Purveyors of fine halos: Re-assessing globular cluster contributions to the Milky Way halo build-up with SDSS-IV

TL;DR

This study estimates that approximately 11% of the Milky Way's halo stars originated from disrupted globular clusters, using chemical signatures from SDSS-IV data to trace their contribution.

Contribution

It provides a refined estimate of the globular cluster contribution to the Galactic halo by analyzing CN-strong stars and accounting for early cluster mass loss.

Findings

Approximately 2.6% of halo stars are CN-strong, indicating GC origin.

Estimated 11% of the halo stems from disrupted GCs, considering early mass loss.

The fraction of GC-origin stars is roughly constant with galactocentric radius.

Abstract

There is ample evidence in the Milky Way for globular cluster (GC) disruption. Hence one may expect that also part of the Galactic halo field stars may once have formed in GCs. We quantify the fraction of halo stars donated by GCs by searching for stars that bear the unique chemical fingerprints typical for a subset of GC stars often dubbed `second-generation stars'. These are stars showing light element abundance anomalies such as a pronounced CN-band strength accompanied by weak CH-bands. Based on this indicator, past studies have placed the fraction of halo stars with a GC origin between a few to up to 50%. Using low-resolution spectra from the most recent data release of the latest extension of the Sloan Digital Sky Survey (SDSS-IV), we were able to identify 118 metal-poor ($-1.8\le$[Fe/H]$\le -1.3$) CN-strong stars in a sample of 4470 halo giant stars out to 50 kpc. This results in an observed fraction of these stars of 2.6$\pm$0.2%. Using an updated formalism to account for the fraction of stars lost early on in the GCs' evolution we estimate the fraction of the halo that stems from disrupted clusters to be 11$\pm$1%. This number represents the case that stars lost from GCs were entirely from the first generation and is thus merely an upper limit. Our conclusions are sensitive to our assumptions of the mass lost early on from the first generation formed in the GCs, the ratio of first-to-second generation stars, and other GC parameters. We carefully test the influence of varying these parameters on the final result and find that, under realistic scenarios, the above fraction depends on the main assumptions at less than 10%. We further recover a flat trend in this fraction with Galactocentric radius, with a marginal indication of a rise beyond 30 kpc that could reflect the ex-situ origin of the outer halo. (abridged)

Figures

Equations

$$S(3839)=-2.5\log \frac{{\int }_{3846}^{3883}{I}_{\lambda }\mathrm{d}\lambda }{{\int }_{3883}^{3916}{I}_{\lambda }\mathrm{d}\lambda },$$

$$s(c_0)$$

$$s(c_1)$$

$$S(CH)=-2.5\log \frac{{\int }_{4280}^{4320}{I}_{\lambda }\mathrm{d}\lambda }{{\int }_{4050}^{4100}{I}_{\lambda }\mathrm{d}\lambda +{\int }_{4330}^{4350}{I}_{\lambda }\mathrm{d}\lambda }$$

$$M_{1G}^{\mathrm{lost}}=\frac{M_{\mathrm{tot}}}{2}\left(\frac{1}{1-f_{1G}^{\mathrm{lost}}}-1\right)=\frac{M_{\mathrm{tot}}{f}_{1G}^{\mathrm{lost}}}{2\left(1-f_{1G}^{\mathrm{lost}}\right)}.$$

$$M_{Diss}$$

$$=$$

$$M_h^{\mathrm{GC}}$$

$$=$$

$$N_{\mathrm{Diss}}=\frac{2f_h^{2G}{M}_{\mathrm{h},\mathrm{tot}}}{<M_{\mathrm{GC}}>}$$

Full text

††offprints: A. Koch;

1 Introduction

In the current picture of hierarchical structure formation, major parts of galactic halos stem from the accretion of small, presumably dark-matter dominated, subgalactic units akin to the progenitors of today’s dwarf satellites (Searle & Zinn, 1978; Dekel & Silk, 1986; Bullock & Johnston, 2005). This channel of halo formation is indeed seen in action via observations of satellite disruption in and outside our own Milky Way (MW; e.g., Ibata et al. 1994; Belokurov et al. 2006; McConnachie et al. 2009; Koch et al. 2012; Ludwig et al. 2012; Shipp et al. 2018; Morales et al. 2018, to name a few).

Moreover, globular clusters (GCs) are progressively gaining consideration as building blocks of yet unknown fractions of the Galactic stellar halo, which is also bolstered by their observed disruption in the tidal field of the MW via tidal tails in the Galactic halo (e.g., Odenkirchen et al., 2001; Lee et al., 2004; Lauchner et al., 2006; Chun et al., 2010; Jordi & Grebel, 2010; Niederste-Ostholt et al., 2010; Sollima et al., 2011; Myeong et al., 2017; Navarrete et al., 2017; Carballo-Bello et al., 2018; Kuzma et al., 2018), the detection of extratidal stars with a likely GC origin based on, e.g., photometric filtering techniques or stellar abundances and velocities (e.g., Jordi & Grebel, 2010; Kunder et al., 2014; Anguiano et al., 2015, 2016; Navin et al., 2016; Simpson et al., 2017b; Kunder et al., 2018), or the discovery of thin streams with possible GC progenitors (e.g., Grillmair & Dionatos, 2006; Grillmair, 2009; Bonaca et al., 2012; Bernard et al., 2014).

GCs stand out in that they show significant light chemical element variations over a broad mass range of cluster masses , as was first noted in the 1970s. Prominent manifestations of these are significant dispersions in Na and O (e.g., Osborn, 1971; Cohen, 1978; Carretta et al., 2009), and bimodalities in their stellar CN abundances (e.g., Popper, 1947; Harding, 1962; Norris & Cottrell, 1979; Kraft et al., 1982; Harbeck et al., 2003; Kayser et al., 2008; Smolinski et al., 2011). Furthermore, a clear correlation between Mg and Al is seen, stemming from the same proton-burning channels (Gratton et al., 2001). All of these lead to clear (anti-)correlations rather than generic abundance spreads alone, despite not all GCs showing Mg spreads, as recently reviewed by Pancino et al. (2017). To higher order, these findings are complemented by later burning stages in the first stellar generation causing Mg, Si, and Zn to anti-correlate as well (e.g., Hanke et al., 2017). Such give-away abundance variations have to date been traced down to the low-mass GC regime (Bragaglia et al., 2017; Simpson et al., 2017a), and were also found in old GCs in external galaxies (e.g., Mucciarelli et al., 2009; Mateluna et al., 2012; Colucci et al., 2014; Larsen et al., 2018), as well as in massive, intermediate-age clusters in the Magellanic Clouds (Hollyhead et al., 2017, 2018, e.g.,) and down to cluster ages of $\sim$2 Gyr (Martocchia et al., 2018a).

It is nowadays accepted that these variations go alongside with multiple stellar populations in GCs, with colour-magnitude diagrams uniquely supporting the presence of two or more populations, possibly separated in age by several $\sim 100$ Myr111 For ancient GCs (ages$>$10 Gyr), an age difference of $\sim$200 Myr is possible, limited by the accuracy in age dating, whereas for the $\sim$2 Gyr old cluster NGC 1978, Martocchia et al. (2018b) found that the two populations are coeval to within an upper limit of 20 Myr., and distinct in other tracers such as variations in He content. However, the origin of these populations is as yet unclear as no model can currently explain all of the observational constraints (e.g., Bastian & Lardo, 2018). In particular, it remains unresolved whether GCs did indeed experience two or more episodes of star formation resulting in the observed abundance anomalies. Nonetheless, we will follow the commonly adopted terminology of calling stars that are enhanced in O and C and that show lower Na and N abundances (in other words, “normal” stars by metal-poor GC standards) “first generation” stars, and those with elevated Na and N levels “second generation” stars. We do so for the sake of convenience and without implying that we favour a particular formation scenario such as repeated star formation. Either way, the ratio of stars in the two main populations in each cluster lies at $\sim 50$% each, with a possible trend toward a higher fraction of the first-generation stars with decreasing cluster mass (Milone et al. 2017; cf. Bastian & Lardo 2015).

Ad-hoc models of GC evolution that are designed to explain multiple populations via multiple epochs of star formation (e.g., D’Ercole et al., 2008; Bastian et al., 2013) predict that, during an initial phase of cluster dissolution, a large fraction of up to 90% of the first generation of cluster stars is lost from a GC and released into the halo. Since these first generation stars, however, bear the chemical imprint of a standard, early chemical evolution, they are indistinguishable from any given halo field star. More generally, several studies suggest GCs have, on average, lost a considerable fraction of their stars since they formed, e.g., around two thirds according to Kruijssen (2015) or about 75–80% according to Baumgardt (2017) and Baumgardt et al. (2019).

Since first-generation stars that end up in the halo are chemically indistinguishable from “normal” halo stars, the second-generation stars are of particular interest since they can be traced through their peculiar chemistry. They are enhanced in N and Na and, in turn, depleted in C and O, a pattern that is qualitatively consistent with proton-capture reactions in a generation of polluters such as intermediate-mass asymptotic giant branch (AGB) stars (D’Ercole et al., 2008), fast-rotating massive stars (Decressin et al., 2007), massive binaries (de Mink et al., 2009), or super-massive stars (Gieles et al., 2018).

In order to assess the actual fraction of the MW halo that is made up by former GC stars, we can use the empirical fact that the aforementioned light element variations are commonly found in GCs, but not in young open clusters or dwarf galaxy field stars, and only rarely in the halo field (Pilachowski et al., 1996; Geisler et al., 2007). If any stars with second-generation-like chemistry (classified by their molecular band strengths as CN-strong and CH-weak) exist in the halo, this indicates that they most likely originated from disrupting GCs.

Large sky surveys such as the Sloan Digital Sky Survey (SDSS) have permitted statistical investigations of the fraction of the MW halo contributed by disrupted GCs based on the discovery of CN-strong and CH-weak field halo stars (e.g., Martell & Grebel, 2010; Martell et al., 2011; Carollo et al., 2013; Tang et al., 2019), with estimates ranging from 17–50%, depending on the assumptions of the ratio of first-to-second generation stars in GCs and the statistics of GC dissolution. Likewise, Carretta et al. (2010) and Ramírez et al. (2012) found candidates with second-generation-like Na- and O-abundance ratios across the metal-poor tails of all MW components, while Lind et al. (2015) identified one potential GC escapee in the Gaia-ESO Survey (GES; Gilmore et al., 2012) of a few hundred halo stars, based on its second-generation-like Mg and Al abundances. This was extended towards a larger fraction of five out of the studied seven metal-rich field stars with Mg-Al anomalies using the SDSS-III APOGEE Survey (Majewski et al., 2017; Fernández-Trincado et al., 2017). Similarly, Martell et al. (2016) employed APOGEE to identify five halo giants enriched in N and Al. These more recent studies typically arrive at estimates of just a few per cent of halo stars with GC cluster origin, suggesting that GC disruption is a minor contributor to the halo field population. On the modeling front, Schaerer & Charbonnel (2011) estimate a contribution of 5–8% of low-mass first generation stars to the halo field population, and possibly as high as 20% if also second-generation stars are accounted for.

While the Galactic bulge is not the target of our current study, we note that also in the Galactic bulge N-rich field stars were discovered (Schiavon et al., 2017). Schiavon et al. (2017) argue that if the N-rich stars are indeed former GC stars, then the mass in destroyed GCs exceeds the mass in surviving GCs by a factor of eight.

In our work, we seek to make use of the latest extensions to the SDSS (Blanton et al., 2017) in order to improve the number statistics of CN-strong stars in the MW halo. While previous studies detected a few tens of such stars in spectroscopic samples of several thousand (leading to a fraction of CN-strong field stars of $\sim 2$%; Martell et al. 2011), the latest generations of massive spectroscopic surveys allow for a potential increase in the number of disrupted GC stars by factors of several. This paper is organized as follows: In Sect. 2 we describe the data set and steps taken to define the bona-fide halo sample. Our spectral index measurements to determine CN- and CH- band strengths are laid out in Sect. 3, and the method to discriminate CN-strong from CN-normal stars is presented in Sect. 4. Next, Sect. 5 is dedicated to the formalism to determine the fraction of the halo that likely originated from dissolved GCs. Our results and their limitations are then discussed in Sect. 6.

2 Data and sample selection

The first statistical endeavour towards the fraction of halo stars born in GCs (Martell & Grebel, 2010) was based on the seventh data release (DR7) of the SDSS, which already included the first important add-on of the Sloan Extension for Galactic Understanding and Exploration (SEGUE) with additional spectra of 240,000 stars (Yanny et al., 2009), taken with a resolving power of R$$\sim2000 over a wavelength range of 3800–9200 Å. The subsequent work of Martell et al. (2011) built upon more numerous data from the next extension within SDSS-III, i.e., SEGUE-2 (with an additional 120,000 stellar spectra). After applying a number of stringent selection criteria, this yielded the discovery of 16 further CN-strong stars, adding to the 49 such objects out of $\sim 2000$ regular halo stars from the previous study.

In our current study, we employed data from the latest phase of the SDSS-IV (Blanton et al., 2017), as drawn from its DR14 catalog (Abolfathi et al., 2018). SDSS-IV’s low-resolution spectroscopy primarily targeted galaxies and quasars from the SDSS project “extended Baryon Oscillation Spectroscopic Survey” (eBOSS; Dawson et al. 2016), which contains on the order of 9% stellar spectra. Moreover, DR14 contains the previously observed spectra from the earlier phases of the SDSS. As in the previous works, we relied on stellar parameter and metallicity measurements provided in the SDSS catalogs, which are, in turn, based on the automated Segue Stellar Parameter Pipeline (SSPP; Lee et al., 2008).

In order to build a representative sample of halo red giants, we apply the same selection criteria as Martell & Grebel (2010) in our SQL query to the SDSS. That is, we preselect only stars with [Fe/H]$\leq-1$ to focus on halo objects. We further demand that the error on metallicity is $\sigma$[Fe/H]$\leq$0.5 and that at least three of the ten independent metallicity determinations within the SSPP were flagged as reliable. Furthermore, only objects with surface gravities constrained to log $g\leq 3$, and respective errors below $\sigma$ log $g\leq 0.5$ were queried. Finally, the mean signal-to-noise ratio (S/N) was required to lie above 20 per pixel, and we employed a colour cut towards cooler giants using $(g-r)_{0}\geq 0.2$, leaving a starting sample of $\sim$15000 halo giants.

Next, we required a S/N above 15 per pixel in the region of 4000–4100 Å, as lower S/N ratios would cloud our measurements of the respective spectral indices below. The ensuing subsample was further refined by dividing the entire sample into metallicity bins of 0.2 dex each. Within each bin, we constructed fiducial lines in diagrams of log $g$ vs. colour (which transpired to yield the clearest separation) and pruned the sample from contaminating AGB, main sequence, and turn-off stars using a smoothed 3$\sigma$-cut along those ridge lines. This is illustrated for each metallicity bin in Fig. 1.

We also ascertained that our field star sample was uncontaminated by present-day GC member stars, as they have not yet been released into the surrounding halo. To this end, we rejected stars that fall within the tidal radii of any object from the catalog of Harris (1996, 2010 version). In this way, we identified 43 giants located in M3, M13, and M15. We were thus left with 6801 halo field candidates.

Finally, in the following, we explicitly ignored the metal-rich ([Fe/H]$>-1.3$ dex) tail of our distribution. This is to avoid any possible false detections of CN-strong stars that are not the progeny of actual GC dissolutions, as suggested by follow-up observations of a subsample of the CN-strong halo stars by Martell et al. (2011), which do not show any signatory Na-enhancement (Martell et al. in prep.). While it is well established that metal-rich GCs do show CN/CH anti-correlations (Harbeck et al., 2003; Kayser et al., 2008) it is strictly not required that a former GC star would need to show both enhanced N and Na-enhancement for a first identification, in particular since, here, we are solely concerned with low-resolution spectra without any means to constrain the Na content of our CN-strong stars. Nonetheless, imposing our additional metallicity cut will ascertain a bona-fide sample for unbiassed identification of the desired GC-like stars halo stars. Furthermore, metal-poor stars below $-1.8$ dex were removed from the sample as elaborated below in Sect. 2.1. This leaves us with a final sample of 4649 stars with halo characteristics in the metallicity range of $-1.3$ to $-1.8$. Fig. 3 shows the full, queried initial and the selected halo subsample.

2.1 Distances

In order to determine the stars’ distances we first computed their $r$-band absolute magnitudes, $M_{r}$, where we resorted to a set of 10-Gyr old Dartmouth isochrones (Dotter et al., 2008) for a broad grid of metallicities from $-1$ to $-2.5$ dex, using no $\alpha$-enhancement, as these provide the best, global representation of metal-poor Galactic GCs (see also Hendricks et al., 2014). These isochrones were interpolated to the observed, dereddened $(g-r)_{0}$ colour as provided by the SDSS. Since the isochrone spacing is getting smaller and less distinguishable towards the lowest metallicities, and with the grid limitation of the Dartmouth tracks to $\geq-$2.5 dex, we follow Martell et al. (2011) in selecting only stars more metal-rich than $-1.8$ dex, which mainly picks up halo giants broadly located around the peak of the halo metallicity distribution function (Schörck et al., 2009). This is further beneficial, as the CN band strength loses its sensitivity to N-abundance at low metallicities (e.g., Boberg et al., 2016a), leaving CN bimodalities largely undetetectable from this tracer.

3 Spectral indices

At the low resolution of the SDSS spectra, measuring band indices in the blue spectral region provides a powerful tool to identify CN-strong and CN-weak stars. In particular, the frequently used S(3839) index, first defined and optimized by Norris et al. (1981) to measure the strength of the CN-band at 3839 Å, is ideal to trace bimodal band strength distributions:

[TABLE]

where $I_{\lambda}$ simply refers to the observed flux in the spectrum.

The run of this CN index versus absolute magnitude (bottom panel), colour (middle), and metallicity (top) is shown in Fig. 2, displaying the trade-mark increase of the CN-band strengths with colour, due to colder (thus redder) stars forming progressively more (CN) molecules.

Similarly, strong bands of carbonaceous molecules such as CH and CN are seen in carbon stars, and, in the metal-poor regime, in carbon-enhanced metal-poor (CEMP) stars (Beers & Christlieb, 2005; Hansen et al., 2016). In this case, the strong bands are rather a result of their strong carbon-overabundance and do not reflect the light element variations that result from the early nucleosynthesis in the GCs to be engulfed into the halo. These objects can be efficiently flagged using indices encompassing the CH- (at 4350 Å) and C2-bands (at 4737 Å) that are mainly sensitive to carbon and only little affected by nitrogen features in the neighbouring spectral regions. These indices read:

[TABLE]

Hence, we discard another 179 stars from further analysis due to their strong C-bands, employing the set of restrictions in $s(c_{0})$, $s(c_{1})$, and [Fe/H] outlined in Martell & Grebel (2010). Separating these by metallicity yields fractions of C-rich stars that are fully compatible with those found by Martell & Grebel (2010), moreover displaying a metallicity distribution function that directly traces that of such objects in the Galactic halo as found in other, large-scale surveys (e.g., Lucatello et al., 2006; Carollo et al., 2012). In particular, the largest fraction of C-stars is found at low metallicities, where 73% of our sample lie below $-2$ dex – the formal boundary of CEMP stars (Beers & Christlieb, 2005).

Finally, in order to cross-identify the “CN-strong” nature of the stars of interest as also being “CH-weak”, we determine the strength of the CH G-band at 4300 Å via the index definition of Martell et al. (2008):

[TABLE]

Throughout our entire work, errors on all measured parameters were determined in a Monte Carlo sense by varying the input quantities ($g_{0}$, $r_{0}$, [Fe/H]) by their respective uncertainty.

4 Separation of CN-weak and -strong stars

In order to identify CN-normal and CN-weak stars, several methods have been devised in the literature. For instance, Gerber et al. (2018) employed separation by spline interpolation in CN-band strength vs. absolute magnitude space. However, their data have higher S/N and smaller errors on individual measurements, and the confirmed membership of their sample stars with a known GC facilitated an accurate $M_{V}$ determination. Furthermore, Boberg et al. (2016b) discuss an accurate treatment of the index-measurement errors, albeit at super-Solar metallicities, which are beyond the range of our halo sample.

For our purpose, we first removed any temperature, gravity, and metallicity trend in the S(3839) measurements via a straight-line fit to the CN-weak sequence in the S(3839) vs.  magnitude space in Fig. 3 (bottom). Computing a vertical distance of each individual star from the best fit then yielded a “corrected” index $\delta$S(3839). Since the slope of this parameter space mildly depends on metallicity, flattening towards the metal-poor regime, we performed the calculation of the $\delta$S(3839) values in independent bins of metallicity, each 0.1 dex wide (Fig. 4).

For each bin, we computed a generalized, i.e., error-weighted histogram of $\delta$S(3839), from which we drew the distinction into CN-weak and CN-strong stars by defining the largest separation in the histogram, aided by a Sobel edge-detection filter. As an independent test, we also applied a heteroscedastic Kayes Mixture Modeling algorithm (Ashman et al., 1994) to every metallicity subsample, which assigns probabilities to each star to belong to either of the CN-strong or CN-weak populations. These probabilities are explicitly assumed to be Gaussian. The resulting distribution (dashed lines in Fig. 5) shows a vast overlap of CN-weak and CN-strong stars and leads to a large, overall ratio of these two populations that is higher than previous estimates in the literature. Considering this overlap and the fact that our first method takes into account the more realistic error distribution of our data, we will not pursue the KMM separation any further.

For the construction of the final sample, we took advantage of the fact that stellar evolution in the progenitors, whether massive or not, produces the phenomenologically observed anticorrelations between CN and CH band strength in GC stars by efficiently converting C into N. For the present purpose this means that strong CN-bands should be accompanied by considerably weakened CH-band strengths. Following Martell et al. (2011), we adopt the mean S(CH) of stars more metal-rich than $-1.3$ dex as a delimiter between CH-normal and CH-weak for the low-metallicity bins that make up our present sample. This selection is again carried out in metallicity bins of 0.1 dex and indicated in Fig. 6.

Fig. 5 displays the combined sample in the corrected $\delta$S(3839) index, also accounting for its error distribution (right panel). Owing to the additional separation criterion in terms of metallicity (Fig. 4), some of the CN strong stars are also CH-strong, while we do not consider them as GC-descendants. Nonetheless, this leads to an overlap in those Figures focusing on CN-strength alone (Figs. 4,5).

A clear bimodality of CN-strong and CN-normal stars is seen, as is commonly found in Galactic and extragalactic GCs (e.g., Kayser et al., 2008; Larsen et al., 2018; Hollyhead et al., 2018). These separate populations will be the base for all our subsequent statistics and number counts. Sample spectra from either group are depicted in Fig. 7, including those of some rejected, metal-rich examples, =demonstrating the success in isolating the relevant stellar tracers based on our spectral index analysis.

5 Halo fractions of globular cluster stars

We find that 118 out of our 4470 halo giant stars are CN-strong and CH-weak, thereby qualifying as second-generation progeny of dissolved GCs. We note that we recover the 65 CN-strong candidates of Martell et al. (2011) as well, which is not surprising given the same selection criteria in this work. This corresponds to an observed fraction of halo stars with second-generation abundance patterns of $f_{h}^{2G}=(2.6\pm 0.2)$%, where the error is solely based on Poisson statistics. We also note that this number would increase to 3.7% if we were to include the entire metallicity range up to $-$1 dex, thereby yielding 252 CN-strong stars. This metallicity dependence of this fraction is illustrated in Fig. 8.

5.1 Formalism

Our goal is to compute the fraction of the halo that was contributed by disrupting GCs, $f_{h}^{\rm GC}$. This is simply the ratio of the total mass in former globular cluster stars in the halo field, $M_{h}^{\rm GC}$, to the total present-day stellar mass of the halo, which we adopt here as $M_{\rm h,tot}=10^{9}$ M*⊙*222Strictly, this number should be scaled down by a factor of four due to the smaller footprint of the SDSS used in this work compared to the entire halo volume. Likewise, a correction factor for our limited distance coverage could be envisioned, which, however, would counteract our investigation of the distance dependence addressed in Sect. 5.3.. We also note that the MW GC system currently accounts for about 2–3% of the stellar halo mass (Forbes et al., 2018).

We will use the following terminology and formalisms, which differ in several details from those of Martell & Grebel (2010); Martell et al. (2011). In our work, “mass loss at early time” refers to the phase of strong loss of first-generation stars from GCs that was proposed to solve the mass budget problem, i.e., the observational evidence that the present stars with primordial signatures (and the respective higher mass stars that have already perished) are insufficient to have produced the amount of light elements required to enrich the second generation stars to the observed levels (e.g., Bastian & Lardo, 2015). During this period, a fraction of $f_{1G}^{\rm lost}$ of mass in the initial globular cluster system is lost. We will discuss the implication of the exact value of this parameter in Sect. 5.1.3 below. Accordingly, $M_{1G}^{\rm lost}$ is the mass lost from the globular cluster system at these early times. In contrast, “late mass loss” is taken as stars escaping from globular clusters after the second generation has formed, whether through internal or external processes.

5.1.1 Ratio of first- to second generation stars

Turning to the present-day GCs, the ratio of first-to-second-generation stars is still debated. Early studies, observationally and theoretically, commonly assigned the GCs with an equal proportion of primordial and enriched populations (e.g., D’Ercole et al., 2008; Carretta et al., 2009). Based on their study of 33 MW CGs Bastian & Lardo (2015) concluded that the fraction of second-generation stars is 68% and independent of cluster parameters such as mass, metallicity, or location within the Galaxy. Conversely, Milone et al. (2017) found a clear trend of the second population with present-day GC mass in the form of a decreasing occurrence of the enriched stars with decreasing mass (see also Gerber et al., 2018). Moreover, the population fractions are expected to vary with distance from each GC’s center (e.g., Milone et al., 2009; Vanderbeke et al., 2015; Nardiello et al., 2018) and change during the clusters’ dynamical evolution (Vesperini et al., 2013). The influence of varying this ratio on the final derived fraction of the halo stemming from dissolved GCs is illustrated in Fig. 9. Finally, Baumgardt (2017) do not find a correlation between the first-generation fraction and the global mass function of GCs, but instead a trend of the escape velocity with the first-generation fraction, which reflects the finding of Milone et al. (2017) of a mass-dependence.

In principle, one can also assume a realistic distribution of GC masses (see Sect. 5.1.2 below) and attach a CN-strong fraction to each mass value via the functional trend implied by Milone et al. (2017). However, as the range of resulting fractions shown in Fig. 9 is fairly small, we adopt for simplicity that the GCs consist of 50% first-generation stars and 50% second-generation stars, which is at the higher end of the values suggested in the literature, noting that this will provide an upper limit in our final results.

5.1.2 Cluster masses and number of present-day GCs

To date, $N_{\rm GC}$ old GCs have been identified in the MW – this is the number of surviving clusters in the Galaxy, for which we adopt a value of 157, corresponding to the number of known GCs in the Harris (1996, 2010 edition) catalog. As we are dealing here with the build-up of the stellar halo, by rights only the halo clusters should be considered, which make up $\sim$75% of this database. This would only mildly decrease the resulting halo-fraction obtained in Sect. 5.3. from 11 to 8%. The influence of this parameter on our final result is shown in the middle panel of Fig. 9.

In order to convert this number into an overall mass of the Galactic GC system, we consulted the catalog of known MW GCs by Harris (1996) and computed cluster luminosities from their absolute magnitudes. For their stellar populations, we assume a stellar mass-to-light ratio of $M/L\,=\,2\,(M/L)_{\odot}$, noting that this may vary to within a factor of about two (Illingworth, 1976; Pryor & Meylan, 1993; Strader et al., 2009). Summing up these values results in a total mass of the GC system of $M_{\rm tot}=3.5\times 10^{7}$ M*⊙. In turn, this yields a simplistic estimate of the mean mass of a typical, present-day MW GC of <$$M_{\rm GC}$$> = $M_{\rm tot}/N_{\rm GC}=2.2\times 10^{5}$ M⊙*.

Alternatively, McLaughlin & van der Marel (2005) determined dynamical masses and mass-to-light ratios of approximately half of the MW’s GCs and found $M/L$ ratios that are consistent with the value of 2 adopted in our work. The average GC mass in their catalog is higher by $\sim$60%. However, this has only a minor influence during the propagation through our formalism below and the final, accreted halo fraction does not change by more than two percentage points. The influence of varying the present-day, mean GC mass on the final derived fraction of the halo stemming from dissolved GCs is illustrated in the bottom panel of Fig. 9.

Now we designate $N_{\rm Diss}$ and $M_{\rm Diss}$ as the number of completely dissolved GCs and the stellar mass lost through complete cluster dissolution, respectively, which are needed to explain the observed fraction of second-generation halo stars ($f_{h}^{2G}$). Thus we can, firstly, determine the mass that has been lost at early times as

[TABLE]

Clusters that dissolve completely contribute, in turn, via their early mass loss, as well as through their final masses, thus:

[TABLE]

Thus the total mass of GC stars in the halo field can be expressed by summing the above as

[TABLE]

5.1.3 Mass loss from the first generation

Previous studies have adopted a large fraction for $f_{1G}^{\rm\,lost}$ of up to 90% early cluster mass loss, preferentially if the clusters were massive. This is based, e.g., on the AGB scenario (D’Ercole et al., 2008; Conroy, 2012). This accounts for cluster evolutionary effects such as tidal disruption, two-body relaxation, energy input from supernovae, or residual gas loss (e.g., Gnedin & Ostriker, 1997), but not effects like “infant mortality”, i.e., the disruption of young clusters already during their formation stages (cf. Bastian & Goodwin, 2006). Likewise, in a scenario where fast rotating, massive stars were the main polluters of the second generation, models predict that the clusters were once more massive by up to factor of 25 ($f_{1G}^{\rm\,lost}=0.96$). However, recent models and observations do not further support such a strong mass loss. For instance, observations of GC populations in dwarf galaxies (Larsen et al., 2012, 2014) and young star clusters in merging galaxies (Cabrera-Ziri et al., 2015) ascertain lower mass-loss fractions of $f_{1G}^{\rm lost}\leq$80%.

Likewise, Baumgardt & Sollima (2017) argued for a loss fraction for a “typical GC” of 75%, which could, however, reach as much as 90% for the most massive objects, based on $N$-body simulations in comparison with the observed mass functions of 35 Galactic GCs. Also the simulations of Webb & Leigh (2015), accounting for orbital evolution, indicate that an average cluster was initially 4.5 times more massive ($f_{1G}^{\rm\,lost}=0.78$). We also note that Kruijssen (2015) considered a two-phase model for GC evolution, according to which only the least massive and/or metal-rich clusters suffered from high mass loss rates, whereas an average system has experienced typically $f_{1G}^{\rm lost}\sim 2/3$.

It stands to further reason that in the mass loss considered above, only first generation stars are lost, not those from the second. While originally hypothesised to solve the mass budget problem, a number of works have since shown that this heavy mass loss of only first generation stars encounters a number of problems (see the discussion in Bastian & Lardo 2018). A strong argument for this is the result from Milone et al. (2017) that the fraction of enriched stars increases with cluster mass, whereas in the heavy mass-loss scenario the opposite trend is expected. This suggests that clusters did not undergo very strong mass loss and that the current fraction is close to the initial fraction – GCs did not preferentially lose large fractions of first generation stars. Reina-Campos et al. (2018) found that clusters with present-day masses in excess of 105 M*⊙* once were only more massive at birth (after accounting for stellar evolution) by factors of 2–4. For our purpose this would imply that, if second generation stars are lost at a similar rate to those from the first population, then one would only need to correct for the relative population fractions (i.e., 50/50), and not any additional factors. For completeness, we chose to follow our previous assumptions and to retain the full correction factors, referring again to Fig. 9 for a quantitative estimate of their variations. Further discussions of the Initial Mass Function and its relevance for GC evolution can be found in Forbes et al. (2018).

5.1.4 Mass loss by stellar evolution

Many of the GC models discussed in Sect. 5.1.3 account for stellar evolution, where about a factor of two comes from stellar evolution and the other half stems from the aforementioned dynamical mass loss, viz., either two-body relaxation or tidal shocking. This equally affects stars that are part of a cluster and those that are lost from the outer regions.

Most importantly, our empirical analysis hinges on the comparison of halo stars with GCs of similar age and metallicity. If we assert that the clusters were two times more massive at birth than now, due to stellar evolution, we must also recognize that also the halo was twice as massive due to the same channels of stellar evolution. Consequentially, the mass loss factors introduced in Sect. 5.1.3 need be lowered by a factor of two. In the following, we will start with the assumption that the initial GCs were 4.5 times as massive as they are today, as argued by Webb & Leigh (2015), who did include stellar evolution. Therefore, we halve this value to 2.25 times larger initial masses, neglecting stellar evolution, which corresponds to our final, adopted fraction of 56% for the mass loss from the first generation.

In Fig. 10 we show the resulting mass fraction of the halo from GC disruption ($f_{h}^{\rm GC}$), as per the calculations concluded in Sect. 5.2, as a function of the adopted mass-loss rate $f_{1G}^{\rm lost}$. Whether the cause lies in the details of the model or in factoring in the effect of stellar evolution is redundant in this figure, as it merely shows the dependence of our results with respect to the quantitative assumption. To this end, we rather highlight three sets of adopted model fractions, each shown for the cases of inclusion and exclusion of stellar evolution.

Even in the hypothetical absence of any such early losses (i.e., Eqs. 9,10 with $f_{1G}^{\rm lost}$=0), one would still end up with a theoretical lower limit of $2\,f_{h}^{2G}$= 5% GC contributions to the present-day stellar halo. This is due to those clusters that have by now fully dissolved and that also contributed to the halo build-up via later mass loss throughout their lives. In fact, in the MW halo, a mass loss fraction of $f_{1G}^{\rm lost}$=0 is certainly conceivable; we note that this does not imply that there was no mass loss from any GC, but rather means that no stars of the first generation were lost, or that the fraction of first and second generation stars lost was roughly equal.

5.2 Resulting halo fraction

At this point, we will consider the actual number of dissolved GCs, $N_{\rm Diss}$, that are required to provide the fraction of second-generation stars, $f_{h}^{2G}$, that we found in the Galactic halo in the previous sections. As elaborated in Martell et al. (2011), this value is given as

[TABLE]

with the factor two stemming from the adopted similar fractions of first- and second-generation stars in the early clusters. It is this factor, which is not strongly constrained by observations, that dominates the final inferred fraction. Therefore we highlighted its influence in Fig. 9 (top); see Sect. 5.1.1. Based on our observed fraction of $f_{h}^{2G}=0.026\pm 0.002$ and the above assumptions, we obtain a large number of 240$\pm$22 clusters to be dissolved. This is more than twice the value found by Martell et al. (2011), but their working hypothesis had been a higher average cluster mass of 5$\times 10^{5}$ M*⊙*.

As a result, we find that the fraction of the stellar halo that originates from disrupted GCs, $f_{h}^{\rm GC}=M_{h}^{\rm GC}/M_{\rm h,tot}=$ 0.11$\pm$0.01, under the assumption of a mass loss fraction (Sect.  5.2) of 56%. The influence of different mass loss prescriptions is shown in Fig. 10 and has been discussed before in Sects. 5.1.3 and 5.1.4. Martell & Grebel (2010) stated that a high fraction of up to 50% of the halo field must have formed in massive star clusters, constituting the CN-strong population observed nowadays, with a further, unknown contribution of CN-weak stars from now fully dissolved systems. Expanding their analysis using larger data sets, and using their finding of a lower $f_{h}^{2G}$ of 2.5%, Martell et al. (2011) estimated a lower limit of 17% of halo stars with both first- and second-generation element patterns, under the omission of low-mass clusters that are long gone. The observed fraction of GC-like halo stars from the latter work is consistent with the value found in our present work, while our inferred value for donated halo stars is slightly smaller. This is, however, chiefly due to the updated statistical treatment and different model assumptions, which we amply addressed through our Figs. 9 and 10.

As a further test, as mentioned in Sect. 5.1.1, we assigned to each present-day GC mass in the compilation of McLaughlin & van der Marel (2005) a corresponding first-to-second generation fraction using the empirical trend from Milone et al. (2017) rather than adopting the generic 50/50 ratio. As a result, we would find $N_{\rm Diss}$=100$\pm$8 dissolved clusters and a donated-halo fraction of 6%. This majorly hinges on the assumption of the present-day mass distribution. Any sophisticated treatment would need to adopt a lower mass limit above which to define a “GC”, initial population fractions á la Reina-Campos et al. (2018), and/or explicit initial mass functions, the latter being highly conjectural at this point, so that we continue our discussion with our above finding of $f_{h}^{\rm GC}$ = 0.11.

We note that all our results are merely upper limits, since we assumed here that all halo stars with second-generation chemical imprints are the result of cluster dissolution. Alternative sources for these chemical patterns could be the effects of post-mass-transfer AGB binaries (e.g., Pols et al., 2012) or internal mixing processes during stellar evolution within the stars themselves (Spite et al., 2005; Stancliffe et al., 2009; Hansen et al., 2016).

5.3 Dependence on distance

Fig. 11 shows the trend of the CN-strong stars in our sample as a function of Galactocentric distance; for the latter we adopted a distance to the Galactic center of 8.34 kpc (Reid et al., 2014). Both the observed fraction of stars with second-generation chemistry (middle panel) and the derived fraction of that portion of the halo that would stem from GCs (bottom panel) show a predominantly flat trend within $\sim$30 kpc, while there is an apparent rise beyond this radius, albeit hampered by the overall small-number statistics and accordingly large error-bars at these large distances.

We further caution that the conversion between these fractions, following Eqs. 5–10, assumes that the distribution of the formerly disrupted GCs (entering via $N_{\rm Diss}$) with Galactocentric radius was isotropic. This also presumes that the orbital history of the entire MW GC system is considered irrelevant in that we reference our formalism to the present-day, total number of GCs. In fact, the MW GCs are rather distributed anisotropically and separated into the underlying Galactic components such as disks, bulge, or halo GCs. This is, however, not crucial to the present analysis as we are mainly concerned with halo GCs and halo stars as per our selection criteria.

The radial trend of Fig. 11 is, qualitatively, reminiscent of those seen in other studies (Carollo et al., 2013) and other halo tracers such as carbon stars (Carollo et al., 2012), RR Lyrae (Medina et al., 2018), and similarly for the radial (metallicity) profiles in the neighbouring Andromeda galaxy M31 (Ibata et al., 2005; Koch et al., 2008) and other external galaxies (e.g., Forbes et al., 2011), albeit the latter examples show generally stronger declines with radius within their inner halos.

Martell et al. (2011) found one CN-strong star beyond 30 kpc, giving rise to an apparent bump in their distance distribution of the CN-strong- to -normal fraction. Such a feature, though not significant is also seen in our profile at 30–35 kpc, which could indicate the presence of a real substructure in the halo at these far distances. Overall, we find 13 second-generation GC stars at distances beyond 30 kpc, with the farthest CN-strong star in our sample lying at 47$\pm$6 kpc.

6 Discussion

Our exploitation of the large-scale, low-resolution spectroscopic surveys of the SDSS has resulted in our detection of more than a hundred stars in the halo field that show strong CN- and weak CH-bands, which are the key signatures of second-generation GC stars. We thus estimate that about one tenth of the present-day MW halo originates from disrupted GC stars; this value lies below previous estimates that were based on SDSS data from earlier releases with smaller numbers of selected stars and that used different formalisms.

Our estimate hinges on several assumptions, some of which pose significant limitations to the extractability of a halo fraction from observations of stars with GC-like chemistry. Amongst these are the:

Ratio of first-to-second generations (Sect. 5.1.1)

The dependence of this parameter on global GC parameters such as mass (be it initial or present-day) or metallicity is still not fully settled. We have adopted here a value of 50 per cent of first-generation stars, which is an upper limit to the values suggested by theories and observations. Our observational finding that second generation stars make up 2.5% of the stellar halo could, effectively, be doubled when correcting for the population ratio. If some mechanism were only to remove the first generation, then our derived fraction would only be a lower limit, with a final number between 5% and 100% depending on the assumed mass loss rate. However, as per our formalism, the change in this value when changing the respective population ratio by a few tens of per cent is marginal.

Mass loss at early times (Sects. 5.1.3, 5.1.4.)

Here, we have adopted a mass loss fraction of 56%. While substantially stronger mass loss is suggested by several theories of GC enrichment and evolution, this would, as per our formalism, imply that, unrealistically, the entire MW halo or more consists of stars formerly hosted by now-disrupted GCs. This problem of “overpopulation” has also been noted for the MW bulge (Schiavon et al., 2017), in the context of mismatches in the metallicity distribution function of the Fornax dwarf spheroidal galaxy’s GC population when scaled to that of its field stars (Larsen et al., 2012), and theoretically addressed by Vesperini et al. (2010). We restate that our adopted value assumes that stellar evolution is not accounted for as it affects stars irrespective of their environment (read: halo and GCs), which prompted the need to halve the literature value from the model adopted in our work.

Mass loss from the second generation

Canonical models of GC evolution and disruption mainly engage mass loss at early times, as also inherent in our formalism. However, it is natural to assume that the second generation stars escape from the GCs at an early stage, as suggested by Schaerer & Charbonnel (2011). The implication of their model (with fast rotating massive stars as the main enrichers) is that the GCs were initially more massive by factors of $\sim$10 times (only first generation lost) or 25 times (also second-generation loss). In the scenario proposed by Schaerer & Charbonnel (2011) this also affects the conclusions drawn on the fraction that present-day GCs have contributed to the low-mass stars in the Galactic halo: while the former mass-loss fraction results in 5–8%, also accounting for the second generation increases this value to the 20% level. Similarly, Baumgardt & Sollima (2017) expect that a typical MW GC (permitting for various mass functions) would have lost about 75% of its mass since formation, while more evolved clusters have already lost more than 90 % and should dissolve over the next 1–2 Gyr, which, however, does not give us a handle on distinguishing stars of the first and second generation in the field. In accordance with our discussion in Sect. 5.1.4, we note that these models did include the effects of stellar evolution.

Stellar halo mass

In our statistics we have explicitly adopted one single number (109 M*⊙*) for the mass of the stellar halo, while more sophisticated correction factors for the footprint of the employed surveys (here, SDSS) could be envisioned – which could be argued for both our target selection and the number of present-day GCs to which we scaled our formalism. Moreover, our approach ignored the orbital histories of the observed MW GCs and assumed an isotropic distribution.

Another potentially aggravating factor is the exact value for the stellar halo mass. On the other hand, many studies have attempted weighing the entire halo (i.e., dark plus stellar) from a variety of tracers (e.g., Wilkinson & Evans, 1999; Sakamoto et al., 2003; Xue et al., 2008; Kafle et al., 2014; Wang et al., 2015; Elias et al., 2018), and the resulting range is less critical in the present analysis. As the halo mass enters inversely in the fraction of the GC-built halo, corrections can be easily implemented.

Present-day GCs (Sect. 5.1.2)

In the comparison of the number of dissolved GCs to the present-day GC population in the MW we have adopted the census of the Harris (1996) catalog. Ever since its latest revision in 2010, more GCs are being discovered towards all major Galactic components including the Galactic halo (e.g., Balbinot et al., 2013; Laevens et al., 2014; Kim et al., 2016; Koposov et al., 2017; Ryu & Lee, 2018). In particular, an estimated dozen objects towards low Galactic latitudes (while not necessarily relevant to studies of the halo) are still awaiting discovery (Ivanov et al., 2005). Since a generous decrease in the number of present-day GCs (excluding disk and bulge objects) or its increase (extrapolating future discoveries) by 25% only amounts to a change of a few percentage points in our results, the exact choice of this parameter is uncritical.

Low-mass clusters

There is now obervational support for a minimum mass on the order of a few $10^{4}$ M*⊙* for GCs to exhibit multiple populations and light element variations (Simpson et al., 2017a; Bragaglia et al., 2017; Bastian & Lardo, 2018). Furthermore, some systems appear to be first-generation only systems (Villanova et al., 2013) without any photometric or chemical evidence for the presence of a second generation, as we are looking for in this present work. However, also the lowest-mass systems and those with peculiar population mixes are likely to have experienced destruction and contributed to the halo build-up. As a consequence, these objects would not spawn any measurable quantity of the enriched second-generation stars, while they could well have contributed first-generation (CN-weak) stars which we generally discarded from consideration. This factor thus leads to an underestimate of our resulting fraction of the halo stars with GC origin by an unknown amount. Indeed, if one assumes that all star formation happens in a clustered manner, we will also miss the contributions of the early counterparts of open clusters and associations, which would not have included second-generation stars. Our current work refers to contributions by GCs with masses of at least a few times $10^{4}$ M*⊙*, which may reasonably be assumed to have formed second-generation stars.

The final a posteriori value of the donated halo fraction $f_{\rm h}^{\rm GC}$ thus relies on these, mainly model-dependent, assumptions, which hampers a clear-cut case distinction. Conversely, as per our formalism above, in particular through Figs. 9 and 10, the parameter space of the early mass-loss fraction, GC mass, and generation ratio could be majorly constrained if models were to independently predict $f_{\rm h}^{\rm GC}$. Kruijssen (2015) used his “end-to-end (yet simple)” model to conclude that the minimum mass for the formation of multiple populations was 105 M*⊙* at $z\geq 2$ under the observational constraint that about 2% of the halo consists of the CN-strong (and enriched in other nucleosynthetic products of the relevant burning processes) stars targeted in this work. The conclusion of Kruijssen (2015) is now bolstered by our present, empirical finding of this fraction lying at the 2% level.

By excluding stellar evolutionary mass loss (occurring both in the halo and the GCs) we lowered the estimated halo fraction from 23% to the 10%-level, which would represent the case that the stars lost from GCs were 100% from the first generation, so our result is clearly a mere upper limit. This also constitutes a significant difference in the interpretation with previous works, but our result it is now based on empirical relations instead of the “arbitrary”, theoretical correction factor required by the scenarios invoking pollution by AGB or fast rotating massive stars. We also reiterate that the early loss of first generation stars is observationally unconstrained and with a larger early mass loss rate, the fraction could still be higher than 11%.

Our findings may provide qualitative evidence for the inner/outer halo dichotomy, which is a consequence of hierarchical galaxy formation where an outer halo is dominated by an ex-situ, accreted component, whereas the inner halo results from both in-situ formation and the accretion of a small number of more massive satellites (Cooper et al., 2013; Pillepich et al., 2015), but we no longer see the pronounced decline in the fraction of stars with a GC origin towards the outer reaches of the inner halo found in Martell et al. (2011).

Cosmological simulations are concerned with the accretion of dark-matter dominated sub-galactic fragments related to progenitors of present-day dwarf spheroidal and dwarf irregular galaxies (which, in turn, can bring in their own GC systems; e.g., Larsen et al. 2001; Law & Majewski 2010; Hendricks et al. 2016; Kruijssen et al. 2018; Myeong et al. 2018; Helmi et al. 2018). Detecting the traces of disrupted GCs (which may include both objects formed in-situ as well as accreted GCs) as a main purveyor of the Galactic halo(s) emphasizes the complexity of disrupting satellites down to the smallest, star cluster scales. We note, however, that small satellites, which make up the outer halo should hardly have contributed any GCs, whereas massive satellites contributing to the inner halo are likely to come with more GCs. Larger and deeper spectroscopic samples are needed in order to verify the potential rise seen in the outer halo in Fig. 11.

Overall, the CN-strong stars we detected in our sample are fairly similar in many regards to their CN-weak halo mates. The latter display a mild radial metallicity gradient, as is also seen in the GC-donated component, although their small numbers frustrate a unique comparison. An important question is whether also the kinematics of these second-generation stars coincide with those of the underlying halo component, as this would provide valuable information on their accretion history and the possible orbits of the progenitor systems (e.g., Roederer et al., 2018). This will be explored in our second paper in this series (Hanke et al., in prep.), exploiting the capabilities of the new Gaia data (Gaia Collaboration et al., 2018).

As we have argued that the CN-strong stars broadly reflect the dichotomy of an inner and outer halo, it can also be envisioned that the stars at large Galactocentric distances could originate from regular mass loss from GCs that have been accreted from satellite dwarf galaxies (cf.  Kruijssen, 2015; Helmi et al., 2018). This tagging is enabled by the fact that, chemically, the GC-stars in dwarf galaxies closely follow the field star population of those dwarfs (Hendricks et al., 2016). In this case, further chemical tagging of the CN-strong objects as purported (accreted) dwarf galaxy GC stars to explore the full chemical abundance space is clearly warranted.

Large spectroscopic surveys are bound to find ever more former GC stars out to large distances, for instance SDSS-V (Kollmeier et al., 2017), or 4MOST (de Jong et al., 2012; Helmi et al., 2019), as their wavelength ranges are able to capture a large number of relevant element abundance tracers (Hansen et al., 2015). This goes in line with the desirability of a broader set of abundance tracers that can ascertain a clear-cut classification as second-generation stars. Similarly, any observed radial trends in the significance of GC contributions to the build-up of the inner and outer Galactic halos will greatly benefit from the recent and future data releases of Gaia, by pinning down the proper motions and the distances to the CN-strong candidates, although Gaia’s reach is limited towards smaller distances in the outer halo.

Acknowledgements.

This work was supported by Sonderforschungsbereich SFB 881 ”The MW System” (subproject A08) of the German Research Foundation (DFG). We are grateful to the referee, N. Bastian, for a very constructive report and helpful discussions. SLM acknowledges support from the Australian Research Council through Discovery Project grant DP180101791. Parts of this research were supported by the Australian Research Council Centre of Excellence for All-Sky Physics in 3 Dimensions (ASTRO 3D), through project number CE170100013. This publication has benefited from the conference on “Multiple populations in stellar clusters” held at the Sexten Center for Astrophysics (http://www.sexten-cfa.eu/). Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.