Open Cluster Chemical Homogeneity Throughout the Milky Way
Vijith Jacob Poovelil, G. Zasowski, S. Hasselquist, A. Seth, John Donor, Rachael L. Beaton, K. Cunha, Peter M. Frinchaboy, D. A. García-Hernández, K. Hawkins, K. M. Kratter, Richard R. Lane, C. Nitschelm
DDraft version September 16, 2020
Typeset using L A TEX twocolumn style in AASTeX63
Open Cluster Chemical Homogeneity Throughout the Milky Way
Vijith Jacob Poovelil, G. Zasowski, S. Hasselquist,
2, 1
A. Seth, John Donor, Rachael L. Beaton, K. Cunha,
5, 6
Peter M. Frinchaboy, D. A. Garc´ıa-Hern´andez,
7, 8
K. Hawkins, K. M. Kratter,
5, 10
Richard R. Lane, and C. Nitschelm Department of Physics & Astronomy, University of Utah, Salt Lake City, UT, 84112, USA NSF Astronomy and Astrophysics Postdoctoral Fellow Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, 76129, USA Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA Steward Observatory, University of Arizona, Tucson, AZ, 85721, USA Observat´orio Nacional, 20921-400 So Crist´ovao, Rio de Janeiro, RJ, Brazil Instituto de Astrof´ısica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain Universidad de La Laguna (ULL), Departamento de Astrof´ısica, E-38206 La Laguna, Tenerife, Spain Department of Astronomy, The University of Texas at Austin, Austin, TX, 78712, USA Department of Astronomy, University of Arizona, Tucson, AZ, 85721, USA Instituto de Astronom´ıa y Ciencias Planetarias, Universidad de Atacama, Copayapu 485, Copiap´o, Chile Centro de Astronom´ıa (CITEVA), Universidad de Antofagasta, Avenida Angamos 601, Antofagasta 1270300, Chile
ABSTRACTThe chemical homogeneity of surviving stellar clusters contains important clues about interstellarmedium (ISM) mixing efficiency, star formation, and the enrichment history of the Galaxy. Existingmeasurements in a handful of open clusters suggest homogeneity in several elements at the 0.03 dexlevel. Here we present (i) a new cluster member catalog based only on APOGEE radial velocitiesand
Gaia -DR2 proper motions, (ii) improved abundance uncertainties for APOGEE cluster members,and (iii) the dependence of cluster homogeneity on Galactic and cluster properties, using abundancesof eight elements from the APOGEE survey for ten high-quality clusters. We find that cluster ho-mogeneity is uncorrelated with Galactocentric distance, | Z | , age, and metallicity. However, velocitydispersion, which is a proxy for cluster mass, is positively correlated with intrinsic scatter at relativelyhigh levels of significance for [Ca/Fe] and [Mg/Fe]. We also see a possible positive correlation at a lowlevel of significance for [Ni/Fe], [Si/Fe], [Al/Fe], and [Fe/H], while [Cr/Fe] and [Mn/Fe] are uncorre-lated. The elements that show a correlation with velocity dispersion are those that are predominantlyproduced by core-collapse supernovae (CCSNe). However, the small sample size and relatively lowcorrelation significance highlight the need for follow-up studies. If borne out by future studies, thesefindings would suggest a quantitative difference between the correlation lengths of elements producedpredominantly by Type Ia SNe versus CCSNe, which would have implications for Galactic chemicalevolution models and the feasibility of chemical tagging. INTRODUCTIONThe chemical composition of stars that we see todayis a consequence of a sequence of past enrichment eventsthat polluted the interstellar medium (ISM). Hence, bystudying stellar chemistry, we can learn how these eventscontributed to enrich the ISM and improve our under-standing about the evolution of the Galaxy over time.Open clusters (OC) are particularly interesting objectssince they consist of stars that were born together fromthe same initial molecular cloud, and hence are believedto be chemically homogeneous. Studying the chemistryof these objects can help us trace the ISM pollution ratesof different nucleosynthetic processes and ISM mixing ef- ficiency in different locations in the Galaxy. One mustalso rely on the assumption of chemical homogeneityof OCs to identify common birth sites using only thechemical signatures of stars, also called chemical tag-ging (Freeman & Bland-Hawthorn, 2002). Measuringthe level of homogeneity of OCs and understanding thefactors that can affect it is crucial for the feasibility ofchemical tagging.Cluster chemical homogeneity has been studied inmany globular clusters (GCs) and a few OCs. GCs areobserved to have inhomogeneities and anti-correlationsin most of the light elements (e.g., Carretta et al., 2010;Milone et al., 2018; M´esz´aros et al., 2020). Chromo-some maps show light element abundance scatter in GCs a r X i v : . [ a s t r o - ph . GA ] S e p Poovelil et al. with masses down to 10 M (cid:12) (Saracino et al., 2019).Heavy element abundance variations are also observed,but only in a small number of massive GCs (e.g., Grat-ton, 2020).The chemistry of OCs, on the other hand, has notbeen as widely explored, and questions remain regard-ing the level — or even presence of — intrinsic chemi-cal scatter. The Hyades is a well-studied cluster thathas been argued to be chemically homogeneous (DeSilva et al., 2006, 2011), although other recent workon the same cluster identified abundance variations ofaround 0.02 dex (Liu et al., 2016b). M67, anotherwell-studied OC, was found to potentially be inhomo-geneous in certain elements from the analysis of twosolar twins in the cluster by Liu et al. (2016a). How-ever, Bovy (2016) showed that the scatter of several el-emental abundances relative to hydrogen within M67,NGC 6819, and NGC 2420 is as low as 0.03 dex, usingAPOGEE spectra. De Silva et al. (2007) demonstratedchemical homogeneity to the 0.05 dex level in seven ele-ments using twelve red giants in the OC Collinder 261,and Bertran de Lis et al. (2016) calculated a scatter of[O/Fe] of (cid:46) M (cid:12) , and a significant fraction ofthose up to 10 M (cid:12) , are expected to be homogeneous.However, large star-forming clouds that form more mas-sive clusters, may be subject to pollution from massivestars that become supernovae before star formation iscomplete. For example, the Sun is suggested to haveformed in a cluster with a high-mass star that becamea supernova while the Sun was still a protostar (Looneyet al., 2006).The many possible mechanisms described above thatinduce abundance scatter within OCs imply that thelevel of scatter may depend on properties like the nu-cleosynthetic groups of elements, range of evolutionarystate, cluster size, cluster mass, etc. Any systematic dif-ference between the levels of homogeneity for differentmetals (e.g., between alpha elements and iron-peak el-ements) may indicate how different enrichment eventscan affect ISM mixing efficiency.Although a few well-studied OCs have been shown tobe chemically homogeneous within the observational un-certainties of large scale surveys, there has not been asurvey that has looked at a large number of clusters andsystematically studied how their chemical homogeneitydepends on various Galactic and cluster properties. Sothen it is necessary to look at these properties to seek outsubtle patterns or behavior that can distinguish amongmechanisms. This paper describes the first such system-atic study of OC chemical homogeneity as a function ofGalactic and cluster parameters such as Galactocentricdistance ( R GC ), vertical height ( | Z | ), age, and mass.The paper is organised as follows: § § § § § § § § § § §
4, we describehow we quantify cluster chemical homogeneity, and § § DATA2.1.
APOGEE
We adopted stellar parameters, chemical abundances,and radial velocities (RVs) from the Apache Point Ob-servatory Galactic Evolution Experiment (APOGEE;Majewski et al., 2017). APOGEE, one of the componentsurveys of the Sloan Digital Sky Survey IV (SDSS-IV;Blanton et al., 2017), is a high resolution, near-infraredspectroscopic survey of ∼ §
3) isbased solely on kinematic properties, initially we onlyrequire reliable kinematical measurements: RVs (dis-cussed here) and PMs ( § § § < − . We also remove a small num-ber of stars with implausibly large velocities by requiring | VHELIO AVG | < − . To remove potential binaries from our sample, whichmay inflate the characteristic velocity signatures in-ferred for our clusters, we remove stars with visit-to-visitRV variations (VSCATTER) > − (Price-Whelanet al., 2020; Badenes et al., 2018) and stars found inthe binary catalog of Price-Whelan et al. (2020). Giventhat the time baseline for the majority of APOGEEsources is less than a year, APOGEE is sensitive to de-tect binaries with periods less than a few years and sep-arated by distances less than a few AU (Price-Whelanet al., 2020). We note that since the VSCATTER limitthat we impose is more sensitive to massive binaries,which tend to be more centrally concentrated, and thatbinary properties are correlated with metallicity (e.g.,Moe et al., 2019; Badenes et al., 2018), it is conceiv-able that these binary rejection cuts could induce somemetallicity-dependent spatial sampling patterns. Weconfirmed that this is not the case in our sample be-cause this limit removes a tiny fraction of stars ( < Re-derived Abundance Uncertainties
Motivation and outline
Earlier studies have highlighted the possibility thatthe uncertainties for some of the APOGEE abundancesin earlier data releases are overestimated (e.g., Nesset al., 2018), and our own preliminary analyses of theabundance dispersions in our clusters supported this as-sessment. Prior to DR16, uncertainties on the abun-dances in the APOGEE data releases were determinedby examining the spread of abundances in well-sampledclusters (Holtzman et al., 2018), which required assum-ing that the cluster had no intrinsic spread. This as-sumption makes the uncertainties unsuitable for thestudy of chemical homogeneity.To address this, we recalculate the random abun-dance uncertainties for the stars in our analysis usingan improved method . We worked closely with theAPOGEE team to subsequently adapt our approachinto the DR16 uncertainty determination. The ap-proach used in DR16 (J¨onsson et al., 2020) relies ona parametric fit to calculate the uncertainties for all theAPOGEE stars. In this paper, however, we adopt a non- We emphasize that this empirical procedure for determiningthe uncertainties in the abundances accounts only for the randomcomponent of the uncertainties, which is essential for deriving theintrinsic abundance scatter in a cluster. Any systematic compo-nents, such as stellar parameter-dependent abundance variationsdue to departures from LTE or hydrostatic equilibrium, or sys-tematics in the atomic data or instrumental distortions, are notcaptured by this procedure.
Poovelil et al. parametric approach because we find that a simple an-alytic function cannot adequately capture the relation-ships between uncertainty and SNR, T eff , and [M/H].In brief, we use the differences in [X/Fe] values de-rived by ASPCAP for independent spectra of the samestar to compute a relationship between the abundanceuncertainties and SNR, T eff , and [M/H] ( § § Calculating uncertainties using multiple visits
In general, the ASPCAP pipeline is run on the stackedspectrum of each star, which comprises all visits to thatstar. For a subset of APOGEE stars, however, ASP-CAP is run on the individual visit-level spectra, provid-ing multiple independent sets of stellar parameter andabundance measurements for single stars . We use thesesets to estimate the random uncertainty of the ASPCAPmeasurements as a function of SNR, T eff , and [M/H].The variations between ASPCAP values for spectra ofthe same star, at the same SNR, provides a more real-istic representation of the random measurement uncer-tainties than the ones derived from cluster dispersionsin earlier APOGEE DRs.We define a sample of stars, hereafter called the Uncer-tainty Training (UT) sample, with ASPCAP solutionsderived from two or more visit spectra with similar SNR(∆SNR/SNR ≤ T eff ≤
100 K) and metallicity (∆[M / H] ≤ .
07 dex)values. These similarity criteria are imposed to en-sure that differences in [X/Fe] are not due to differentglobal spectral fits. We restrict our analysis to giantstars (using the ASPCAP CLASS column and a limit oflog g < > ≈ T eff –[M/H],within these fixed SNR ranges, to ensure both reliablemeasurements of the uncertainties in less populated re-gions of the parameter space, and high resolution mea- These measurements are contained in the “allCal” file as partof APOGEE’s data releases. surements where possible. The python package vorbin (Cappellari & Copin, 2003) is used to group the UT sam-ple into 2D bins of T eff and [M/H], targeting at least 30stars per bin. The final bins are populated with betweennine and 69 stars per bin, with an average of around 33.The differences between pairs of visit-level [X/Fe] val-ues for individual stars can be used to compute thestandard deviation of the distribution from which thepairs were originally drawn. We assume this distributionto represent the intrinsic ASPCAP random uncertainty.The quantities are related bye [X / Fe] , k = √ π | [X / Fe] i − [X / Fe] j | ) , (1)where e [X / Fe] , k is the abundance uncertainty associatedwith the k th bin of T eff and [M/H] at a given SNR, and[X / Fe] i and [X / Fe] j refer to abundance measurementsderived from two independent visit spectra of the samestar. The top row of Figure 1 shows the distributionof UT stars in [M/H] and T eff , in bins of SNR, coloredby the e [Mg / Fe] , k values. This demonstrates the complexpattern of e [Mg / Fe] , k derived in this way and the diffi-culty of describing such behavior with simple analyticalexpressions. Similar figures for all elements we analyzein § e [X / Fe] , k on[X/Fe] itself — e.g., that stars with enhanced [Mg/Fe]may have different uncertainties than stars with solar[Mg/Fe] at the same T eff , [M/H], and SNR — by de-riving e [X / Fe] , k in the same manner as above, but sepa-rately for stars with high and low [Mg/Fe]. We found nosignificant differences in the e [X / Fe] , k ( T eff , [M/H], SNR)patterns. We also found no difference in the results dis-cussed in § Assigning uncertainties to stars
Given the computed array of e [X / Fe] , k for each bin of T eff , [M/H], and SNR, we can then sort any other starinto a bin and assign it e [X / Fe] , k values. We perform thissorting by training a Gaussian Naive Bayes classifier al-gorithm (Pedregosa et al., 2011) on the UT sample, andthen applying the trained classifier to our cluster mem-ber sample ( § e [ X/F e ] = (cid:88) k p k e [ X/F e ] ,k , (2)where k is the bin index, p k is the probability of bin k forthis star, and e [X / Fe] is the final uncertainty for the star.Adopting this weighted average uncertainty ensures thatall stars falling within a range of stellar parameters willnot be assigned identical values for their abundance un-certainties due solely to the binning scheme. This ap-proach also smooths the transitions between the binedges. Ultimately, the uncertainties assigned to a starwith stellar parameters near a bin edge are not drivenby the distribution of the bins, but by the uncertain-ties estimated from the UT sample that fall within aneighboring area of the star in [M/H] and T eff .The bottom 3 rows of Figure 1 show examples ofthese rederived uncertainties for [Mg/Fe], [Ni/Fe], and[Na/Fe] (note the differences in color scaling) along[M/H] and T eff , in bins of SNR. All show the ex-pected improvement in precision with higher SNR.Other generic patterns are also clearly visible — for ex-ample, the increase in uncertainty at low metallicitiesand/or high temperatures, where lines become weaker,and at very low temperatures, where lines become in-creasingly blended. Mg and Ni have lower uncertaintiescompared to Na, which is expected due to the difficultyin measuring Na lines in APOGEE. Each element alsohas its own unique patterns, reflecting the range of diffi-culty in measuring lines of different elements in differentparts of stellar parameter space.The DR16 uncertainties are not systematically higheror lower than the uncertainties derived here for stars inour cluster sample ( § § Proper Motions
For the cluster membership selection in §
3, we useproper motions (PMs) from DR2 of the
Gaia mission(Gaia Collaboration et al., 2018). We require that theerrors in the proper motion measurements be smallerthan 2.0 mas yr − and the renormalized unit weighterror (RUWE) be less than 1.4 (Ziegler et al., 2020).In addition, cluster-specific limits are imposed on thespatial distribution, magnitude, and color of the stars,as described in § Stellar Distances
For our analysis in §
5, we use spectrophotomet-ric distances calculated using the method described inRojas-Arriagada et al. (2017, RA17). We also use theStarHorse (Queiroz et al., 2018, 2019) and astroNN (Le-ung & Bovy, 2019) distances to compare with our RA17estimates. The results of this paper are not affectedby the choice of the distance catalog used to determinecluster distances. Further discussion can be found in § Literature Cluster Parameters
We adopt the Milky Way Star Clusters catalog(Kharchenko et al., 2013, hereafter K13) as the basecatalog for our membership search §
3. We use K13 clus-ter center coordinates and angular radii to define thesearch limits, and we consider the cataloged distances,ages, and metallicities (in conjuntion with APOGEE-derived values) when assessing our membership selec-tion. From the total sample of 3208 clusters in K13,we only consider the 366 clusters that have six or moreAPOGEE stars ( § § § CLUSTER MEMBERSHIPThe first step of our open cluster analysis is to iden-tify cluster members in the APOGEE sample. Numer-ous methods have been demonstrated in the literature,typically adopting some combination of RVs, propermotions, metallicities, and position in the CMD (e.g.,Frinchaboy & Majewski, 2008; M´esz´aros et al., 2013;Donor et al., 2018). As we are interested in the chemi-cal homogeneity of the clusters, we design our member-ship selection around kinematical information only: RVsfrom APOGEE ( § Gaia -DR2 ( § Gaia -DR2 information only.Figure 2 shows the distribution of the
Gaia -DR2 G -band magnitude of stars with (blue) and without(red) Gaia/RVS data, compared to the APOGEE stars(green) in the vicinity of several of our cluster candi-dates. This figure highlights why APOGEE RVs arenecessary for the objects in our sample; due to a combi-nation of distance and extinction, most of our stars aretoo faint to have Gaia -DR2 RVS radial velocities.3.1.
Method
Figures 3–5 demonstrate the procedure described be-low for a well-studied open cluster (NGC 6819), apoorly-studied cluster (FSR 0494), and a K13 clusternot recovered by our membership method (ASCC 116),respectively. 3.1.1.
Cluster Coordinates
For each cluster, we start our membership search withAPOGEE and
Gaia -DR2 stars within twice the clus-ter radius, 2 R cluster , using central coordinates and “to-tal” cluster radii (their r = R cluster ) from K13 ( § R cluster ) define the cluster’skinematical signature, and the “annulus stars” (between1.5–2 R cluster ) define the background distribution (e.g.,Figure 3a-b). We only consider the 366 K13 clusters that Poovelil et al.
Figure 1.
First row: the Uncertainty Training (UT) sample, divided by SNR and Voronoi-binned by T eff –[M/H], as describedin the text ( § e [X / Fe] for that bin; [Mg/Fe] is shown here as an example.Note that many adjacent bins have nearly identical e values and are indistinguishable in this representation. Second row:Weighted uncertainties for [Mg/Fe] of the cluster member sample ( § have six or more stars within 1 R cluster in the APOGEEcatalog that meet the quality criteria above.3.1.2. Radial Velocities
We search for RV peaks associated with co-movingstars in each cluster (e.g., Figure 3c) location by sub-tracting a kernel density estimate (KDE) of the annulusstellar RV distribution (shown in green) from that ofthe central stars (shown in blue). The residual (shown in red) is then fit with a Gaussian to determine the cen-tral RV ( (cid:104) RV (cid:105) ) and the width ( σ RV ) of the dominantpeak. We also measure the ratio of the Gaussian am-plitude ( A RV ) to the standard deviation of the residuals( σ resid ) more than 3 σ RV away from the Gaussian cen-ter; this metric quantifies the strength of the RV signal.Visual inspection demonstrates that for our clusters, an A RV /σ resid > . Figure 2.
Gaia -DR2 G -band magnitude of stars with(blue) and without (red) Gaia /RVS data (normalized sepa-rately), compared to the APOGEE stars (green) belongingto our clusters. Since
Gaia -DR2 only has RVs for stars with G (cid:46)
13, and most of our clusters have RGB stars fainter thanthis, we do not use
Gaia /RVS for the RVs in our selection.
Smaller values tend to be dominated by noisy residualsdriven by a low number of annulus stars.3.1.3.
Proper Motions
We obtain proper motion information for all starswithin 2 R cluster using the Gaia
TAP+ query from theastroquery package in python and keep stars that passthe quality cuts mentioned in § Gaia -DR2 data sample hasthe same color-magnitude range as the APOGEE starsby matching to the ‘apogeeObject’ files used in theAPOGEE targeting pipeline, which contain the 2MASS(Skrutskie et al., 2006),
Spitzer –IRAC GLIMPSE (Ben-jamin et al., 2005; Churchwell et al., 2009), and AllWISE(Wright et al., 2010; Cutri et al., 2013) photometry usedto calculate extinction (Majewski et al., 2011; Zasowskiet al., 2013a; Zasowski et al., 2017). We then restrictthe
Gaia -DR2 stars to the same ( J − K s ) and H limitssampled by the APOGEE stars in the vicinity of thatcluster (generally ( J − K s ) ≥ . ≤ H < . Gaia -DR2 stars is an accurate represen-tation of the APOGEE stars that we are consideringfor membership. However, we compare the membershipwith and without using this cut for all the ten clus-ters studied in §
5. Although the PM distribution isaltered slightly, the final cluster members determinedare the same for these clusters irrespective of the color-magnitude cut.In a small fraction of cases (6%), the apogeeObjectfiles do not span the full background annulus region,but we have confirmed that the distributions of µ RA and µ Dec do not change across the small angular scalesof our clusters, so we consider even these partial annulito be representative of the background distributions.As with the RVs ( § µ RA × µ Dec ,shown in Figure 3d). Because the annular PM distribu-tion is much less noisy than in case of RV, we model theentire central PM distribution (shown in blue) as thesum of a 2D Gaussian and a scaled copy of the annularPM distribution (shown in green). The best-fit Gaus-sian (shown in red) center ( (cid:104) PM (cid:105) ) and 2D dispersion( σ PM (RA, DEC)) are taken as the PM distribution ofthe co-moving cluster stars.3.1.4. Computing Membership Probabilities
We first compute cluster membership probabilities,based on RVs and PMs, for each star within 2 R cluster ofa cluster. These probabilities are the values of Gaussiandistributions with the means and standard deviationsderived from the RV and PM fitting in § § σ window(shown in purple in Figures 3–5) on the combined RV–PM probability. We give equal weighting to each kine-matic dimension while calculating the combined prob-ability, since weighting each dimension on how distinctit is from the background did not yield any changes inthe final selected cluster members. We choose a selec-tion window of 2 σ on the combined probability for theanalysis in § Gaia -DR2 stars usedfor the PM background in gray points. The top row(panels a and b) show the on-sky distribution of stars,with the inner R cluster in a blue circle and the outerannulus enclosed in green circles at 1.5 and 2 R cluster .Panel a shows the stars used in characterizing the clus-ter ( § § § § Poovelil et al.
Figure 3 shows the recovery of the well-studied clusterNGC 6819 (e.g., Hole et al., 2009; Platais et al., 2013;Yang et al., 2013; Wu et al., 2014; Lee-Brown et al.,2015), Figure 4 shows the recovery of the less-studiedcluster FSR 0494 (Froebrich et al., 2007; Zasowski et al.,2013b; Donor et al., 2018), and Figure 5 shows the non-recovery of the cluster catalogued as ASCC 166 (e.g.,Kharchenko et al., 2005; Cantat-Gaudin et al., 2018).
Figure 3.
Proof-of-concept membership selection for NGC6819: APOGEE stars within annulus and central regionsare shown in green and blue, respectively, while final clustermembers are shown in purple. (a) and (b): Stellar distri-bution in RA and DEC. APOGEE and
Gaia -DR2 stars areshown as triangles and points, respectively. (c) and (d): Dis-tribution of RVs and PMs. Fits for the subtracted distribu-tions in RV and PM are shown in red. Diagnostic plots forfinal cluster members: (e) Color-magnitude diagram alongwith a Padova isochrone corresponding to the cluster; (f)Metallicity distribution of cluster stars as compared to an-nulus stars. See text for details.
Validation
Figure 4.
Same as Figure 3, but for FSR 0494, a lesserstudied OC.
In the membership selection examples in Figures 3–5, the left side of the bottom row (panel e) shows the( J − K s , H ) color–magnitude diagram of the clustermembers and background stars, along with a shiftedPARSEC isochrone (Bressan et al., 2012; Marigo et al.,2017) corresponding to the cluster’s distance, metallic-ity, and extinction, either known from K13 or approxi-mated from the cluster members themselves. The rightside of the bottom row (panel f) shows the APOGEEmetallicity distributions of the annulus stars (green) andthe kinematically-selected member stars (purple). Weuse these two pieces of data when setting reliability flagsfor clusters in the final catalog ( § Figure 5.
Same as Figure 3, but for ASCC 116, shownhere as an example of a cluster where the diagnostic plots donot confirm the presence of an OC. gories based on our confidence in the recovery of genuinecluster members: • GOOD: Clusters that have distinct kinematics( A RV /σ resid > . § • WARN: Clusters that have distinct kinematics( A RV /σ resid > . § • INSUFFICIENT DATA: Clusters that have dis-tinct kinematics ( A RV /σ resid > . § • UNRECOVERED: Clusters that do not have dis-tinct kinematics ( A RV /σ resid < . § §
5, weonly use clusters that have a “GOOD” validation flag.3.3.
Catalog
We generate two catalogs based on the kinematicmembership selection above. One contains all of thestars within 2 R cluster that meet the membership cri-teria described in § § § § R cluster , 34 are included with the GOOD flag,38 have WARN, 11 have INSUFFICIENT DATA, and283 are flagged as UNRECOVERED.Figure 6 summarizes several properties of the GOODclusters from our catalog. Figure 6a shows the clusters’Galactic R GC – Z distribution, and Figure 6b shows thedistribution of their mean [M/H] and log(age) values.In Figure 6c, we plot the distribution of mean [M/H]and [Mg/Fe] over a background of APOGEE stars withsimilar Galactic radius and height ( R GC = 5 −
15 kpcand | Z | < § §
5. Figure 6d shows a histogramof the number of cluster members identified, with the0
Poovelil et al. cutoff of nine members used in § − . ± .
016 dex kpc − for the sample,spanning R GC = 7 −
12 kpc and | Z GC | < − . ± .
005 and − . ± .
019 dex kpc − ;Donor et al., 2018; Jacobson et al., 2011).We also compared our membership with the C18 mem-bership for our GOOD clusters. Considering stars withAPOGEE observations, C18 has about 5% more mem-bers for each cluster than we do, but these stars typicallyhave RVs inconsistent with the peak of the cluster. Fora few clusters, we find additional members (about 4%of the total) that are not present in C18. These starsdo not have measured Gaia -DR2 parallaxes, and we be-lieve that this is the reason they have been excludedfrom C18. However, these additional members we finddo have measured RA17, StarHorse, and astroNN dis-tances ( § § QUANTIFYING CLUSTER HOMOGENEITYTo study the chemical homogeneity of the kinemati-cally identified cluster members in §
3, we need a robusthomogeneity metric that takes into account the mem-bers’ non-uniform abundance uncertainties ( § χ -like mea-surement of the distance between pairs of stars in an N -dimensional chemical space (Ness et al., 2018).We adopt a Maximum Likelihood Estimator (MLE)approach to determining the intrinsic abundance scatterof a group of stars, similar to the MLE in Kovalev et al.(2019). This choice is based on the speed and simplicityof the method, combined with its consistency with othertested metrics (see below).Given a distribution of abundances [X/Fe] with theircorresponding uncertainties, we can estimate the like-lihood that these values were drawn from a Gaussiandistribution centered at µ [X / Fe] with a standard devia-tion of σ [X / Fe] using: L ≡ n (cid:89) i =1 √ π ( σ / Fe] + e i ) / exp (cid:32) − ( x i − µ [X / Fe] ) σ / Fe] + e i ) (cid:33) , (3) where x i is the chemical abundance of a particular el-ement for a cluster member and e i is the correspond-ing abundance uncertainty. By finding where the max-imum of this function lies in the µ [X / Fe] − σ [X / Fe] planeshown in Figure 7, we can estimate the parameters ofthe Gaussian distribution from which these data pointsare drawn. Here, we are most interested in the valueof σ [X / Fe] , since it represents the intrinsic scatter of theabundances within the cluster. We estimate the asym-metric uncertainty in the value of σ [X / Fe] using the distri-bution of the likelihood function along the σ [X / Fe] axis.We take the first and third quartile ranges of this dis-tribution as the lower and upper uncertainty limits on σ [X / Fe] .We verified that this method can recover an input σ [X / Fe] value from mock abundances that have been per-turbed by uncertainties assigned from stars in several ofour clusters for a given element. During this test, we no-ticed the existence of a bias for the MLE estimator withrespect to the number of stars in each cluster – specif-ically, clusters with fewer stars (
N <
15) were system-atically estimated to have lower scatter than the actualvalue. We resolved this issue by fitting this bias with anexponential function and scaling the derived MLE scat-ter based on the number of members in each cluster.We looked at the distribution of individual stellarAPOGEE RVs versus abundances in clusters to ensurethat the calculated value of σ [X / Fe] was not being drivenby outlier stars in each dimension. We ensured thatthere was no evident trend between intrinsic scatterand dispersion of T eff or logg for the clusters that westudy. We verified for multiple clusters that the el-emental abundance distributions followed a Gaussiandistribution since this is an assumption intrinsic to theMLE method. We also studied how the σ [X / Fe] changedfor stars that belonged to different evolutionary stageswithin the same cluster.As a consistency check, we compared the MLE-based σ [X / Fe] to that estimated from other metrics. One othermetric we considered compares the cumulative distri-bution of pairwise distances in N -dimensional chemicalspace of simulated abundances with real cluster data.This metric is more computationally expensive than theMLE method but produces results that are entirely con-sistent. RESULTS5.1.
Final selection of elements and cluster members
We select elements for our analysis from the full setavailable in APOGEE using a variety of criteria. Someelements are known to have issues with accurate abun-dance determinations with ASPCAP, at least in certain1
APOGEE ID CLUSTER RA DEC NO SIGMAS RV NO SIGMA PM DIST CENTERdeg deg arcmin2M00000068+5710233 NGC 7789 0.0029 57.1732 37.79 24.49 33.992M00001199+6114138 NGC 7790 0.0500 61.2372 12.24 3.93 13.362M00001328+5725563 NGC 7789 0.0554 57.4323 8.70 5.09 47.912M00002012+5612368 NGC 7789 0.0839 56.2102 33.14 2.58 39.472M00002853+6119307 NGC 7790 0.1189 61.3252 5.35 1.33 16.94
Table 1.
Sample table of cluster members selected using our membership selection § Note —Table 1 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding itsform and content.Column DescriptionNAME Name of clusterCENTER RA Central right ascension [deg]CENTER DEC Central declination [deg]RADIUS Adopted cluster radius [arcmin]DISTANCE APOGEE Median RA17 spectrophotometric distance of cluster members [kpc] ( § [dex]LOG AGE ERR Uncertainty in log(age) of cluster [dex]M H Mean [M/H] of cluster members [dex] ( § § § § µ α of best-fit Gaussian to µ α × µ δ [mas/year] ( § µ δ of best-fit Gaussian to µ α × µ δ [mas/year] ( § µ α × µ δ [mas/year] ( § µ α × µ δ [mas/year] ( § µ α × µ δ ( § § § § § § § § Table 2.
Columns from the table of catalog clusters. From K13
Note —Table 2 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding itsform and content. Poovelil et al.
NAME DISTANCE APOGEE ± RV FIT MEAN ± PM FIT RA MEAN ± PM FIT DEC MEAN ± NUM MEMBERS M H ± MG FE ± DISTANCE DISP APOGEE RV FIT STD PM FIT RA STD PM FIT DEC STD M H DISP MG FE DISP kpc km s − mas yr − mas yr − dex dexNGC 1245 3.19 ± .
19 -29.18 ± .
79 0.55 ± .
57 -1.67 ± .
49 26 -0.080 ± .
025 -0.028 ± . ± .
18 -41.96 ± .
33 -2.32 ± .
54 -0.94 ± .
52 29 0.100 ± .
029 0.033 ± . ± .
19 92.09 ± .
01 -0.54 ± .
55 1.96 ± .
51 27 -0.282 ± .
096 0.014 ± . ± .
43 74.22 ± .
93 -1.15 ± .
50 -2.16 ± .
59 18 -0.201 ± .
067 0.004 ± . ± .
13 34.05 ± .
66 -10.98 ± .
55 -2.95 ± .
56 381 -0.007 ± .
058 0.004 ± . ± .
61 35.51 ± .
65 -2.31 ± .
29 -5.05 ± .
79 15 0.172 ± .
056 -0.058 ± . ± .
95 -47.05 ± .
39 -0.42 ± .
52 -2.27 ± .
51 59 0.346 ± .
050 0.099 ± . ± .
61 2.74 ± .
18 -2.93 ± .
54 -3.88 ± .
57 48 0.057 ± .
099 -0.008 ± . ± .
76 -54.77 ± .
12 -0.91 ± .
51 -1.95 ± .
53 25 -0.018 ± .
085 -0.017 ± . ± .
53 -31.89 ± .
68 -6.00 ± .
67 0.19 ± .
72 13 0.152 ± .
071 -0.038 ± . Table 3.
A subsample of columns from Table 2 for the ten clusters used in §
5. Shown are the mean cluster heliocentricdistances, metallicities, and [Mg/Fe] abundances, and the means of the Gaussian fits for each kinematic dimension, along withtheir standard deviations. ‘VDB 131’ is short for VDBERGH-HAGEN 131.
Figure 6. Summary of cluster catalog ( § Panel (a) shows the distribution in R GC and Z of clusters flagged asGOOD, using heliocentric distance estimates from the APOGEE member stars. Panel (b) shows the distribution of GOODclusters in [M/H] (from the APOGEE member stars) and log(age) (from K13). Panel (c) shows the distribution of GOODclusters in [M/H] and [Mg/Fe] (against a background of MW stars). Panel (d) shows the histogram of the number of clustermembers in the GOOD clusters. For the analysis in §
5, we only use clusters with at least nine members, shown by the verticaldashed line. Figure 7.
Example of the µ [X / Fe] − σ [X / Fe] plane of thelikelihood function (Eq. 3) used to determine the intrinsicscatter ( σ [X / Fe] ) for [Mg/Fe] in NGC 6791. ranges of stellar parameter relevant to our stars (e.g., S,K, Na, and Ti; Hawkins et al., 2016), and we discardthese. We also remove C, N, and O from further anal-ysis since the abundances of these elements are affectedby different stages of dredge-up over the course of theevolution of the star.We use the re-derived uncertainties ( § σ [X / Fe] )used in this section are derived from GOOD clusters( § § R cluster from the cluster center and that meetthe following APOGEE bitmask criteria: • BRIGHT NEIGHBOR and VERY BRIGHT NEIGHBOR== 0 (STARFLAG bits 2 and 3) • SUSPECT BROAD LINES==0 (STARFLAG bit17) • METALS BAD==0 (ASPCAPFLAG bit 19) • ALPHAFE BAD==0 (ASPCAPFLAG bit 20) • STAR BAD==0 (ASPCAPFLAG bit 23) We further restrict our sample to giant stars (using theASPCAP CLASS designation and a limit of log g < >
50. This log g limit is implemented to re-move stars whose abundances could potentially be af-fected by atomic diffusion (Souto et al., 2019; Semenovaet al., 2020). Finally, we remove stars that lie in rangesof T eff , [M/H], and SNR in which the distribution ofobserved visit-to-visit abundance variations ( § ∼ > § B. Note that most of the outliers in theMDFs of the clusters (panel f, shown in purple) fail topass the quality cuts mentioned above and so are notincluded in the analysis.5.2.
Cluster distances
We use stellar distances to compute median cluster he-liocentric distances, which are used to calculate Galac-tocentric distance ( R GC ), height above the midplane( | Z | ) ( § § § Gaia -DR2 parallax of the cluster members.The two exceptions are VDBERGH-HAGEN 131 andNGC 6705, where the four catalogs give median dis-tances that vary by a factor of ∼
2. VDBERGH-HAGEN 131 stands out as being the most heavilyreddened ( E ( J − K s ) ∼ . σ E ( J − K s ) ∼ . Gaia -DR2 parallax-based distance values.4
Poovelil et al.
So we adopt the RA17 distances for these two clusters,and for consistency for all of the clusters. We emphasizethat the results described below are independent of thecatalog used to calculate the distance.5.3.
Abundance scatter in clusters
We calculate the abundance scatter in ten OCs for 8elements (Mg, Al, Si, Ca, Fe, Si, Mn, and Ni) using themethod discussed in §
4. We measure non-zero intrin-sic scatter ( σ [X / Fe] ) in most cases. From Table 4, wesee that all clusters except NGC 2204, NGC 6791, andVDBERGH-HAGEN 131 have σ [Fe / H] very close to pre-viously determined limits for scatter in [Fe/H] (a rangeof 0.02 – 0.04 dex; Bovy, 2016; De Silva et al., 2007;Kovalev et al., 2019). Two of these three have σ [Fe / H] less than 0.05 dex, with the exception of VDBERGH-HAGEN 131, which is a lesser studied cluster with noprevious abundance determinations or abundance scat-ter studies performed.VDBERGH-HAGEN 131 also exceeds the limit (0.03dex) predicted by Bovy (2016) for σ [Al / Fe] . Althoughchemical abundances have been determined for some redgiants in NGC 2204 (e.g., Jacobson et al., 2011; Carlberget al., 2016), there have been no studies focused on itschemical homogeneity. We find σ [Mg / Fe] , σ [Al / Fe] , and σ [Si / Fe] in NGC 2204 to be higher than average literaturelimits ( ∼ σ [Mn / Fe] for NGC 6791 that is very high com-pared to the σ [Mn / Fe] values for the rest of our clusters.The σ [X / Fe] values for the other elements in NGC 6791fall within the limits quoted by Bovy (2016), except for σ [Al / Fe] (limit ∼ σ [Mn / Fe] is not a result ofnon-members with discrepant [M/H] measurements thatmay have been selected as members (e.g., σ [Fe / H] < . T eff at high [M/H]. We also find no systematicincrease in random uncertainties at higher [M/H] norany systematic shift in [Mn/Fe] abundances with T eff .We compared abundance scatter between elementsthat are observed to have a high abundance variationsin GCs and those that are not. Of the elements thatare included in our study, Mg, Al and in few cases Si are those that have confirmed observations of significantabundance scatter and anti-correlations in GCs (Grat-ton, 2020). As described above, the abundance scatterin Mg, Al, and Si for NGC 2204 stands out above theliterature limits for OCs. However, we do not observea selectively higher abundance scatter in these elementsfor any of our other OCs.5.4. Galactic position, age, and metallicity
We find that cluster abundance scatter is uncorrelatedwith Galactocentric distance and vertical height fromthe plane of the Milky Way for all the elements we con-sider. Figure 8a–b shows examples of the trend of clus-ter scatter in [Mg/Fe] with respect to Galactocentricdistance and vertical height, respectively.For ages we use values from the K13 catalog that havereported uncertainties in their age measurements (sevenout of the ten clusters). We find that cluster scatteris uncorrelated with cluster age. An example plot isshown for [Mg/Fe] in Figure 8c. We calculate the meanmetallicity ([M/H]) of each cluster, using its APOGEEmembers, and find that metallicity is uncorrelated withcluster scatter. An example plot is shown for [Mg/Fe]in Figure 8d.In Figure 8b, although we see a relatively higher cor-relation coefficient compared to the rest of the subplots,we do not believe that this shows the presence of a sig-nificant correlation since this trend is not evident in anyother element ([X/Fe] or [Fe/H]) that we consider. Wealso looked for correlations between chemical scatter andthese Galactic/cluster properties in selected subgroups,such as thin and thick disk clusters, but did not findanything of significance.We examined whether cluster scatter was correlatedwith physical cluster size, which we calculated using theangular cluster radius from K13 and the median stellardistance, and found no relationship. However, we notethat we consider these size values to be highly uncertain,since they depend on the choice of angular radius defi-nition and in at least some cases, clearly do not matchthe kinematically-clumped stars at that location.5.5.
Velocity dispersion (cluster mass)
Correlation with velocity dispersion
We calculate the 3D velocity dispersion of a cluster, aproxy for cluster mass, from its RV and PM dispersionsand heliocentric distance using the following equation: σ tot = (cid:113) σ RV + ( σ µ α + σ µ δ ) d helio (4)where σ tot is the space velocity dispersion, correctedby the uncertainties as described in § σ RV , σ µ α , and5 Cluster σ [Fe / H] σ [Mg / Fe] σ [Al / Fe] σ [Si / Fe] σ [Ca / Fe] σ [Cr / Fe] σ [Mn / Fe] σ [Ni / Fe] σ tot dex dex dex dex dex dex dex dex km s − NGC 1245 ± . .
002 0.0246 ± . .
003 0.0233 ± . .
005 0.0154 ± . .
002 0.0252 ± . .
003 0.0582 ± . .
008 0.0000 ± . .
003 0.0127 ± . .
002 5.41 ± . NGC 188 ± . .
004 0.0143 ± . .
004 0.0341 ± . .
008 0.0000 ± . .
002 0.0148 ± . .
004 0.0135 ± . .
008 0.0240 ± . .
006 0.0074 ± . .
003 3.10 ± . NGC 2204 ± . .
006 0.0414 ± . .
006 0.0511 ± . .
009 0.0443 ± . .
007 0.0224 ± . .
005 0.0000 ± . .
006 0.0134 ± . .
006 0.0068 ± . .
004 6.49 ± . NGC 2420 ± . .
006 0.0160 ± . .
004 0.0210 ± . .
006 0.0000 ± . .
002 0.0202 ± . .
005 0.0430 ± . .
011 0.0157 ± . .
005 0.0000 ± . .
002 4.18 ± . NGC 2682 ± . .
003 0.0148 ± . .
003 0.0132 ± . .
005 0.0153 ± . .
003 0.0000 ± . .
002 0.0728 ± . .
010 0.0134 ± . .
004 0.0028 ± . .
002 1.68 ± . NGC 6705 ± . .
006 0.0124 ± . .
003 0.0275 ± . .
006 0.0112 ± . .
003 0.0161 ± . .
003 0.0326 ± . .
007 0.0096 ± . .
005 0.0072 ± . .
004 3.50 ± . NGC 6791 ± . .
004 0.0268 ± . .
003 0.0709 ± . .
006 0.0205 ± . .
002 0.0263 ± . .
003 0.0693 ± . .
007 0.1146 ± . .
010 0.0285 ± . .
003 7.59 ± . NGC 6819 ± . .
003 0.0081 ± . .
002 0.0329 ± . .
003 0.0211 ± . .
002 0.0174 ± . .
002 0.0246 ± . .
005 0.0252 ± . .
003 0.0100 ± . .
003 4.24 ± . NGC 7789 ± . .
004 0.0043 ± . .
003 0.0300 ± . .
005 0.0102 ± . .
003 0.0128 ± . .
003 0.0000 ± . .
006 0.0245 ± . .
004 0.0000 ± . .
002 3.23 ± . VDB 131 ± . .
014 0.0205 ± . .
007 0.0576 ± . .
012 0.0123 ± . .
004 0.0183 ± . .
005 0.0357 ± . .
011 0.0331 ± . .
007 0.0161 ± . .
005 5.81 ± . Table 4.
Intrinsic abundance scatter ( §
4) and space velocity dispersion ( σ tot ; Equation 4) for the OCs analyzed in §
5. ‘VDB131’ is short for VDBERGH-HAGEN 131.
Figure 8.
Dependence of cluster [Mg/Fe] homogeneity on Galactocentric distance, vertical height, log(age), and metallicityof the cluster. The Spearman correlation coefficient (C) and corresponding p-value (p) are shown for each property. σ µ δ are the dispersions in the cluster for each kinematicdimension; and d helio is the heliocentric distance, as-signed as the median of the stellar member distancesfrom RA17 ( § σ tot is not being driven by any onedimension alone.We find that the cluster chemical scatter is positivelycorrelated with the space velocity dispersion of the clus-ter at relatively high levels of significance ( p < . . < p < . p > .
38) for [Cr/Fe] and [Mn/Fe]. Figure 9 shows theintrinsic scatter in [Fe/H] and rest of the abundances asa function of space velocity dispersion, along with theassociated Spearman correlation coefficients (C) and p -values.To understand why only certain elements show thistrend between intrinsic scatter and σ tot , we look for nat-ural ways to group elements based on their properties.For example, we notice that this trend is not exclusive to the α -elements that we study. Although intrinsic scat-ter is positively correlated with σ tot in Mg, Ca, and Si(albeit at low significance), we observe a similar trendin an odd-Z element (Al) and an iron-peak element (Ni)at lower significance. In § f cc ) for each element from Wein-berg et al. (2019). Figure 10 shows the Spearman cor-relation coefficients from Figure 9 against f cc , with thepoints colored by the p -value of their correlation. Here f cc represents the fraction of each element contributed6 Poovelil et al. by CCSNe at a given metallicity [Mg/H], assuming thatthese elements are produced exclusively by Type Ia SNeand CCSNe. We calculate f cc from Equation 11 in Wein-berg et al. (2019), using the median [Mg/H] value foreach of our clusters.From Figure 10, in addition to metallicity (traced by[Fe/H]), the elements that show a correlation betweenintrinsic abundance scatter and cluster velocity disper-sion (with C > p < . . < p < . Caveats of the significance of the correlations
While these correlations between abundance scatterand space velocity dispersion are interesting, we notethat the statistical analysis is done using only ten clus-ters and the elements that we list as correlated havevarying levels of significance ( p -values). Here we explorethe caveats associated with these correlations. One ef-fect of the low sample size is seen when we randomlyremove any one cluster from the analysis using a jack-knife resampling. For certain elements, the correla-tion becomes insignificant if we remove a specific cluster(e.g., removing NGC 2204 in the case of Si or removingNGC 6791 in the case of Ni) from the analysis. However,we found that no one cluster is responsible for system-atically reducing the significance across the set of allthe elements. Since we arrive at this cluster sample bypreferentially selecting clusters with high quality mem-bership and reliable abundance uncertainties ( § p -values up to 0.07, which reinforces ourclassification of these elements as possible correlations.However, Mg and Ca scatters are significantly correlatedwith velocity dispersion irrespective of the metric used,while Mn and Cr remain uncorrelated.5.5.3. Potential Implications
As discussed in § § < >
40 pc) will also yield ho-mogeneous stellar chemistry since the variations span arange larger than the typical cloud size. However, metalsthat are correlated on intermediate lengths in the ISM(6 −
40 pc) can have higher scatter in the stellar abun-dances of their final clusters. So with this reasoning,elements that have correlation lengths within the inter-mediate range in the initial cloud may be expected tohave higher abundance scatter in the final stellar mem-bers for massive clusters.Furthermore, since elements belonging to different nu-cleosynthetic groups have been shown by Krumholz &Ting (2018) to have different correlation lengths in theinitial cloud, we may observe this trend only in certainelements or nucleosynthetic groups. They propose thatthere should be no significant differences between thecorrelation lengths of Type Ia SNe and CCSNe sinceboth types of explosions have comparable energy bud-gets. However, Figure 10 suggests the presence of aquantitative difference between the correlation lengthsof these two mechanisms that pollute the ISM, and thatthis difference may manifest itself in the abundance scat-ter of nucleosynthetic element groups in the final stellarpopulations. SUMMARYWe have identified cluster members for a large numberof open clusters in the Kharchenko et al. (2013) catalogusing only their kinematic information: radial veloci-ties from APOGEE and proper motions from
Gaia -DR2.We provide a catalog of cluster properties and membersfor 83 clusters with a range of detection quality ( § ® Poovelil et al.
Figure 9.
Dependence of cluster [X/Fe] homogeneity on space velocity dispersion. The Spearman correlation coefficients (C)and corresponding p-values (p) are shown for each element.
Figure 10.
Fractional contribution from CCSNe vs theSpearman correlation coefficient of space velocity dispersionwith respect to intrinsic [X/Fe] scatter.
Smithsonian Center for Astrophysics, Instituto de As-trof´ısica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics ofthe Universe (IPMU) / University of Tokyo, the Ko-rean Participation Group, Lawrence Berkeley NationalLaboratory, Leibniz Institut f¨ur Astrophysik Potsdam(AIP), Max-Planck-Institut f¨ur Astronomie (MPIA Hei-delberg), Max-Planck-Institut f¨ur Astrophysik (MPAGarching), Max-Planck-Institut f¨ur ExtraterrestrischePhysik (MPE), National Astronomical Observatories ofChina, New Mexico State University, New York Uni-versity, University of Notre Dame, Observat´ario Na-cional / MCTI, The Ohio State University, Pennsylva-nia State University, Shanghai Astronomical Observa-tory, United Kingdom Participation Group, UniversidadNacional Aut´onoma de M´exico, University of Arizona,University of Colorado Boulder, University of Oxford,University of Portsmouth, University of Utah, Univer-sity of Virginia, University of Washington, University ofWisconsin, Vanderbilt University, and Yale University.REFERENCES
Ahumada, R., Allende Prieto, C., Almeida, A., et al. 2019,arXiv e-prints, arXiv:1912.02905.https://arxiv.org/abs/1912.02905Allende Prieto, C., Beers, T. C., Wilhelm, R., et al. 2006,ApJ, 636, 804, doi: 10.1086/498131Armillotta, L., Krumholz, M. R., & Fujimoto, Y. 2018, s,481, 5000, doi: 10.1093/mnras/sty2625 Badenes, C., Mazzola, C., Thompson, T. A., et al. 2018,ApJ, 854, 147, doi: 10.3847/1538-4357/aaa765Benjamin, R. A., Churchwell, E., Babler, B. L., et al. 2005,ApJL, 630, L149, doi: 10.1086/491785Bertran de Lis, S., Allende Prieto, C., Majewski, S. R.,et al. 2016, A&A, 590, A74,doi: 10.1051/0004-6361/201527827 Blanco-Cuaresma, S., Soubiran, C., Heiter, U., et al. 2015,A&A, 577, A47, doi: 10.1051/0004-6361/201425232Bland-Hawthorn, J., Krumholz, M. R., & Freeman, K.2010, ApJ, 713, 166, doi: 10.1088/0004-637X/713/1/166Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017,AJ, 154, 28, doi: 10.3847/1538-3881/aa7567Bovy, J. 2016, ApJ, 817, 49,doi: 10.3847/0004-637X/817/1/49Bowen, I. S., & Vaughan, Jr., A. H. 1973, ApOpt, 12, 1430,doi: 10.1364/AO.12.001430Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS,427, 127, doi: 10.1111/j.1365-2966.2012.21948.xCantat-Gaudin, T., Jordi, C., Vallenari, A., et al. 2018,A&A, 618, A93, doi: 10.1051/0004-6361/201833476Cappellari, M., & Copin, Y. 2003, MNRAS, 342, 345,doi: 10.1046/j.1365-8711.2003.06541.xCarlberg, J. K., Cunha, K., & Smith, V. V. 2016, ApJ, 827,129, doi: 10.3847/0004-637X/827/2/129Carretta, E., Bragaglia, A., Gratton, R. G., et al. 2010,A&A, 516, A55, doi: 10.1051/0004-6361/200913451Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009,PASP, 121, 213, doi: 10.1086/597811Cunha, K., Smith, V. V., Johnson, J. A., et al. 2015, TheAstrophysical Journal, 798, L41,doi: 10.1088/2041-8205/798/2/l41Cutri, R. M., Wright, E. L., Conrow, T., et al. 2013,Explanatory Supplement to the AllWISE Data ReleaseProducts, Explanatory Supplement to the AllWISE DataRelease ProductsDe Silva, G. M., Freeman, K. C., Asplund, M., et al. 2007,AJ, 133, 1161, doi: 10.1086/511182De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., et al.2011, MNRAS, 415, 563,doi: 10.1111/j.1365-2966.2011.18728.xDe Silva, G. M., Sneden, C., Paulson, D. B., et al. 2006,AJ, 131, 455, doi: 10.1086/497968Donor, J., Frinchaboy, P. M., Cunha, K., et al. 2018, AJ,156, 142, doi: 10.3847/1538-3881/aad635—. 2020, AJ, 159, 199, doi: 10.3847/1538-3881/ab77bcFreeman, K., & Bland-Hawthorn, J. 2002, Annual Reviewof Astronomy and Astrophysics, Vol. 40, 487,doi: 10.1146/annurev.astro.40.060401.093840Frinchaboy, P. M., & Majewski, S. R. 2008, AJ, 136, 118,doi: 10.1088/0004-6256/136/1/118Froebrich, D., Scholz, A., & Raftery, C. L. 2007, MNRAS,374, 399, doi: 10.1111/j.1365-2966.2006.11148.xFujii, M. S. 2015, PASJ, 67, 59, doi: 10.1093/pasj/psu137Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al.2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051 Garcia-Dias, R., Allende Prieto, C., S´anchez Almeida, J., &Alonso Palicio, P. 2019, A&A, 629, A34,doi: 10.1051/0004-6361/201935223Garc´ıa P´erez, A. E., Allende Prieto, C., Holtzman, J. A.,et al. 2016, AJ, 151, 144,doi: 10.3847/0004-6256/151/6/144Gratton, R. 2020, in IAU Symposium, Vol. 351, IAUSymposium, ed. A. Bragaglia, M. Davies, A. Sills, &E. Vesperini, 241–250, doi: 10.1017/S1743921319007877Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006,AJ, 131, 2332, doi: 10.1086/500975Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008,A&A, 486, 951, doi: 10.1051/0004-6361:200809724Hawkins, K., Masseron, T., Jofr´e, P., et al. 2016, A&A,594, A43, doi: 10.1051/0004-6361/201628812Hole, K. T., Geller, A. M., Mathieu, R. D., et al. 2009, AJ,138, 159, doi: 10.1088/0004-6256/138/1/159Holtzman, J. A., Hasselquist, S., Shetrone, M., et al. 2018,AJ, 156, 125, doi: 10.3847/1538-3881/aad4f9Jacobson, H. R., Friel, E. D., & Pilachowski, C. A. 2011,AJ, 141, 58, doi: 10.1088/0004-6256/141/2/58Jacobson, H. R., Pilachowski, C. A., & Friel, E. D. 2011,The Astronomical Journal, 142, 59,doi: 10.1088/0004-6256/142/2/59J¨onsson, H., Allende Prieto, C., Holtzman, J. A., et al.2018, AJ, 156, 126, doi: 10.3847/1538-3881/aad4f5J¨onsson, H., Holtzman, J. A., Allende Prieto, C., et al.2020, arXiv e-prints, arXiv:2007.05537.https://arxiv.org/abs/2007.05537Kharchenko, N. V., Piskunov, A. E., R¨oser, S., Schilbach,E., & Scholz, R.-D. 2005, A&A, 438, 1163,doi: 10.1051/0004-6361:20042523Kharchenko, N. V., Piskunov, A. E., Schilbach, E., R¨oser,S., & Scholz, R.-D. 2013, A&A, 558, A53,doi: 10.1051/0004-6361/201322302Kounkel, M., & Covey, K. 2019, AJ, 158, 122,doi: 10.3847/1538-3881/ab339aKovalev, M., Bergemann, M., Ting, Y.-S., & Rix, H.-W.2019, A&A, 628, A54, doi: 10.1051/0004-6361/201935861Krumholz, M. R., McKee, C. F., & Bland -Hawthorn, J.2019, ARA&A, 57, 227,doi: 10.1146/annurev-astro-091918-104430Krumholz, M. R., & Ting, Y.-S. 2018, MNRAS, 475, 2236,doi: 10.1093/mnras/stx3286Lee-Brown, D. B., Anthony-Twarog, B. J., Deliyannis,C. P., Rich, E., & Twarog, B. A. 2015, AJ, 149, 121,doi: 10.1088/0004-6256/149/4/121Leung, H. W., & Bovy, J. 2019, MNRAS, 489, 2079,doi: 10.1093/mnras/stz2245 Poovelil et al.
Liu, F., Asplund, M., Yong, D., et al. 2016a, MNRAS, 463,696, doi: 10.1093/mnras/stw2045Liu, F., Yong, D., Asplund, M., Ram´ırez, I., & Mel´endez, J.2016b, MNRAS, 457, 3934, doi: 10.1093/mnras/stw247Looney, L. W., Tobin, J. J., & Fields, B. D. 2006, ApJ,652, 1755, doi: 10.1086/508407Majewski, S. R., Zasowski, G., & Nidever, D. L. 2011, ApJ,739, 25, doi: 10.1088/0004-637X/739/1/25Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al.2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784dMarigo, P., Girardi, L., Bressan, A., et al. 2017, ApJ, 835,77, doi: 10.3847/1538-4357/835/1/77M´esz´aros, S., Holtzman, J., Garc´ıa P´erez, A. E., et al. 2013,AJ, 146, 133, doi: 10.1088/0004-6256/146/5/133M´esz´aros, S., Masseron, T., Garc´ıa-Hern´andez, D. A., et al.2020, MNRAS, 492, 1641, doi: 10.1093/mnras/stz3496Milone, A. P., Marino, A. F., Renzini, A., et al. 2018,MNRAS, 481, 5098, doi: 10.1093/mnras/sty2573Moe, M., Kratter, K. M., & Badenes, C. 2019, ApJ, 875,61, doi: 10.3847/1538-4357/ab0d88Ness, M., Rix, H. W., Hogg, D. W., et al. 2018, ApJ, 853,198, doi: 10.3847/1538-4357/aa9d8eNidever, D. L., Holtzman, J. A., Allende Prieto, C., et al.2015, AJ, 150, 173, doi: 10.1088/0004-6256/150/6/173Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011,Journal of Machine Learning Research, 12, 2825Platais, I., Gosnell, N. M., Meibom, S., et al. 2013, AJ, 146,43, doi: 10.1088/0004-6256/146/2/43Plez, B. 2012, Turbospectrum: Code for spectral synthesis.http://ascl.net/1205.004Price-Whelan, A. M., Hogg, D. W., Rix, H.-W., et al. 2020,ApJ, 895, 2, doi: 10.3847/1538-4357/ab8accQueiroz, A. B. A., Anders, F., Santiago, B. X., et al. 2018,MNRAS, 476, 2556, doi: 10.1093/mnras/sty330Queiroz, A. B. A., Anders, F., Chiappini, C., et al. 2019,arXiv e-prints, arXiv:1912.09778.https://arxiv.org/abs/1912.09778 Rojas-Arriagada, A., Recio-Blanco, A., de Laverny, P.,et al. 2017, A&A, 601, A140,doi: 10.1051/0004-6361/201629160Saracino, S., Bastian, N., Kozhurina-Platais, V., et al. 2019,MNRAS, 489, L97, doi: 10.1093/mnrasl/slz135Semenova, E., Bergemann, M., Deal, M., et al. 2020, arXive-prints, arXiv:2007.09153.https://arxiv.org/abs/2007.09153Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ,131, 1163, doi: 10.1086/498708Souto, D., Allende Prieto, C., Cunha, K., et al. 2019, ApJ,874, 97, doi: 10.3847/1538-4357/ab0b43Spina, L., Mel´endez, J., Casey, A. R., Karakas, A. I., &Tucci-Maia, M. 2018, ApJ, 863, 179,doi: 10.3847/1538-4357/aad190Weinberg, D. H., Holtzman, J. A., Hasselquist, S., et al.2019, ApJ, 874, 102, doi: 10.3847/1538-4357/ab07c7Wilson, J. C., Hearty, F. R., Skrutskie, M. F., et al. 2019,PASP, 131, 055001, doi: 10.1088/1538-3873/ab0075Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al.2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868Wu, T., Li, Y., & Hekker, S. 2014, ApJ, 786, 10,doi: 10.1088/0004-637X/786/1/10Yang, S.-C., Sarajedini, A., Deliyannis, C. P., et al. 2013,ApJ, 762, 3, doi: 10.1088/0004-637X/762/1/3Zasowski, G., Johnson, J. A., Frinchaboy, P. M., et al.2013a, AJ, 146, 81, doi: 10.1088/0004-6256/146/4/81Zasowski, G., Beaton, R. L., Hamm, K. K., et al. 2013b,AJ, 146, 64, doi: 10.1088/0004-6256/146/3/64Zasowski, G., Cohen, R. E., Chojnowski, S. D., et al. 2017,AJ, 154, 198.http://stacks.iop.org/1538-3881/154/i=5/a=198Ziegler, C., Tokovinin, A., Brice˜no, C., et al. 2020, AJ, 159,19, doi: 10.3847/1538-3881/ab55e9 A. Figure 11.
The Uncertainty Training (UT) sample for [Fe/H], [Ca/Fe], [Si/Fe], and [Ni/Fe], similar to first row of Figure 1. Poovelil et al.
Figure 12.
The Uncertainty Training (UT) sample for [Al/Fe], [Mn/Fe], and [Cr/Fe], similar to first row of Figure 1. B. Here we show the membership plots for all of the clusters that we use in the final analysis in § Poovelil et al.
Figure 13.
Same as Figure 3, but for NGC 1245.
Figure 14.
Same as Figure 3, but for NGC 2204.
Figure 15.
Same as Figure 3, but for NGC 2420.
Figure 16.
Same as Figure 3, but for NGC 2682. Figure 17.
Same as Figure 3, but for NGC 6705.
Figure 18.
Same as Figure 3, but for NGC 6791.
Figure 19.
Same as Figure 3, but for NGC 7789.
Figure 20.
Same as Figure 3, but for NGC 188. Poovelil et al.