The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. V. Constraints on Formation Scenarios
A. Renzini, F. D'Antona, S. Cassisi, I. R. King, A. P. Milone, P. Ventura, J. Anderson, L. R. Bedin, A. Bellini, T. M. Brown, G. Piotto, R. P. van der Marel, B. Barbuy, E. Dalessandro, S. Hidalgo, A. F. Marino, S. Ortolani, M. Salaris, A. Sarajedini
aa r X i v : . [ a s t r o - ph . GA ] O c t Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 7 October 2015 (MN L A TEX style file v2.2)
The
Hubble Space Telescope
UV Legacy Survey of Galactic GlobularClusters. V. Constraints on Formation Scenarios. ⋆ A. Renzini, F. D’Antona, S. Cassisi, I. R. King, A. P. Milone, P. Ventura, , J. Anderson, L. R. Bedin, A. Bellini, T. M. Brown, G. Piotto, R. P. van der Marel, B. Barbuy, E. Dalessandro, S. Hidalgo, , A. F. Marino, S. Ortolani, M. Salaris, and A. Sarajedini INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy INAF-Osservatorio Astronomico di Roma, Via Frascati 33, I-00040 Monteporzio Catone, Roma, Italy INAF-Osservatorio Astronomico di Teramo, Via Mentore Maggini s.n.c., I-64100 Teramo, Italy Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195-1580 Research School of Astronomy and Astrophysics, The Australian National University, Cotter Road, Weston, ACT, 2611, Australia Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universit`a di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy Universidade de Sao Paulo, IAG, Rua do Matao 1226, Cidade Universitaria, Sao Paulo 05508-900, Brazil Dipartimento di Fisica e Astronomia, Universit`a di Bologna, Viale Berti Pichat 6 /
2, I-40127 Bologna, Italy Instituto de Astrofisica de Canarias, E-38200 La Laguna, Tenerife, Canary Islands, Spain Department of Astrophysics, University of La Laguna, E-38200 La Laguna, Tenerife, Canary Islands, Spain Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, IC2 Building, 146 Brownlow Hill, Liverpool L3 5RF, UK Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA
Accepted September 29, 2015; Received July 8, 2015 in original form
ABSTRACT
We build on the evidence provided by our Legacy Survey of Galactic globular clusters (GC) tosubmit to a crucial test four scenarios currently entertained for the formation of multiple stel-lar generations in GCs. The observational constraints on multiple generations to be fulfilledare manifold, including GC specificity, ubiquity, variety, predominance, discreteness, super-nova avoidance, p -capture processing, helium enrichment and mass budget. We argue thatscenarios appealing to supermassive stars, fast rotating massive stars and massive interactivebinaries violate in an irreparable fashion two or more among such constraints. Also the sce-nario appealing to AGB stars as producers of the material for next generation stars encounterssevere di ffi culties, specifically concerning the mass budget problem and the detailed chemicalcomposition of second generation stars. We qualitatively explore ways possibly allowing oneto save the AGB scenario, specifically appealing to a possible revision of the cross section ofa critical reaction rate destroying sodium, or alternatively by a more extensive exploration ofthe vast parameter space controlling the evolutionary behavior of AGB stellar models. Still,we cannot ensure success for these e ff orts and totally new scenarios may have to be inventedto understand how GCs formed in the early Universe. Key words: globular clusters: general — stars: formation — stars: evolution
Globular Clusters (GC) have always been among the most inten-sively studied stellar systems, and also among those whose imagesare so familiar to all astronomers. Yet, we have never really under-stood why it was so easy to produce such massive and extremelydense stellar aggregates, with over 100,000 stars per cubic parsec, ⋆ Based on observations with the NASA / ESA
Hubble Space Telescope ,obtained at the Space Telescope Science Institute, which is operated byAURA, Inc., under NASA contract NAS 5-26555. and generate them in such a widespread fashion, no matter whetherin a metal-poor or a metal-rich environment. We still have to un-derstand how they formed, why they are so common around giantellipticals such as M 87, or spirals such as the MW Galaxy, or evenin dwarfs such as Fornax or Sagittarius. Then, with the discoveryof their multiple stellar populations, answering these questions be-came even harder than ever before.In this series of papers we report the results of the
Hub-ble Space Telescope UV Legacy Survey of Galactic GCs dedi-cated to the observation of 48 GCs through the filters F275W,F336W, F438W of the Wide Field Camera 3 (WFC3) on board
HST c (cid:13) A. Renzini et al. (Piotto et al. 2015, hereafter Paper I ), which complements the ex-isting F606W and F814W photometry from the Advanced Camerafor Survey, or ACS (Sarajedini et al. 2007; Anderson et al. 2008)and is specifically designed to map multiple stellar populations inGCs. This set of filters, have proved to be most e ff ective in dis-entangling the various sub-population, as these bands sample dif-ferent molecular absorptions, such as OH, NH, CH and CN, hencecan distinguish stars with di ff erent degrees of p -capture processing(e.g., Milone et al. 2012). Together with similar data already ob-tained in previous HST cycles, our survey brings to 57 the numberof GCs with such a homogeneous, multiband database which al-lows us to resolve such GCs in their multiple populations. As partof this project, the prototypical examples of M2 and NGC 2808and that of NGC 6352 have been already published (Milone et al.2015a,b; Nardiello et al. 2015, respectively paper II, III and IV).Photometric and spectroscopic evidence accumulated over theyears has shown that secondary generations (2G) in GCs are madeof materials enriched in helium, nitrogen and sodium and depletedin carbon and oxygen, hence implying that they have been ex-posed to proton-capture reactions at high temperatures ( ∼ − p -capture materials areproduced at such temperatures and then likely ejected. Thus, thecandidate producers of the raw 2G material have been, in or-der of decreasing mass: i) supermassive stars (SMS, ∼ M ⊙ ,Denissenkov & Hartwick 2014), ii) massive interacting binaries(MIB, e.g., 15 + M ⊙ , de Mink et al. 2009; Bastian et al. 2013),iii) fast-rotating massive stars (FRMS, ∼ − M ⊙ , Krause et al.2013) and iv) asymptotic giant branch (AGB) and super-AGB stars(hereafter collectively, AGB, ∼ − M ⊙ , e.g., D’Ercole et al.2010). Each of these candidate 1G donors is then part of its corre-sponding scenario depicting how the 1G-processed material mightbe incorporated into 2G stars. In the present paper we concentrateon exploiting the evidence presented in the earlier papers of this se-ries to set constraints on these GC formation scenarios. In the lastsection we briefly mention other possible observational constraints. In Paper I we listed the main constraints on 2G formation that areimposed by the photometric and spectroscopic evidence. Here werecall them and add a few more. • GC Specificity.
The presence of 2G stars, with their chem-ical characteristics, is common within GCs, but stars with suchcharacteristics are very rare in the Milky Way field. Their smallnumber in the field is consistent with them having been generatedwithin GCs and then lost by them through tidal interactions (e.g.,Vesperini, McMillan & D’Antona 2010; Martell et al. 2011). Thisindicates that the (proto-)GC environment may be indispensablefor the production of stars with such special composition. In anyevent, every scenario aiming at accounting for GC multiple pop-ulations must at the same time account for the rarity of 2G-likestars in the field, i.e., it must be GC specific. Young massive clus-ters (YMC, with mass up to ∼ M ⊙ ) are occasionally forming inthe local Universe, but do not appear to be brewing 2G stars (e.g.,Bastian et al. 2013). So, special conditions encountered only in theearly Universe appear to be instrumental for the occurrence of theGC multiple population phenomenon. • Ubiquity.
In almost all GCs studied in su ffi cient photometric and / or spectroscopic detail, evidence has been uncovered for thepresence of 2G stars (in particular in the unprecedented sample ex-plored by our Legacy Survey). This suggests that the productionof multiple populations is an unescapable outcome of the very for-mation process of GCs. None of the proposed scenarios is in ob-vious tension with this constraint, hence ubiquity is not consideredany further in this paper. However, it remains essential for any GCformation theory to account for the formation of multiple stellargenerations as an almost inescapable outcome, as opposed to a for-tuitous event taking place only in a few cases and under specialcircumstances. • Variety.
While virtually all GCs harbor multiple populations,no two GCs are alike, i.e., each cluster has its own specific patternof multiple populations, ranging from a minimum of two, up toseven and possibly more, each with specific chemical composition.Thus, there must be large cluster-to-cluster di ff erences in the wayin which materials from the 1G donors are eventually incorporatedinto 2G stars and / or in the chemical composition of such materials. • Predominance.
2G stars are not a minor component in mostGCs, but may even dominate especially in the central regions wheretheir fraction can largely exceed ∼ ∼
23% of the cluster population (PaperIII). • Discreteness.
A major characteristic of multiple populationsis that within each cluster they can be separated into quite distinct sequences in various color-magnitude diagrams (CMD) and / or inappropriate two-color plots, as opposed to a continuous spread .To be sure, for quite some time spectroscopic evidence has insteadbeen consistent with a continuous spread in chemical compositions,particularly suggestive in the case of the ubiquitous O-Na anticor-relation (e.g., Carretta et al. 2009). However, the apparent continu-ity of spectroscopic abundances has been widely suspected of be-ing due to measurement errors blurring an underlying discreteness,which is so evident in photometric data (e.g., Renzini 2013). Quiterecently, Carretta (2014) was indeed able to show that in the caseof NGC 2808, with more accurate abundances, the earlier contin-uous O-Na anticorrelation indeed splits into at least three separateclumps. (For a previous example of spectroscopic discreteness seeMarino et al. 2008) Discreteness is quite powerful at discriminatingamong competing scenarios and therefore we expand on it furtherin Appendix A. • Supernova avoidance.
In most GCs the various multiple (2G)populations share the same metallicity [Fe / H] with the primary(1G) population, and do so within better than ∼ . ω Cen and Terzan 5, but lessextreme metallicity di ff erences are now documented for quite afew other clusters such as M2, M22, M54, NGC 185, NGC 5286and NGC 5824 (see Paper I and Marino et al. 2011, for references).Still, even in the case of ω Cen to enrich 2G stars to their observediron content it is su ffi cient that only ∼
2% of the iron ejecta ofthe core-collapse supernovae from the 1G were retained and incor-porated into 2G stars, while 98% of such ejecta were lost by thesystem (Renzini 2013). Indeed, the main metal rich component ofthis cluster contains just ∼ M ⊙ of additional iron compared tothe iron content of the 1G component (Renzini 2008). The corecollapse supernovae from the 1G population of ∼ × M ⊙ at ori-gin have instead produced ∼ , M ⊙ of iron, with most havingbeen ejected and only ∼
2% retained in 2G stars. This estimate isbased on the present mass of the 1G component, so it is only anupper limit; if the 1G was substantially more massive at its origin, c (cid:13) , 000–000 lobular Cluster Formation a smaller fraction would su ffi ce. Thus, in all GCs, 2G stars have ex-perienced very little contamination by supernova products, or noneat all, with only a very small fraction of such products having beenincorporated into 2G stars. Every GC-formation scenario needs toaccount for such avoidance of supernova ejecta. • Hot CNO and NeNa processing.
A distinctive characteristicof 2G stars is the chemical composition that results from CNO-cycling and p -capture processes at high temperatures. All candidate1G donors have indeed been chosen purposely because they are asite of such processes. Thus, every scenario should quantitativelyaccount for the variety of composition patterns exhibited by 2Gstars in all GCs that have been studied. Here, however, each sce-nario depends on the specific nucleosynthesis yields of the invoked1G donors, which all are extremely (stellar-) model-dependent. Forexample, theoretical AGB yields di ff er dramatically from one setof AGB models to another: some sodium is produced by the AGBmodels of Ventura et al. (2013) but it is instead mostly destroyedin the models of Doherty et al. (2014), and comparable uncertain-ties are likely to a ff ect the yields of the other candidate polluters.Actually, Bastian et al. (2015) argue that none of the yields used ineach of the four scenarios is able to reproduce the observed abun-dance patterns, even by appealing to an ad hoc dilution with pristinematerial. This does not necessarily invalidate any of the scenarios;instead it clearly calls into question the stellar models used to cal-culate those yields. It is important to realize that such theoreticalyields depend on several parameters needed to describe bulk mo-tions of matter inside stars (e.g., rotation, convection, mixing, massloss) and that only a tiny fraction of this parameter space has beenexplored so far (Renzini 2014). For these reasons we believe that atthis stage arguments based uniquely on the chemical compositionof 2G stars cannot be conclusive, either for or against any of theproposed scenarios. • Helium enrichment.
The discovery of the helium-rich 2Gstars, first in ω Cen and in NGC 2808, and then in virtually allother GCs that have been studied, has been bewildering and hascompletely changed our view of GCs and their formation (see ref-erences in the previous papers of this series). The ubiquity of thehelium enrichment in 2G stars is extensively documented by themulti-band database provided by our Legacy Survey. All invoked1G donors do meet the requirement of shedding helium-enrichedmaterial out of which 2G stars may form, though they may predictdi ff erent yields of helium relative to other elements, most notablyoxygen and sodium. • Mass Budget.
The mentioned predominance of the 2G com-ponent in many GCs is a challenge for all possible scenarios,as only a small fraction of the initial 1G mass is deliveredwith the composition required for 2G stars. For example, with aKroupa / Chabrier-like IMF the ∼ − M ⊙ AGB stars deliver only ∼
10% of the initial total mass of the first generation. A way outfrom this di ffi culty is to postulate that the progenitors of todayGCs were substantially more massive than their present-day GCprogeny, with a strict lower limit of a factor of ∼ ∼
20 or more. This is to say that GC progenitorswould have lost at least ∼ −
90% of their mass before deliver-ing the naked clusters as we see them today. Especially demandingis the presence of oxygen depleted populations, which imply thatsuch stars formed from material that was fully processed through1G stars. For example, in the central field of NGC 2808 the oxygendepleted populations account for ∼
50% of the total mass. Thus,depletion is more demanding for the mass budget than pollution,as e.g., a high sodium enhancement could in principle be achieved by polluting pristine gas with a relatively small mass of materialhighly enriched in sodium.
In this section we first sketch the four scenarios that have been men-tioned and then confront each of them with each of the binding con-straints, checking whether they can fulfill them as they are, or onlywith major modification in some of the ingredients (e.g., the stellaryields), or whether by their nature there is no way they could satisfysome constraint. These three di ff erent grades of (im)plausibility arereferred to in Table 1 as ”OK”, ”TBD”, and ”Nix”, respectively.The four scenarios are now examined in detail, in order of decreas-ing mass of the 1G donor. In doing so we will not discuss whether aparticular scenario is physically plausible on general grounds, e.g.,whether or not a SMS can form, or whether low-mass stars canform in an extruding disk, etc., even if some of these scenarios re-main highly conjectural at this stage. As stated, we limit ourselvesto checking whether the binding constraints can be fulfilled. Denissenkov & Hartwick (2014) and Denissenkov et al. (2015)build on the idea that within a young GC the most massive starswill sink to the center by dynamical friction and coalesce there,hence forming a SMS of ∼ M ⊙ . An object of this kind wouldbe fully convective, with a luminosity close to or exceeding the Ed-dington luminosity, hence would lose mass at high rate. Since fullconvection makes the SMS chemically homogeneous, as it evolvesits wind would be progressively enriched in helium and of productsof CNO cycling and p -capture reactions: the kind of compositionone wants for 2G stars. This scenario quite naturally fulfills the“GC specific” requirement, as the GC environment is indeed in-strumental for the formation of the central SMS. Variety may beexpected, e.g., from di ff erent possible masses of the SMS and fromdi ff erent timing of the 2G star formation. Discreteness of the multi-ple populations may be accommodated appealing to separate burstsof star formation, that take place at di ff erent stages of pollution ofthe ISM by the SMS. Supernova avoidance is much more di ffi cultto accommodate in this scenario, because the SMS and 2G starsshould both form before a fraction of a percent of massive starscould explode. Because of this contrived timing, we give a Nixfor this constraint. Denissenkov & Hartwick want the SMS to bein a very precise range around ∼ M ⊙ , and should be “.. nei-ther ∼ M ⊙ nor > ∼ M ⊙ ”, otherwise their central temperatureswould be either too low or too high to produce p -capture elementsin the right mix. In Denissenkov et al. (2015) the SMS mass is cho-sen to be 7 × M ⊙ , because its central temperature of ∼ × K ensures a sizable oxygen (and magnesium) depletion without de-stroying sodium. Moreover, it is assumed that the SMS fragmentsand falls apart when helium has increased to Y = .
4, the upperlimit of the helium abundance in 2G stars. This scenario faces aninsurmountable di ffi culty with the mass budget constraint: for ex-ample, the major 2G population in ω Cen has a mass of ∼ M ⊙ and has been enriched in helium by ∆ Y ∼ . ∼ M ⊙ of fresh helium is required. So, the limit im-posed to the mass of the SMS makes it impossible for them to de-liver the required amount of helium and we give a Nix to both themass budget and the helium constraints. Moreover, the helium-rich2G stars are also highly depleted in oxygen, implying that all theirmaterial was previously processed through 1G donor stars. Again, c (cid:13) , 000–000 A. Renzini et al. the same argument for the excess helium can be spent for the oxy-gen depletion: SMSs do produce helium and destroy oxygen, but afew × M ⊙ SMS is simply not massive enough to produce heliumenhancements and oxygen depletions on the scale that is observedin 2G stars in GCs. Appealing to multiple SMSs would not workeither, as by the same token dynamical friction would force themto coalesce even faster than massive stars would do.
In the current version of this scenario (Krause et al. 2013), 2G starsform within the extruding disks of FRMS, with or without dilu-tion with pristine materials that are supposed to exist in their vicin-ity. As such, if the process exists in nature, it is not specific toGCs but to all FRMSs, whether in a GC or not. So if this processworked, the result would be that stars with the chemical patters of2G stars in GCs would be nearly as frequent in the Galactic-halofield as in GCs, which is at variance with the observations. Hencewe give a Nix for GC specificity. Given the star-by-star formationprocess, one may expect little variation from one batch of 2G starsto another, as 2Gs would arise from the contribution of very manyFRMSs; but perhaps the scenario could be tuned to do that, so weassign a TBD to the variety constraint.Discreteness of 2G populations is, on the other hand, an in-surmountable di ffi culty for this scenario, since Krause et al. (2013)admit that ”a consequence of this way of star formation is that thedistribution of abundances will always be continuous.” Supernovaavoidance is also a major problem. The fast winds from massivestars, and from their supernova explosions, make the extremelycrowded central regions of GCs too harsh an environment for ex-truding disks to avoid contamination by supernova products or evenfor them to survive at all. The mass budget and detailed abundancesof 2Gs are also a problem for this scenario, as for all others, but asin the case of the other 1G donors, we cannot exclude the possibil-ity that the actual yields may be di ff erent from those computed sofar and that the mass-budget problem could thus be solved. Hencethese last constraints do not result in a fatal argument against thisscenario. This scenario was first proposed by de Mink et al. (2009) and hasbeen further elaborated by Bastian et al. (2013). In MIBs the forcedrotation of the primary envelope would cause mixing, which, ifreaching down to the hydrogen-burning shell, would result in CNOand p -capture processing of the whole envelope, hence leading tohelium enhancement, oxygen depletion, etc. The processed enve-lope would then be shed in a subsequent common-envelope phaseof the MIB, thereby going to replenish the ISM. In the original deMink et al. scenario 2G stars would then form out of this material.In the Bastian et al. (2013) version, MIB ejecta would instead beswept up by the circumstellar disks of young, low-mass stars andeventually dumped onto the stars themselves. The scenario is cer-tainly GC-specific, as the high density of a GC is needed to ensurea su ffi ciently high density of the ISM to be built up for appreciableaccretion to take place.Variety, i.e., large cluster to cluster di ff erences, might be ac-commodated in this scenario, that instead encounters insurmount-able di ffi culties in producing multiple GC populations that are dis-crete. The problem is that large yet continuous star-to-star di ff er-ences in the amount of swept / accreted material are naturally ex-pected in this scenario, while there is no known mechanism that would lead to quantized accretions resulting in the sharp discrete-ness exhibited by the composition of 2G stars in all GCs, with theextreme cases like ω Cen, M2, and NGC 2808, with their more thanfive distinct populations. Moreover, there is no way to establish andmaintain the observed 1G /
2G dichotomy, because the surviving 1Gshould have avoided accretion completely, while the 2G stars wouldhave been dominated by it, with no intermediate cases (but see Ap-pendix A for still a possible role for accretion).Dichotomy / discreteness is indeed a killing argument for anyaccretion scenario for the origin of multiple GC populations (e.g.,Renzini 2013). Supernova avoidance is another insurmountable dif-ficulty for this scenario too (and for its original de Mink et al. ver-sion as well), as the MIB 1G donors would inevitably coexist withthe supernovae from single stars as well as from MIBs themselves,so the ISM could not be made exclusively of the preferred MIBcommon-envelope ejecta. Bastian et al. (2015) argue that the avail-able yields plus dilution cannot account for the detailed composi-tion patterns that are exhibited by GC multiple populations, but weregard this as a minor concern compared with those just mentioned.The mass-budget problem may a ffl ict this scenario as it does theothers, but again this is not necessarily a fatal flaw. AGB stars have long been entertained as the possible origin, firstof GC composition anomalies (e.g., D’Antona, Gratton & Chie ffi ∼ − M ⊙ to ∼ M ⊙ experience the socalled hot bottom burning (HBB) process (see e.g., Ventura et al.2013, whereby very high temperatures are reached at the bottomof the convective envelope, thus allowing e ffi cient p -capture nu-clear processing. This mass range should be regarded as indicative,because it is somewhat model dependent, e.g., on whether over-shooting from convective cores is assumed and on its extension.Below ∼ M ⊙ the HBB process does not operate and the AGB ispopulated by carbon stars. Since none of the 2Gs so far discov-ered is made of carbon stars one is forced to conclude that in thisscenario the 2G formation must be completed before < ∼ M ⊙ starsevolve into the AGB phase. It is important to note that the maxi-mum temperature reached at the base of the convective envelope isa strong function of stellar mass, e.g., in the low-metallicity modelsof Ventura et al. (2013) it increases from ∼ × K in 3 M ⊙ mod-els to ∼ × K in 7 . M ⊙ models. Moreover, these values areextremely sensitive to the treatment of envelope convection, whichremains a major source of uncertainty. The mentioned mass rangemay be extended up to ∼ M ⊙ by including among the 1G donorsthe so-called super-AGB stars, i.e., stars that ignite carbon in thecore, shed large amount of helium and CNO-processed material,and die either as ONeMg white dwarfs or electron-capture super-novae (e.g., Ritossa, Garcia-Berro & Iben 1996). Thus, in this sce-nario the fact that stars in a wide range of stellar masses contributethe material to form 2G stars ensures that p -processing takes placeover a wide range of temperatures, with e.g., sodium being mostlyprovided by lower mass stars and oxygen-depleted material by themore massive ones.In the specific model of D’Ercole et al. (2010) a massive GCprogenitor has a major episode of star formation leading to the first(1G) generation, but is then emptied of residual gas by supernovafeedback. At the end of the supernova era, AGB (and Super-AGB)ejecta start to accumulate within the potential well of the system, c (cid:13) , 000–000 lobular Cluster Formation since their ejection velocity ( ∼
10 km s − ) is lower than the escapevelocity. A cooling flow is then established, leading to accumula-tion of gas within the original nucleus, until one or more starburstsmake the 2G stars. Dilution with pristine gas was also invoked inthe attempt to better reproduce the observed O-Na anticorrelation.In the subsequent dynamical evolution of the system most of 1Gstars would be lost e.g., via tidal interactions with the MW (orparent) galaxy, leaving a naked GC with comparable fractions of1G and 2G stars. We consider here only the main features of thisscenario, rather than its specific incarnation in a particular model.For example, rather than a more massive, compact GC the progen-itor may have been a nucleated dwarf galaxy (as suggested by e.g.,Bekki & Norris 2006),GC-specificity, variety, and discreteness are probably not aproblem for this scenario. The deep potential well of the progen-itor is instrumental in retaining the AGB ejecta, thus allowing sub-sequent star formation events to take place from this material. Inthe GC progenitor the chemical composition of the ISM is rapidlychanging as it gets replenished by the ejecta of AGB stars of pro-gressively lower initial mass; hence each star-formation burst willhave a specific composition. Thus, discreteness arises from burstsof 2G star formation being separated by periods of (relative) inac-tivity. Variety in di ff erent GCs can arise from di ff erent numbers ofbursts and their di ff erent timings. Thus, the intimate stocharsticityof star formation would ensure variety. The AGB era during which2G stars would form is indeed bound in time by the end of the core-collapse supernovae on one side and by the ultimate gas removal(by either Type Ia supernovae or interaction with the environment)on the other. This time interval, of the order of ∼ years, maywell change from one cluster to another, depending on the detailedstar formation history that led to the first generation. Similar argu-ments can be applied to other scenarios as well, where 2G stars areproduced in star formation events.Avoidance of contamination by 1G core-collapse supernovaeis automatically fulfilled, but if there is more than one 2G star-burst, supernovae from stars of the first 2G burst may contaminatethe later-formed generations, an aspect that is further discussed in afollowing section. The postulated dilution with pristine gas remainsproblematical: where was such material stored in the meantime,and how did it avoid being contaminated by 1G supernovae? Thesequestions remain unanswered.The mass budget is a problem that is solved by appealing to asu ffi ciently massive precursor. Quantitative estimates of how mas-sive this precursor needs to be depend on several uncertain factorssuch as the mass range of the 1G AGB donors, the star formatione ffi ciency, the 2G IMF and the incidence of the postulated dilution.Particularly critical is the star formation e ffi ciency, i.e., the fractionof the available gas from 1G ejecta that is e ff ectively turned into 2Gstars (e.g., Renzini 2013). To minimize the mass budget D’Ercoleet al. assume that the IMF of 2G stars is truncated at a value < ∼ M ⊙ ,which also ensures supernova avoidance from one 2G starburst tothe next. Moreover, the absence of 2G supernovae would preventgas that is not used by a 2G star-formation episode from being ex-pelled from the system, hence keeping it available for subsequentstar-formation events. Thus, even if the star formation e ffi ciency ofindividual bursts is low (say ∼ − ∼ −
10 times the presentmass of a GC. Yet, the nature of GC progenitors remains a criticalproblem for this as for all other scenarios. In Section 4.1 we furtheraddress this issue. One enduring problem with AGB stars as 1G donors is thatthey tend to produce a correlation between oxygen and sodium,rather than an anticorrelation , as actually observed. (See e.g., Fig-ure 3 in D’Antona et al. 2011.) Assuming that the mass range ofAGB producers of p -capture elements is somewhere between ∼ ∼ − M ⊙ , towards the low mass end of this range these AGBmodels shed material that is both O rich and Na rich. At the oppo-site mass end they shed material that is both O- and Na-depleted.This makes it di ffi cult to match the observed anticorrelation,especially in cases of extreme oxygen depletion. However, AGByields are extremely sensitive to several, interlaced parameters de-scribing processes such as convection, mixing and mass loss. So,future calculations may deliver yields more compatible with thesurvival of sodium in matter processed by HBB at high tempera-tures. In Section 4 we recall what are the main physical processesa ff ecting the AGB yields and we speculate on how AGB modelsmight be tuned to produce yields in better agreement with the ob-servational requirements. All in all, there appears to be no blatantshow-stopper for this scenario and, as reported in Table 1, no Nixis assigned to it. In all scenarios discussed above, except one, more than one starformation event takes place, a first one out of pristine material (1G)and one or more subsequent events where 2G stars form out of ma-terial processed by 1G stars. The exception is the case of the sce-nario where ejecta from massive interacting binaries are accretedby the circumstellar disks of lower mass stars. In such case there isindeed only one star formation episode, i.e., only one stellar gen-eration (1G), but some of the 1G stars are polluted by the ejecta ofmore massive stars of the same generation. However, by its very na-ture any accretion scenario is incapable of producing distinct, mul-tiple stellar populations within individual GCs such as those beingdocumented by the present Legacy Survey. Thus, we consider GC“multiple stellar populations” and “multiple stellar generations” assynonyms and may use the two expressions interchangeably.
Table 1 summarizes the results of these cross checks. In the table wedistinguish the two versions of the MIB scenario, one with circum-stellar disk accretion (MIB
Acc ) and another with possibly discreteevents of star formation (MIB SF ). Three scenarios, namely SMS,FRMS and MIB Acc , fail to meet two or more constraints and doso because of their intrinsic nature, i.e., such failure does not ap-pear curable by fine tuning parameters. Supernova avoidance anddiscreteness are the constraints which are more widely violated,and to which insu ffi cient attention, or none, has been dedicated bythe proponents of such scenarios. The MIB SF option clearly vio-lates only the supernova avoidance constraint. The AGB is the onlyscenario that does not appear to irreparably violate the seven con-straints. Yet, it is still far from providing an adequate, quantitativeaccount for the specific composition patterns so far documented inthe first papers of this series and in the references therein. The massbudget problem remains, along with the still unknown nature of theGC precursors, i.e. the systems that nursed GCs as we eventuallysee them today. Whether the AGB scenario could be upgraded tomeet the observed patterns quantitatively is addressed in the nextsection. c (cid:13) , 000–000 A. Renzini et al.
Table 1.
The cross-check of the four scenarios discussed in the text vs the observational constraints set by the properties of the second generations.Scenario GC Specific Variety Discreteness SN Avoidance Mass budget Hot p-captures HeliumSMS OK OK TBD Nix Nix Nix NixFRMS Nix TBD Nix Nix TBD TBD TBDMIB
Acc
OK OK Nix Nix TBD TBD TBDMIB SF OK OK OK Nix TBD TBD TBDAGB OK OK OK OK TBD TBD TBD
The binding constraints from our Legacy Survey are su ffi cient toclearly falsify three of the four examined scenarios, but still do notprovide fatal evidence against the AGB scenario. Yet, even if we didnot assign any ”Nix” to the AGB option, this scenario encountersif not fatal, at least severe di ffi culties in accounting for all the ac-cumulated evidence on the multiple populations of GCs. The massbudget is one, the detailed chemical composition of 2G stars is an-other. In this section we speculate on whether possible ways mayexist of upgrading this scenario to better match the binding con-straints. We emphasize that we do so for a lack, at least temporarily,of any better alternative. A possible solution (or alleviation) of the mass budget problem hasalready been mentioned, i.e., the D’Ercole et al. (2010) postulate ofa di ff erent IMF between 1G and 2G stars, with that of 2Gs beingtruncated at a mass close to or below ∼ M ⊙ . This ansatz has threebeneficial e ff ects, it reduces the mass budget directly as well as in-directly (by allowing a virtually ∼ ffi ciency)and avoids supernova pollution from one 2G to another. Yet it re-mains unproved.One possible reason for a di ff erent IMF for 2G stars comesfrom the fact that such stars have to form in an environment al-ready densely occupied by 1G stars. The typical central density ofa massive GC is ∼ M ⊙ pc − , corresponding to a number densityof atoms n ≃ cm − . Moreover, 1G and 2G stars have compa-rable number density in a GC central region and often the 2G evenprevails. With a Chabrier / Kroupa IMF, ∼
150 stars (more massivethan 0 . M ⊙ ) are formed every 100 M ⊙ of gas that goes into stars,hence central densities exceed 10 stars per cubic parsec (and mighthave been even higher at formation time). Thus, 2G star formationtakes place in an environment already inhabited by an extremelydense stellar system. This may well be a di ff erent mode of star for-mation, compared to the case of a molecular cloud virtually devoidof pre-existing stars (Renzini 2013). To our knowledge, star forma-tion in an extremely densely populated stellar system is a mode ofstar formation never explored so far. Yet, this must be the mode toform 2G stars in virtually all GCs. For the time being, we can saythat if there is a situation in which star formation takes place with adi ff erent IMF, this may well be the core of a proto-GC. Might mas-sive star formation be inhibited in such environment? This does notappear to be the case in the vicinity of the Galactic center, wherestellar densities may be even higher, and where massive stars ap-pear to have formed, either by coalescence of less massive ones orin counter-rotating disks (Genzel et al. 2003), though conditions inthe Galactic center may not be representative of those in proto-GCs.Besides helping with the Na-O anticorrelation, the postulated dilution with pristine material also has the beneficial e ff ect of some-what alleviating the mass budget issue. However, its origin remainsproblematical along with its supernova avoidance. One less contro-versial form of dilution which must occur to some extent is via theejecta of common-envelope binaries of intermediate mass stars, asadvocated by Vanbeveren, Mennekens & De Greve (2012).How over ∼
80% of the progenitor mass would have been re-moved remains problematical. There appears to be no correlationof the 2G /
1G ratio with galactocentric distance (Bastian & Lardo2015), confirmed by the larger and homogeneous dataset of ourLegacy survey (Milone et al. in preparation). This may argueagainst the progenitor being a compact, just more massive GC andmay favor the nucleated dwarf galaxy option, with the less boundbody of such an object being more easily stripped.Larsen, Strader & Brodie (2012) have argued that the FornaxdSph galaxy with its own GCs may set an upper limit to the possi-ble mass budget. Based on two O-poor / Na-rich stars found in twoamong the four metal poor GCs (from Letarte et al. 2006) it is in-ferred that also Fornax GCs harbor multiple stellar populations.Larsen et al. note that the metal poor component of this galaxy isonly ∼ − ∼
26 times that of the MW galaxy, which suggests that alsoFornax may have lost a significant fraction of its original stellarmass. This may be even more the case for its metal poor com-ponent, given that the specific GC frequency jumps to ∼
400 ifthe calculation is restricted to only the metal poor component. So,we regard as interesting but not yet compelling the proposed upperlimit for the mass budget.
As mentioned in Section 3.4, the main di ffi culty encountered bythe AGB scenario consists in predicting the observed chemical pat-terns observed in 2G stars, most notably the oxygen-sodium anti-correlation. Thus, it is worth expanding a bit on the physics of whythis happens. Upon arrival on the AGB, stars in this mass range areonly slightly depleted in oxygen and somewhat enriched in sodium.They are also slightly depleted in carbon and enriched in nitro-gen and helium. All this is due essentially to the second dredge-up (2DU), when envelope convection penetrates through the ex-tinguished hydrogen shell into helium layers that were processedby the hydrogen-burning shell during the previous evolutionaryphases. Indeed, in this shell oxygen was highly depleted in favorof nitrogen while sodium had been produced by the Ne( p , γ ) Nareaction, with Ne being also replenished by two successive p -captures on Ne. Since initially Ne is more abundant than Na c (cid:13) , 000–000 lobular Cluster Formation Figure 1.
The rates of the O( p , γ ) F and Na( p , α ) Ne reactions as afunction of temperature, showing that for T . K oxygen is destroyedfaster than sodium, whereas sodium is destroyed faster above this tempera-ture. and Ne is ∼
100 times more abundant, even a relatively smallreduction in the abundance of Ne isotopes can result in a factorof ∼
10 increase in the surface abundance of Na. Upon settlingon the AGB, these stars start experiencing the HBB process andnow the whole convective envelope works as a reservoir of neonisotopes ready to be turned into Na. Thus, brought by convec-tion to the HBB layers, part of these neon isotopes are then con-verted to Na, further enhancing the surface abundance of sodium(see e.g., Figure 6 in Ventura & D’Antona 2005a). However, as thesodium abundance increases, so does the rate at which it is de-stroyed by its own p -captures, via the reactions Na( p , γ ) Mg and Na( p , α ) Ne. At the same time oxygen is being destroyed by thereaction O( p , γ ) F and subsequent reactions, eventually turningthis oxygen into nitrogen. So, after an initial spike of Na produc-tion, both sodium and oxygen tend to be destroyed, which is whyit happens that way in, e.g., the AGB models of D’Antona et al.(2011) and Doherty et al. (2014).Therefore, what matters is ultimately the relative rate at whichoxygen and sodium are destroyed and on the timing in the inter-ruption of these processes when the envelope is eventually lost ina (super)wind and the Post-AGB phase begins. The existence ofoxygen-poor and sodium-rich stars among the 2G stars of manyGCs argues for oxygen being destroyed faster than sodium. Howcould this happen? Figure 1 shows the rates of the O( p , γ ) F and Na( p , α ) Ne reactions as a function of temperature (this latterbeing the dominant channel for p -captures on Na). Thus, at lowertemperatures ( T < ∼ K) oxygen is destroyed faster than sodium:a result of the lower tunneling probability through the Coulombbarrier of sodium compared to that of oxygen. However, at highertemperatures the di ff erence in tunneling probabilities decreases andwhat becomes dominant is the fully nuclear part of the cross sec-tion: the destruction of sodium becomes faster than that of oxygenbecause the destruction reaction is mediated by the strong interac-tions (revealed by the emission of an α particle) whereas the oxygen destruction reaction is mediated by the much weaker electromag-netic interactions (as revealed by the emission of a γ photon). Thus,above ∼ K sodium is destroyed faster than oxygen. By the sametoken, it is clear that the AGB evolution should end before thisNe-Na cycle has reached equilibrium, i.e., near equality betweenproduction and destruction rates of neon and sodium isotopes. For,equilibrium disfavors sodium as it is produced by electromagnetic nuclear reactions and destroyed by strong nuclear reactions.This means that if one wants to produce AGB yields that areoxygen depleted and still sodium rich, then the HBB should workat temperatures below ∼ K in a suitable fraction of the AGBstars. Incidentally, this is precisely why Denissenkov et al. (2015)want their SMSs to work at ∼ × K. Actually, the AGBscenario o ff ers an important opportunity, in that the AGB yieldsresult from the contribution of stars in and extended mass range(within roughly ∼ ∼ M ⊙ ), hence with an extended rangeof temperatures at which the HBB process has operated, becausesuch temperature is a strong function of stellar mass, metallicityand changes in the course of the evolution of each individual AGBstar (e.g., Renzini & Voli 1981). In the most massive AGB stars theHBB temperature may indeed be so high that even the abundanceof Mg, Al, Si, and K can be a ff ected by p -capture reactions, andindeed demanded by the observed abundances of these elements inthe 2G stars of some GCs (e.g., Carretta et al. 2009; Carretta 2014;Cohen & Kirby 2012; Mucciarelli et al. 2012).This is illustrated in Figure 2, where the temperatures abovewhich the various p -capture reactions e ff ectively operate is shown,including those producing Al, Si and K at the expenses of respec-tively Mg, Al and Ar (Ventura et al. 2011, 2012), an oppor-tunity that only the AGB scenario can potentially o ff er. The figureshows that models of either MIBs or FRMSs operate at tempera-tures not exceeding ∼ × K, so they can easily process oxygento nitrogen and do not destroy sodium, but fail to appreciably turnmagnesium into aluminum. The preferred central temperature forthe SMS models is indicated by the blue vertical bar at ∼ × K,su ffi cient to destroy O while preserving Na and ensuring some con-version of Mg into Al, but being too low to allow production ofSi and K. Finally, the HBB temperature range potentially coveredby AGB stars extends from well below to somewhat above ∼ K, encompassing a wide variety of situations, from oxygen deple-tion and sodium production, to Al, Si and K production. However,stars producing these heavier p -capture elements will necessarilydestroy sodium, hence other, less massive AGB stars should pro-duce it while still destroying oxygen. As mentioned above, so farnone of the incarnations of the AGB scenario has fully accountedfor the detailed abundance patterns exhibited by 2G stars.We see two potential ways of saving this scenario, i.e., to makeit to produce p -capture elements (and helium) in the observed pro-portions. The simplest way is to assume that the actual cross sectionof the Na( p , α ) Ne reaction is somewhat lower that the recom-mended value by Angulo et al. (1999). Indeed, with a factor of ∼ ∼ × K to over ∼ × K, as illus-trated in Figure 2. The selective reduction of just this cross sectionwould su ffi ce to establish a Na-O anticorrelation in better agree-ment with the observations, without a ff ecting other successes ofcurrent AGB models, such as the p -capture production of Al, Siand K (Ventura et al. 2012, 2013).The alternative, assuming current cross sections to be cor-rect, would be to attribute the mismatch to insu ffi cient explo-ration of the AGB parameter space, a rather laborious possibil-ity to pursue. AGB models rely on assumptions concerning mass c (cid:13) , 000–000 A. Renzini et al.
Figure 2.
As in Figure 1, the figure shows as a function of the temperaturethe rates of the two reactions which mainly determine the O / Na ratios inAGB stars. The rate of the Na burning is the lower limit allowed by theNACRE reaction rates as compiled by Angulo et al. (1999), i.e., a factor ∼ ffi ciently operate (see text). The green shadedtemperature range corresponds to the maximum temperature in lower massAGB models (e.g., Ventura et al. 2013), where only marginal oxygen deple-tion may take place. loss, mixing and superadiabatic convection, all poorly understoodprocesses. Therefore, it is not surprising if existing AGB modelscome tantalizingly close, but not quite enough, to produce chemi-cal yields that satisfy the 2G requirements. The residual mismatchcould then be due to insu ffi ciencies in the adopted parametriza-tions of these processes and / or in the parameter combinations sofar explored. In D’Antona et al. (2011), Ventura et al. (2013) andDoherty et al. (2014) AGB models, above ∼ − M ⊙ , the HBBprocess burns at T > ∼ K, hence destroys both oxygen and sodium,whereas at lower masses sodium is produced but not much oxy-gen is destroyed. The divide between these two mass ranges de-pends strongly on the adopted e ffi ciency envelope convection: themore e ffi cient convection, the higher the HBB temperature, hencethe lower the mass at which burning works at T ∼ K (e.g.,Renzini & Voli 1981; Ventura & D’Antona 2005b). Existing AGBmodels in which HBB burning operates at T < ∼ K show a stronge ff ect of the third dredge up (3DU), so that their C + N + O increases,oxygen is less depleted, or increases too, and sodium increases eventoo much (e.g., Fenner et al. 2004). Thus, acting solely on convec-tive e ffi ciency may help with sodium, but at the expense of wors-ening the match to e.g., the global CNO abundance. A possiblesolution would require both to extend the AGB lifetime (e.g., byworking on the assumptions made for the mass loss processes), inorder to achieve a certain level of oxygen depletion, while at thesame time reduce the e ffi ciency of mixing via the 3DU. Indeed,the three parametrized processes, envelope convection (hence e ffi -ciency of the HBB process for a given mass), 3DU mixing and mass loss, all influence each other in a closely entangled fashion (Renzini2014), and all together concur in determining the AGB lifetime, lu-minosity excursion and eventually chemical yields, all as a func-tion of stellar mass. This is to say that the exploration of the AGBmodel parameter space is not a simple task and whether one canaccommodate even Si and K production in the most massive AGBstars while still delivering Na-rich yields from the whole AGB massrange remains to be demonstrated. If this approach should succeed,the need for the postulated dilution with pristine material could alsobe reassessed. Anyway, if so far AGB models have failed to fullyreproduce the composition of GC 2Gs, then what we can do is turnthe obstacle around, and see what GC 2Gs can tell us about theevolution of AGB stars, and use them as a guide to improve uponthe construction of AGB models. Hopefully, if such an endeavorsucceeds, we will gather a better understanding of both GC forma-tion and of AGB evolution – which are perhaps one and the sameproblem. A potential problem that at this point in time appears to be com-mon to all suggested polluters, i.e., that large oxygen depletions aretypically accompanied by a large helium enhancement. Instead, insome cases such as the GC 47 Tuc, a sizable depletion in oxygen byat least a factor of ∼ ∆ Y ≃ .
03 increase in helium abundance (Milone et al.2012). Bastian et al. (2015) have expanded on this issue, arguingthat it is intrinsic to nuclear processing to have oxygen destructionand helium production to be closely correlated and they seem tobelieve that other than nuclear processes are responsible for the ob-served anomaly . Before appealing to more exotic physics, again itmay be worth exploring whether insu ffi ciencies in the models or intheir implementation may have been responsible for the mismatchwith the observations.In this respect, it is worth recalling that most of the heliumenrichment in AGB stars is due to the 2DU, which brings heliumto the surface in stars more massive than ∼ ∼ M ⊙ , depend-ing on composition (Becker & Iben 1979). Oxygen is instead de-pleted via the HBB process, that operates in stars more massivethan ∼ ∼ M ⊙ , depending on composition and the assumed ef-ficiency of envelope convection. In the case of all the other donors,CNO processing occurs in the interior of hydrogen-burning mainsequence stars, so unavoidably it is strictly linked to the heliumproduction. The helium and O–Na yields of AGB stars are insteadnot so tightly bound to each other, as these elements are processedat di ff erent times in the course of evolution (by the 2DU and HBB,respectively), and in a mass dependent fashion. In principle, it isindeed possible that a mass range exists in which not much heliumis brought to the surface by the 2DU whereas oxygen is signifi-cantly depleted by the HBB. The amount of helium produced bythe HBB is indeed quite small. Of course, appealing to a reducedmass range of AGB donors would somewhat exacerbate the massbudget problem. In this paper we have first summarized the most salient propertiesof multiple generations in globular clusters, as they have emergedfrom the many observational studies of the last decade which haveculminated with our
HST
Legacy Survey of Galactic Globular Clus-ters (Paper I). Such properties include GC Specificity, Ubiquity, c (cid:13) , 000–000 lobular Cluster Formation Variety, Discreteness, Supernova Avoidance, Hot CNO / NeNa Pro-cessing, Helium Enrichment and Mass Budget. Such observationalevidence is used to check whether four scenarios for the formationof multiple populations are consistent with each of the constraints,or whether they violate them in a possibly curable or incurable way.The four scenarios di ff er for the nature of the stars producingthe material used to form the second populations / generations ofstars, namely supermassive stars (few 10 M ⊙ , Denissenkov et al.2015, fast rotating massive stars (25 to 120 M ⊙ , Krause et al. 2013,massive interacting binaries ( ∼ + M ⊙ , de Mink et al. 2009 andAGB ( + Super-AGB) stars ( ∼ ∼ − M ⊙ , e.g., D’Ercole et al.2010). Our cross-check examination (summarized in Table 1) in-dicates that the first three scenarios encounter unsurmountable dif-ficulties in fulfilling one or more of the above observational con-straints, and we conclude that they are untenable (at least in theircurrent form). Only the AGB scenario survives, but barely.The main di ffi culties encountered by the AGB option concernthe mass budget and the detailed chemical composition of secondgeneration stars. For the AGB scenario to work, the mass of theparent stellar system (dwarf nucleated galaxy? super star cluster?)needs to have been at least ∼
10 times more massive than currentGC survivors, i.e., with masses up to several 10 M ⊙ and possiblymore. So, suitable proto-GCs remain to be firmly identified. Forthe chemical composition issue, the problem is that 2G stars whichare depleted in oxygen and enriched in sodium are rather common,whereas current AGB models deliver materials that if are depletedin oxygen then they are also depleted in sodium. This seem to usthe most serious di ffi culty, hence we ignore minor ones such as theabundances of lithium or s-process elements.One way of alleviating the mass budget problem is to assumethat the 2G stars form with a di ff erent IMF compared to 1G stars(D’Ercole et al. 2010), in particular assuming that 2Gs consist onlyof stars less massive than ∼ M ⊙ . This would also allow super-nova avoidance between one 2G and the next and could possiblyallow a full conversion of AGB ejecta into 2G stars with ∼ ffi ciency. We emphasize that forming the 2G stars in an environ-ment already extremely packed with 1G stars (i.e., over 10 starsper cubic parsec) is a star formation mode quite di ff erent from thatprevailing under normal circumstances. We then speculate that suchan as-yet-unexplored mode of star formation may lead to an IMFwhich is devoid of massive stars. Even so, the nature of the GCprogenitors and how they would have lost most of their stellar massremain puzzling. The lack of a correlation of the 2G /
1G ratio withgalactocentric distance suggests that tidal stripping of a massiveand compact progenitor may not solve the budget problem.Concerning the chemistry, we note that the reason that cur-rent AGB models fail may be that CNO and NeNa cycles oper-ate in them at temperatures above ∼ K, when sodium is ac-tually destroyed faster than oxygen. This discrepancy would bemuch alleviated if the cross section of the sodium-destroying re-action Na( p , α ) Ne were actually a factor of a few lower thancurrently estimated, a possibility that future experiments may test.This simplest solution of the problem of the Na-O anticorrelationhas the advantage of avoiding to jeopardize other successes of cur-rent AGB models, such as the extension to Al, Si and K of theinvolvement in p -capture processing, which requires temperatureswell in excess of 10 K.Alternatively, we argue that tuning envelope convection to re-duce somewhat below this limit the temperature at the base of theenvelope –in a majority of AGB stars– may result in AGB chem-ical yields with low oxygen and still high sodium, hence in bet-ter agreement with the observations. Yet, this cannot be achieved without concurrently acting on the other parametrized processes,i.e., the third dredge up and mass loss, in such a way to ensure asuitable extension of the AGB lifetimes while avoiding excessiveCNO and s-process enhancements via the 3DU. In other words,we suggest to put the AGB scenario under intensive care, and seewhether it can be saved by an extensive exploration of the param-eter space. Success is by no means guaranteed. If the AGB optionwere also to fail, we would be left without any viable scenario: anew, totally di ff erent formation scenario for GCs and their multi-ple populations would have to be invented. One may argue that onescenario does not necessarily exclude another, and that two or more1G donors may operate together. For the time being, however, weprefer to avoid the intricacies that may arise in such a composite op-tion. Young massive clusters in the nearby galaxies show no signsof being forming 2G stars, whereas 2Gs are ubiquitous among our ∼
12 Gyr old GCs. Clearly, YMCs and GCs may not form in thesame way. This suggests that special conditions prevailing only inthe early Universe may have been determinant in leading to GCformation with their multiple generations.What is really striking is the prolificacy with which Naturehas made so many complex systems, in contrast with our persis-tent inability to understand how they formed and evolved to theirpresent state. Even the least implausible solution appears quite con-trived and relies on several unproven assumptions. However, explo-ration of Galactic GCs has made great progress in recent years, andthe evidence is now fairly well documented, both photometricallyand spectroscopically. Perhaps a new day is dawning, with new op-portunities, such as the spectroscopic follow-up of photometricallyselected sub-populations and of their spatial distribution and kine-matic di ff erences within each cluster. This is what our team is set-ting out to pursue, starting with NGC 2808 (Bellini et al. 2015b,Marino et al., in preparation), and continuing with a host of otherGCs (see Paper I).The spatial distribution of the various sub-populations withineach cluster is not discussed in this paper, because our Legacy Sur-vey data pertain only to the central regions of the studied GCs.Yet, in a few cases we know that radial gradients exist, with 2Gstars being more centrally concentrated than 1G stars, e.g., in ω Cen (Sollima et al. 2007) and in 47 Tuc (Milone et al. 2012). Map-ping the radial trends of the 2G /
1G population ratios in most of the
Legacy Survey clusters is an obvious next step in the study of mul-tiple populations and may add further critical constraints on forma-tion scenarios.There is also new territory to explore, concerning the GC pop-ulations in other galaxies. This could tell us whether the multiple-population phenomenon is also common within other GC families,and whether its frequency depends on the nature of the host galaxy,thus giving us new hints about, or constraints on, how GCs form.In this direction, Bellini et al. (2015a) have combined
HST opticaland UV data to study almost 2,000 GCs in the core of the giantelliptical galaxy M87, in the hope of finding whether some of themmay host UV-bright multiple stellar generations. Their experimenthas reached only partial success, but we believe that this kind ofstudy can give us important clues on GC formation and should bepursued.Finally, a real breakthrough would be to catch GCs while theyare still forming (or shortly thereafter), i.e., at redshifts beyond 2 or3, at a lookback time of 10–13 Gyr. If their parent stellar systemswere really as massive as 10 to 10 M ⊙ , then their light shouldbe observable by JWST and by the next generation of extremelylarge telescopes on the Earth’s surface. Massive galaxies at these c (cid:13) , 000–000 A. Renzini et al. redshifts may well be encircled by a swarm of forming / young GCswhich may not remain below detection threshold for long. ACKNOWLEDGMENTS
APM acknowledges support by the Australian Research Councilthrough Discovery Early Career Researcher Award DE150101816.AR, SC, and GP acknowledge partial support by PRIN-INAF 2014,and GP acknowledges partial support by ”Progetto di Ateneo”(Universit’a di Padova) 2014. AB and IK acknowledge supportfrom STScI grant GO-13297, provided by the Space Telescope Sci-ence Institute, which is operated by AURA, Inc., under NASA con-tract NAS 5-26555.
Appendix: On Discreteness
To illustrate what we mean by discreteness , Figure 3 shows thecomposite multicolor plot for the red giants in the GC NGC2808, replicated from Paper III where the indices ∆ F336W , F438W and ∆ F275W , F814W are defined. Similar plots, that we nickname chro-mosomic maps , are now being constructed for all 57 GCs in this
Legacy Survey plus its pathfinders. We have chosen this particularcluster to illustrate the case, because it is one of those for whichsomewhat deeper integrations have been used, resulting in verysmall photometric errors ( ∼ .
01 mag) that have allowed us to dis-tinguish at least five and possibly as many as seven distinct sub-populations. (A rigorous statistical estimate of the number of sub-populations just confirms what just an eye examination suggests.).While the presence of distinct sub-populations is evident, one im-portant issue is whether each of them is a simple stellar population ,i.e., whether all stars in each of the clumps in the chromosomic maphave the same composition, or whether there is an intrinsic disper-sion internal to each clump, possibly leading to marginal overlapbetween adjacent clumps. The reddening of the cluster is fairlyhigh – E ( B − V ) = .
24– hence di ff erential reddening of order of ∼ .
03 mag could be expected. Although a di ff erential reddeningcorrection has been applied before constructing the indices shownin Figure 3 (see Paper III and references therein), still we suspectthat errors in such corrections are larger than pure photometric er-rors, resulting in combined errors of order of ∼ . − .
03 mag.This estimated error is still substantially smaller than the widthof individual peaks in the histograms shown in Figure 2 and, unlessthere are other unaccounted sources of error, we suspect that in-dividual clumps are not made of stars with identical composition,but a small dispersion exists among them. Such a dispersion canoriginate in two possible ways. One is that the individual bursts ofstar formation had a finite duration, hence stars formed at di ff er-ent phases of the burst were made of material with slightly di ff er-ent composition, as indeed the composition of the ISM was con-tinuously changing being the ISM continuously fed by AGB starof di ff erent mass. Moreover, in between bursts star formation mayhave not vanished entirely, so one burst partially overlapped withthe next one. Besides an intra-clump dispersion due to the detailedstar formation history, accretion may add further dispersion, bothon top of 1G and 2G stars. Indeed, if the Bondi formula applies onewould expect appreciable accretion to take place during the first ∼ years (cf. Renzini 2013).As documented in Paper III, Population A + B in Figure 3 rep-resents the 1G of NGC 2808. Clearly, the elongated and clumpydistribution of this feature of the chromosomic map suggests thateven the 1G stars are not chemically homogeneous, possibly by marginal contamination of some stars by supernova products by1G itself, or by accretion of AGB ejecta, or both.
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Reproduction from Milone et al (2015b) of the ∆ F336W , F438W vs. ∆ F275W , F814W diagram of NGC 2808. Stars in the A, B, C, D, and E groups arecolored green, orange, yellow, cyan, and blue, respectively (lower-left). The corresponding Hess diagram is plotted in the upper-right panel. The histogramsof the normalized ∆ F275W , F814W and ∆ F336W , F438W distributions for all the analyzed RGB stars are plotted in black in the upper-left and lower-right panel,respectively. The shaded colored histograms show the distributions for each of the five populations defined in the lower-left panel.
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