The self-enrichment scenario in intermediate metallicity globular clusters
aa r X i v : . [ a s t r o - ph ] D ec Astronomy&Astrophysicsmanuscript no. agb c (cid:13)
ESO 2018November 15, 2018
The self-enrichment scenario in intermediate metallicity globularclusters
P. Ventura and F. D’Antona
INAF - Observatory of Rome, Via Frascati 33, 00040 MontePorzio Catone (RM) - Italy e-mail: ventura, [email protected]
Preprint online version: November 15, 2018
ABSTRACT
Context.
We present stellar yields computed from detailed models of intermediate mass asymptotic giant branch stars of low metallicity. Inthis work, the whole main microphysics inputs have been updated, and in particular α − enhancement is explicitly taken into account both in theopacities and equation of state. Aims.
The target of this work is to provide a basis to test the reliability of the AGB self-enrichment scenario for Globular Clusters ofintermediate metallicity. These Globular Clusters exhibit well defined abundance patterns, which have often been interpreted as a consequenceof the pollution of the interstellar medium by the ejecta of massive AGBs.
Methods.
We calculated a grid of intermediate mass models with metallicity Z = Results.
The predictions of our models show an encouraging agreement with the demand of the self-enrichment scenario for what concernsthe abundances of oxygen, aluminum, fluorine and magnesium. The question of sodium is more tricky, due to the large uncertainties of thecross-sections of the Ne-Na cycle. The present results show that only a relatively small range of initial masses ( M = , M ⊙ ) can be responsiblefor the self enrichment. Key words.
Stars: abundances – Stars: AGB and post-AGB – Stars: evolution – Stars: chemically peculiar – Globular Clusters: general
1. Introduction
Deep spectroscopic investigations in the last decades haveshown that Globular Clusters (GC) stars are not chemicallyhomogeneous samples, rather they show clear trends involvingthe chemical abundances of some light elements (Kraft 1994),like magnesium, aluminum, oxygen, fluorine and sodium; thesame behaviour is not followed by halo field stars, whichpresent star to star variations limited to carbon and nitrogen,i.e. those elements whose surface abundances are expected tochange following the first dredge-up and the mixing possiblyfollowing the bump on the red giant branch (hereinafter RGB).In almost the totality of the GCs investigated, is present a mainstellar population, whose surface chemistry is in agreementwith the standard α − enhanced abundances, and a second com-ponent, whose surface abundances of the afore mentioned ele-ments define well determined patterns (for a recent update, seeCarretta 2006; Smith et al. 2005). These stars show depletionof oxygen and fluorine, while the abundances of sodium andaluminum are enhanced with respect to the solar values; thequestion of a possible depletion of magnesium by ∼ . Send o ff print requests to : P. Ventura ture of all the GCs investigated is that the C + N + O sum is con-stant within a factor ∼ .The capability of the DPS to fully explain the observedabundance patterns was seriously undermined by the detection Here we do not consider the alternative SES proposed by Maeder& Meynet (2006), Prantzos & Charbonnel (2006) and described byDecressin et al. (2007), namely that self-enrichment is produced bythe envelopes of fast rotating massive stars. Ventura & D’Antona: AGB models of intermediate metallicity of the same chemical anomalies even in main sequence andsub-giant stars of some GCs (Gratton et al. 2001), because theinterior of these stars is not expected to reach temperatures sohigh to ignite a very advanced nucleosynthesis.The question concerning the SES is still open, basicallybecause many ingredients used in the stellar evolution theory,whose physical formulation is not directly based on first prin-ciples (e.g. convection, mass loss rate, extra-mixing), have astrong impact on the physical and chemical aspects of the AGBevolution (Ventura & D’Antona 2005a;b); also, for one of theelements involved in the observed trends, i.e. sodium, the un-certainties associated to the relevant cross-sections ( ∼ + N + Oabundances, and inhibits the depletion of oxygen (Fenner etal. 2004; Denissenkov & Herwig 2003). On the other hand,Ventura & D’Antona (2005b), studying the e ff ects of chang-ing the treatment of convection on the AGB modeling, showthat when the Full Spectrum of Turbulence (FST, Canuto &Mazzitelli 1991) is used to model the convective regions, theFST high e ffi ciency of convection favours higher tempera-tures at the bottom of the convective envelope, thus an ad-vanced nucleosynthesis (which is usually referred to as “HotBottom Burning”, HBB), a larger luminosity, and consequentlya smaller number of TDU episodes, thus keeping the C + N + Osum almost constant.An appealing prediction of the SES, and more generally ofthe role which AGBs may play in the pollution of the interstel-lar medium within GCs, is that their yields are expected to behelium rich, as a consequence of the deep second dredge up(hereinafter II DUP) experienced particularly by the most mas-sive models. A helium content Y > .
30, as found in previousinvestigations (Ventura et al. 2001), may be at least partiallyconsistent with the existence of helium rich stellar populationsin GCs, which allow the interpretation of the morphology of ex-tended horizontal branches in some GCs (D’Antona et al. 2002;D’Antona & Caloi 2004; Lee et al. 2005); the presence of a he-lium rich population was also invoked to explain the presenceof a blue main sequence in NGC 2808 (D’Antona et al. 2005b;Piotto et al. 2007) and ω Cen (Bedin et al. 2004; Piotto et al.2005).The possibility that DPS and SES might act together in or-der to explain the O-Na anticorrelation observed in a few giantsof M13 has recently been explored by D’Antona & Ventura(2007), and was previously suggested by Denissenkov et al.(1998) to account for the Mg-Al trend in the same cluster.
Any SES model faces with a serious problem: it isdi ffi cult to understand how is it possible that the self–enriched population is very abundant in most of theexamined clusters —see, e.g., D’Antona & Caloi(2007),concerning the ratio of the normal to self–enriched popu-lations derived from the analysis of the Horizontal Branch (HB) morphology. In particular, for NGC 2808, both theHB —D’Antona & Caloi(2004), D’Antona et al.(2005b)—the main sequence splittings —D’Antona et al.(2005b),Piotto et al.(2007)— and the spectroscopic evidence —Carretta et al.(2006)— indicate that about half of thecluster stars is self–enriched. In order to accomplishthis we need that: 1) either the initial mass function(IMF) of the first generation stars is highly anomalous,and is peaked at the intermediate mass stars; 2) or theIMF is more or less normal, the initial cluster mass ismuch larger, by about a factor 10, than the final mass,and the stars of the first generation have been preferen-tially lost, as discussed, e.g., in D’Antona & Caloi(2004)and Prantzos & Charbonnel(2006). In addition,Bekki et al.(2007) suggest that all GCs formed withindwarf galaxies, so that the cluster formation may take ad-vantage of the infall from all the gas lost by massive AGBsevolving in the galaxy and falling into the protoclusterpotential well. In this paper we model the AGB evolution by releasingsome of the approximations of our previous works. We fo-cus on an intermediate metallicity ([Fe / H] ∼ − . = α − enhanced mix-ture. We compare the yields of the individual elements with theabundances observed in the GCs having metallicity appropriatefor the present investigation, taking care to restrict our compar-ison to those stars which are scarcely evolved, to rule out anypossible contamination from canonical or non-canonical extra-mixing which the stars may experience during the RGB evo-lution. The e ff ects of the uncertainties related to mass loss andthe nuclear reaction rates of the Ne-Na cycle and the Mg-Alchain are also examined.
2. The ATON stellar evolution code
The stellar evolution code used in this work is ATON3.1; a fulldescription of the numerical structure can be found in Venturaet al. (1998). Here we briefly recall the main physics inputs,with the most recent updates.
We adopt the latest opacities by Alexander & Ferguson (2005)at temperatures smaller than 10000 K and the OPAL opaci-ties in the version documented by Iglesias & Rogers (1996).For both the above treatments we have the choice between theopacities corresponding to solar mixture (Grevesse & Sauval1998), and to an α − enhanced mixture [ α / Fe] = . ff e.rssi.ru / astro / conduct / ), and are harmonically added to the radiative opacities. entura & D’Antona: AGB models of intermediate metallicity 3 Tables of the equation of state are generated in the (gas)pressure-temperature plane, according to the method describedin D’Antona et al. (2005a). For mixtures including hydrogen,we use the latest OPAL EOS (2005), overwritten in the pres-sure ionization regime by the EOS by Saumon, Chabrier & VanHorn (1995). The EOS is extended to the high density, hightemperature domain according to the treatment by Stoltzmann& Bl¨ocker (2000). After these large tables are written, for agiven Z , six values of each physical quantity are computed forsix di ff erent X values. A cubic unidimensional spline providesthe interpolation for any input value of X. The six tables forH / He and given Z are supplemented by 15 tables of He / C / O inwhich the EOS is directly computed according to Stolzmann& Blocker (2000) as the non-ionized regions are not presentin stellar structure following helium ignition. The interpolationamong the 15 tables is performed using triangles in the planeC / O, as the stechiometric condition is Y = − X C − X O . The thermodynamic description of the regions unstable to con-vective motions can be addressed either within the context ofthe traditional MLT formulation (Vitense 1953), or by the FSTmodel (Canuto et al. 1996).
Mixing of chemicals within convective zones can be addressedwithin the instantaneous mixing framework or by a di ff usiveapproach. In this case, for each chemical species a di ff usive-like equation (Cloutman & Eoll 1976) is solved: dX i dt = (cid:16) ∂ X i ∂ t (cid:17) nucl + ∂∂ m r h (4 π r ρ ) D ∂ X i ∂ m r i (1)where D is the di ff usion coe ffi cient, for which, given the con-vective velocity v and the scale of mixing l , a local approxima-tion ( D ∼ vl ) is adopted.The borders of the convective regions are fixed accordingto the Schwarzschild criterium. It is also possible to considerextra mixing, by allowing convective velocities to decay ex-ponentially from the formal border, with an e-folding distancedescribed by the free-parameter ζ (see Ventura et al. (1998) fora complete discussion regarding the variation of convective ve-locities in the proximities of the convective borders). Mass loss can be treated according to di ff erent prescriptions.It is possible to adopt the classic Reimers’ treatment, theVassiliadis & Wood (1993) formulation, or the prescriptiongiven by Bl¨ocker (1995). In this latter case the strong increaseof the mass loss rate during the AGB evolution is modeled bymultiplying the Reimers’ rate by an ad hoc luminosity power:the final expression is˙ M = . × − η R M − . L . R (2) where η R is the free parameter entering the Reimers’ prescrip-tion. The nuclear network includes 30 elements (up to P) and 64reactions. The full list of the 30 chemicals and of the reactionsincluded can be found in Ventura & D’Antona (2005a).The relevant cross section are taken from the NACRE com-pilation (Angulo et al. 1999), with only the following excep-tions:1. N(p, γ ) O (Formicola et al. 2004)2. Ne(p, γ ) Na (Hale et al. 2002)3. Na(p, γ ) Mg (Hale et al. 2004)4. Na(p, α ) Ne (Hale et al. 2004)
3. The results of the most recent spectroscopicsurveys of intermediate metallicity GC
Several clusters of intermediate metallicity (i.e. − . ≤ [Fe / H] ≤ − .
2) have been investigated spectroscopically in thelast decade: among these, the most extensively studied areM3,M4,M5,M13,NGC6752 and NGC6218. The first analyseswere focused on bright giants, and only in past few years turn-o ff (TO) and sub-giant branch (SGB) stars were studied. Brightgiants are of little help for the main target of this paper, sincethe abundances observed might be the result of some mix-ing episode from the bottom of the convective envelope tak-ing place during the RGB evolution; on the other hand, TOand SGB stars never reach internal temperatures su ffi cientlyhigh to trigger any advanced nuclesynthesis, so any chemicalanomaly must have been imprinted in the matter from whichthey formed. Studies focused on the TO and SGB stars aretherefore the most useful for the present investigation.In the analysis of the observational results, we will considerthe uncertainties associated to the data, and the constant o ff setsamong the di ff erent observers, mainly due to di ff erences in theassumed solar abundances and in the temperature scale.The oxygen-sodium and magnesium-aluminum anticorre-lations are by far the most studied trends. For NGC 6752,the works related to TO and SGB stars (Gratton et al. 2001;Carretta et al. 2005) and to bump stars (Gratton et al. 2005),evidentiated a well defined stellar population in which the oxy-gen was depleted up to 0.8 dex ([O / Fe] ∼ − .
4) compared tothe “standard” abundance ([O / Fe] ∼ + . ∼ . = , a factor of 2 smaller than the valuedetected in the stars with standard sodium.The O-Na anticorrelation was recently confirmed in theinvestigation of NGC 6218 performed by the same group We use the notation A(Li) = log(Li / H) +
12 (in number) Ventura & D’Antona: AGB models of intermediate metallicity (Carretta et al. 2006): for the stars below the RGB bump, theauthors find a maximum extent of the oxygen depletion by ∼ / Fe] = δ [O / Fe] ∼ . / Fe] = / Fe] = ff set, which may be understoodin the left-upper panel of their fig.4) and of the aluminum en-hancement found by Ivans et al. (1999); they also found a clearanticorrelation between sodium and fluorine, the most sodiumrich stars being depleted in fluorine by [F / Fe] = -0.8 dex.M3 and M13 have been extensively studied in the literature.Sneden et al. (2004) evidentiated a clear O-Na anticorrelation,which, for the high gravity stars (i.e. those well below the RGBbump) extends to [O / Fe] ∼ − .
4, and [Na / Fe] =+ / Fe] =
1. The authors also claim the detectionin both clusters of a magnesium - aluminum anticorrelation,but this result has been recently argued by Cohen & Melendez(2005), who confirm the extent of the oxygen depletion foundby Sneden et al. (2004), but also limit the sodium enhancementfor the stars below the RGB bump to [Na / Fe] =+ δ [ O / Fe ] ∼ .
82. The most aluminum rich stars show up an Al abundanceof [Al / Fe] =
13. Sodium is anticorrelated to oxygen. The extent of thelargest sodium enhancement is [Na / Fe] =
4. The physical properties of the intermediatemass models
The models were evolved from the pre-MS through the wholeAGB phase. The chemistry adopted is typical of the interme-diate metallicity GCs, i.e. Z = = α − enhanced, with [ α / Fe] =+ M ⊙ ≤ M ≤ . M ⊙ ; the limitswere chosen to restrict the analysis to stars achieving HBBduring the AGB phase, and not undergoing any carbon igni-tion in the interior. Convection was modelled according to theFST treatment. Due to the importance that CNO burning withinthe most internal part of the convective envelope may have onthe AGB evolution (Herwig 2005; Mazzitelli et al 1999), weadopted the di ff usive treatment in all the models presented here.In the phases preceeding the AGB evolution, a free parameter ζ = .
02 was used to model the exponential decay of velocitieswithin regions stable against convection; this is in agreementwith the calibration in Ventura et al. (1998). For the whole AGBphase no extra-mixing was assumed from any convective bor-der. Mass loss was modelled according to Bl¨ocker (1995), withthe free parameter entering eq.2 set to η R = .
02, according tothe calibration given in Ventura et al. (2000).The main physical properties of the models are reported inTable 1. Cols. 2 to 4 show the duration of the core H- and He-burning phases (Myr) and of the AGB phase (Kyr).Within stars of intermediate mass, after the extinction ofthe CNO burning shell following the core He-burning phase,the bottom of the convective envelope sinks inwards, down tolayers precedently touched by nuclear burning; this is the sec-ond dredge-up (Iben 1991) Col.5 reports the total mass previ-ously involved in CNO burning mixed with the convective en-velope during the II DUP; in the most massive models, wherethe amount of dredged-up matter is higher, the surface chem-istry is altered, with a decrease of the surface oxygen abun-dance and an increase of the sodium and helium mass fractions.These results are consistent with the old models calculatedwith the same metallicity, presented in Ventura & D’Antona(2005b, see Table 1). In cols. 6-10 of Table 1 we give somedetails of the AGB evolution, namely the core mass at the be-ginning of the Thermal Pulses (TPs) phase, the maximum lu-minosity and the maximum temperature reached at the bottomof the convective zone ( T bce ), the number of the first TP fol-lowed by a TDU episode, and the maximum e ffi ciency of theTDU during the whole stellar AGB life .Fig.1 shows the variation with mass (decreasing during theevolution) of the luminosity and T bce in some of our models.We note in all cases, with the only possible exception of the3 M ⊙ model, a rapid increase of the luminosity after the veryfirst TPs, associated to an increase of T bce . This is a conse-quence of the high e ffi ciency of the convective model adopted,as correctly predicted by Bl¨ocker & Sch¨onberner (1991), and We use here the usual descriprion of the e ffi ciency of the TDUin the terms of the quantity λ , defined as the ratio of the total mat-ter dredge-up after a TP to the mass by which the H-exhausted coreadvanced from the previous TPentura & D’Antona: AGB models of intermediate metallicity 5 Table 1.
Evolutionary properties of intermediate mass models M / M ⊙ τ H / τ He / τ AGB / δ ( M ) M core / M ⊙ log( L / L ⊙ ) max T bcemax N pulse (TDU) λ Fig. 1.
Variation with the total mass of the luminosity (Left) and Temperature at the bottom of the convective envelope (Right)of some intermediate mass models during the AGB phase. For clarity reasons, only models corresponding to initial masses3,4,5,6 M ⊙ are shown.later confirmed by D’Antona & Mazzitelli (1996) and Venturaet al. (2000). A detailed comparison of the results obtained withvarious e ffi ciencies of the convective model can be found inVentura & D’Antona (2005b).The large luminosities attained by our models have two im-portant consequences:1. A fast decrease of the mass of the envelope, with a conse-quent small number of TPs, and therefore of TDUs2. A very advanced nucleosynthesis at the bottom of the en-velopeIn the most massive models, mass loss is so large that theyreach their maximum luminosity after a few TPs; they loosetheir envelope so rapidly, that TDU takes place only in thelatest stages of their AGB evolution, and with a very modeste ffi ciency (see col.10 of Table 1). We stress that the larger isthe luminosity, the faster is the general cooling of the structuredetermined by the gradual loss of the mass of the envelope:the maximum temperature achieved at the bottom of the ex-ternal convective zone reaches a maximum asymptotic value(see col.8 of Table 1), which, for large M, turns out to be in-dependent of the total initial mass of the star; in the presentcomputations, this upper limit is T bce =
5. The chemistry of the ejecta
For each model, we calculate the average mass fractions in theejecta, for the chemical elements included in our network. Theresults for the species of interest for this work, are presentedin Table 2. For any isotope A, we give the quantity [A / Fe], de-fined as [A / Fe] = log(A / Fe) ejecta − log(A / Fe) ⊙ ; the abundancesare mass fractions. The only exceptions are helium and lithium,for which we list, respectively, the mass fraction Y and the stan-dard A(Li) quantity. Note that Mg in col.9 refers to the totalmagnesium abundance, and R(CNO) in the last column givesthe ratio between the total C + N + O in the ejecta and the initialvalue.
The depletion of the surface oxygen abundance requires astrong HBB at the bottom of the convective envelope, as the ac- tivation of the full CNO cycle demands temperatures approach-ing 100MK, which, within the context of the AGB modelling,are attainable only via a very e ffi cient description of convec-tion (Ventura & D’Antona 2005b). The present models havebeen calculated with the FST prescription, thus, at least in themost massive models, we expect to reach such a high T bce , ascan be seen in the right panel of Fig.1.The left panel of Fig.2 shows the variation with the totalmass of the surface oxygen abundance for the masses examinedhere, with the only exception of the 6.3 M ⊙ model, which wasomitted for clarity reasons, being very similar to the 6 M ⊙ case.We see that oxygen burning starts e ffi ciently shortly after thebeginning of the AGB phase in all the models more massivethan 4 M ⊙ . In the same panel we may easily note the e ff ects ofthe TDU, which, when su ffi ciently e ffi cient, increases the oxy-gen content of the envelope, because carbon and oxygen richmaterial is dredged-up from the ashes of the precedent 3 α burn-ing shell which forms during each TP. A strong oxygen deple-tion is thus inhibited by repeated and e ffi cient TDU episodes,so that in the less massive models, which undergo many TDUs,and hardly reach the temperatures requested to ignite oxygenburning, the oxygen is indeed produced rather than destroyedwithin their envelopes. With increasing mass, we shift progres-sively to a situation where the final oxygen abundance is a del-icate compromise between the depletion triggered by the acti-vation of the full CNO cycle and the increase due to the TDU(4.5 M ⊙ ≤ M ≤ M ⊙ ), to end up with the most massive models( M ≥ M ⊙ ), in which oxygen can be eventually depleted by afactor ∼
20 compared to the initial value (see the track corre-sponding to the 6 M ⊙ model in the left panel of Fig.2).In the right panel of Fig.2 we show the oxygen content ofthe ejecta of the models calculated, in terms of [O / Fe], to al-low a more straight comparison with the observations outlinedin Sect.2. We note a very high oxygen content in the ejectaof the models with masses M < M ⊙ , consistently with theprevious discussion; the model with initial mass 4 M ⊙ shows anoxygen content unchanged compared to the initial α − enhancedvalue. The mass-oxygen trend is progressively decreasing withmass, and reaches a plateau value of [O / Fe] ∼ − . M > M ⊙ . The reasons why this lower limit ex-ists is twofold: a) on the one hand (see col.8 in Table 1), we Ventura & D’Antona: AGB models of intermediate metallicity
Table 2.
Chemical composition of the ejecta of intermediate mass models M / M ⊙ η R Y A(Li) [ C / Fe] [ N / Fe] [ O / Fe] [ F / Fe] [ Na / Fe] [Mg / Fe] [ Al / Fe] R(CNO)3.0 0.02 .248 2.77 0.84 2.21 0.92 0.10 1.16 0.57 0.65 9.63.5 0.02 .265 2.43 0.51 2.18 0.77 -0.26 1.30 0.55 0.66 7.94.0 0.02 .281 2.20 0.14 2.02 0.44 -0.61 1.18 0.48 0.55 4.94.5 0.02 .310 2.00 0.12 1.89 0.19 -0.90 0.97 0.43 0.85 3.15.0 0.02 .324 1.98 0.13 1.70 -0.06 -1.16 0.60 0.35 1.02 2.15.5 0.02 .334 1.93 -0.41 1.51 -0.35 -1.39 0.37 0.28 1.10 1.36.0 0.02 .343 2.02 -0.62 1.35 -0.40 -1.36 0.31 0.29 1.04 0.976.3 0.02 .348 2.06 -0.68 1.33 -0.37 -1.28 0.30 0.30 0.99 0.945.0 0.01 .327 1.79 0.00 1.83 -0.14 -1.30 0.67 0.40 1.20 2.775.0 0.04 .323 2.49 -0.37 1.58 -0.05 -1.00 0.70 0.39 0.80 1.716.0 0.01 .345 1.83 -0.40 1.49 -0.42 -1.45 0.27 0.22 1.07 1.29
Fig. 2.
Left: Variation with the total mass of the surface oxygen mass fraction of the AGB models with masses 3 M ⊙ ≤ M ≤ M ⊙ ;the strong depletion in the most massive models is a clear signature of strong HBB at the bottom of the convective envelope.Right: oxygen content of the ejecta as a function of the initial mass; a plateau value of [O / Fe] = -0.4 is reached for the highestmassessaw that there is an upper limit for T bce , which therefore limitsthe degree of O-burning which may be achieved at the bottomof the envelope; b) the luminosity in the most massive mod-els is so high that they loose mass rapidly, already from thevery first TPs, when the oxygen abundance is still large (seethe di ff erent slope of the Oxygen-Mass relation characterizingthe 6 M ⊙ model compared to the other masses in the left panelof Fig.2). We will show that changing the mass loss descrip-tion does not change substantially this conclusion. Finally, wenote that this lower limit for [O / Fe]is in good agreement withthe lowest oxygen abundances measured in TO and SGB starsbelonging to intermediate metallicity GCs.
Cols. 10 and 11 of Table 2 report the Mg and Al content ofthe ejecta. While the observed spread in the Mg abundance, asoutlined in Sect.3, is still debated, and in any case restrictedto 0.2-0.4 dex, the stars in GCs showing up the largest degreeof oxygen depletion are also strongly enriched in aluminum,with [Al / Fe] = Al (Denissenkov & Herwig 2003; Ventura & D’Antona2005a). Also TDU plays a role which is not negligible, as adeep penetration of the convective envelope within the regionprecedently touched by helium burning may bring to the sur-face Mg and Mg synthetized via α − captures by Ne nu-clei; these isotopes, once the CNO burning shell is reactivated,undergo proton capture and produce aluminum.Fig.3 shows the evolution of the surface aluminum contentin the models presented here. We note in all cases a trend in-creasing during the evolution; in the most massive models, due
Fig. 3.
The variation during the AGB phase of the surface alu-minum abundance, for the same models reported in fig.2. Notethe combined e ff ects of HBB and of TDU to increase the sur-face aluminum contentto the stronger nucleosynthesis activated, the aluminum pro-duction is larger. Even in this case, as it was for the depletion ofoxygen, we note an upper limit to the aluminum enhancement,which can also be seen in col.10 of Table 2 to be [Al / Fe] = T bce = ff ered from these modelsat the beginning of the AGB phase, which favours the ejectioninto the ISM of material which is not aluminum rich.We see from col.11 of Table 2 that the ejecta of all the mod-els are characterized by 0 . ≤ [Al / Fe] ≤
1, and are thereforefully consistent with the aluminum content of the stars with theanomalous chemistry outlined by the spectrospic investigationspresented in Sect.3.The total magnesium abundance, as it is evident from theprevious discussion, is the result of the balance between the in-crease of Mg determined by the TDU, and the depletion due toproton captures during HBB. This explains the negative trendwith mass which can be seen in col.9 of Table 2.We underline here the striking di ff erence between our find-ings and the results obtained by Fenner et al. (2004, see thebottom panel of their fig.1), where they found that the most Al-rich stars were also magnesium rich. This was a result of thee ff ects of many TDUs, enriching the envelope with the heavymagnesium isotopes produced in the 3 α shell; it is the di ff erenttreatment of convection between the two sets of models leadingto this discrepancy, because the use of the FST model reducesthe number of TPs and TDUs.Contrary to oxygen, the predictive power of our results forAl is undermined by the range of uncertainties related to the entura & D’Antona: AGB models of intermediate metallicity 7 Fig. 4.
Variation with mass of the surface sodium abundancewithin our standard models
Fig. 5.
Variation of the sodium surface content within modelswith initial masses 4,5,6 M ⊙ calculated with the recommendedvalues of the cross-sections of the Ne-Na cycle (dotted), andthose maximising sodium production (see text for details). Thedashed tracks show the results obtained when the upper limitsof the α − capture reactions by Ne nuclei are adopted.relevant cross-sections. Izzard et al. (2007) evidentiated that inmassive AGBs the yields of Al is a ff ected by the uncertaintiesconnected to both the Mg(p, γ ) Al and Al(p, γ ) Si reactionrates: we used the upper NACRE limit for these reactions inthe present investigation, but we keep in mind that these resultshave an associated uncertainty which may be estimated to bearound 0.3-0.4 dex.
The debate regarding the amount of sodium which may be syn-thesized within AGBs is still open, due to the large uncertain-ties associated to a) the cross-sections of the reactions involvedin the Ne-Na cycle; b) the cross sections of the α − captures by Ne; c) other physical inputs which play a role in determiningthe sodium content within the envelope of these stars.As outlined by Ventura & D’Antona (2006), the surfacesodium abundance first increases due to the II DUP, then, par-ticularly in AGB models calculated with an e ffi cient convec-tive model, it is further produced by burning of the dredged-up Ne, and is later decreased when the rate of destruction ex-ceeds that of production. Any TDU favours sodium production,due to dredging up of primary Ne synthesized via α − capturewithin the convective shell which forms during the TP. Thisbehaviour is confirmed by Fig.4, which shows the variation ofthe surface sodium abundance of the evolutionary models. Thebehaviour of the M ≤ M ⊙ stars is in qualitative agreement withthe AGB models used by Fenner et al.(2004) (see the upperpanel of their Fig.1): we note a great increase of the sodiumabundance, due to the dredge-up of Ne which is later con-verted to sodium. Contrary to their findings, our more massivemodels show an opposite behaviour, because the FST convec-tive model favours a more advanced nucleosynthesis, with apartial destruction of the sodium precedently created; also, werecall that the higher mass loss favours a smaller number ofTPs, thus acting against sodium production.The precedent discussion explains the clearly negativetrend with mass of the [Na / Fe] values in the 9th column ofTable 2. We focus our attention on the most massive models,which produce yields which we saw to be aluminum rich andoxygen poor: the sodium content of their ejecta is in the range0.3-0.4 dex, which is consistent with the sodium abundancesderived by most of the research groups for the stars with themost anomalous chemical composition.The uncertainties connected to the cross sections havea dramatic impact on the value of [Na / Fe] of the ejecta, even more than we saw for aluminum. Concerning HBB,the main problems are associated to the cross section of the Ne(p, γ ) Na reaction, which is uncertain by a factor ∼ Na(p, α ) Ne, has amargin of uncertainty, which is however smaller ( ∼ ran three models with initial masses 4,5,6 M ⊙ , wherewe used the lower limit for the Ne(p, γ ) Na reaction, andthe upper limit for Na(p, α ) Ne. The comparison betweenthese simulations (dotted tracks) and those described in Table2 (solid) is shown in Fig.5. We note that when the cross sec-tions minimizing the sodium production are used, with theonly exception of the II DUP, sodium is destroyed when T bce becomes su ffi ciently large to ignite proton capture by Nanuclei. The sodium contents which we get are considerablylower, i.e. [Na / Fe] = M ⊙ model, [Na / Fe] = = M ⊙ case, and [Na / Fe] = -0.2 for M = M ⊙ ; these values aresmaller than those reported in Table 2 by 0.6 dex. Note that thisis not proportional to the reduction factor of the Ne(p, γ ) Nareaction, because, as pointed out by Izzard et al. (2007), once Ne is destroyed at the bottom of the envelope, no furthersodium can be created, despite the use of a cross section for Ne burning which is a factor ∼ Na(p, α ) Ne reactionby a factor 2 could reconcile better the sodium content of theejecta of the most massive AGBs of intermediate metallicitywith the spectrospic measurements of GC stars.For the models experiencing TDU, another source of un-certainty for the sodium yield is provided by the cross sectionsof the α − capture reactions by Ne nuclei, whose upper limitis 3 orders of magnitude higher than the recommended values(Angulo et al. 1999). These reactions determine the Ne con-tent in the convective shell which forms during the TP, hencethe amount of Ne which may be dredged-up in the after-pulse phase, and therefore the quantity of sodium which maybe sinthesized at the bottom of the envelope via proton captureby Ne nuclei.The dashed tracks in Fig.5 show the results of the surfacesodium abundance when these upper limits are used: for the4 and 5 M ⊙ the overall sodium abundance is clearly reduced.Di ff erently from the previous case, the associated uncertain-ties on the sodium yields are not uniform with mass, but rathershow a decreasing trend, ranging from a null e ff ect for the mostmassive models, to δ [ Na / Fe ] ∼ . M = M ⊙ , up to δ [ Na / Fe ] ∼ . M = M ⊙ ; these results are actuallynot surprising, since dredging up of Ne becomes progres-sively more important in determining the sodium abundancethe smaller is the stellar mass.The yields of sodium from these sources are still highlyuncertain; only a more solid estimate of the relevant cross-sections may help increasing the reliability of these investiga-tions.
Ventura & D’Antona: AGB models of intermediate metallicity
Fig. 6.
Left: Variation as a function of the total stellar mass of the surface lithium content of the intermediate mass models duringthe whole AGB evolution. Right: The lithium content of the ejecta, as a function of the initial mass.
Lithium is synthesized at the bottom of the convective envelopeof AGBs at temperatures exceeding 40 × K via the Cameron& Fowler (1971) mechanism. Sackmann & Boothroyd (1992)first showed that the use of a di ff usive approach was mandatoryto describe such a delicate interplay among nuclear and mix-ing time scales, which could eventually lead to lithium produc-tion. Ventura et al. (2000) used this approach to reproduce thelithium vs. luminosity trend observed in the Large MagellanicCloud.The key factor to achieve lithium production is the activa-tion of the He( α, γ ) Be reaction at the bottom of the convec-tive envelope, which is possible when T bce > × K.The left panel of Fig.6 shows that all our models attain tem-peratures at the bottom of the convective envelope su ffi cientlyhigh to ignit the Cameron & Fowler mechanism; the most mas-sive stars undergo a rapid consumpion of the whole He avail-able in the envelope, so that the surface lithium content, afterreaching a maximum value A(Li) ∼
4, rapidly declines to ex-tremely low abundances. This process becomes progressivelyslower as the mass decreases; we end up with the 3 M ⊙ model,which is still lithium rich at the end of its AGB evolution. Thisdiscusion explains the relation between the initial mass of thestar and the lithium content of its ejecta, shown in the rightpanel of Fig.6; all the massive models have A(Li) ∼
2, in ex-cellent agreement with the lithium abundance of the oxygenpoor TO stars in NGC 6752 (Pasquini et al. 2005).
The AGB models discussed here experience a small number ofTPs, thus most of the helium enrichment of the envelope takesplace during the II DUP. Since this latter is deeper the higheris the initial mass of the star (see col.5 of Table 1) we expectthe helium enrichment to increase with mass, as it is confirmedby the results reported in col.3 of Table 2. We find a small in-crease (compared to the standard Big Bang value, Y = M < M ⊙ ; the maximum enrichment,for the masses close to the limit for carbon ignition, is Y = ffi ciency of the II DUP. Ventura et al. (2002) presented models for the evolution of starsof intermediate mass at various metallicities, ranging from Z = × − to Z = .
01. We compare the yields of the present workwith the results of that investigation, for the metallicity Z = . ∼ .
04, as can be seen by comparing the thirdcolumn of Table 2 with the dashed curve giving the helium- mass trend in fig.4 in Ventura et al. (2002). This results may beunderstood in terms of the extra-mixing from the bottom of theconvective envelope which was assumed in the present models,and which was neglected in Ventura et al. (2002).The combined e ff ects of the overshooting from the enve-lope and the di ff erent mixture adopted (solar in Ventura et al.(2002), α − enhanced here), favours smaller core masses in thepresent models, so that a given model here can be comparedwith a model 0 . M ⊙ less massive in Ventura et al. (2002).Even with this assumption, we note di ff erences in the CNOyields, the overall C + N + O contribution being higher here com-pared to the corresponding values in Ventura et al. (2002) (seefig.6 in Ventura et al. 2002, to be compared with columns 5to 7 in Table 2). The reason for such discrepancy is the di ff er-ent e ffi ciency of the TDU found in the two sets of models: wefind a maximum e ffi ciency of λ = . λ = . λ could hardly reach 0.5. This change, favoured bythe di ff erent mixture adopted, determines the di ff erences in theyields obtained.The detailed comparison of the other yields is rendered hardby the di ff erences in the nuclear cross-sections adopted for therelevant reactions; Ventura et al. (2002) used the NACRE com-pilation, whereas here we use the most updated releases presentin the literature.
6. The uncertainties related to mass loss
Mass loss plays a fundamental role in the context of AGB evo-lution: it is the reduction of the convective envelope via stel-lar winds which eventually halts the TP phase, and leads toPN ejection. Also, the description of mass loss determines thenumber of TPs experienced by the star, and, in turn, the numberof TDUs (Sch¨onberner 1979).Ventura et al.(2000) calibrated the parameter η R enteringeq.(2) by reproducing the luminosity function of lithium richstars in the Magellanic Clouds; the chemistry of the stars ex-amined in the present work is di ff erent, thus leaving some roomfor a possible variation of η R . It is therefore essential to under-stand to which extent the yields which we obtain depend onthis choice.On the physical side, a larger mass loss leads the starevolve at lower luminosities; the degree of the nucleosynthesisachieved at the bottom of the convective envelope is reduced,because we have smaller temperatures. This is confirmed byfig.7, where we show the evolution of the luminosity and of T bce in models with initial masses 5 and 6 M ⊙ , calculated withdi ff erent η R s.Chemically, the situation is complex, and not all the iso-topes follow the same trend with ˙ M ; this is dependent on themodality with which any chemical species is synthesized (ordestroyed) within the convective envelope. The last three linesof Table 2 report the chemistry of the ejecta of the models of 5 entura & D’Antona: AGB models of intermediate metallicity 9 and 6 M ⊙ calculated with a di ff erent mass loss rate with respectto our standard case.The behaviour of lithium is the most linear. As can be seenin the left panel of fig.8, lithium is produced only during thefirst TPs, so that the average lithium content of the ejecta isdetermined essentially by the mass lost by the star during thisphase. A large ˙ M allows a larger release of lithium rich mate-rial during the early phases of the AGB evolution, with a conse-quent increase of A(Li): for a given mass, we see in Table 2 analmost linear trend A(Li)- η R . A similar, straight path is also fol-lowed by fluorine, which is destroyed during the very first TPs,so that the overall yield is determined by the strength of thestellar winds during the first TPs; in this case the slope of the[F / Fe]- η R relation is lower compared to lithium, because thefluorine consumption is faster than the duration of the wholephase of lithium production and destruction.Other elements show up a less defined behaviour, becausetheir yield is determined by the nucleosynthesis at the bottomof the envelope during the whole AGB phase, and also by theTDU. Interestingly, we find that in some cases the yields arenot very sensitive to the mass loss rate adopted. A typical ex-ample is oxygen, for which we show the variation of the sur-face abundance in the right panel of fig.8. When mass loss isreduced, the tendency of the oxygen abundance of the ejectato diminish (less oxygen-rich matter during the first TPs is lostby the star) is partly compensated by the larger number of TPs,which act to increase the surface oxygen content. The clear-est example is the 6 M ⊙ model, for which a smaller η R (dottedtrack) leads to a smaller surface oxygen abundance until thetotal mass of the star drops to 3 M ⊙ , but to a larger mass frac-tion in the latest evolutionary phases, when the TDU becomese ffi cient. As can be seen in Table 2, the oxygen content of theejecta is almost independent of η R , and so is the general con-clusion which we reached in Sect.5.1 concerning the maximumdepletion of oxygen obtainable by these models: playing withmass loss leaves unchanged the maximum depletion of oxygenobtainable at these metallicites, leading to a minimum oxygencontent of the ejecta [O / Fe] = -0.4.A behaviour similar to oxygen is also followed by sodium,again because its abundance in the envelope is a balance be-tween destruction via proton capture and production via dredg-ing up of Ne. Independently of mass, the related uncertaintyis δ [Na / Fe] ∼ . M ,because a larger mass loss favours a larger release of mass at thebeginning of the AGB phase, when the aluminum has not yetbeen synthesized in great amounts. The smaller number of TPsat large ˙ M tends to increase the Al abundance indirectly, viadredge-up of the heavy magnesium isotopes, which later formaluminum via proton capture. The variation of [Al / Fe]with themass loss rate is ( δ [ Al / Fe ] ∼ . substantial change of its surfaceabundance takes place during the II DUP, and remains approx-imately constant during the whole following AGB phase.Finally, we note from the last column of Table 2 that theCNO ratio has a negative trend with mass loss, which is a mere Fig. 7.
Comparison between the variation with the total mass ofthe luminosity (top) and temperature at the bottom of the con-vective envelope (bottom) of models with initial masses 5,6 M ⊙ ,calculated with di ff erent values of the parameter η R eneteringeq.2consequence of the fact that when ˙ M is high the star experiencea smaller number of TPs.We may summarize the e ff ects of the uncertainties of massloss during the AGB phase on the chemistry of the ejecta asfollows:1. Oxygen is not sensitive to the mass loss rate adopted2. Sodium and aluminum show a positive trend with massloss, but the uncertainty associated with the adopted de-scription of mass loss is considerably smaller than the in-determination due to the unknown relevant cross-sections3. Lithium and fluorine are more sensitive to mass loss, witha linear positive trend4. The CNO content of the ejecta is sensitive to mass loss,because a stronger ˙ M diminishes the number of TPs ex-perienced by the stars, thus favouring a smaller C + N + Oabundance
7. Discussion: theory vs. observations
We discuss the self-enrichment scenario hypothesis for inter-mediate metallicity clusters, by asking whether the ejecta ofthe most massive AGBs can account for the chemical patternstraced by the abundances of the GC stars with the most anoma-lous chemistry. We restrict our attention on the least evolvedstars (i.e. TO and SGB sources, or giants well below the RGBbump), despite the di ffi culties presented by their spectroscpicanalysis, because this allows to rule out any possible changeof the surface chemistry due to some non-canonical extra mix-ing while ascending the RGB; we therefore disentangle the pri-mordial from the evolutionary e ff ects, and focus only on theabundance patterns present directly in the matter from whichthe stars formed.Our goal is to test the possibility that our ejecta can repro-duce the observed O-Na and O-Al trends, and that the starsshowing the strongest oxygen depletion are fluorine poor andpossibly sligthly depleted in magnesium. Finally, we compareour results with the recent analysis of the lithium abundances inNGC 6752, which indicate that oxygen poor stars deviate fromthe Spite’s plateau, having a lithium content a factor 2 smallerthan the standard value (Pasquini et al. 2005).In making this comparison, we keep in mind that the oxy-gen abundances predictions are very robust, that the aluminumand even more sodium mass fractions are made uncertain bythe poor knowledge of the relevant cross-sections in the rangeof temperatures of interest here (T ∼ ff ering in Fig. 8.
Variation with the total mass of the star of the lithium (Left) and oxygen (Right) surface abundances within models ofinitial mass 5 and 6 M ⊙ calculated with di ff erent mass loss rates. Note the straightforward dependency of lithium on mass loss,compared to the more tricky behaviour of oxygen, whose destruction is first amplified by a lower mass loss rate, and laterprevented by TDU episodesthe chosen cross-sections for the reactions involving sodium:the upper solid track refers to models calculated with the up-per limits for the Ne(p, γ ) Na and the lower limits for the Na(p, α ) Ne reactions, while the lower refers to models cal-culated with the recommended values for the same reactions;the dashed track indicates the results obtained by maximizingthe rates of the α − capture reactions by Ne.According to our interpretation, the observed points insidethe squared box in the right lower portion of the plane rep-resent stars born with the original chemistry, while those be-longing to the 2nd generation, whose initial chemistry tracesthe pollution by AGBs, are included within the squared boxin the left-upper part. The remaining points, with high sodiumand normal oxygen, may be stars formed by processed mat-ter mixed with remnant primordial gas (Decressin et al. 2007).The uncertainties related to the cross-sections strongly limit thepredictive power of the results obtained, and the observationalspread ( δ [Na / Fe] ∼ . / Fe]) makes the compar-ison not straightforward. However, we note that the ejecta ofmodels with masses M ≥ M ⊙ might account for the oxy-gen and sodium abundances detected in the 2nd generation ofstars. Notice that here we are touching again the problemof the mass budget: if only the envelopes of stars from 5up to 6.3 M ⊙ —or at most up to 7-8 M ⊙ , if we can assumethat also the superAGBs contribute with similar yields—can form the self–enriched stars, the gas contained in thismass range, for reasonable IMFs, is only a few percent ofthe total initial cluster mass. As we remarked in the in-troduction, we must then hypothize that the initial clustermass was much larger than the present mass, and that pref-erentially the second generation stars have been lost duringthe long term cluster evolution. The right panel of Fig.9 reports the observed points in theO-Al plane. Even in this case we report two theoretical lines,obtained with di ff erent choices of the rates of the Mg-Al chainreactions (the upper line refers to models calculated with themaximum allowed values of the cross-section of the protoncapture reactions by the two heavy magnesium isotopes). Inthis case the observed trend is well reproduced, in particularfor the chemistry of the most oxygen poor stars, which evi-dentiate an aluminum enhancement by [Al / Fe] ∼
1. In the caseof aluminum the comparison is more straightforward, becausethe theoretical uncertainties related to the cross-sections aresmaller. The two squares in the figure have the same meaningas in the left panel.A welcome result from this investigation is that the lithiumcontent of the ejecta of the most massive models, those showingthe strongest depletion of oxygen, is A(Li) ∼ / Fe] < . δ [Mg / Fe] ∼ . M ⊙ . Thisis in agreement with a recent investigation focused on M4 gi-ants (Smith et al. 2005); a robust confirm of this scenario wouldbe the determination of fluorine abundances in TO and SGBstars.
8. Conclusions
We present updated model for the evolution of AGB stars of3 M ⊙ ≤ M ≤ . M ⊙ , Y = = α − enhanced mixture, to describe self-consistentlythe chemistry of the first generation of stars which form in theGCs.The high e ffi ciency of the convective model adopted con-firms an important result obtained by this research group re-garding the AGB evolution of intermediate mass stars, i.e. thepossibility of a strong nucleosynthesis at the bottom of the ex-ternal convective zone for all the masses M > M ⊙ ; this HBBalso favours a fast increase of the luminosity, a higher massloss, and therefore reduces the number of thermal pulses ex-perienced by the star during the AGB phase. The present in-vestigation indicate that for this metallicity a maximum T bce = ff ered by the most massive models,limits the extent of the nucleosynthesis which may be achievedwithin the envelope.The combination of HBB and TDU in the most massivemodels favours a strong depletion of oxygen and fluorine, amodest reduction of magnesium, and a large production of alu-minum. Sodium is also produced, via a delicate compromisebetween production by neon burning and destruction by protoncapture. It is confirmed that lithium can be produced at the be-ginning of the AGB phase via the Cameron-Fowler mechanism,to be later destroyed due to He consumption within the enve-lope. The matter ejected by these models is helium rich, whicha maximum enrichment of Y = M ⊙ model.On the basis of the results of this work, the strongest pointin favour of the self-enrichment scenario is the oxygen deple-tion, for which both the observations an the theoretical predic-tions indicate a maximum limit of [O / Fe] = − .
4; the theoreti- entura & D’Antona: AGB models of intermediate metallicity 11
Fig. 9.
Left: The observed Oxygen-sodium trend in stars in GCs. The solid lines indicate the content of the ejecta of our models,obtained with the recommended cross-sections for the reactions involved in the Ne-Na cycle (lower track), and with the reactionsrates maximizing sodium production (upper lines); the dashed track shows the abundances of the ejecta from the models calcu-lated with the enhanced cross sections for the α − captures by Ne. Right: The observed Oxygen-Aluminum anticorrelation. Thetwo solid lines indicate the results from our models, accroding to the choices made for the cross-section of the Mg-Al reactions.The observed points refer to the following works. Full triangles: NGC 6752 (Gratton et al. 2001); Open squares: M5 stars with V >
16 (Ramirez & Cohen 2003); Stars: M13 stars with V >
15 (Cohen & Melendez 2005); Open triangles: M3 stars with V >
15 (Cohen & Melendez 2005); Full points: NGC 6218 stars (Carretta et al. 2006); Open squares: High gravity M3 giants(Sneden et al. 2004); Full squares: High gravity M13 giants (Sneden et al. 2004)cal oxygen yield is robust, as it turns out to be approximatelyindependent of the details of the mass loss description, and therelevant cross-sections are known with su ffi cient accuracy.The O-Al trend is confirmed by the present investigation,though the extent of the aluminum enrichment of the ejecta issensitive to the assumptions regarding the cross-sections of theproton capture reactions by the heavy magnesium isotopes andby Al: note that the largest enrichment, [Al / Fe] = Ne nu-clei are adopted, the most oxygen poor ejecta are also sodiumrich, but the exact extent of the sodium enrichment, and theconfirm that a clear anticorrelation exists, can be hardly fixedwith the present cross-sections: the theoretical uncertainties re-lated to the sodium content amount to 0.6 dex.The yield of lithium and fluorine are most sensitive to themass loss rate adopted. With our standard choice, our modelspredict a O-Li trend which is in excellent agreeent with a recentinvestigation based on the lithium content of TO stars in NGC6752. The fluorine content is expected to be extremely poor inany case, the exact abundance being determined by the detailsof the mass loss description.
References