.5–5160.0 + .
225 0.035[Cr / Fe]4250.0–4292.0 − .
004 0.0104350.0–4400.0 − .
134 0.0164520.0–4660.0 + .
006 0.0055235.0–5330.0 + .
026 0.0055342.0–5351.0 − .
235 0.0255407.0–5413.0 − .
344 0.045[Mn / Fe]4750.0–4790.0 − .
375 0.0156010.0–6030.0 − .
364 0.020[Ba / Fe]4551.0–4560.0 + .
286 0.0154929.0–4939.0 + .
365 0.0215849.0–5859.0 + .
436 0.0306135.0–6145.0 + .
306 0.021
Article number, page 25 of 35 & A proofs: manuscript no. larsen
Table A.3.
Individual abundance measurements for NGC 6254 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
472 0.0054400.0–4600.0 − .
492 0.0054600.0–4800.0 − .
482 0.0054800.0–5000.0 − .
503 0.0065000.0–5150.0 − .
462 0.0055250.0–5400.0 − .
423 0.0065400.0–5600.0 − .
513 0.0065600.0–5800.0 − .
542 0.0056000.0–6200.0 − .
442 0.005[Na / Fe]5677.0–5695.0 − .
040 0.0256149.0–6166.0 − .
032 0.051[Mg / Fe]4347.0–4357.0 + .
538 0.0514565.0–4576.0 + .
270 0.0364700.0–4707.0 + .
339 0.0255523.0–5531.5 + .
379 0.0255705.0–5715.0 + .
429 0.025[Ca / Fe]4222.0–4232.0 + .
379 0.0104280.0–4320.0 + .
470 0.0204420.0–4460.0 + .
410 0.0104575.0–4591.0 + .
068 0.0214873.0–4883.0 + .
960 0.0705259.0–5268.0 + .
610 0.0165580.0–5610.0 + .
458 0.0116100.0–6175.0 + .
270 0.005[Sc / Fe]4290.0–4330.0 + .
049 0.0254350.0–4440.0 + .
090 0.0214665.0–4675.0 + .
229 0.0415026.0–5036.0 + .
029 0.0365521.0–5531.0 + .
139 0.0305638.0–5690.0 + .
199 0.016[Ti / Fe]4292.0–4320.0 + .
470 0.0104386.0–4420.0 + .
530 0.0164440.0–4474.0 + .
349 0.0164532.0–4574.0 + .
410 0.0054587.0–4593.0 + .
869 0.0414650.0–4715.0 + .
270 0.0164750.0–4850.0 + .
358 0.0164980.0–5045.0 + .
358 0.0115152.5–5160.0 + .
538 0.030[Cr / Fe]4250.0–4292.0 − .
100 0.0204350.0–4400.0 − .
231 0.0304520.0–4660.0 − .
021 0.0115235.0–5330.0 − .
051 0.0115342.0–5351.0 + .
069 0.0305407.0–5413.0 + .
159 0.021[Mn / Fe]4750.0–4790.0 − .
340 0.0206010.0–6030.0 − .
610 0.030[Ba / Fe]4551.0–4560.0 + .
300 0.0214929.0–4939.0 + .
399 0.0255849.0–5859.0 + .
500 0.0356135.0–6145.0 + .
500 0.020
Article number, page 26 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table A.4.
Individual abundance measurements for NGC 6388 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
521 0.0024400.0–4600.0 − .
472 0.0024600.0–4800.0 − .
470 0.0044800.0–5000.0 − .
521 0.0015000.0–5150.0 − .
531 0.0015250.0–5400.0 − .
502 0.0035400.0–5600.0 − .
542 0.0015600.0–5800.0 − .
573 0.0046000.0–6200.0 − .
426 0.005[Na / Fe]5677.0–5695.0 + .
343 0.0106149.0–6166.0 + .
369 0.010[Mg / Fe]4347.0–4357.0 − .
255 0.0304565.0–4576.0 − .
006 0.0154700.0–4707.0 + .
158 0.0055523.0–5531.5 + .
149 0.0085705.0–5715.0 + .
115 0.009[Ca / Fe]4222.0–4232.0 + .
033 0.0104280.0–4320.0 + .
367 0.0054420.0–4460.0 + .
189 0.0054575.0–4591.0 + .
136 0.0165259.0–5268.0 + .
683 0.0105580.0–5610.0 + .
283 0.0076100.0–6175.0 + .
127 0.005[Sc / Fe]4290.0–4330.0 + .
360 0.0164350.0–4440.0 + .
355 0.0204665.0–4675.0 − .
414 0.0355026.0–5036.0 + .
026 0.0305521.0–5531.0 + .
155 0.0265638.0–5690.0 + .
026 0.005[Ti / Fe]4292.0–4320.0 + .
385 0.0124386.0–4420.0 + .
336 0.0034440.0–4474.0 + .
126 0.0084532.0–4574.0 + .
197 0.0104587.0–4593.0 − .
120 0.0364650.0–4715.0 + .
317 0.0094750.0–4850.0 + .
155 0.0014980.0–5045.0 + .
406 0.009[Cr / Fe]4250.0–4292.0 + .
069 0.0044350.0–4400.0 − .
016 0.0164520.0–4660.0 − .
004 0.0045235.0–5330.0 + .
074 0.0045342.0–5351.0 − .
525 0.0095407.0–5413.0 + .
255 0.013[Mn / Fe]4750.0–4790.0 − .
005 0.0106010.0–6030.0 − .
304 0.011[Ba / Fe]4551.0–4560.0 − .
095 0.0114929.0–4939.0 + .
334 0.0155849.0–5859.0 + .
606 0.0216135.0–6145.0 + .
257 0.016
Article number, page 27 of 35 & A proofs: manuscript no. larsen
Table A.5.
Individual abundance measurements for NGC 6752 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
861 0.0054400.0–4600.0 − .
841 0.0054600.0–4800.0 − .
861 0.0054800.0–5000.0 − .
881 0.0055000.0–5150.0 − .
910 0.0055250.0–5400.0 − .
941 0.0055400.0–5600.0 − .
951 0.0115600.0–5800.0 − .
861 0.0056000.0–6200.0 − .
841 0.011[Na / Fe]5677.0–5695.0 + .
291 0.0116149.0–6166.0 + .
352 0.030[Mg / Fe]4347.0–4357.0 + .
461 0.0264565.0–4576.0 + .
152 0.0304700.0–4707.0 + .
371 0.0155523.0–5531.5 + .
262 0.0205705.0–5715.0 + .
551 0.016[Ca / Fe]4222.0–4232.0 + .
242 0.0054280.0–4320.0 + .
332 0.0054420.0–4460.0 + .
392 0.0114575.0–4591.0 + .
322 0.0164873.0–4883.0 + .
772 0.0305259.0–5268.0 + .
483 0.0155580.0–5610.0 + .
493 0.0106100.0–6175.0 + .
252 0.010[Sc / Fe]4290.0–4330.0 + .
203 0.0104350.0–4440.0 + .
103 0.0104665.0–4675.0 + .
002 0.0305026.0–5036.0 + .
113 0.0265521.0–5531.0 − .
038 0.0265638.0–5690.0 + .
123 0.010[Ti / Fe]4292.0–4320.0 + .
452 0.0114386.0–4420.0 + .
461 0.0104440.0–4474.0 + .
402 0.0104532.0–4574.0 + .
332 0.0114587.0–4593.0 + .
683 0.0264650.0–4715.0 + .
212 0.0114750.0–4850.0 + .
371 0.0114980.0–5045.0 + .
171 0.005[Cr / Fe]4250.0–4292.0 − .
087 0.0154350.0–4400.0 − .
167 0.0164520.0–4660.0 − .
018 0.0115235.0–5330.0 − .
087 0.0115342.0–5351.0 − .
218 0.0255407.0–5413.0 − .
248 0.030[Mn / Fe]4750.0–4790.0 − .
337 0.0106010.0–6030.0 − .
468 0.025[Ba / Fe]4551.0–4560.0 + .
313 0.0164929.0–4939.0 + .
061 0.0205849.0–5859.0 + .
112 0.0306135.0–6145.0 + .
132 0.025
Article number, page 28 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table A.6.
Individual abundance measurements for NGC 7078 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
405 0.0054400.0–4600.0 − .
376 0.0114600.0–4800.0 − .
435 0.0114800.0–5000.0 − .
425 0.0055000.0–5150.0 − .
315 0.0055250.0–5400.0 − .
376 0.0065400.0–5600.0 − .
425 0.0115600.0–5800.0 − .
415 0.0156000.0–6200.0 − .
325 0.011[Na / Fe]5677.0–5695.0 + .
154 0.051[Mg / Fe]4347.0–4357.0 + .
074 0.0454565.0–4576.0 + .
414 0.0354700.0–4707.0 + .
093 0.0265523.0–5531.5 + .
135 0.0205705.0–5715.0 + .
414 0.060[Ca / Fe]4222.0–4232.0 + .
305 0.0164280.0–4320.0 + .
324 0.0214420.0–4460.0 + .
295 0.0164575.0–4591.0 + .
183 0.0364873.0–4883.0 + .
535 0.0555259.0–5268.0 + .
483 0.0205580.0–5610.0 + .
364 0.0116100.0–6175.0 + .
284 0.010[Sc / Fe]4290.0–4330.0 + .
364 0.0204350.0–4440.0 + .
215 0.0204665.0–4675.0 + .
234 0.0415026.0–5036.0 + .
003 0.0405521.0–5531.0 + .
114 0.0415638.0–5690.0 + .
154 0.025[Ti / Fe]4292.0–4320.0 + .
525 0.0154386.0–4420.0 + .
483 0.0164440.0–4474.0 + .
414 0.0164532.0–4574.0 + .
384 0.0114587.0–4593.0 + .
715 0.0364650.0–4715.0 + .
414 0.0214750.0–4850.0 + .
445 0.0214980.0–5045.0 + .
234 0.0165152.5–5160.0 + .
464 0.041[Cr / Fe]4250.0–4292.0 − .
216 0.0204350.0–4400.0 − .
325 0.0414520.0–4660.0 − .
216 0.0155235.0–5330.0 − .
085 0.0205342.0–5351.0 − .
176 0.0415407.0–5413.0 − .
115 0.040[Mn / Fe]4750.0–4790.0 − .
387 0.0306010.0–6030.0 − .
125 0.075[Ba / Fe]4551.0–4560.0 + .
465 0.0254929.0–4939.0 + .
375 0.0205849.0–5859.0 + .
525 0.0416135.0–6145.0 + .
465 0.030
Article number, page 29 of 35 & A proofs: manuscript no. larsen
Table A.7.
Individual abundance measurements for NGC 7099 (standard analysis)
Wavelength [Å] Value Error[Fe / H]4200.0–4400.0 − .
475 0.0114400.0–4600.0 − .
416 0.0054600.0–4800.0 − .
436 0.0054800.0–5000.0 − .
466 0.0065000.0–5150.0 − .
336 0.0055250.0–5400.0 − .
376 0.0115400.0–5600.0 − .
426 0.0055600.0–5800.0 − .
336 0.0166000.0–6200.0 − .
297 0.011[Na / Fe]5677.0–5695.0 + .
230 0.0466149.0–6166.0 + .
250 0.155[Mg / Fe]4347.0–4357.0 − .
099 0.0554565.0–4576.0 + .
479 0.0414700.0–4707.0 + .
309 0.0265523.0–5531.5 + .
230 0.0255705.0–5715.0 + .
441 0.051[Ca / Fe]4222.0–4232.0 + .
121 0.0154280.0–4320.0 + .
380 0.0164420.0–4460.0 + .
301 0.0114575.0–4591.0 + .
121 0.0364873.0–4883.0 + .
380 0.0515259.0–5268.0 + .
370 0.0255580.0–5610.0 + .
410 0.0106100.0–6175.0 + .
280 0.010[Sc / Fe]4290.0–4330.0 + .
320 0.0214350.0–4440.0 + .
121 0.0214665.0–4675.0 + .
030 0.0565026.0–5036.0 + .
030 0.0415521.0–5531.0 + .
179 0.0415638.0–5690.0 + .
221 0.025[Ti / Fe]4292.0–4320.0 + .
470 0.0114386.0–4420.0 + .
431 0.0104440.0–4474.0 + .
380 0.0114532.0–4574.0 + .
291 0.0054587.0–4593.0 + .
561 0.0514650.0–4715.0 + .
301 0.0214750.0–4850.0 + .
470 0.0164980.0–5045.0 + .
291 0.0105152.5–5160.0 + .
380 0.041[Cr / Fe]4250.0–4292.0 − .
210 0.0204350.0–4400.0 − .
579 0.0514520.0–4660.0 − .
200 0.0165235.0–5330.0 + .
010 0.0165342.0–5351.0 − .
129 0.0255407.0–5413.0 − .
149 0.041[Mn / Fe]4750.0–4790.0 − .
339 0.0206010.0–6030.0 − .
489 0.126[Ba / Fe]4551.0–4560.0 + .
301 0.0304929.0–4939.0 − .
089 0.0305849.0–5859.0 − .
079 0.0456135.0–6145.0 − .
030 0.035
Article number, page 30 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table B.1.
Abundance measurements using stars in slit scan areas. For each abundance ratio, the second line lists the weighted r.m.s. and thenumber of individual measurements.
NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099[Fe / H] − . − . − . − . − . − . − . w (N) 0 .
037 (9) 0 .
041 (9) 0 .
027 (9) 0 .
036 (9) 0 .
041 (9) 0 .
040 (9) 0 .
057 (9)[Na / Fe] 0 . − .
002 0 .
006 0 .
376 0 .
259 0 .
162 0 . w (N) 0 .
007 (2) 0 .
014 (2) 0 .
012 (2) 0 .
006 (2) 0 .
046 (2) . . . (1) 0 .
003 (2)[Mg / Fe] 0 .
459 0 .
211 0 .
412 0 .
143 0 .
347 0 .
181 0 . w (N) 0 .
076 (5) 0 .
105 (5) 0 .
069 (5) 0 .
094 (5) 0 .
107 (5) 0 .
127 (5) 0 .
147 (5)[Ca / Fe] 0 .
414 0 .
276 0 .
395 0 .
243 0 .
344 0 .
336 0 . w (N) 0 .
108 (7) 0 .
139 (8) 0 .
140 (8) 0 .
178 (7) 0 .
112 (8) 0 .
060 (8) 0 .
101 (8)[Sc / Fe] 0 .
209 0 .
078 0 .
085 0 .
068 0 .
149 0 .
194 0 . w (N) 0 .
174 (6) 0 .
143 (6) 0 .
068 (6) 0 .
183 (6) 0 .
059 (6) 0 .
108 (6) 0 .
106 (6)[Ti / Fe] 0 .
369 0 .
313 0 .
374 0 .
228 0 .
394 0 .
405 0 . w (N) 0 .
115 (8) 0 .
090 (9) 0 .
100 (9) 0 .
122 (8) 0 .
095 (8) 0 .
090 (9) 0 .
077 (9)[Cr / Fe] − . − .
051 0 .
097 0 . − . − . − . w (N) 0 .
135 (6) 0 .
106 (6) 0 .
415 (6) 0 .
203 (6) 0 .
063 (6) 0 .
068 (6) 0 .
132 (6)[Mn / Fe] − . − . − . − . − . − . − . w (N) 0 .
090 (2) 0 .
032 (2) 0 .
128 (2) 0 .
131 (2) 0 .
029 (2) 0 .
091 (2) 0 .
033 (2)[Ba / Fe] 0 .
153 0 .
229 0 .
333 0 .
194 0 .
314 0 .
402 0 . w (N) 0 .
072 (4) 0 .
043 (4) 0 .
063 (4) 0 .
234 (4) 0 .
091 (4) 0 .
055 (4) 0 .
179 (4)
Article number, page 31 of 35 & A proofs: manuscript no. larsen
Table B.2.
Abundance measurements using the Kurucz line list as of 18 Feb 2016. For each abundance ratio, the second line lists the weightedr.m.s. and the number of individual measurements.
NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099[Fe / H] − . − . − . − . − . − . − . w (N) 0 .
053 (9) 0 .
036 (9) 0 .
047 (9) 0 .
030 (9) 0 .
045 (9) 0 .
040 (9) 0 .
047 (9)[Na / Fe] 0 . − . − .
016 0 .
354 0 .
322 0 .
158 0 . w (N) 0 .
010 (2) 0 .
009 (2) 0 .
000 (2) 0 .
005 (2) 0 .
023 (2) . . . (1) 0 .
007 (2)[Mg / Fe] 0 .
539 0 .
249 0 .
427 0 .
191 0 .
442 0 .
242 0 . w (N) 0 .
097 (5) 0 .
167 (5) 0 .
070 (5) 0 .
130 (5) 0 .
071 (5) 0 .
099 (5) 0 .
151 (5)[Ca / Fe] 0 .
411 0 .
302 0 .
421 0 .
250 0 .
363 0 .
349 0 . w (N) 0 .
145 (7) 0 .
183 (8) 0 .
175 (8) 0 .
249 (7) 0 .
133 (8) 0 .
061 (8) 0 .
103 (8)[Sc / Fe] 0 .
308 0 .
221 0 .
248 0 .
261 0 .
198 0 .
295 0 . w (N) 0 .
056 (6) 0 .
052 (6) 0 .
111 (6) 0 .
069 (6) 0 .
065 (6) 0 .
087 (6) 0 .
074 (6)[Ti / Fe] 0 .
393 0 .
348 0 .
397 0 .
284 0 .
341 0 .
395 0 . w (N) 0 .
116 (8) 0 .
086 (9) 0 .
100 (9) 0 .
120 (8) 0 .
105 (8) 0 .
110 (9) 0 .
080 (9)[Cr / Fe] − . − .
062 0 .
093 0 . − . − . − . w (N) 0 .
115 (6) 0 .
130 (6) 0 .
399 (6) 0 .
256 (6) 0 .
023 (6) 0 .
083 (6) 0 .
123 (6)[Mn / Fe] − . − . − . − . − . − . − . w (N) 0 .
029 (2) 0 .
095 (2) 0 .
035 (2) 0 .
017 (2) 0 .
000 (2) 0 .
142 (2) 0 .
005 (2)[Ba / Fe] 0 .
220 0 .
423 0 .
508 0 .
233 0 .
288 0 .
576 0 . w (N) 0 .
098 (4) 0 .
034 (4) 0 .
051 (4) 0 .
074 (4) 0 .
129 (4) 0 .
041 (4) 0 .
141 (4)
Article number, page 32 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table B.3.
Abundance measurements based on theoretical isochrones. For each abundance ratio, the second line lists the weighted r.m.s. and thenumber of individual measurements.
NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099[Fe / H] − . − . − . − . − . − . − . w (N) 0 .
039 (9) 0 .
044 (9) 0 .
028 (9) 0 .
044 (9) 0 .
038 (9) 0 .
041 (9) 0 .
069 (9)[Na / Fe] 0 . − .
018 0 .
012 0 .
403 0 .
287 0 .
175 0 . w (N) 0 .
009 (2) 0 .
013 (2) 0 .
008 (2) 0 .
025 (2) 0 .
042 (2) . . . (1) 0 .
002 (2)[Mg / Fe] 0 .
436 0 .
190 0 .
370 0 .
164 0 .
369 0 .
177 0 . w (N) 0 .
095 (5) 0 .
088 (5) 0 .
082 (5) 0 .
107 (5) 0 .
120 (5) 0 .
115 (5) 0 .
147 (5)[Ca / Fe] 0 .
375 0 .
207 0 .
344 0 .
207 0 .
361 0 .
322 0 . w (N) 0 .
104 (7) 0 .
136 (8) 0 .
154 (8) 0 .
196 (7) 0 .
105 (8) 0 .
080 (8) 0 .
081 (8)[Sc / Fe] 0 .
230 0 .
135 0 .
176 0 .
105 0 .
040 0 .
243 0 . w (N) 0 .
148 (6) 0 .
054 (6) 0 .
093 (6) 0 .
143 (6) 0 .
067 (6) 0 .
096 (6) 0 .
103 (6)[Ti / Fe] 0 .
369 0 .
328 0 .
392 0 .
255 0 .
316 0 .
409 0 . w (N) 0 .
115 (8) 0 .
057 (9) 0 .
105 (9) 0 .
088 (8) 0 .
092 (8) 0 .
113 (9) 0 .
061 (9)[Cr / Fe] − . − .
050 0 . − . − . − . − . w (N) 0 .
132 (6) 0 .
101 (6) 0 .
399 (6) 0 .
196 (6) 0 .
068 (6) 0 .
071 (6) 0 .
143 (6)[Mn / Fe] − . − . − . − . − . − . − . w (N) 0 .
068 (2) 0 .
024 (2) 0 .
123 (2) 0 .
112 (2) 0 .
039 (2) 0 .
094 (2) 0 .
026 (2)[Ba / Fe] 0 .
178 0 .
376 0 .
367 0 .
193 0 .
150 0 . − . w (N) 0 .
094 (4) 0 .
043 (4) 0 .
099 (4) 0 .
228 (4) 0 .
096 (4) 0 .
070 (4) 0 .
153 (4)
Article number, page 33 of 35 & A proofs: manuscript no. larsen
Table B.4. Di ff erences between standard analysis and abundances based on stars in slit scan areas. NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099 ∆ scn − std [Fe / H] 0 . − . − . − .
064 0 . − . − . ∆ scn − std [Na / Fe] − .
001 0 .
043 0 .
044 0 . − .
043 0 . − . ∆ scn − std [Mg / Fe] 0 .
017 0 .
061 0 .
034 0 . − .
044 0 . − . ∆ scn − std [Ca / Fe] 0 .
003 0 .
003 0 . − . − .
011 0 . − . ∆ scn − std [Sc / Fe] − . − . − . − .
050 0 . − .
027 0 . ∆ scn − std [Ti / Fe] − . − . − . − .
031 0 . − . − . ∆ scn − std [Cr / Fe] − . − . − .
007 0 .
027 0 .
031 0 .
004 0 . ∆ scn − std [Mn / Fe] − . − . − .
006 0 .
022 0 .
006 0 . − . ∆ scn − std [Ba / Fe] − . − . − . − .
006 0 . − . − . Article number, page 34 of 35. S. Larsen et al.: Detailed abundances from integrated-light spectroscopy: Milky Way globular clusters
Table B.5. Di ff erences between standard analysis and abundances based on Kurucz line list. NGC 104 NGC 362 NGC 6254 NGC 6388 NGC 6752 NGC 7078 NGC 7099 ∆ kur − std [Fe / H] − . − . − . − . − . − . − . ∆ kur − std [Na / Fe] 0 .
003 0 .
015 0 . − .
003 0 .
020 0 .
004 0 . ∆ kur − std [Mg / Fe] 0 .
097 0 .
100 0 .
049 0 .
083 0 .
051 0 .
065 0 . ∆ kur − std [Ca / Fe] − .
001 0 .
029 0 . − .
010 0 .
009 0 . − . ∆ kur − std [Sc / Fe] 0 .
089 0 .
104 0 .
118 0 .
143 0 .
079 0 .
074 0 . ∆ kur − std [Ti / Fe] 0 .
022 0 . − .
016 0 . − . − .
027 0 . ∆ kur − std [Cr / Fe] 0 . − . − .
011 0 .
133 0 .
025 0 .
025 0 . ∆ kur − std [Mn / Fe] 0 .
038 0 .
088 0 .
067 0 .
038 0 .
063 0 .
053 0 . ∆ kur − std [Ba / Fe] 0 .
066 0 .
093 0 .
096 0 .
033 0 .
106 0 .
140 0 .103