Exploring Anticorrelations and Light Element Variations in Northern Globular Clusters Observed by the APOGEE Survey
Szabolcs Meszaros, Sarah L. Martell, Matthew Shetrone, Sara Lucatello, Nicholas W. Troup, Jo Bovy, Katia Cunha, Domingo A. Garcia-Hernandez, Jamie C. Overbeek, Carlos Allende Prieto, Timothy C. Beers, Peter M. Frinchaboy, Ana E. Garcia Perez, Fred R. Hearty, Jon Holtzman, Steven R. Majewski, David L. Nidever, Ricardo P. Schiavon, Donald P. Schneider, Jennifer S. Sobeck, Verne V. Smith, Olga Zamora, Gail Zasowski
aa r X i v : . [ a s t r o - ph . S R ] A p r Draft version October 17, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
EXPLORING ANTICORRLELATIONS AND LIGHT ELEMENT VARIATIONS IN NORTHERN GLOBULARCLUSTERS OBSERVED BY THE APOGEE SURVEY
Szabolcs M´esz´aros , Sarah L. Martell , Matthew Shetrone , Sara Lucatello , Nicholas W. Troup ,Jo Bovy , Katia Cunha , Domingo A. Garc´ıa-Hern´andez , Jamie C. Overbeek , Carlos Allende Prieto ,Timothy C. Beers , Peter M. Frinchaboy , Ana E. Garc´ıa P´erez , Fred R. Hearty , Jon Holtzman ,Steven R. Majewski , David L. Nidever , Ricardo P. Schiavon , Donald P. Schneider , Jennifer S. Sobeck ,Verne V. Smith , Olga Zamora , Gail Zasowski Draft version October 17, 2018
ABSTRACTWe investigate the light-element behavior of red giant stars in Northern globular clusters (GCs)observed by the SDSS-III Apache Point Observatory Galactic Evolution Experiment (APOGEE). Wederive abundances of nine elements (Fe, C, N, O, Mg, Al, Si, Ca, and Ti) for 428 red giant stars in10 globular clusters. The intrinsic abundance range relative to measurement errors is examined, andthe well-known C-N and Mg-Al anticorrelations are explored using an extreme-deconvolution code forthe first time in a consistent way. We find that Mg and Al drive the population membership in mostclusters, except in M107 and M71, the two most metal-rich clusters in our study, where the groupingis most sensitive to N. We also find a diversity in the abundance distributions, with some clustersexhibiting clear abundance bimodalities (for example M3 and M53) while others show extended distri-butions. The spread of Al abundances increases significantly as cluster average metallicity decreasesas previously found by other works, which we take as evidence that low metallicity, intermediate massAGB polluters were more common in the more metal poor clusters. The statistically significant cor-relation of [Al/Fe] with [Si/Fe] in M15 suggests that Si leakage has occurred in this cluster. We alsopresent C, N and O abundances for stars cooler than 4500 K and examine the behavior of A(C+N+O)in each cluster as a function of temperature and [Al/Fe]. The scatter of A(C+N+O) is close to itsestimated uncertainty in all clusters and independent on stellar temperature. A(C+N+O) exhibitssmall correlations and anticorrelations with [Al/Fe] in M3 and M13, but we cannot be certain aboutthese relations given the size of our abundance uncertainties. Star-to-star variations of α − elements(Si, Ca, Ti) abundances are comparable to our estimated errors in all clusters. INTRODUCTION ELTE Gothard Astrophysical Observatory, H-9704 Szombat-hely, Szent Imre Herceg st. 112, Hungary Dept. of Astronomy, Indiana University, Bloomington, IN47405, USA Dept. of Astrophysics, School of Physics, University of NewSouth Wales, Sydney, NSW 2052, Australia University of Texas at Austin, McDonald Observatory, FortDavis, TX 79734, USA INAF-Osservatorio Astronomico di Padova, vicolo dellOsser-vatorio 5, 35122 Padova, Italy Dept. of Astronomy, University of Virginia, Charlottesville,VA 22904-4325, USA Institute for Advanced Study, Einstein Drive, Princeton, NJ08540, USA University of Arizona, Tucson, AZ 85719, USA Observat´orio Nacional, S˜ao Crist´ov˜ao, Rio de Janeiro, Brazil Instituto de Astrof´ısica de Canarias (IAC), E-38200 La La-guna, Tenerife, Spain Universidad de La Laguna, Departamento de Astrof´ısica,38206 La Laguna, Tenerife, Spain Dept. of Physics and JINA Center for the Evolution of theElements, Univ. of Notre Dame, Notre Dame, IN 46556 USA Texas Christian University, Fort Worth, TX 76129, USA Dept. of Astronomy and Astrophysics, The PennsylvaniaState University, University Park, PA 16802, USA New Mexico State University, Las Cruces, NM 88003, USA Dept. of Astronomy, University of Michigan, Ann Arbor,MI 48109, USA Astrophysics Research Institute, IC2, Liverpool SciencePark, Liverpool John Moores University, 146 Brownlow Hill, Liv-erpool, L3 5RF, UK Institute for Gravitation and the Cosmos, The PennsylvaniaState University, University Park, PA 16802, USA
Over the last two decades, the long lasting idea ofglobular clusters hosting single, simple stellar popula-tions has changed dramatically. The classical paradigmof GCs being an excellent example of a simple stellarpopulation, defined as a coeval and initially chemicallyhomogeneous assembly of stars, has been challenged byobservational evidence. The presence of chemical in-homogeneities, in most cases limited to the light ele-ments (the chemical pairs C-N, O-Na, and Mg-Al anti-correlated with each other), have been known for decadesand recognized to be the signature of high-temperatureH-burning. This was initially framed within a stellar evo-lutionary scenario (see, e.g., Kraft 1994, and referencestherein) given that GC abundance work based on high-quality data was limited to bright, evolved giants. It wasonly at the turn of the century that the availability ofhigh-resolution spectrographs mounted on 8 m class tele-scopes made it possible to carry out studies on the com-positions of stars down to the main-sequence, which re-vealed light elements variations analogous to those foundamong giants (Briley et al. 1996; Gratton et al. 2001;Ram´ırez & Cohen 2002). Given that the atmospheres ofwarm main-sequence stars in large part retain the com-position of the gas from which they were formed, theunavoidable conclusion was that the abundance inhomo-geneities are of primordial origin.The most extensive spectroscopic survey of GCs un-dertaken so far (Carretta et al. 2009a,b,c) revealed thatthese inhomogeneities are ubiquitous in Galactic GCs,though they do not appear to occur in other star for-mation environments. However, the extent of the in-homogeneity varies from cluster to cluster, and appearsto correlate strongly with the present-day total mass ofthe GCs, and also with metallicity. The improvementin available instrumentation and techniques has also ledto the discovery of a much higher degree of complexityof GC color-magnitude diagrams. In fact, while someclusters seem to photometrically comply with the simplestellar population paradigm, a growing number of themare found to be characterized by multiple main sequencesand/or subgiant and/or giant branches, (Piotto et al.2007; Milone et al. 2008, e.g.,), which have been associ-ated to variations in the content of He and CNO, as wellas age spread (DAntona et al. 2005; Cassisi et al. 2008).This observational evidence led to a general scenariowhere GCs host multiple stellar populations. These areoften assumed to be associated with different stellar gen-erations: the ejecta of the slightly older stars, probablymixed with varying amounts of gas from the original starforming cloud, creates subsequent younger generationof stars (see e.g., Decressin et al. 2007; D’Ercole et al.2008), though alternative scenarios are also being con-sidered (see, e.g., Bastian et al. 2013). It is believed thatonly a fraction of the first-generation of stars can con-tribute to the internal enrichment. The difference in agesamong the stellar generations is actually relatively smallfor the majority of the clusters (with a few exceptionssuch as e.g., ω Cen or M22) and is confined to a coupleof hundreds Myr.The details of this formation scenario are still far frombeing understood. The origin of the polluting materialremains to be established and it has obvious bearingson the timescales for the formation of the cluster it-self and its mass budget. The observed wide star-to-star variations in C, N, O, Na, and Al found in eachGalactic GCs, coupled with the uniformity in Fe and Ca(apart from a few notable exceptions) provide quite strin-gent constraints and argue against anything but a minorcontribution from supernovae (Carretta et al. 2009a).Proposed candidate polluters include intermediate massstars in their asymptotic giant branch (AGB) phase(Ventura et al. 2001), fast rotating massive stars losingmass during their main sequence phase (Decressin et al.2007), novae (Maccarone & Zurek 2012) and massive bi-naries (de Mink et al. 2009). These potential contribu-tions obviously operate on different time scales and re-quire a different amount of stellar mass in the first-generation. All of the candidates proposed so far fallshort of reproducing the full variety of observations. Ad-vances in the theoretical modeling of star formation andevolution are likely needed to improve our understandingof these issues, including the spanning of a larger rangeof the parameter space (e.g., mass, metallicity, and massloss). However, from an observational point of view, theincrease in the high-quality abundance work availablefor GCs, both in the sheer number of stars and clus-ters, as well as in terms of chemical species considered, isparamount, as it creates a more complete picture of thephenomena involved. National Optical Astronomy Observatory, Tucson, AZ 85719,USA Johns Hopkins University, Baltimore, MD, 21218, USA
The Apache Point Observatory Galactic Evolution Ex-periment (APOGEE Majewski et al. 2015) is a threeyear, near-infrared (15,090 to 16,990 ˚A; Wilson et al.2012), high-resolution spectroscopic survey of about100,000 red giant stars included as part of the 3rd SloanDigital Sky Survey (SDSS-III Eisenstein et al. 2011).With a nominal resolving power of 22,500, APOGEEis deriving abundances of up to 15 elements for nearly100,000 stars, although fewer elements are generally de-tected in weak-lined metal-poor stars. APOGEE is in aunique position among the various Galactic spectroscopicsurveys such as Gaia-ESO, (Gilmore et al. 2012), RAVE(Steinmetz et al. 2006), and GALAH (Freeman 2012), asit uses the Sloan 2.5m telescope at Apache Point Obser-vatory (Gunn et al. 2006), and thereby has access to thenorthern hemisphere. APOGEE observes a large sampleof northern globular clusters, something that makes itpossible to analyse these clusters in a homogeneous way,which has not been done before for these objects.The study of GCs with APOGEE plays an importantrole not just because it has access to many northern GCs.Its high-resolution near-IR spectra allow the simultane-ous determination of many elemental abundances gen-erally not available in optical spectroscopic work of GCstars. C and N, which are elements heavily affected bythe pollution phenomenon in GCs, are often not includedin studies of metal poor stars because the strongest fea-tures (CH and CN) lie in the near-UV, far from the op-tical lines of Na, Mg and Al, and thus multiple detectorsor setups are required to obtain both sets. In addition,because these studies usually focus on fairly red starslonger exposure times are required to acquire sufficientSNR to analyse the near-UV features.The spectra used in this paper are publicly availableas part of the tenth data release (DR10, Ahn et al. 2014)of SDSS-III. The initial set of stars selected were thesame used by Meszaros et al. (2013) to check the accu-racy and precision of APOGEE parameters published inDR10. However, instead of using the automatic ASP-CAP pipeline, we will make use of photometry and theo-retical isochrones to constrain the effective temperature(T eff ) and surface gravity log g , and use an independentsemi-automated method for elemental abundance deter-mination for 10 northern GCs. Some of these clusters arewell studied, such as M3, M13, M92, M15, while othershave been poorly studied (NGC 5466), or been only re-cently discussed in the literature, such as M2 (Yong et al.2014). ABUNDANCE ANALYSIS
Target Selection
Table 1 lists the globular clusters APOGEE observedin its first year, along with the adopted [Fe/H], E( B − V ),and ages from the literature. Targets were selected ascluster members if 1) there is published abundance infor-mation on the star as a cluster member, 2) the star is aradial velocity member, or 3) if it has a probability > eff − log g dia-gram based on APOGEE observations and deleted thosethat were not red giant branch (RGB) stars. Stars thathave metallicity 0.3 dex (typically 3 σ scatter) larger or Table 1
Properties of Clusters from the LiteratureID Name N a [Fe/H] b E(B − V)Ref. c NGC 7078 M15 23 -2.37 ± ± ± ± ± ± ± ± ± ± a N is the number of stars observed in each cluster. b [Fe/H] references: Harris 1996 (2010 edition), clusters arelisted in order of the average cluster metallicity determinedin this paper. c E(B − V) references: (1) Harris 1996 (2010 edition). smaller than the cluster average also need to be deleted,but this last step resulted in no rejections. The clus-ter target selection process is described in more detailin Zasowski et al. (2013). The final sample consists of428 stars from 10 globular clusters. High S/N spectraare essential to determine abundances from atomic andmolecular features, thus all selected targets have at leastS/N=70 as determined by Meszaros et al. (2013).
Atmospheric Parameters
Abundances presented in this paper are defined foreach individual element X heavier than helium as[
X/H ] = log ( n X /n H ) star − log ( n X /n H ) ⊙ (1)where n X and n H are respectively the number of atomsof element X and hydrogen, per unit volume in the stellarphotosphere.To derive abundances from stellar spectra, we firsthave to estimate four main atmospheric parameters: T eff ,log g , microturbulent velocity, and overall metallic-ity ([Fe/H]). In the following sub-sections we presentour methodology for determining these parameters andour reasons for not using the values available for eachstar from the APOGEE Stellar Parameters and Chemi-cal Abundances Pipeline (ASPCAP; Garc´ıa P´erez et al.2014) in DR10. In order to evaluate the accuracy andprecision of the ASPCAP parameters, Meszaros et al.(2013) carried out a careful comparison with literaturevalues using 559 stars in 20 open and globular clusters.These clusters were chosen to cover most of the pa-rameter range of stars APOGEE is expected to observe.Meszaros et al. (2013) provided a detailed explanation ofthe accuracy and precision of these parameters, and alsoderived empirical calibrations for T eff , log g , and [M/H]using literature data. In the sections below we will brieflyreview these calibrations along with their limitations. The Effective Temperature
We adopt a photometric effective temperatures cal-culated from the J − K s colors using the equations ofGonz´alez Hern´andez & Bonifacio (2009). Their calibra-tion was chosen because of its proximity of only 30 −
40 Kto the absolute temperature scale. De-reddened J − K s were calculated the same way as by Meszaros et al.(2013), from E ( B − V ), listed in Table 1 for each cluster,using E ( J − K s ) = 0 . · E ( B − V ).The ASPCAP DR10 effective temperatures werecompared with photometric ones using calibrationsby Gonz´alez Hern´andez & Bonifacio (2009) basedon 2MASS J − K s colors (Strutskie et al. 2006).Meszaros et al. (2013) found that small systematicdifferences, in the range of 100 − eff were also comparedto literature spectroscopic temperatures, and theaverage of these differences were found to be negli-gible. The corrected ASPCAP DR10 temperatureswere calculated between 3500 K and 5500 K usinga calibration relation derived from the comparisonwith the Gonz´alez Hern´andez & Bonifacio (2009) scale.ASPCAP DR10 raw temperatures above 5000 K inmetal-poor stars showed significant, 300 −
500 K offsetscompared to photometry, and are thus believed to benot accurate enough for abundance analysis. This issueis mostly limited to metal poor stars, and does notaffect stars at [Fe/H] > −
1, where the vast majority ofAPOGEE targets are.The adoption of a purely photometric temperaturescale enables us to be somewhat independent of ASP-CAP (while still using the same spectra), which gives im-portant comparison data for future ASPCAP validation.Besides providing an independent comparison dataset forAPOGEE, the photometric temperatures allowed us toinclude stars in the sample that are hotter than 5000 K.Because of these reasons, the final results presented inthis paper are based on the photometric temperatures,and we only use the ASPCAP DR10 raw temperaturesto estimate our errors related to the atmospheric param-eters.
The Metallicity
The APOGEE DR10 release contains metallicities de-rived by ASPCAP for all stars analysed, thus provid-ing an alternative scale to manually derived metallici-ties. That metallicity, [M/H], tracks all metals relativeto the Sun, and gives the overall metallicity of the starsbecause it was derived by fitting the entire wavelengthregion covered by the APOGEE spectrograph. This isdifferent from most literature publications that use Felines to track metallicity in a stellar atmosphere. We use[Fe/H] in this paper whenever we refer to metallicity pre-sented here, because we use Fe I lines to measure it. Forthe most part, one can treat values of [M/H] as if theywere [Fe/H]. When ASPCAP metallicity was comparedwith individual values from high-resolution observationsfrom the literature, a difference of 0.1 dex is found below[M/H]= −
1, and this discrepancy increased with decreas-ing metallicity reaching 0.2 − − Table 2
Properties of Stars Analyzed2MASS ID Cluster v helio T eff log g [Fe/H] [C/Fe] [N/Fe] [O/Fe] [Mg/Fe] [Al/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]2M21301565+1208229 M15 -104.5 4836 1.56 -2.12 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · -0.45 0.63 0.60 0.35 · · · · · · · · · · · · -0.11 0.75 0.41 · · · · · · · · · Note . — This table is available in its entirety in machine-readable form in the online journal. A portion is shown here for guidance regarding its formand content. ter mean metallicity before starting the calculations, af-ter which small wavelength windows around the Fe lineslisted in Table 3 were used to revise the individual starmetallicities.
The Surface Gravity
In this study we adopt gravities from stellar evolutioncalculations. Following Meszaros et al. (2013), we derivegravities for our sample using isochrones from the Padovagroup (Bertelli et al. 2008, 2009). The cluster metallic-ities collected from the literature used in the isochronesare listed in Table 1, while the ages of all clusters werechosen to be 10 Gyr. The final set of temperatures andgravities corresponding to them from the isochrones arelisted in Table 2.The ASPCAP DR10 surface gravities were com-pared to both isochrones and Kepler (Borucki et al.2010) asteroseismic targets observed by APOGEE(Pinsonneault, et al. 2014) to estimate their accuracyand precision. An average difference of 0.3 dex wasfound at solar metallicity in both cases, but this in-creased to almost 1 dex for very metal poor stars. Theasteroseismic gravities are believed to have errors in therange of 0.01 − > − < − < The microturbulent velocity
A relation between microturbulent velocity and surfacegravity, v micro = 2 . − . × log g , was used for ASPCAPanalyses in DR10 (Meszaros et al. 2013). For consistencywith ASPCAP, and for easier future comparisons withAPOGEE results, we adopted that equation in this work. AUTOSYNTH
The program called autosynth was developed especiallyfor this project to simplify the large amount of synthe-sis required for abundance determination. The programtakes atmospheric parameters as input and carries out spectral synthesis to derive elemental abundances. Thecore of autosynth is MOOG2013 (Sneden 1973), whichdoes the spectrum synthesis, while autosynth comparesthe synthetic spectrum with the observed spectrum anddetermines the best abundances with χ minimization inwavelength windows specified by the user. The programcan read the MOOG formatted ATLAS and MARCSmodel atmospheres, and can also convert the originalATLAS and MARCS formats into a MOOG compatibleformat.The line list adopted for this study includes bothatomic and molecular species. It is an updated ver-sion of what was used for the DR10 results, versionm201312160900 (also used for DR12, APOGEE’s nextpublic data release; Alam et al. 2015; Holtzman et al.2015), and includes atomic and molecular species. Themolecular line list is a compilation of literature sourcesincluding transitions of CO, OH, CN, C , H , and SiH.All molecular data are adopted without change with theexception of a few obvious typographical corrections.The atomic line list was compiled from a number of liter-ature sources and includes theoretical, astrophysical andlaboratory oscillator strength values. These literatureline positions, oscillator strengths, and damping valueswere allowed to vary in order to fit to the solar spectrumand the spectrum of Arcturus, thus generating a tunedastrophysical line list. The solution is weighted such thatthe solar solution has twice the weight as the Arcturussolution to properly consider the fact that the abundanceratios in Arcturus are more poorly understood than thoseof the Sun. The code used for this process was based onthe LTE spectral synthesis code MOOG (Sneden 1973)but adapted to our unique needs. For lines with labora-tory oscillator strengths, we did not allow the astrophys-ical gf value to vary beyond twice the error quoted bythe source. A more detailed description of this processand the line list can be found in Shetrone et al. (2015).The choice for the local continuum set can greatly af-fect the derived abundances, thus we needed a reliableautomated way to determine the continuum placement.This was done with a separate χ minimization fromthe one that was used for the abundance determina-tion. Continuum normalized observation points around1 are multiplied by a factor between 0.7 and 1.1 with0.001 steps for each synthesis emulating slightly differentchoices for the location of the local continuum. Multipli-cation is necessary because it preserves the original spec-trum. The χ near the continuum is calculated and com-pared to the continuum of the observation and minimized separately for every abundance step. The χ calculationfor the abundances determination happens between cer-tain flux ranges (usually between 0.3 and 1.1) using thecontinuum placement determined in the previous step. Individual Abundances
The individual abundances were determined using the1D Local Thermodynamic Equilibrium (LTE) model at-mospheres calculated with ATLAS9 (Kurucz 1979). Themodel atmospheres were generated using solar referenceabundances from Asplund et al. (2005), the same way asthe main APOGEE model atmosphere database was gen-erated (Meszaros et al. 2012). Because the overall metal-licity of these clusters were well known from the litera-ture, initially we calculated atmospheres using the av-erage literature metallicity for each cluster adopting thephotometric effective temperatures and isochrone gravi-ties. These initial model atmospheres were later revisedto have consistency with the synthesis.The windows used to derive the individual abundanceswere determined based on the analysis of FTS stars inthe H − band using the APOGEE line list by Smith et al.(2013). In the case of Fe we measured [Fe/M], relative tothe literature cluster metallicity for each line. The abun-dance of Na is very important in discussing the spread ofO in GCs, and two Na lines are available in the APOGEEspectral band. However, these two Na lines are weak evenat solar metallicities. We carried out a number of testsattempting to derive Na abundances, but we found thatthe two Na lines become very weak around [Fe/H]= − − .
7, thus we were notable to determine Na abundances for any of our targets.The list of wavelength regions used in our analysis, andthe solar reference values for each element is listed in Ta-ble 3. Figures 1 and 2 show examples of observed Fe, Mg,Al, OH, CO, and CN line profiles and their fitted syn-thesis for one star from M71 and M13. The wavelengthregions shown in these figures are only a fraction of whathas been used from Table 3.CN lines spread over most of the H − band, hence it isimportant to calculate the CNO abundances before theatomic ones. It is also important to use self consistentmodel atmospheres, because stars in globular clusters ex-hibit low carbon and high α − content, which significantlyalters the structure of the atmosphere compared to a so-lar scaled one (Meszaros et al. 2012). Taking into ac-count all this, we developed the following procedure toproduce the final abundances for each star:1. A model atmosphere is generated using literaturecluster average metallicities, the photometric tem-perature and an isochrone gravity. Because allof our targets are RGB stars, we choose [C/Fe]= − .
5, [O/Fe] = 0 .
3, and [N/Fe] = 0 . autosynth , and anaverage [Fe/H] is calculated for each star.3. A new model atmosphere is calculated using thisnew [Fe/H] value, but still using the starting CNOabundances.4. We set the abundances of C, N and O before theremaining elements, because they can have a sig- Table 3
Wavelength RegionsElement log(N) a Wavelength (˚A) b Fe 7.45 15210-15213.5; 15397-15401; 15651-1565415966-15973; 16044-16048; 16156-1616016168-16171C 8.39 15572-15606; 15772-15791; 15980-1603716172-16248; 16617-16677; 16839-16870N 7.78 15240-15417O 8.66 15267-15272; 15281-15288; 15372-1538015386-15390; 15394-15397; 15404-1541415499-15502; 15508-15511; 15539-1554215561-15566; 15569-15574; 15887-1590416188-16198; 16207-16213; 16233-1623716244-16247; 16251-16261; 16300-1630516314-16319; 16707-16714; 16718-1672016731-16735; 16888-16892; 16898-16912Mg 7.53 15741-15757; 15767-15773Al 6.37 16720-16727; 16751-16759; 16765-16770Si 7.51 15962-15966; 16062-16066; 16097-1610116218-16223; 16683-16687; 16830-16834Ca 6.31 16139-16143; 16153.5-16164Ti 4.90 15546.5-15549.5; 15718-15721.5 a The Solar reference abundances are from Asplund et al. (2005). b Vacuum wavelength. nificant effect on the atmospheric structure in coolstars. Since molecular features generally disappearfrom metal-poor spectra above 4500 K, we divideour stars into two temperature groups. For thestars cooler than 4500 K, we first determine [O/Fe]using OH lines, then create a new model atmo-sphere with [ α /Fe] equal to [O/Fe]. We then de-termine C and O abundances from CO lines, thenrecreate the model atmosphere again with thesenew [C/Fe] and [O/Fe] abundances. Finally, we de-rive N abundance using CN lines. For stars hotterthan 4500 K, we leave the C, N, and O abundancesat their inital values.5. The abundances of the remaining elements (Mg,Al, Si, Ca and Ti) are determined with autosynth ,using the stellar parameters, metallicities, and C,N and O abundances previously determined.For each element, we average together the abundanceresults from the different wavelength regions to obtainfinal values. Although the size of each region is differ-ent, we did not find it necessary to use weights basedon their ranges or line strengths, because that approachdid not produce abundances significantly different from astraightforward average. Data reduction errors or miss-ing data affected some of these regions, resulting in er-roneous fits, and because of this we carefully examinedeach fit by eye. These wavelength regions were not in-cluded when constructing the final average abundances.The final abundance values are listed in Table 2. Uncertainty Calculations
Systematic Uncertainties
The uncertainty in the atmospheric parametersstrongly affects the final abundances derived from someof the spectral features we consider. To test the sensi-tivity of abundances due to changes in the atmosphericparameters we used the results from the ASPCAP raw R e l a t i v e F l u x Min. [Fe/M] = -0.40Best [Fe/M] = 0.16Max. [Fe/M] = 0.40
Min. [Fe/M] = -0.40Best [Fe/M] = 0.07Max. [Fe/M] = 0.40 R e l a t i v e F l u x T eff = 3913Klog g = 0.71 Min. [Al/M] = -0.50Best [Al/M] = 0.36Max. [Al/M] = 1.50 eff = 3959Klog g = 0.40
Min. [Al/M] = -0.50Best [Al/M] = 0.07Max. [Al/M] = 1.50 R e l a t i v e F l u x Wavelength (A)
Min. [Mg/M] = -0.30Best [Mg/M] = 0.46Max. [Mg/M] = 0.60
Min. [Mg/M] = -0.30Best [Mg/M] = 0.28Max. [Mg/M] = 0.60
Figure 1.
Example spectra and the fitted synthesis of Fe, Al, and Mg lines for two stars from M71 and M13. Abundances were fittedbetween the labelled minimum and maximum values using a step of 0.01 dex. The printed best fitted abundance values might not be thesame as in Table 2, because the table contains averaged values, not individual fits. temperature scale. The same exact steps described inthe previous section were followed, but instead of adopt-ing the photometric temperature scale we adopt the AS-PCAP DR10 raw temperature scale, which results innew surface gravities and microturbulent velocities. Thisway we could track systematics uncertainties sensitive tothese parameters as well.The differences in abundances as a function of photo-metric temperatures are demonstrated in Figure 3. Thetop left panel displays the differences in the measuredabundances by using ASPCAP and photometric temper- ature, while the rest of the panels are assigned to eachelement. The color scale in all panels represents ∆ T eff .We defined the estimated errors associated with the at-mospheric parameters based on the standard deviationaround the mean differences between the two tempera-ture scales. The calculated standard deviation in of thedifferences in temperatures is 146 K (which we round to150 K). This standard deviation corresponds to the sumof the uncertainty in the photometric temperature andthe ASPCAP temperature in quadrature.In order to estimate the uncertainty of just the photo- R e l a t i v e F l u x Min. [O/M] = -0.30Best [O/M] = 0.33Max. [O/M] = 0.70
Min. [O/M] = -0.30Best [O/M] = 0.55Max. [O/M] = 0.70 R e l a t i v e F l u x Min. [C/M] = -0.40Best [C/M] = -0.37Max. [C/M] = 0.40
Min. [C/M] = -0.70Best [C/M] = -0.49Max. [C/M] = 0.40 R e l a t i v e F l u x Wavelength (A)T eff = 3913Klog g = 0.71
Min. [N/M] = -0.50Best [N/M] = 1.17Max. [N/M] = 1.50 eff = 3959Klog g = 0.40
Min. [N/M] = -0.50Best [N/M] = 1.22Max. [N/M] = 1.50
Figure 2.
Example spectra and the fitted synthesis of OH, CO, and CN lines for two stars from M71 and M13. For more explanation seecaption of Figure 1 and Section 3.1. metric temperature component, we carried out calcula-tions of temperatures with varied J − Ks colors, redden-ings and metallicities for M107. M107 was chosen be-cause it is the cluster with the highest reddening in oursample. The uncertainty of 2MASS photometry is usu-ally between 0.025 − − Ks color. Changing J − Ks by0.05 magnitudes typically produces a change of 80 K inthe photometric temperature. The reddening of M107was changed by 0.03, simulating a 10% uncertainty inreddening, and this produced a difference of about 40 K in the photometric temperature. A change of 0.1 dexin metallicity results in 1 K or less uncertainty in tem-perature; thus the uncertainties in metallicity can be ne-glected. By adding the uncertainty from photometry andreddening in quadrature, we estimate the uncertainty ofthe photometric temperature to be about 100 K. The toppanel of Table 4 lists uncertainties associated with both150 and 100 K changes in temperature.In our methodology a 100 K change in temperaturealso introduces an 0.3 dex systematic difference in sur-face gravity, and 0.1 km/s in microturbulent velocity, soby coupling these two parameters to T eff , our system- Table 4
Estimated Abundance UncertaintiesCluster Fe C N O Mg Al Si Ca TiSystematic uncertainties from atmospheric parameters∆T eff eff autosynth M15 0.11 0.21 0.30 0.06 0.08 0.16 0.13 0.19 0.26M92 0.10 0.18 0.30 0.05 0.07 0.12 0.12 0.22 0.17M53 0.06 0.16 0.12 0.05 0.06 0.14 0.11 0.11 0.18N5466 0.06 0.18 0.15 0.03 0.07 0.03 0.07 0.14 0.17M13 0.05 0.12 0.06 0.05 0.05 0.12 0.07 0.06 0.12M2 0.04 0.11 0.06 0.04 0.07 0.10 0.09 0.05 0.09M3 0.04 0.12 0.08 0.05 0.03 0.10 0.08 0.05 0.12M5 0.04 0.08 0.05 0.05 0.04 0.06 0.07 0.04 0.09M107 0.04 0.04 0.03 0.05 0.04 0.08 0.07 0.04 0.10M71 0.02 0.03 0.04 0.04 0.04 0.05 0.07 0.06 0.07Final combined uncertaintiesM15 0.12 0.22 0.32 0.13 0.09 0.17 0.13 0.19 0.28M92 0.11 0.20 0.32 0.13 0.09 0.13 0.12 0.22 0.20M53 0.08 0.18 0.16 0.13 0.07 0.15 0.11 0.12 0.21N5466 0.08 0.20 0.19 0.12 0.08 0.06 0.08 0.15 0.20M13 0.07 0.14 0.13 0.13 0.06 0.13 0.08 0.07 0.16M2 0.06 0.14 0.13 0.13 0.08 0.11 0.09 0.06 0.13M3 0.06 0.14 0.14 0.13 0.04 0.11 0.09 0.06 0.16M5 0.06 0.11 0.12 0.13 0.05 0.08 0.08 0.06 0.13M107 0.06 0.09 0.11 0.13 0.05 0.09 0.08 0.06 0.14M71 0.05 0.09 0.12 0.13 0.05 0.07 0.08 0.07 0.12
Note . — Top panel: Systematic uncertainty estimates from changes inT eff , log g , and v micro . Middle panel: Average random uncertainties re-ported by autosynth . Bottom panel: The final uncertainties are the sumof uncertainties in quadrature from the middle panel and uncertainties for∆T eff =100K, ∆ log g =0.3, and ∆ v micro =0.1 km/s. atic uncertainties include the investigation of abundancesensitivity to these parameters as well. Internal Uncertainties
Besides the uncertainty coming from the adopted at-mospheric parameters, the uncertainty of the fit was alsocalculated using the σ of the residuals between the bestfit synthesis and the observation. These calculations esti-mate random uncertainties. This σ of the fit is calculatedwithin the windows used in the χ calculation. For de-termining the uncertainty of the fit, we multiply the ob-served spectra by 1+ σ and 1- σ which simulates two spec-tra slightly different from the original spectrum. Then,the fit of each line is repeated while keeping all otherparameters unchanged. The average differences betweenthese two new fits and the original best-fit spectrum isthe defined uncertainty associated with the fit itself. Thisuncertainty estimate is mainly sensitive to variations ofnoise in the spectrum in the defined windows for the χ fit. If its value is close to 0, then the (1 + σ ) × spectrumand (1 − σ ) × spectrum give very similar, or the sameabundances. This is expected when working at high S/Nand with a well defined continuum.While this uncertainty estimation method is reliablein most cases, it has its limitations for very noisy spec-tra, very weak lines, or when abundances are near upperlimits. Uncertainties are usually overestimated for noisyspectra, while they are underestimated for weak lines Uncertainty Estimation, T eff < 5400K -600-400-2000200400600800 400045005000 ∆ T e ff ∆ T eff = 46.4 +/- 146.4 -400-2000200400 -1-0.500.51 400045005000 ∆ [ F e / H ] ∆ [Fe/H] = 0.02 +/- 0.08-1-0.500.51 400045005000 ∆ [ C / F e ] ∆ [C/Fe] = 0.03 +/- 0.12-1-0.500.51 400045005000 ∆ [ O / F e ] ∆ [O/Fe] = 0.04 +/- 0.18 -1-0.500.51 400045005000 ∆ [ N / F e ] ∆ [N/Fe] = 0.02 +/- 0.16-1-0.500.51 400045005000 ∆ [ A l / F e ] ∆ [Al/Fe] = 0.009 +/- 0.07 -1-0.500.51 400045005000 ∆ [ M g / F e ] ∆ [Mg/Fe] = 0.002 +/- 0.04-1-0.500.51 400045005000 ∆ [ S i / F e ] ∆ [Si/Fe] = -0.0005 +/- 0.05-1-0.500.51 400045005000 ∆ [ C a / F e ] T eff photo ∆ [Ca/Fe] = -0.003 +/- 0.06 -1-0.500.51 400045005000 ∆ [ T i / F e ] T eff photo ∆ [Ti/Fe] = 0.03 +/- 0.15 Figure 3.
Differences in abundances produced by two runs adopt-ing different temperatures: photometric and ASPCAP tempera-tures; otherwise the same calculation method was used. The pointsare color coded by the differences between the photometric andASPCAP temperatures. The ± errors give the standard deviationaround the mean of the differences. and upper limits. Thus, we decided to use one uncer-tainty from autosynth per element per cluster by simplyaveraging together all uncertainties reported by the pro-gram. This resulted in one uncertainty estimate for ev-ery element in each cluster. Autosynth uncertainties arelisted in the middle section of Table 4. The final esti-mated uncertainties were calculated by adding togetherin quadrature the uncertainties for 100 K difference intemperature (also 0.3 dex systematic difference in log g , and 0.1 km/s in microturbulent velocity), and the aver-age autosynth values that estimate random uncertainties.These final estimations for each element per cluster aregiven in the bottom panel of Table 4. LITERATURE COMPARISONS
We take [X/Fe] abundance values for C, N, O, Mg, Al,Si, Ca and Ti from high-resolution spectroscopic stud-ies in the literature as a point of comparison for ourabundance determinations. We use the same literaturesources as Meszaros et al. (2013), and added more re-cently published papers listed in Table 5. The deriva-tion of stellar parameters T eff and log g are describedin detail in Section 2; and they were also compared tothe literature. Our goal for these comparisons is not to Table 5
Identifiers, stellar parameters and elemental abundances from the literature for stars in our sample2MASS ID Cluster T eff log g [Fe/H] [C/Fe] [N/Fe] [O/Fe] [Mg/Fe] [Al/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe] alt. ID Source2M21290843+1209118 M15 · · · · · · -2.37 · · · · · · · · · · · · · · · · · · · · · · · · -2.37 · · · · · · · · · · · · · · · · · · · · · K22 h2M21293871+1211530 M15 · · · · · · -2.37 · · · · · · · · · · · · · · · · · · · · ·
K47 h2M21294979+1211058 M15 · · · · · · -2.40 · · · · · · · · · · · · · · · · · ·
K144 h2M21294979+1211058 M15 · · · · · · -2.27 · · · · · · · · · · · · · · · · · ·
K144 i
Note . — This table is available in its entirety in machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.Individual star references: (a) O’Connell et al. (2011); (b) Carretta et al. (2009a); (c) Johnson & Pilachowski (2012); (d) Sneden et al. (2004); (e) Yong et al. (2006a);(f) Cohen & Mel´endez (2005); (g) Cavallo & Nagar (2000); (h) Sneden et al. (2000); (i) Minniti et al. (1996); (j) Otsuki et al. (2006); (k) Sneden et al. (1991); (l)Sneden et al. (1997); (m) Sobeck et al. (2011); (n) Kraft & Ivans (2003); (o) Kraft et al. (1992); (p) Johnson et al. (2005); (q) Lai et al. (2011); (r) Ivans et al.(2001); (s) Koch & McWilliam (2010); (t) Sneden et al. (1992); (u) Ram´ırez & Cohen (2003); (v) Yong et al. (2008); (w) Mel´endez & Cohen (2009); (x) Briley et al.(1997); (y) Shetrone (1996); (z) Smith et al. (2007); (aa) Lee et al. (2004); (ab) Ram´ırez & Cohen (2002); (ac) Yong et al. (2006b); (ad) Sneden et al. (2000); (ae)Roederer & Sneden (2011) cross-calibrate our new abundance determinations withthe literature; rather, we are looking for cases where ourabundances are systematically different from the litera-ture, or particular clusters or elements for which our ho-mogeneously observed and analysed data set can clarifyconflicts in the literature.Cross-identification between the globular cluster starsin the DR10 APOGEE data set and the literature wasperformed using the Simbad online service , based on2MASS identifiers and ( α , δ ) coordinates. Because thereis a large and heterogeneous literature on chemical abun-dances in globular cluster stars, we are providing ourcross-identifications as a resource for the community. Ta-ble 5 lists 2MASS ID and position, and alternate stellaridentifiers from literature abundance studies for all of thestars considered in this study.Figure 4 shows comparisons of our stellar parametersand abundances against the literature values. Differ-ent globular clusters are represented by different coloredpoints. In general, we find a systematic offset of ∼ eff values and the spectro-scopic effective temperatures from the literature, with areasonably small scatter. This is similar to the typicaldifference between spectroscopic and photometric tem-peratures reported by Meszaros et al. (2013). Becauseof the degeneracies in deriving stellar parameters, theslightly higher temperatures in the literature are accom-panied by a systematic offset of ∼ +0 . g .There are a few systematic differences between ourabundance results and those in the literature. These canmainly be traced back to a change in the Solar abundancescale as derived by Asplund et al. (2005). As one exam-ple, the [Fe/H] metallicities we derive are typically 0 . ⊙ from 7 . .
45 (Asplund et al. 2005).Also, the Solar abundance of oxygen was revised signif-icantly, from A(O) ⊙ =8.93 (Anders & Grevesse 1989) to8.66 (Asplund et al. 2005). Since we use the more re-cent Solar abundance values from Asplund et al. (2005)whereas our earlier literature sources do not, we expectthe ∼ . http://simbad.u-strasbg.fr/simbad/ which this explanation does not hold: although theSolar abundance was revised down, from A(C) ⊙ =8.56(Anders & Grevesse 1989) to 8 .
39 (Asplund et al. 2005),our [C/Fe] values are typically lower than the literaturevalues. Unfortunately, literature values are available foronly a subset of our stars, which makes it difficult toverify precisely any systematic behavior.In the other elements we consider in the present study,there is generally good agreement between our resultsand those from the literature, which is encouraging.However, we find significant differences in Al abundancesin stars with below-Solar metallicities. This is mainlydriven by stars in M3, where the [Al/Fe] abundancesfrom Johnson et al. (2005) are larger than in the otherliterature sources. We also see significant scatter in[Ca/Fe] and [Ti/Fe] at low abundances; this is likelycaused by our abundance determination method havingdifficulty with weak lines.The [Mg/Fe] versus [Al/Fe] relations in M3, M13 andM5 provide useful examples of how our new data setcompares with the literature. In M3, our abundance de-terminations show a clear bimodality in the Mg-Al dis-tribution. The study of Cavallo & Nagar (2000) founda similar bimodality, but Johnson et al. (2005) found asmooth distribution. In M13 we find an extended an-ticorrelation between [Mg/Fe] and [Al/Fe], and the lit-erature abundances lie within it. We have seven starsin common with Sneden et al. (2004), and they span thefull anticorrelation, while the three and two stars, respec-tively, that we have in common with Cohen & Mel´endez(2005) and Cavallo & Nagar (2000) are consistent withour abundance results but happen to inhabit small re-gions of abundance space. M5 is a similar case, whereour [Al/Fe] values span a range of − − VARIATIONS IN INDIVIDUAL ELEMENT ABUNDANCES
Although there are well-known abundance patternswithin globular clusters, large homogeneous studies thatinclude a wide range of abundances are rare. Since wecan determine abundances of most of the light elementsfor the stars in our sample, we examine the behaviorof the known abundance patterns across a wide range0
Literature Comparisons T e ff li t e r a t u r e T eff photometric 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 l ogg li t e r a t u r e logg photometric -2.5-2-1.5-1-0.5 -2.5 -2 -1.5 -1 -0.5 [ F e / H ] li t e r a t u r e [Fe/H] this study M15M92M13M3M5M107M71 -1-0.8-0.6-0.4-0.2 0 0.2 0.4 -1 -0.5 0 [ C / F e ] li t e r a t u r e [C/Fe] this study 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.5 1 1.5 [ N / F e ] li t e r a t u r e [N/Fe] this study -0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 -0.5 0 0.5 [ O / F e ] li t e r a t u r e [O/Fe] this study-0.4-0.2 0 0.2 0.4 0.6 0.8 0 0.5 [ M g / F e ] li t e r a t u r e [Mg/Fe] this study -0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 [ A l / F e ] li t e r a t u r e [Al/Fe] this study 0 0.2 0.4 0.6 0.8 1 0 0.5 1 [ S i / F e ] li t e r a t u r e [Si/Fe] this study-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.5 [ C a / F e ] li t e r a t u r e [Ca/Fe] this study -0.2 0 0.2 0.4 0.6 0.8 0 0.5 [ T i / F e ] li t e r a t u r e [Ti/Fe] this study Figure 4. T eff , log g , [Fe/H], [C/Fe], [N/Fe], [Mg/Fe], [Al/Fe], [Si/Fe], [Ca/Fe], [Ti/Fe] compared to literature sources. Different colorsdenote different clusters, for an explanation of the colors see upper right panel. Solid lines show the 1:1 relation, while dashed lines denote ±
100 K for T eff , and ± g and individual abundances. A detailed discussion can be found in Section 4. in cluster metallicity, and search for unexpected varia-tions in the α − elements. In this section we focus on therange of abundance within each cluster, to separate realabundance variations, bimodalities and trends from pos-sible measurement errors. Table 6 lists the average andstandard deviation for each elemental abundance in eachcluster. Correlations with T eff In Figures 5-7 we show all nine derived abundancesas a function of effective temperature. From Figure 5we conclude that we measure constant Fe abundances in all of the clusters. Mg and Al abundances show a largerange of values in some clusters (as discussed in Section2, and further in Section 6), but no significant trendswith T eff except in M107 and M71. This trend is veryweak in M71, and data are consistent with showing notrend within the uncertainties. However, in M107 thetrend is stronger. We currently do not fully understandwhere these small correlations come from. We suspectthat this is a result of a combination of effects. Onesuch effect may be the use of model atmospheres that as-sume local thermodynamic equilibrium (LTE), but that1 Table 6
Abundance Averages and ScatterCluster [Fe/H] [C/Fe] [N/Fe] [O/Fe] A(C+N+O) [Mg/Fe] [Al/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]AveragesM15 -2.28 -0.41 0.95 0.54 7.09 0.11 0.34 0.44 0.16 0.15M92 -2.23 -0.41 0.93 0.58 7.19 0.14 0.42 0.45 0.10 0.09M53 -1.95 -0.50 1.06 0.56 7.49 0.11 0.37 0.41 0.23 0.28N5466 -1.82 -0.56 0.84 0.63 7.60 0.14 -0.24 0.29 0.04 0.29M13 -1.50 -0.53 0.89 0.28 7.69 0.13 0.61 0.40 0.26 0.20M2 -1.49 -0.48 0.90 0.41 7.76 0.26 0.45 0.35 0.24 0.27M3 -1.40 -0.46 0.69 0.40 7.84 0.15 0.21 0.30 0.12 0.11M5 -1.24 -0.46 0.76 0.27 7.85 0.23 0.36 0.34 0.20 0.26M107 -1.01 -0.21 0.69 0.33 8.15 0.24 0.47 0.48 0.15 0.21M71 -0.68 -0.10 0.91 0.51 8.65 0.38 0.51 0.39 0.21 0.42ScatterM15 0.10 0.13 0.35 0.19 0.14 0.24 0.52 0.16 0.25 0.08M92 0.10 0.11 0.23 0.19 0.13 0.23 0.48 0.12 0.17 0.20M53 0.07 0.16 0.21 0.06 0.09 0.08 0.51 0.05 0.17 0.13N5466 0.08 0.01 0.10 0.04 0.08 0.06 0.35 0.09 0.25 0.14M13 0.07 0.07 a a a M3 0.08 0.08 a a a M107 0.06 0.09 0.27 0.15 0.15 0.10 a a a Standard deviation around the linear fit. [Fe/H], [Mg/Fe], [Al/Fe] as a function of T eff , T eff < 5400K -2-1 [ F e / H ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 -2-1 [ F e / H ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ M g / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 [ M g / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ A l / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205
01 400045005000 [ A l / F e ] T eff M2, N7089 eff
M3, N5272 eff
M5, N5904 eff
M107, N6171 eff
M71, N6838
Figure 5. [Fe/H], [Mg/Fe], and [Al/Fe] as a function of photometric T eff for all ten clusters. The error bars represent our final combineduncertainties from Table 4. The linear fit is plotted over [Mg/Fe] for M107 and M71 to remove the visible linear trend (see Section 5.1 fordiscussion). non-LTE effects (Bergemann & Nordlander 2014) act to make the strong Mg lines in these metal-rich stars give2 [C/Fe], [O/Fe], [N/Fe] as a function of T eff , T eff < 4520K -10 [ C / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 -10 [ C / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ N / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 [ N / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ O / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205
01 40004500 [ O / F e ] T eff M2, N7089 eff
M3, N5272 eff
M5, N5904 eff
M107, N6171 eff
M71, N6838
Figure 6. [C/Fe], [N/Fe], and [O/Fe] as a function of photometric T eff for all ten clusters. Open triangles mark upper limits for [C/Fe] andlower limits for [N/Fe], while the real detections are plotted using filled red dots. The error bars represent our final combined uncertaintiesfrom Table 4. The linear correlation in [C/Fe] as a function of T eff in M13, M2, M3 and M5 is the effect of CNO burning on the RGB.The fitted lines are used to remove the trend in order to estimate the scatter in these clusters (see Section 5.1 for discussion). the appearance of higher abundance in the cooler stars.Other possible effects are small systematic errors fromestimating T eff and log g culminating during the synthe-sis. Abundances are also sensitive to the microturbulentvelosity, so if the log g − v micro expression used is not soaccurate in this metallicity range, or the surface gravityis badly estimated, this propagates into systematicallyoff abundances through v micro .The minimum [C/Fe] (Figure 6) that can be measuredfrom the CO lines strongly depends on temperature. Be-cause RGB stars in GCs generally have low carbon abun-dances, we can only set upper limits for a number ofour stars. Our [C/Fe] values are an average of the de-rived abundances from five CO windows. As a resultdetermining the upper limit is more challenging becauseCO lines in certain windows disappear faster with risingtemperature than in others. We carefully checked ev-ery CO window fit and selected upper limits if the COband head was not visible in more than three windows bylooking at the flatness of the χ fit around the minimumvalue. Because the derived abundance of N from the CNlines is anticorrelated with the value of [C/Fe] used, allstars with upper limits in [C/Fe] have also lower limitsin [N/Fe]. These upper limits for [C/Fe] and lower limitsof [N/Fe] are identified with open triangles in all figures.We see clear correlations between [C/Fe] and T eff in M13, M3, M2, and M5 when omitting upper lim-its. We interpret these as a sign of “deep mixing”,a nonconvective mixing process that causes steady de- pletion of surface carbon abundance and an enhance-ment in nitrogen abundance in all low-mass RGB stars(Gratton et al. 2004). We derive only upper limits on[C/Fe] for M15, M92, M53 and NGC 5466 because theCO bands are quite weak at such low metallicity. Withonly upper limits, it is not possible to identify abun-dance trends in these clusters. However, previous studies(Angelou et al. 2012; Shetrone et al. 2010; Martell et al.2008) have found signs of the same deep mixing processin action in those clusters.The only cluster in which we see a sign of nitrogenenrichment with declining temperature is M13. Possibletrends in nitrogen are not necessarily a result of astro-physics, because in our methodology small systematicerrors in temperature can result in systematic errors inN abundance because deriving [N/Fe] is challenging fromthe CN lines. Other than the relatively large errors ofN, one also has to be careful with possible correlationsof C and N with temperature, because they can be gen-erated on the RGB as part of deep mixing and also in aprevious stellar evolution event that are responsible forthe pollution.In Figure 7 there is a weak trend, on par with the er-ror, visible in the Si abundance in M13, but not in theother clusters. While Ca does not show any correlationwith temperature, it does show temperature-dependentscatter in most of the GCs. The three Ca lines usedin our analysis are generally weak, and get significantlyweaker above 4700 K, which leads to higher errors re-3 [Si/Fe], [Ca/Fe], [Ti/Fe] as a function of T eff , T eff < 5400K [ S i / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 [ S i / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ C a / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205 [ C a / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ T i / F e ] M15, N7078 M92, N6341 M53, N5024 NGC 5466 M13, N6205
01 400045005000 [ T i / F e ] T eff M2, N7089 eff
M3, N5272 eff
M5, N5904 eff
M107, N6171 eff
M71, N6838
Figure 7. [Si/Fe], [Ca/Fe], and [Ti/Fe] as a function of photometric T eff for all ten clusters. The error bars represent our final combineduncertainties from Table 4. Trends in Ti for M2 and M5 are removed using the plotted lines when calculating the internal scatter (seeSection 5.1 for discussion). lated to increased sensitivity to the uncertainty in thecontinuum placement. Titanium, unexpectedly, showsa decline with decreasing temperature in M2, M5 and(marginally) in M107 in Figure 7. We suspect that in-accuracies in our analysis of the hotter star spectra aredriving this apparent trend, since the S/N is lower forthose stars than for the cooler, brighter giants. Becausethese trends in Mg (Figure 5), Si and Ti (Figure 7) onlyshow up in a handful of clusters, we believe that they area result of difficulties in data analysis for certain lines incertain stars and not any systematic mishandling in, e.g.,v micro estimation.We choose to fit these various observed trends witha linear equation, regardless of their origin, in order toexplore the scatter around the trend. We fit lines to[Mg/Fe] in M107 and M71, [C/Fe] in M13, M2, M3 andM5, and [Ti/Fe] in M2 and M5. We are only using thesefits to determine the internal scatter, which we define asthe standard deviation about the fitted line. Through-out the rest of this paper we use the abundance valuesdirectly, except when discussing the CN anticorrelationsin Section 6.4. Scatter and Errors
An internal abundance scatter significantly larger thanthe estimated errors suggests an astrophysical origin. Infact, significant scatter in N, O, Mg and Al is well doc-umented in literature (Gratton et al. 2012). The largestar-to-star variations in these elements are the result ofthe CNO, Ne-Na, and Mg-Al cycles, which play an im- portant role in the nuclear fusion processes at the earlystages of RGB (CNO) and AGB (Ne-Na, Mg-Al) evo-lution. Figure 8 shows the internal scatter calculatedas the standard deviation around the mean values (insome cases around a fitted linear equation, as explainedearlier), and the final combined estimated uncertaintiesfrom Table 4, as a function of cluster average metallic-ity. We note that the small number of stars analysed inNGC 5466 limits our ability to make a detailed analysisof C, N, and O in this cluster: because we were only ableto measure the abundance of these elements in the threestars that have temperatures below 4500K, the scatter isunrealistically higher than the calculated uncertainty.The star-to-star scatter in [Fe/H] is quite similar toour measurement uncertainties, indicating that no signif-icant metallicity variations in the clusters are detected inthis study. Recently, Yong et al. (2014) have discoveredthree distinctive groups with different iron abundancesin M2. The first group has a dominant peak at [Fe/H]=-1.7, while the second and third have smaller peaks at1.5 and 1.0, but the membership for the latter group isnot conclusive. We see no such behaviour in M2. Thediscrepancy between these two studies is most likely theresult of a selection effect. Yong et al. (2014) selectedstars that belong to a second RGB (Lardo et al. 2012)within the cluster, while our sample selection were basedupon previous observations (Zasowski et al. 2013) and allof our stars belong to the main RGB of this cluster.The α − elements Si and Ti also show constant dis-4 Cluster internal scatter compared to uncertainties S c a tt e r M71M107M5M3M2M13N5466M53M92M15 [Fe/H] scatter[Fe/H] uncertainty 00.10.20.30.4 [C/Fe] scatter[C/Fe] uncertainty00.10.20.30.40.50.6 S c a tt e r [N/Fe] scatter[N/Fe] uncertainty 00.10.20.30.4 [O/Fe] scatter[O/Fe] uncertainty00.10.20.30.4 S c a tt e r [Mg/Fe] scatter[Mg/Fe] uncertainty 00.10.20.30.40.50.6 [Al/Fe] scatter[Al/Fe] uncertainty00.10.20.30.4 -2.5 -2 -1.5 -1 -0.5 S c a tt e r [Fe/H] average [Si/Fe] scatter[Si/Fe] uncertainty[Ti/Fe] scatter[Ti/Fe] uncertainty 00.10.20.30.4 -2.5 -2 -1.5 -1 -0.5[Fe/H] average [Ca/Fe] scatter[Ca/Fe] uncertainty Figure 8.
The internal scatter in each cluster from Table 6 (red dots) compared to our estimated final combined errors from Table 4 (bluedots). tribution, but the scatter in [Ca/Fe] is larger than ourmeasurement uncertainties for most clusters in our sam-ple. We attribute this to an increasing inaccuracy in[Ca/Fe] with rising temperature, as discussed in Section5.1, and not a real range in calcium abundance. Little tono range in iron and α − elements is what we expect fornormal globular clusters, although the clusters in whichthese abundances do vary are an intriguing puzzle (see,e.g., Marino et al. 2013). M107 stands out as havingthe largest discrepancy between the scatter of [Ca/Fe]and its estimated uncertainty. However, the large inter-nal scatter is not related to astrophysics, but to spectralcontamination from telluric OH lines. Due to the clus-ter’s radial velocity, two of the three Ca lines lie on top ofatmospheric OH lines. Because the telluric correction isnot perfect, the Ca lines are compromised in a way thatis not included in our uncertainty estimation.We do see scatter above the level of the uncertaintiesin some of the light-element abundances. In the case ofcarbon, we find that the scatter around the overall car-bon depletion trend for M13, M2, M3 and M5 (as shownby dashed lines in Figure 6) is fairly small, although ourmeasurement uncertainties get quite large at low metal-licity. We do not see clear carbon depletion in M107 orM71; however, as discussed in Martell et al. (2008), therate of carbon depletion due to deep mixing is lower inhigher-metallicity stars.The range in [N/Fe] abundance (Figure 8, second panelfrom the top, in the left column) in M71, M107, M5,M3, M13, and M2 is clearly larger than the estimated uncertainties. However, the difference between the scat-ter and the uncertainty decreases with decreasing clustermetallicity, and below [Fe/H]= − Table 7
Averages of PopulationsCluster Pop. a N b R c [Fe/H] [C/Fe] [N/Fe] [O/Fe] [Mg/Fe] [Al/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]M15 1 10 0.43 -2.31 -0.49 0.78 0.64 0.20 -0.19 0.31 0.08 0.112 13 0.57 -2.26 -0.33 1.11 0.43 0.04 0.75 0.53 0.24 0.17M92 1 14 0.30 -2.23 -0.42 0.89 0.67 0.33 -0.23 0.41 0.08 0.092 33 0.70 -2.23 -0.38 1.03 0.40 0.05 0.70 0.47 0.11 0.09M53 1 8 0.50 -1.96 -0.43 0.91 0.59 0.38 -0.11 0.42 0.23 0.242 8 0.50 -1.95 -0.54 1.13 0.55 0.25 0.84 0.41 0.23 0.31N5466 1 6 · · · -1.83 -0.56 0.84 0.64 0.15 -0.42 0.28 0.14 0.292 2 · · · -1.79 -0.56 0.86 0.62 0.11 0.31 0.30 -0.16 · · · M13 1 32 0.40 -1.50 -0.44 0.83 0.56 0.21 0.04 0.38 0.24 0.182 49 0.60 -1.49 -0.58 0.92 0.12 0.09 0.99 0.40 0.28 0.21M2 1 7 0.39 -1.46 -0.45 0.75 0.56 0.30 -0.10 0.35 0.19 0.262 11 0.61 -1.50 -0.49 1.01 0.30 0.24 0.79 0.35 0.27 0.27M3 1 39 0.66 -1.40 -0.42 0.59 0.53 0.18 -0.08 0.30 0.13 0.112 20 0.34 -1.38 -0.54 0.86 0.16 0.10 0.79 0.29 0.10 0.12M5 1 60 0.49 -1.24 -0.41 0.62 0.41 0.24 0.06 0.34 0.20 0.242 62 0.51 -1.24 -0.50 0.87 0.16 0.21 0.64 0.35 0.20 0.28M107 d · · · -1.04 -0.16 0.47 0.38 0.36 0.51 0.50 0.21 0.122 6 · · · -1.00 -0.25 0.92 0.29 0.37 0.53 0.45 0.22 0.16M71 d · · · -0.72 0.00 0.57 0.53 0.46 0.44 0.41 0.24 0.382 4 · · · -0.69 -0.17 1.16 0.49 0.44 0.53 0.38 0.21 0.45 a Population 1 is denoted by red, while population 2 is denoted by blue in Figures 8 − b N: the number of stars in each population. c R: the ratio of number of stars in a population and the overall number of stars analysed. d Populations are found using N instead of Al. ties, suggesting that the O-Na anticorrelation is not asextended as in the rest of the clusters. A clear spreadis visible in M5, M3, M2, M13, M15 and M92, whilein M53 the O abundances are constant and the scatteris significantly smaller than what is expected from theuncertainties.The effects of the Mg-Al cycle are very noticeable forall clusters except M71 and M107 (Figure 8, second pan-els from the bottom). The scatter in Mg abundance inthose clusters is close to the estimated uncertainties af-ter taking the linear correlations with T eff into account(Figure 5). In other clusters the scatter of [Mg/Fe] alsoclosely follows the uncertainties, except for M15 and M92where the most Mg poor stars can be found. We see noAl enrichment in M107 and M71; however, as the aver-age metallicity decreases, the amount of internal scatterrapidly starts to deviate from the error, and we see a largespread in Al in all other GCs. A more detailed analysisof the Mg-Al anticorrelations and Al populations can befound in Section 6.2 and 6.3.Based on the examination of the spread of N andAl abundances, we conclude that all clusters possessmultiple stellar populations either based on N or Al,or both. We examine these populations in more de-tail in the next section. The derived α − element abun-dances are also fairly constant in all globular clusterspresented here, similar to what is reported in the litera-ture (Gratton et al. 2004). MULTIPLE POPULATIONS
Most light elements show star-to-star variations in allGCs. These large variations are generally interpreted asthe result of chemical feedback from an earlier generationof stars (Gratton et al. 2001; Cohen et al. 2002), ratherthan inhomogeneities in the original stellar cloud thesestars formed from. Thus, the current scenario of GC evo-lution generally assumes that more than one populationof stars were formed in each cluster. The first generation of GC stars formed from gas that had been enriched bysupernovae in the very early Universe, while the secondformed by combining gas from the original star-formingcloud with ejecta from the first-generation stars. Onlythe fraction of first-generation stars contribute to the pol-lution, and the time scale of the formation of these secondgeneration stars depend on the nature of polluters; it is acouple of hundred Myr in the case of intermediate-massAGB stars, but it is only a few Myr for fast rotatingmassive stars and massive binaries.These first-generation pollutors are thought tohave been fast rotating massive stars (Decressin et al.2007), or intermediate mass (M star > ⊙ )AGB stars (D’Ercole et al. 2008), or massive binaries(de Mink et al. 2009). Our data reveal the expectedsignatures of pollution from material enriched from thehot hydrogen burning cycles such as the CNO, NeNa,or MgAl cycles in all globular clusters in our sample.In this section we explore the various correlations be-tween these elements, and we discuss individual star for-mation, and/or pollution events suggested by separategroups found in the C-N and Mg-Al anticorrelations. Identifying Multiple Populations
To separate the various populations under study, wefollow an approach similar to that of Gratton et al.(2011), who used K -means clustering (Steinhaus 1956)to identify multiple populations in ω Cen. Here, we usethe extreme-deconvolution (XD) method of Bovy et al.(2011) to identify population groups and assign mem-bership. This method fits the distribution of a vectorquantity, here the elemental abundances, as a sum of K Gaussian populations, whose amplitudes, centers andcovariance matrices are left entirely free. The algorithmcan be applied to noisy or incomplete data, thus making Code available at http://github.com/jobovy/extreme-deconvolution . Table 8
Statistics of CorrelationsCluster ∆ a e∆ b σ c ∆ e∆ σ [Mg/Fe] [Mg/Fe] [Si/Fe] [Si/Fe]M15 0.16 0.037 4.3 0.22 0.055 4.0M92 0.28 0.029 9.7 0.06 0.038 1.6M53 0.13 0.035 3.7 0.01 0.055 < < < < a Difference of the average Mg and Si abundance of populations. b The estimated error of the difference. c Detection significance in σ . the best possible use of all available data. In the currentapplication, XD’s main advantage is the latter, since weare not able to measure abundances for all nine elementsin all stars in our sample. Similar to the K -means, thenumber K of populations to fit is an input to the algo-rithm; XD itself does not determine the optimal numberof components to fit the distribution.Briefly, the XD algorithm works by optimizing the like-lihood of the Gaussian mixture model of the data. Theoptimization proceeds by an iterative procedure consist-ing of repeated expectation (E) and maximization (M)steps. In the E step, each datum is probabilistically as-signed (a) membership in each population and (b) error-free values of each noisy or missing elemental abundance;in the M step, each Gaussian’s parameters are updatedusing its members’ mean abundances and covariance cal-culated from the error-free values obtained in the E step.These steps are repeated until the likelihood stops in-creasing to within a small tolerance. The algorithm isproven to increase the likelihood in each EM-step.We analyse each globular cluster in our sample us-ing this algorithm, with the [Mg/Fe],[Al/Fe], [Si/Fe],[Ca/Fe], [Ti/Fe] abundances as well as only [Mg/Fe] and[Al/Fe]. We find that the two separate analyses providenearly identical results, indicating that Si, Ca, and Ti donot drive the populations. For M71 and M107 we used[N/Fe] instead of [Al/Fe], because Al does not show anyspread in these two clusters. We run XD using uncertain-ties given by the ‘Final combined errors ′ section in Table4, and also without any uncertainties, and found thatthe two different runs produce identical results. We in-clude missing abundance measurements by using a largeuncertainty for these measurements. Group membershipfor each star is determined using the best-fit Gaussianmixture by calculating the posterior probability for eachstar to be a member of each population based on its ele-mental abundances and their uncertainties; stars are thenassigned to the population for which this probability isthe largest. These membership assignments are typicallyunambiguous (probabilities &
99 % in most cases), withonly a few cases for which the maximum probability isbelow 90 %. The abundance averages of populations arelisted in Table 7. In the next few subsections we discussthe results from the population fitting in more detail foreach individual cluster.
The Mg-Al anticorrelation
In order for the Mg-Al cycle to operate, hightemperatures above 70 million Kelvin are required(Charbonnel & Prantzos 2006). Because current clus-ter main-sequence stars are unable to reach these tem-peratures, the high [Al/Fe] abundances we see in someglobular cluster stars imply that a previous generationof higher-mass or evolved stars must have contributed totheir chemical composition.Figure 9 shows [Mg/Fe] versus [Al/Fe] for all ten clus-ters in our study. The two XD populations are plotted inred and blue, and a representative error bar is included inthe top right corner of each panel. As noted previously,stars in M107 and M71 do not show a strong Mg-Al an-ticorrelation, and their XD population assignments arebased on N abundances. The light blue points in thepanels for M107 and M71 are stars that are warmer than4500 K, and thus have no CNO measurements.The extended distribution of Mg and Al abundancesapparent in Figure 9 is typical for globular clusters, and itshows the influence of the Mg-Al fusion cycle, which con-verts Mg into Al. However, there is a variety in the struc-ture of this relationship that has not been thoroughly ex-plored before: in some clusters (M92, M53, NGC 5466,M2 and M3), there are two distinct abundance groupswith a gap, while in other clusters (M15, M13 and M5)there is no gap. This result strongly suggests that thereis diversity in the process of stellar chemical feedback andstar formation in globular clusters, which may relate tothe larger environment in which they formed.To date, the largest homogeneous study of Mg and Alabundances was carried out by Carretta et al. (2009a).We have several clusters in common, M15, M5, M107 andM71 which enables a direct comparison. M107 and M71do not show any anticorrelation in either of the stud-ies. Carretta et al. (2009a) only have upper limits forAl and Mg in M15, while we were able to make directmeasurements, but even with upper limits the two stud-ies show similar anticorrelations with largest spreads inboth Al and Mg from the whole sample of clusters. Thelargest difference between the two studies can be seen incase of M5, where our values span a range of − − σ detection iseach difference. We find that in M15 (4.3 σ ), M92 (9.7 σ ),M13 (8.6 σ ), and M3 (7.3 σ ) the differences are statis-tically significant and the Mg-Al anticorrelation exists.Two clusters, M53 (3.7 σ ) and M5 (3.8 σ ), also show large σ detections, however, we would like to use a more con-servative approach to the detection of anticorrelationsout of a concern that our errors may be underestimated,given the degeneracies between stellar parameters andabundances in our analysis. M2 stands out as having nostatistically significant Mg-Al anticorrelation.The summed abundance A(Mg+Al) is expected to be7 Mg-Al anti-correlations, T eff < 5400K [ A l / F e ] M15, N7078 M92, N6341 NGC 5466M53, N5024 M13, N620501 -0.5 0 0.5 [ A l / F e ] [Mg/Fe]M2, N7089 -0.5 0 0.5[Mg/Fe]M3, N5272 -0.5 0 0.5[Mg/Fe]M5, N5904 -0.5 0 0.5[Mg/Fe]M107, N6171 -0.5 0 0.5[Mg/Fe]M71, N6838 Figure 9.
Mg-Al anticorrelations. Colors mark the populations found with the XD code, first population is denoted by red, and thesecond-generation denoted by blue points. Because [N/Fe] was used to identify populations in M107 and M71, not all stars could becatalogued, these are denoted by light blue. The same colors denote the same stellar groupings in Figures 9-13.
A(Mg+Al) as a function of T eff A ( M g + A l ) M15, N7078 M92, N6341 NGC 5466M53, N5024 M13, N62055.06.07.0 40005000 A ( M g + A l ) T eff M2, N7089 40005000T eff
M3, N5272 40005000T eff
M5, N5904 40005000T eff
M107, N6171 40005000T eff
M71, N6838
Figure 10.
The combined abundance of A(Mg+Al) as a functionof effective temperature. constant as a function of T eff when material is completelyprocessed through the Mg-Al cycle, and that is what ourresults show in Figure 10. The only exception is M107,but the slight correlation is due Mg correlating with tem-perature (see Figure 5), and this trend was not removedhere.Al is expected to correlate with elements enhanced byproton-capture reactions (N, Na; Figure 11) and anti-correlate with those depleted in H-burning at high tem-perature (O, Mg; Figure 11). The Al-O anticorrelationsand Mg-O correlations can be clearly seen in our data in Figure 11 for all clusters except M53, M107 and M71.The small number of stars observed in NGC 5466 doesnot allow us to investigate the correlations in that clus-ter in detail. However, the slight correlation of Al withSi that can be seen in M15 in Fig. 11 is the evidence of Si leaking from the Mg-Al cycle, which is an intriguingresult. Si participating in the light-element abundancepattern was first reported in NGC 6752 by Yong et al.(2005). Since then, Carretta et al. (2009a) have alsofound Si enhancement correlated with Al in NGC 2808.Those authors’ interpretation was that it is only in low-metallilcity clusters, where the AGB stars burn slightlyhotter, or in high-mass clusters, where the chemical en-richment is more efficient, that a Si enhancement will beobserved in second-generation GC stars. The differencein Si abundance between the two XD-identified popu-lations, listed in in Table 8, is significant relative to theerror on that measurement. The Si-Al correlation in M15is also accompanied by a Si-Mg anticorrelation (Figure11), which is further evidence of Si being produced byhot bottom burning in AGB stars (Karakas & Lattanzio2003).
The spread of Al abundances
The spread of Al abundances (Figure 8) also increasessignificantly below [Fe/H]= − −
70 million K, play anincreasingly larger role in more metal-poor cluster. Thisbehaviour of Al abundances was previously observed by8
Si and O (anti-)correlations [ A l / F e ] M15N7078 M92N6341 NGC 5466 M53N5024 M13N6205 [ A l / F e ] M2N7089 M3N5272 M5, N5904 M107, N6171 M71, N6838 [ N / F e ] M15, N7078 M92, N6341 NGC 5466 M53, N5024 M13, N6205 [ N / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ M g / F e ] M15, N7078 M92, N6341 NGC 5466 M53, N5024 M13, N6205
01 0 1 [ M g / F e ] [Si/Fe] M2, N7089
M3, N5272
M5, N5904
M107, N6171
M71, N6838 [ A l / F e ] M15, N7078 M92, N6341 NGC 5466 M53, N5024 M13, N6205 [ A l / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ N / F e ] M15, N7078 M92, N6341 NGC 5466 M53, N5024 M13, N6205 [ N / F e ] M2, N7089 M3, N5272 M5, N5904 M107, N6171 M71, N6838 [ M g / F e ] M15, N7078 M92, N6341 NGC 5466 M53, N5024 M13, N6205
01 0 1 [ M g / F e ] [O/Fe] M2, N7089
M3, N5272
M5, N5904
M107, N6171
M71, N6838
Figure 11.
Si and O (anti)correlations with Al, N, and Mg. For explanation of color coding, please see description of Figure 9.
Carretta et al. (2009a), but the larger range of Al valuespresented in this paper make this correlation clearer.Theoretical AGB nucleosynthesis modeling indeed pre- dict this behavior (Ventura et al. 2001, 2013). The high-mass AGB stars reach higher temperatures at the bottomof the convective envelope; i.e., stronger HBB and ad-9
CN anti-correlations, T eff < 4520K [ N / F e ] M15, N7078 M92, N6341 NGC 5466M53, N5024 M13, N6205 ***01 -1 0 [ N / F e ] [C/Fe]M2, N7089 *** -1 0[C/Fe]M3, N5272 *** -1 0[C/Fe]M5, N5904 *** -1 0[C/Fe]M107, N6171 -1 0[C/Fe]M71, N6838 Figure 12.
CN anticorrelations. Correlations of [C/Fe] with temperature associated with deep mixing were removed in clusters markedby ***. Upper limits are denoted by open triangles. vanced (Mg-Al) nucleosynthesis occurs with decreasingmetallicity. We are seeing very advanced Mg-Al nucle-osynthesis in the most metal poor clusters such as M15and M92, while the most metal-rich clusters like M107and M71 do not show this, as theoretically expected, ifthe high-mass AGB stars are the polluters. Also, this iscorroborated by the Al-O anticorrelation; the most Al-rich stars are O-poor showing the effects of very stronghot bottom burning (HBB), because HBB proceeds com-pletely and destroys O.An other related issue is that HBB is activated forlower masses with decreasing metallicity. High-mass andvery low-metallicity AGB stars don not exists in GCs to-day due to their extremely short lifetimes, but this trendseems to be confirmed both theoretically (Ventura et al.2001, 2013) and observationally at least for solar metal-licities down to that of the Magellanic Clouds. Fromthe observational point of view, we know that high-massAGB stars in the Small Magellanic Cloud ([Fe/H]= − > ⊙ ) lowerthan their solar metallicity counterparts (M > ⊙ )(Garc´ıa-Hern´andez et al. 2006, 2009). Thus, at the low-est metallicities in M15 and M92 we also would expectmore HBB AGB stars (i.e., with several degrees of HBBand Mg-Al nucleosynthesis), because the minimum stel-lar mass to activate the HBB process (and advanced Mg-Al nucleosynthesis) decreases with decreasing metallicity.Thus, we conclude that more polluted material would bepresent at the lowest metallicities.Because of these reasons, we believe that our results support and add some evidence to the high-mass AGBsas GCs polluters. C-N
Carbon, nitrogen and sometimes oxygen are influencedby two independent processes in GC giants: a primordialanticorrelation, with the same first-generation sources asthe O-Na and Mg-Al patterns; and also stellar evolution,driven by circulation between the hydrogen-burning shelland the surface (Sweigart & Mengel 1979; Angelou et al.2012). As discussed in the previous section, we see largestar-to-star variations in N abundance in all clusters;however, our inability to measure C abundances below[Fe/H]=-1.7 dex leads us to only having upper limits,and therefore we restrict the discussion of C-N anticor-relations to the more metal-rich clusters.Figure 12 shows [N/Fe] versus [C/Fe] for all clusters.Deep mixing has to be taken into account when dis-cussing the CN anticorrelations, so in M13, M2, M3, andM5, where we see deep mixing clearly, the correlation of[C/Fe] with T eff was removed. Because deep mixing isnot visible in M107 and M71, we used the original values.A clear anticorrelation cannot be seen in any of the clus-ters. While M107 and M71 show weak anticorrelations,neither of these is statistically significant. The anticorre-lation itself may be obscured by the relatively large errorsfor [C/Fe] and [N/Fe]. As mentioned in Section 5.1, wesee correlations of [C/Fe] with temperature in M13, M3,M2, and M5, but these are not accompanied by increas-ing [N/Fe] at the same time. We believe that this is due0 A(C+N+O) as a function of T eff and [Al/Fe] A ( C + N + O ) M15, N7078 M92, N6341 NGC 5466M53, N5024 M13, N6205 A ( C + N + O ) T eff M2, N7089 eff
M3, N5272 eff
M5, N5904 eff
M107, N6171 eff
M71, N6838 A ( C + N + O ) M15, N7078 M92, N6341 NGC 5466M53, N5024 M13, N6205 A ( C + N + O ) [Al/H] M2, N7089 -2 -1 0[Al/H]
M3, N5272 -2 -1 0[Al/H]
M5, N5904 -2 -1 0[Al/H]
M107, N6171 -2 -1 0[Al/H]
M71, N6838
Figure 13.
Upper panels: The sum of C, N and O as a function ofeffective temperature. Upper limits are denoted by open triangles.For explanation of color coding, please see description of Figure8. Lower panels: The sum of C, N and O as a function of [Al/H].A clear correlation is visible in M13, M2, M3, and M5, for morediscussion see Section 6.4. to our inability to measure C and N accurately: most ofour abundance determinations are upper limits or closeto them. If the anticorrelations exist, they must spanranges smaller than our uncertainties, which are alwayshigher than 0.14 dex in [C/Fe] and 0.12 dex in [N/Fe].It is interesting to note that in M3, M107 and M71 thereis a clear CN weak and CN strong group of stars, whilein all more metal poor clusters, N abundances fill out abroad distribution.
C+N+O
We have C, N, and O abundances available for alarge number of stars, thus we are able to investi-gate the C+N+O content in each cluster in detail.Studies from the literature showed that the C+N+Ocontent in globular clusters are fairly constant towithin 0.3 dex (Ivans et al. 1999; Carretta et al. 2005;Smith et al. 1996), except for N1851 where Yong et al.(2009) find a spread of 0.57 dex. According to Yong et al.(2009) the large spread in C+N+O in N1851 is probablyattributed to larger than usual pollution from lower massAGB stars than in other clusters, but these results werequestioned by Villanova et al. (2010) as they did not seespread of C+N+O larger than 0.3 dex. We also see near constant C+N+O in our sample,which is consistent with the material in these stars havingundergone CNO cycling in the first-generation of stars inthe RGB phase. In Figure 13 we show A(C+N+O) as afunction of T eff . The spread is significantly larger thanwhat is reported in literature, between 0.4 and 0.6 dexfor M13, M2, M3, and M5. The spread in these clustersis at the level of what has been found in N1851, but wethink this is mostly associated with large uncertainties of[N/Fe] measurements. We do not find clear separation inthe amount of A(C+N+O) between the two populationsfound in any of the clusters.As previously mentioned, there are currently two lead-ing models to explain the nature of the polluters: thefirst assumes that intermediate-mass AGB stars that arethermally pulsing and undergoing hot bottom burningexpel material to the intra-cluster medium by strongmass loss (Ventura et al. 2001), while the second as-sumes that the pollution comes from hot, fast rotat-ing stars (Decressin et al. 2007). According to the firsttheory, intermediate-mass HBB-AGB stars could pro-duce or not produce large C+N+O variations (see, e.g.,Yong et al. 2009, and references therein). This is becausethe C+N+O predictions (which basically depend onthe number of third dredge-up episodes) for these starsare extremely dependent on the theoretical modelling,the convective model and the mass loss prescriptionused (see, e.g., DAntona & Ventura 2008; Karakas et al.2012). A (C+N+O)-Al correlation is not clearly visiblein the lower panel of Figure 10.According to the first theory, AGB stars may explaina large spread in A(C+N+O) because they are expectedto produce a substantial increase in the C+N+O abun-dance as they enhance Na and Al and deplete O and Mg(Yong et al. 2009). This should result in a (C+N+O)-Al correlation, which is not clearly visible in the lowerpanel of Figure 13. Weak correlations in M107 and M71,and weak anticorrelations in M13 and M3 are visible, butthey are probably the result of large uncertainties in Cand N. More accurate measurements of [N/Fe] will helpto clarify the possible (C+N+O)-Al correlation. SUMMARY
We investigated the abundances of nine elements for428 stars in ten globular clusters using APOGEE DR10spectra. A homogeneous analysis of these GCs has notbeen accomplished previously, something that APOGEEis uniquely able to do because it can observe all the brightGCs in the northern hemisphere. A semi automated codecalled autosynth was developed to provide abundancesindependent of those derived by ASPCAP. Our main goalwas to examine the stellar populations in each clusterusing a homogeneous dataset. Based on our abundances,we find the following:1. From the examination of the star-to-star scatter in α − REFERENCESAhn, C. P., Alexandroff, R., Allende Prieto, C. et al. 2014, ApJS,211, 17Alam, S., Albareti, F. D., Allende Prieto, C. et al. 2015, arXiv,1501.00963Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53,197Angelou, G. C., Stancliffe, R. J., Church, R. P., Lattanzio, J. C.,& Smith, G. H. 2012, ApJ, 749, 128Asplund, M., Grevesse, N. & Sauval, A. J. 2005, ASPC, 336, 25Bastian, N., Lamers, H. J. G. L. M., de Mink, S. E., et al. 2013,MNRAS, 436, 2398Bergemann, M. & Nordlander, T. 2014, 2014arXiv1403.3088BBertelli, G., Girardi, L., Marigo, P., & Nasi, E. 2008, A&A, 484,815Bertelli, G., Nasi, E., Girardi, L., & Marigo, P. 2009, A&A, 508,355Borucki, W.J., Koch, D., Basri, G. et al. 2010, Science, 327, 977Bovy. J., Hogg, D. W., & Roweis, S. T. 2011, Ann. Appl. Stat., 5,1657Briley, M. M., Smith, V. V., King, J., & Lambert, D. L. 1997, AJ,113, 306Briley, M. M., Smith, V. V., Suntzeff, N. B., et al. 1996, Nature,383, 604Cassisi, S., Salaris, M., Pietrinferni, A. et al. 2008, ApJ, 672, L115Carretta, E., Gratton, R. G., Lucatello, S., Bragaglia, A., &Bonifacio, P. 2005, A&A, 433, 597Carretta, E., Bragaglia, A., Gratton, R., & Lucatello, S. 2009a,A&A, 505, 139Carretta, E., Bragaglia, A., Gratton, R. G., et al. 2009b, A&A,505, 117Carretta, E., Bragaglia, A., Gratton, R., D’Orazi, V., &Lucatello, S. 2009c, A&A, 508, 695Cavallo, R. M., & Nagar, N. M. 2000, AJ, 120, 1364Charbonnel, C., & Prantzos, N. 2006, arXiv: astro-ph/0606220Cohen, J. G., Briley, M. M., & Stetson, P. B. 2002, AJ, 123, 2525Cohen, J. G., & Mel´endez, J. 2005, AJ, 129, 303Decressin, T., Meynet, G., Charbonnel, C., Prantzos, N., &Ekstr¨om, S. 2007, A&A, 464, 1029DAntona, F., Bellazzini, M., Caloi, V. et al. 2005, ApJ, 631, 868DAntona, F. & Ventura, P. 2008, Messenger, 134, 18D’Ercole, A., Vesperini, E., D’Antona, F., McMillan, S. L. W., &Recchi, S. 2008, MNRAS, 391, 8252