Chemical yields from low-and intermediate-mass stars: model predictions and basic observational

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December 12, 2000
Chemical yields from low- and intermediate-mass stars:
model predictions and basic observational constraints
Paola Marigo
Dipartimento diAstronomia, Universita(cid:18) di Padova, Vicolo dell’Osservatorio 2, I-35122 Padova, Italia
Received14 September2000 / Accepted
Abstract. In this work we analyse the role of low- and forest clouds (e.g. Lu 1991; Crotts et al. 1994, Tytler &
intermediate-mass stars in contributing to the chemical Fan 1994).
enrichment of the interstellar medium. First we present Thechemicalhistoryofboththeseelementsinagalaxy
new sets of stellar yields basing on the results of updated is quite complex, as it depends, besides other factors, on
evolutionary calculations, which extend from the ZAMS the relative contributions of stars with di(cid:11)erent masses,
up to the end of the AGB phase (Girardi et al. 2000; hence releasing their yields at di(cid:11)erent timescales. In the
Marigoetal.1999a).Thesenewyields,thatpresentasig- caseof12Ctherelativeroleoflow-andintermediate-mass
ni(cid:12)cant dependence on metallicity, are then compared to stars, or rather of metal-rich, mass-losing massive stars,
those of other available sets (Renzini & Voli 1981; van de in the carbon enrichment at late galactic epochs is still
Hoek &Groenewegen1997).The resultingdi(cid:11)erences are a matter of debate (Prantzos et al. 1994). In the case of
explained in terms of di(cid:11)erent model assumptions { i.e. 14N, large uncertainties a(cid:11)ect the theoretical predictions
treatmentof convectiveboundaries,massloss,dredge-up, on both the secondaryand primarynucleosynthesis of ni-
hot-bottom burning { and further discussed on the basis trogen in low- and intermediate-mass stars, and the pos-
ofimportantempiricalconstraintswhichshouldberepro- sible contribution of primary nitrogen from massive stars
ducedbytheory{i.e.theinitial-(cid:12)nalmassrelation,white (Woosley&Weaver1982,Maeder1983;seealsothereview
dwarf mass distribution, carbon star luminosity function, by Maeder & Meynet 2000).
and chemical abundances of planetary nebulae. We show Itfollowsthat,inordertotracethehistoryofchemical
thatpresentmodelsareabletoreproducesuchconstraints evolution and of star formation in the Universe { which
in a satisfactory way. the observations of high red-shift systems are intended
to infer { it is quite important to analyse in detail the
Keywords:Stars:evolution{Stars:AGBandpost-AGB nucleosynthesisof theseelementstakingplaceinlow-and
{ Stars: mass-loss { Planetary nebulae: general { ISM: intermediate-mass stars. The contribution of these stars
abundances { Galaxies: abundances to the chemical enrichment of the ISM essentially occurs
during the RGB and AGB phases, both characterized by
the occurrenceofmasslossandeventsofsurfacechemical
pollution (dredge-up episodes).
1. Introduction
WhereasmodellingtheevolutionofastarontheRGB
Low-andintermediate-massstars(withmasses0.8M(cid:12) <(cid:24) is rather easy by means of modern stellar evolutionary
M <(cid:24)5(cid:0)8M(cid:12),dependingonmodeldetails)playanimpor- codes, dealing with the most advanced stages { charac-
tantroleingalacticchemicalevolution,thankstotheejec- terised bythe occurrenceof thermal pulses(the TP-AGB
tion into the interstellar medium (ISM) of material con- phase) { is quite a di(cid:14)cult task, due to both the high
taining newly synthesized nuclear products, mainly 4He, complexity of the physics involved, and the remarkable
12C, and 14N, and possibly 16O. requirementofcomputingtime.Then,analternativetheo-
The interest in the nucleosynthetic history of 12C and reticalapproachiso(cid:11)eredbysyntheticmodels,whichsum-
14N, in particular, has recently increased thanks to the marisetheresultsofcompletestellarcalculationsthrough
simpleandpracticalanalyticalrelations.Thisallowsquick
observations of high red-shift systems. For instance, it is
computingofthemodelsandreadyanalysisoftheresults.
possibletomeasurethe nitrogenabundanceandthe N/O
ratiointhedampedLy-(cid:11)systems(e.g.Pettinietal.1995; Historically, the (cid:12)rst most signi(cid:12)cant AGB synthetic
Lu et al. 1998), whereas carbon is detected in the Ly-(cid:11) models were those developed by Iben & Truran (1978)
and Renzini & Voli (1981). These pioneer works focused
Send o(cid:11)print requests to: Paola Marigo on the contribution of low- and intermediate-mass stars
e-mail: [email protected] to the element enrichment of the ISM. In particular, the
2 P. Marigo
sets of stellar yields presented by Renzini & Voli (1981) (cid:11) = 2:50. This parameter mainly a(cid:11)ects the predicted
havebeenextensivelyusedinchemicalevolutionmodelsof production of 14N and 4He due to HBB (See Sect. 4.1).
galaxies, providing almost the only available data source The (cid:12)nal part of this work (Sect. 5) is dedicated to
up to recent years. compareourresultswiththeyieldscalculatedbyotherau-
ItisimportanttoremarkthatinRenzini&Voli(1981) thors,i.e.Renzini&Voli(1981),andvandeHoek&Groe-
syntheticAGBmodelthefundamentalparameters(essen- newegen (1997). In the attempt to single out the causes
tiallymass-lossanddredge-up)werespeci(cid:12)edaccordingto of the main di(cid:11)erences, we analyse the e(cid:11)ect of di(cid:11)erent
theindicationsfromthecurrentknowledgeoftheinvolved model prescriptions (e.g. mass-loss, dredge-up, HBB) on
physical processes and available complete stellar calcula- the predicted yields, testing at the same time the capa-
tions. In this sense the model was uncalibrated. That ap- bility of amodeltosatisfybasicobservationalconstraints
proach had the merit of supplying a testing tool for com- (e.g. initial-(cid:12)nal mass relations, white dwarf mass distri-
plete stellar models, as it pointed out at some fundamen- bution, carbon star luminosity functions, chemical abun-
tal inadequacies in the predictions (e.g. too low e(cid:14)ciency dances of planetary nebulae).
of the third dredge-up), and assumed prescriptions (e.g.
too low mass-loss rates), which led to clear discrepancies
2. Evolutionary models
between theory and observations (see, for instance, Iben
1981; Iben & Renzini 1983; Bragagliaet al. 1995). 2.1. Some de(cid:12)nitions
Withawarenessofthat,thelatersyntheticAGBmod-
Letus(cid:12)rstde(cid:12)nesomequantitieswhichwillbeoftenused
els(e.g.Groenewegen&deJong1993;Marigoetal.1996,
throughout this paper to indicate critical masses for the
1999a)havemadethe nextstepahead,thatisupdatethe
occurrenceof particularphysicalprocesses.These quanti-
input prescriptions and calibrate the model parameters
ties are: M , M , Mmin , Mmin, and Mmin.
in order to reproduce fundamental observables (e.g. the HeF up HBB dred c
The(cid:12)rstone,M ,denotesthemaximuminitialmass
carbonstarluminosityfunctions,the initial-(cid:12)nalmassre- HeF
for a star to develop a degenerate He-core, hence expe-
lation). Basing on the results of these model calibrations,
rience the He-(cid:13)ash at the tip of the Red Gian Branch
various sets of stellar yields from low- and intermediate-
(RGB), and is comprised between 1.7 { 2.5 M(cid:12) depend-
mass stars have been presented in recent years as an al-
ing on metallicity and model details.
ternative to Renzini & Voli (1981), namely: Marigo et al.
The second one, M , is de(cid:12)ned as the critical stellar
(1996,1998),vandeHoek&Groenewegen(1997);seealso up
massoverwhichcarbonignitionoccursinnon-degenerate
Forestini & Charbonnel (1997), and Boothroyd & Sack-
conditions, marking the boundary between intermediate-
mann (1999).
massandmassivestars.Itisworthrecallingthatthismass
To the above reference list we will now add the new
limit is usually comprised within 5 { 8 M(cid:12), being signif-
homogeneous sets of stellar yields presented in this work.
icantly a(cid:11)ected by the adopted treatment of convective
With respect to our previous calculations (Marigo et al.
boundaries, as discussed in Sect. 5.
1996, 1998), the present yields are derived from stellar The third one, Mmin , corresponds to the minimum
HBB
models with updated input prescriptions and improved
initial mass for a star to undergo HBB during the TP-
treatmentoftherelevantprocessesinvolved(i.e.thethird
AGB phase. Stellar evolution calculations indicate that
dredge-up, see Marigo et al. 1999afor all details). Mi >(cid:24) MHmBinB (cid:24) 3:5(cid:0) 4:5M(cid:12), depending on metallicity
Speci(cid:12)cally, we follow the evolution of low- and (see, for instance, Marigo 1998b).
intermediate-mass stars, coupling the results of complete The fourth one, Mmin, denotes the minimum initial
dred
stellarmodels(Girardietal.2000){thatcovertheevolu- mass for a star to experience the third dredge-up during
tion from the zero age main sequence (ZAMS) up to the the TP-AGB phase. Observations of carbon stars suggest
onset of the thermally pulsing asymptotic giant branch thatMdmreind (cid:24)1:1(cid:0)1:5M(cid:12),decreasingwiththemetallicity
(TP-AGB) { with synthetic TP-AGB models (Marigo (see, for instance, Marigo et al. 1999a).
1998ab;Marigoet al. 1999a)that extend the calculations Finally, we recall the basic parameters of the third
up to the end of this phase. Relevant model prescriptions dredge-up: (cid:21) and Mmin. The parameter (cid:21) is intended to
c
are brie(cid:13)y recalled in Sect. 2. measure the e(cid:14)ciency the third dredge-up, being de(cid:12)ned
With the aid of these evolutionary calculations, we asthefractionoftheincrementofcoremassoveraninter-
then derive the stellar yields (H, He, and main CNO ele- pulseperiodwhichisdredged-uptothesurfaceatthesub-
ments; refer to Sects. 3 and 4) for a dense grid of initial sequent thermal pulse. The actual values for (cid:21) are still a
stellar masses (in the range 0:8M(cid:12) { 5M(cid:12)) and various matterofdebateamongtheoreticians,andcanrangefrom
metallicities (Z =0.004, 0.008, 0.019). For the most mas- (cid:21)(cid:24)0 to (cid:21)>(cid:24)1, depending both on stellar properties(e.g.
sive stars, experiencing hot-bottom burning (hereinafter massandmetallicity)andmodeldetails(e.g.treatmentof
HBB, or envelope burning) during the TP-AGB phase, convective boundaries).
the corresponding yields are given for three values of the TheparameterMmin referstotheminimumcoremass
c
mixing-length parameter, i.e. (cid:11) = 1:68, (cid:11) = 2:00, and for the occurrence of the third dredge-up, and is a(cid:11)ected
Yields from low- andintermediate-mass stars 3
by several factors as well. In general, theoretical models 3. Derivation of the wind contributions
would predict that Mmin decreases { so that the third
c Following the classical de(cid:12)nition by Tinsley (1980), the
dredge-up is favoured { at increasing mass and mixing-
stellar yield, p (M), of agivenchemical element k, is the
length parameter, and decreasing metallicity (see, for in- k i
mass fraction of a star with initial mass M that is con-
stance, Wood 1981; Marigo et al. 1999a). i
vertedintothe elementk andreturnedtotheISMduring
its entire lifetime, (cid:28)(M). Tables A1 { A12 give the quan-
i
2.2. Input physics tities:
Inthisworkweconsiderlow-andintermediate-massstars,
M (k)=M p (M) (1)
y i k i
i.e. those with initial masses in the range from about
0:8M(cid:12) to Mup (cid:24) 5:0M(cid:12) and and three choices of the expressed in solar masses, for all the chemical elements
original compositions (i.e. [Y = 0:273;Z = 0:019], [Y = considered, as function of the initial stellar mass M,
i
0:250;Z =0:008], [Y =0:240;Z =0:004]). metallicity Z, and mixing-length parameter (cid:11).
TheirevolutionfromtheZAMSuptothebeginningof Accordingtothede(cid:12)nitionofstellaryieldwecanwrite:
the TP-AGB phase is taken from the Padua stellar mod-
els (Girardi et al. 2000), that include moderate overshoot M (k)= (cid:28)(Mi)[X(k)(cid:0)X0(k)] dMdt (2)
from core and external convection (Chiosi et al. 1992; y Z dt
0
Alongi et al. 1993). The reader should refer to Girardi et
where dM=dt is the current mass-loss rate; X(k) and
al. (2000) for more details of the adopted input physics.
X0(k) refer to the current and initial surface abundance
The models by Girardi et al. (2000) provide the ex-
of the element k, respectively.
pected changesin the surface abundanceof severalchem-
Thankstothe fact that the surfacechemicalcomposi-
ical elements (H, 3He, 4He, 12C, 13C, 14N, 15N, 16O,
tionofstarsnotsu(cid:11)eringHBBduringtheTP-AGBphase
17O,18O,20Ne,22Ne,25Mg)causedbythe(cid:12)rstandsecond
dredge-upepisodes, i.e.priortothe onset of the TP-AGB (i.e.withinitialmassesMi <(cid:24)MHmBinB),isalteredbytheoc-
currence of discrete and quasi-instantaneous episodes of
phase. It should be also remarked that these models do
convective dredge-up, that alternate with periods of con-
not assume any ad-hoc \extra-mixing mechanism", e.g.
tinuous mass-loss, the evaluation of stellar yields can be
theso-calledcool-bottomprocess(Wasserburgetal.1995;
simpli(cid:12)ed as follows.
see also Charbonnel 1995; Boothroyd & Sackmann 1999;
Denoting by X1(k), X2(k), Xj(k), the abundance of
Weissetal.2000),whichisinvokedtoreconcilediscrepant
the species k afterthe (cid:12)rst dredge-up,the second dredge-
predictionsof surfaceabundances with those measuredin
up, and the jth dredge-up event during the TP-AGB
(cid:12)eld Population II stars, galactic globular clusters, and
phase, respectively, we get:
Magellanic Clouds clusters (see, for instance, the results
by Gratton et al. 2000 in their chemical analysis of (cid:12)eld
My(k)=My(k)RGB+My(k)E(cid:0)AGB+My(k)TP(cid:0)AGB (3)
metal-poor stars).
Mass loss by stellar winds su(cid:11)ered by low-mass stars where
(withMi (cid:20)MHeF (cid:24)1:7(cid:0)2:2M(cid:12))ontheascentofRGB,is M (k) =[X1(k)(cid:0)X0(k)] (cid:1)Mej (4)
analyticallyincludedapplyingtheclassicalReimers(1975) y RGB RGB
formula to the evolutionary tracks calculated at constant
mass by Girardi et al. (2000). An e(cid:14)ciency parameter My(k)E(cid:0)AGB =[X2(k)(cid:0)X0(k)] (cid:1)MEej(cid:0)AGB (5)
(cid:17) =0:45isadoptedtoful(cid:12)ltheclassicalobservationalcon-
straintprovidedbythemorphologyofhorizontalbranches My(k)TP(cid:0)AGB = [Xj(k)(cid:0)X0(k)] (cid:1)MTj;Pej(cid:0)AGB (6)
in Galactic Globular Clusters. Xj
Finally, once the the (cid:12)rst signi(cid:12)cant thermal pulse
is singled out in each evolutionary sequence calculated In Eq.(4) (cid:1)Mej isthe massof the envelope ejected
RGB
by Girardi et al. (2000), that point is assumed to de- during the entire RGB phase (de(cid:12)ned only for low-mass
(cid:12)ne the starting conditions for synthetic calculations of stars). It is worth noticing that most of (cid:1)Mej is lost
RGB
theTP-AGBphase(followingthe modelprescriptionsde- close to the tip of the RGB, that is after the occurrence
scribedinMarigo1998ab,andMarigoetal.1999a),which of the (cid:12)rst dredge-up, so that Eq. (4) is a good approxi-
are carried on up to the complete ejection of the enve- mation of Eq. (2).
lope by stellar winds. Mass loss is included according to As far as mass loss on the AGB is concerned, we re-
the semi-empirical formalism developed by Vassiliadis & mark that, with the adopted prescription for M_ (Vassil-
Wood (1993).Nucleosynthesis occurringin the innermost iadis & Wood 1993), the amount mass lost during the
envelope layers of TP-AGB stars with HBB is followed E-AGB phase is indeed negligible so that we can assume
adopting the Caughlan & Fowler (1988) compilation of (cid:1)Mej =0 in Eq. (5).
E(cid:0)AGB
reaction rates for CNO and p-p reactions. The electron- The contribution of the TP-AGB phase is evaluated
screening factors are those of Graboske et al. (1973). with Eq. (6), that sums all the partial contributions of
4 P. Marigo
the pulse cycles, the generic jth one consisting of a ther- { The third dredge-up determines the surface enrich-
mal pulse { when the jth dredge-uppossibly occurs { fol- ment mainly of 4He, 12C, and 16O. The adopted in-
lowed by the inter-pulse period, during which the mass tershellabundancesare[X(4He)=0:76;X(12C)=0:22;
(cid:1)Mj;ej is ejected. X(4He)= 0:02] according to Boothroyd & Sackmann
TP(cid:0)AGB
It shouldbe noticed that this approximationholdsfor (1988b).Theprocessismoree(cid:14)cient(i.e.higher(cid:21))at
TP-AGBstarswhichexperienceonlythethirddredge-up. lower Z;
For more massive TP-AGB stars (with M >Mmin ) also { HBBoperatesviatheCNO-cycle,henceessentiallyin-
i HBB
su(cid:11)ering HBB, the changes in the surface chemical com- creasingthe surface abundances of 4He, and 14N. The
position and mass lossare concomitantprocesses, sothat process is more e(cid:14)cient at higher M (provided that
thecalculationofstellaryieldsrequirestheadoptionofin- M >Mmin ), lower Z, and larger (cid:11).
HBB
tegration time steps shorter than the inter-pulse periods. { mass loss is, in general, less e(cid:14)cient (i.e. lower M_ ) at
Ingeneral,negativeM (k)correspondtothoseelemen- decreasing Z and increasing (cid:11). In fact, both factors
y
tal species which are prevalently destroyed and diluted in tend to produce hotter tracks, and generally M_ anti-
theenvelope,sothattheirabundancesintheejectedmate- correlateswith T .Asaconsequence,lowermass-loss
e(cid:11)
rialarelowerwithrespecttothemainsequencevalues.On rates correspond to longer TP-AGB lifetimes, hence
the contrary,positive M (k)correspondtothoseelements greaternumberofthirddredge-upeventsandalonger
y
which are prevalently produced so that a net enrichment duration of HBB.
of their abundances in the ejecta is predicted.
The expected trend of M (k) for the elements un-
Figures 1 and 2 show the quantities M (k) for all the y
y der consideration as a function of the stellar initial mass,
chemical elements considered, as a function of M and Z.
i metallicity, and mixing-length parameter is shown in
ForstarsexperiencingHBBresultsaregivenforthreeval-
Figs. 1-3. We can notice the following:
ues of the mixing-length parameter.
Finally,forthesakeofclarity,weremindthattheCNO { H and 4He
cycle does not change the total number of CNO nuclei The net yields of these elements have mirror-like
involved as catalysts in the conversion of H into 4He, i.e. trends, being negative for H, and positive for 4He.
YCNO = kXkCNO=Ak = constant. It follows that the The maximum of 4He production at around 2(cid:0)3M(cid:12)
(cid:12)rst and Psecond dredge-up, though a(cid:11)ecting the surface (depending on metallicity) is explained considering
abundances of the CNO isotopes, do not alter their total the e(cid:11)ect of the increase of the number of thermal
abundance by number. In fact, the material injected into pulses(hencedredge-upepisodes)withstellarmassfor
theenvelopehasexperiencedtheCNOcycleinvolvingonly 0:8M(cid:12) <Mi <(cid:24)2(cid:0)3M(cid:12)(seeFig.5).Thispeakismore
isotopes already present in the original composition. On pronounced at lower metallicities due to longer TP-
the contrary,the constancy of YCNO breaks down assoon AGB duration (Fig. 5) and larger number of thermal
asthedredge-upofprimarycarbonandoxygen,produced pulses (Fig. 6) for given stellar mass. The subsequent
by (cid:11)-capture reactions at thermal pulses, occurs. increase of 4He production towards higher masses,
However, in all cases the total abundance by mass of 4M(cid:12) <(cid:24) Mi (cid:20) 5M(cid:12), is caused by the occurrence of
the CNO isotopes is somewhat changed because of the HBB in addition to the third dredge-up. The yield of
conversion of these elements mainly into 14N, so that a 4He is larger for lower metallicities and higher values
small positive CNO yield (in mass fraction), is expected, of the mixing-length parameter, re(cid:13)ecting the greater
for example, from the RGB phase (see Tables A1 { A3). e(cid:14)ciency of both the third dredge-up and HBB.
The quantity, My(CNO), referring to the total net yield { 3He
of all CNO isotopes, is shown in Fig. 3. The net yield of this element presents a pronounced
peak at very low masses, say at Mi (cid:24) 1M(cid:12), and de-
4. Stellar yields as a function of Mi, Z, and (cid:11) creases at higher masses. This trend is explained con-
sideringthat the maincontribution tothe yield is due
Model predictions can be understood more easily consid-
tothe(cid:12)rstdredge-up,andthatboththerelatedsurface
eringthatthestellaryieldofagivenelementisessentially enrichmentof3Heandtheamountofmasslostduring
determined by the e(cid:14)ciency and duration/frequency of: the RGB phase are inversely proportional to the stel-
lar mass in the low-mass domain. At higher masses,
{ the nucleosynthesis/mixing processes (e.g. dredge-up
events, HBB) whichalterits abundancein the surface (Mi >(cid:24)3M(cid:12)), the net yield becomes even slightly neg-
ative because of HBB.
layers;
{ 12C
{ the mass-loss process which ejects the surface layers
The net positive yield increases with the initial mass,
into the ISM
up to a maximum located at about 2(cid:0)3M(cid:12), corre-
Accordingtothephysicalprescriptionsadoptedinthis spondingto largestnumber of dredge-up episodessuf-
work for the TP-AGB phase (see also Sect. 5.1) we can fered during the TP-AGB phase, provided that HBB
summarise the following points: has not operated.
Yields from low- andintermediate-mass stars 5
Fig.1. Net yields My(k) (in M(cid:12)) for each indicated chemical element (H, 3He, 4He, 12C, and 13C) as a function of the initial
mass (in M(cid:12)) of the star. The solid, dashed, and dotted lines correspond to the metallicity sets Z = 0:019, Z = 0:008, and
Z =0:004, respectively.Panels along each columnrefer to the same value of the mixing-lengthparameter.
The subsequent decline towards higher masses is ini- { 13C
tially due to fewer dredge-up events, and then to the The (cid:12)rst dredge-up causes an increase of the 13C sur-
prevailinge(cid:11)ectof HBB.Itfollowsthatnosubstantial faceabundanceinstarsofallmasses,andtheresulting
enrichment of 12C is provided from the most massive yields are positive. A further contribution is provided
AGB stars. by mild HBB, as long as creation of 13C via the re-
This general trend is more marked at lower metallic- action 12C(p;(cid:13))13C prevails over destruction via the
ities, because of the longer TP-AGB phases, and the reaction 13C(p;(cid:13))14N. The results also depend on the
greater e(cid:14)ciency of the third dredge-up and HBB. interplaybetween the strength of HBB and mass loss.
6 P. Marigo
Fig.2. Net stellar yields My(k) (in M(cid:12)) for each indicated chemical element (14N, 15N, 16O, 17O, and 18O) as a function of
the initial stellar mass (inM(cid:12)). The notation is the same as inFig. 1.
The most favourable cases correspond to the mod- weak 13C is not signi(cid:12)cantlycreated, else if somewhat
els [e.g. (4M(cid:12);Z = 0:019;(cid:11) = 2:00), (3:5M(cid:12);Z = too strong 13C is quickly destroyed in favour of 14N.
0:004;(cid:11) = 1:68)], in which the e(cid:14)ciency of reactions { 14N
allows the synthesis of 13C for a long time before the It turnsout that HBB playsthe dominant rolefor the
drastic reduction of the envelope causes the extinc- synthesisof14N.Thepositiveyieldasafunctionofthe
tion of nuclear burning. The spikes of 13C production stellar mass depends on both the e(cid:14)ciency and dura-
forthesemodelswouldsuggestthatapropertuningof tion of nuclear burning. It follows that lowermetallic-
HBBisrequired:Ifnuclearreactionsaresomewhattoo ities and higher values of the mixing-length parame-
ter concur to favour nitrogen production. The contri-
Yields from low- andintermediate-mass stars 7
Fig.3.Netstellar yields of all CNO elements as a function of the initial stellar mass. The notation is the same as inFig. 1.
bution from low- and intermediate-mass stars to the a(cid:11)ected by various other factors (e.g. number and ef-
galactic enrichment of nitrogen may result important, (cid:12)ciency of dredge-up episodes; see also Sect. 6).
assuggestedbychemicalevolutionarymodelsofgalax- Anyhow, regardless of its abundance in the dredged-
ies (e.g. Portinari et al. 1998). up material, the trend of 16O, as a function of M and
{ 15N Z, is expected to be qualitatively similar to that of
The net yield of this element is mostly negative. For 12C. Moreover, according to the present calculations,
stars with initial masses in the range, 0:8M(cid:12) <(cid:24) Mi <(cid:24) a notable dependence on metallicity comes out. The
3:5M(cid:12), the depletion of 15N is due to the e(cid:11)ect of the increasing positive trend with decreasing metallicities
(cid:12)rst and second dredge-up. For higher mass stars, the essentiallyre(cid:13)ectsthe longerdurationof theTP-AGB
results are a(cid:11)ected by HBB, depending on the degree phase, and hence the greater number of dredge-up
of CNO cycling attained in the burning regions. This episodes, in combination with their larger e(cid:14)ciency.
element has the shortest nuclearlifetime, after that of { 17O
18O,sothatitquicklyattainsnuclearequilibriumwith AcertainproductionofthiselementisprovidedbyTP-
14N.Wenotethatthedepletionof15Nismuchmoreef- AGBstarswithHBB,aslongasthechainofreactions
(cid:12)cientathighermetallicitiesduetotheincreaseofthe 16O(p;(cid:13))17F((cid:12)+(cid:23))17O prevails over nuclear destruc-
CNO-cycling, which implies a more e(cid:14)cient destruc- tion via the reactions 17O(p;(cid:13))18F and 17O(p;(cid:11))14N.
tion of this element. The predicted trend of the 15N Thebehaviourresemblesthatof13C,inthesensethat
yield mirrors, to some extent, that of the secondary undersome(cid:12)ne-tunedconditions{forparticularcom-
component of 14N (cf. Sect. 4.1). binations of the stellar mass and metallicity { a pro-
{ 16O duction spike of 17O can result.
The net yield of this element is positive for stars with { 18O
0:8M(cid:12) <(cid:24)Mi <(cid:24)3:5M(cid:12) thanks tothe dredge-upevents This element has the shortest nuclear lifetime against
during the TP-AGB phase, whereas it becomes nega- proton captures, so that it easily burns even at mild
tive at higher masses because of HBB. temperatures, quickly attaining the nuclear equilib-
The synthesis of fresh 16O occurs via the reaction rium with 17O. The net yield of 18O is negative for
12C((cid:11);(cid:13))16O during thermal pulses, so that the yield all masses, with a trend mirroring that of 17O. More-
of this element depends, among other factors, on its over,asinthecaseof15N,thedepletionof18Oismore
abundance in the dredged-up material. According to pronounced at higher metallicities due to the more ef-
recent TP-AGB calculations { which include deep (cid:12)cient CNO cycling.
overshooting from all convective boundaries { Herwig
et al. (1997) (cid:12)nd that the 16O abundance in the con-
vectiveintershellisroughlytentimeshigher,X(16O)(cid:24) 4.1. Secondary and primary components
0:25, than previously predicted, i.e. X(12C)(cid:24) 0:02 by
AsfarastheCNOnucleiareconcerned,wecandistinguish
Boothroyd& Sackmann1988b(standard case). Then,
for each element k the secondary, MS(k), and primary,
adopting Herwig et al. indications, oxygenproduction y
MP(k), components of the stellar yield
by low- and intermediate-mass stars may be favoured y
with respect to the standard case, but it is worth re-
calling that, in general, the (cid:12)nal yields are crucially
M (k)=MS(k)+MP(k) (7)
y y y
8 P. Marigo
calculated with (see Eq. (2)) Thesecond(2.) casecorrespondstobothprimaryand
secondary production. In stars with M > Mmin it ap-
(cid:28)(Mi) dM i HBB
MS(k)= [XS(k)(cid:0)XS;0(k)] dt (8) plies, for instance, to 13C, 17O, and 14N. In general, for
y Z dt
0 these elements a positive secondary contribution may be
and providedbythe (cid:12)rst(andpossiblysecond)dredge-upand
(cid:28)(Mi) dM HBB,the latterprocessbeingalsoresponsibleforthepri-
MP(k)= [XP(k)(cid:0)XP;0(k)] dt (9) mary synthesis of these elements (starting from primary
y Z dt
0 12C and 16O injected by the third dredge-up).
where XS(k) and XP(k) denote the secondary and pri- As far as 13C is concerned (see also Sect. 4) we notice
mary current surfaceabundances, respectively. Moreover, that a suitable interplay between the strength of HBB
we have XS;0(k) = X0(k) and XP;0(k) = 0, as follows and mass loss can occasionally result in very favourable
fromthede(cid:12)nitionsofsecondaryandprimaryabundances. conditions for the production of 13C, giving a peak of the
WenoticethatMyP(k)canbeonly(cid:21)0,whereasMyS(k) relatedyields(forinstance,at themodel 4M(cid:12) in the case
can be either (cid:21)0 or <0, in the respective cases that the Z =0:019;(cid:11)=2:0).
mass-averagedsecondaryabundanceoftheelementinthe Concerning the yields of 14N, it should be remarked
ejecta is greater, equal or smaller than its original value. that the contribution from intermediate-mass stars may
A few basic remarks should be made at this point. be relevant in view of interpreting, with the aid of chem-
Both the (cid:12)rst and second dredge-up a(cid:11)ect (by increasing ical evolutionary models of galaxies, the observed trend
ordecreasing)onlythesecondarycomponentsoftheCNO in the log(N/O) vs. log(O/H) diagram (see, for instance,
surfaceabundances.Infact,intheseepisodestheenvelope Vila-Costas& Edmunds 1993;Henryet al. 2000b),where
ispollutedbymaterialwhichhasundergoneCNO-cycling, thelargescatterofdatapointstowardslowermetallicities
with a net change in the relative abundances of the CNO wouldimplytheexistenceofasigni(cid:12)cantprimarycompo-
isotopessynthesizedfrommetalseedsoriginallypresentin nent in the measured nitrogen abundances.
thestar.Onthecontrary,thethirddredge-upenrichesthe The third (3.) possibility corresponds to a dominant
chemicalcompositionoftheenvelopewith 12Cand16Oof primary production. In stars with initial masses Mmin <(cid:24)
dred
primary origin (synthesized by (cid:11)-capture reactions). Fi- Mi <(cid:24) MHmBinB, this case applies to 12C surface abundance,
nally,HBBa(cid:11)ectstheabundancedistributionoftheCNO which is (cid:12)rst decreased by the negative secondary con-
isotopes of both secondary and primary synthesis. tribution from the (cid:12)rst and second dredge-up, and subse-
Keeping in mind these concepts, it turns out that: quentlyincreasedbythethirddredge-upinjectingprimary
nucleiintotheenvelope.Asimilarsituationoccursforthe
{ stars with initial masses M < Mmin can produce
i dred yield 16Ointhe samerangeofstellarmasses,asthee(cid:11)ect
CNO yields of secondary origin only;
of the third dredge-up prevails over that of the previous
{ ftohre sytiaerlsdswoitfh12iCnitaianldm16aOssesshoMudlmdreindin<(cid:24)cludMeia<(cid:24)prMimHmaBirnBy mixFiningaelplyi,sothdeesfo(u(cid:12)rrtsht (a4n.d)csaesceoncdor)r.espondstoadominant
secondary depletion. This refers to 15N, 18O for stars of
component, as a consequence of the third dredge-up
during the TP-AGB phase; and allmasses,andto16OforstarswithMi >(cid:24)MHmBinB ifthere-
duction of the originalabundance caused by the (cid:12)rst and
{ for stars with initial masses Mi >(cid:24) MHmBinB undergoing osexcyognedndvrieadgthe-eupthdirodmidnraetdegseo-uvper(tehveeninjpeoctsisoibnlyofpparrimtiaalrlyy
HBBduringtheTP-AGBphase,theyieldsoftheCNO
destroyed by HBB). Under these circumstances, no en-
isotopes should all display primary components, be-
cause of the injection of primary 12C and 16O nuclei richment of the interstellar medium is expected for these
elemental species.
(ateachdredge-upevent)intoregionswherethe CNO
TablesA10{A12givethenetyieldforeachelementof
cycle is operating.
the CNOgroup(Tentry),togetherwiththesecondary(S
Comparing the secondaryand primary components of entry) and primary (P entry) components, for stars with
the CNO yields four cases can be met (Tables A1 { A12; initial masses 3:5M(cid:12) (cid:20) Mi (cid:20) 5M(cid:12), for various values of
see also Marigo 1998b): the original metallicity and mixing length parameter.
1. MS 6=0 and MP =0 so that M =MS
y y y y
2. MyS >0 and MyP >0 so that My >0 5. Comparison with other calculations
3. MS <0 and MP >0 so that M >0
y y y We will compare the stellar yields presented in this work
4. MS <0 and MP >0 so that M <0
y y y (hereinafter alsoM2K) with thoseavailablein twowidely
The(cid:12)rst(1.)caseappliestolow-massstarswith M < used studies, namely the pioneer work by Renzini & Voli
i
Mmin, i.e. never experiencing the third dredge-up dur- (1981;RV81), andthe morerecentoneby vande Hoek&
dred
ing the TP-AGB phase. No primary component of stellar Groenewegen (1997;HG97). Before making a direct com-
yields is expected. parisonbetweentheyieldsofvariouselementalspecies,we
Yields from low- andintermediate-mass stars 9
Table 1.Summaryof the main prescriptions adopted inthe syntheticTP-AGB models here considered for comparison.
PROCESS/QUANTITY MODELPRESCRIPTION
RV81 HG97 M2K (this work)
Mup 8 M(cid:12) 7 M(cid:12) 5 M(cid:12)
Mc(cid:0)L relation, Mc(cid:0)Tip relation no metallicity dependence with metallicity dependence with metallicity dependence
mass loss Reimers (1975) (cid:17)=1=3(cid:0)2=3 Reimers (1975) (cid:17)=5 Vassiliadis & Wood(1993)
3 D.up:e(cid:14)ciency (cid:21) (cid:24)0:3(cid:0)0:5 0.75 0.65 for Z =0:004, anyM
function of Mc,any Z for anyZ, M 0.55 for Z =0:008, anyM
3 D.up:minimum core mass Mcmin 0.60 M(cid:12) 0.58 M(cid:12) from envelopeintegrations
for anyZ, M for any Z,M function of M andZ
HBB: overluminosity no no yes
HBB: nucleosynthesis nuclearnetwork parameterised approx. nuclearnetwork
consider it useful (cid:12)rst to recall the relevant prescriptions be included in galactic models of chemical evolution, at-
adoptedinthementionedAGBmodels,andconsequently tention should be paid to correctly match sets of yields
analyse their e(cid:11)ects by showing how the predictions of of di(cid:11)erent mass intervals (i.e. low, intermediate, high).
di(cid:11)erent models compare with basic observables. If the models do not belong to a homogeneous grid of
stellar calculations, one should at least care to combine
stellaryields of di(cid:11)erent origin (i.e. stellar code) but with
5.1. Model prescriptions
the same predicted valuefor M . Otherwise,the relative
up
Table 1 summarises the relevant assumptions adopted in weightof starsbelongingtodi(cid:11)erentclasses(i.e.with dif-
the AGB calculations, which the three di(cid:11)erent sets of ferentnucleosynthetichistories)totheintegratedchemical
stellar yields under consideration are derived from. For enrichment may be substantially mistaken (for instance,
further details the reader should refer to the original pa- by over- or under- estimating the role of supernovae).
pers and references therein.
5.1.2. Analytical relations
5.1.1. The limiting mass M
up
Fundamental relations in synthetic AGB models are the
First of all, let us consider the quantity M (see also
up coremass-luminosity(M (cid:0)L),andcoremass-interpulse
c
Sect. 2.1), that corresponds to the maximum initial mass
period(M (cid:0)T )relations.Predictionsofstellaryieldsare
c ip
of a star to develop a degenerate C-O core, hence experi-
signi(cid:12)cantly in(cid:13)uenced by these input prescriptions, i.e.
ence the AGB phase. This critical mass heavily depends
theluminositya(cid:11)ectsthemass-lossratesontheTP-AGB,
on the previous evolutionary history, mainly the exten-
andinterpulse-periodsdeterminethe temporal recurrence
sion of the convective core during the H-burning phase.
of the third dredge-up.
Evolutionary models (classical models) that adopt the
With respect to RV81 prescriptions (Iben & Truran
Schwarzschild criterion to de(cid:12)ne the convective bound-
1978(IT78),seeFig.4),M2KandHG97modelsarebased
aries (e.g. Dominguez et al. 1999) predict higher values
on more recent relations (Boothroyd & Sackmann 1988a;
for M than those models that assume some overshoot
up
Wagenhuber&Groenewegen1998)inwhichanotableim-
beyond the last formally stable layer against convection
provement is the inclusion of a composition dependence.
(e.g. Girardi et al. 2000).
For a given core mass, the quiescent luminosity / inter-
Both RV81 and HG97 yields are based on classical
pulse period of a TP-AGB star is found to increase / de-
models and have Mup (cid:24) 7(cid:0)8M(cid:12), whereas the pre-AGB
creaseatincreasingmetallicity.Accordingtoevolutionary
evolutionarymodelsusedinthiswork(M2K)adoptacon-
calculations by Boothroyd & Sackmann (1988a), for in-
vectiveovershootschemesothatMup (cid:24)5M(cid:12).Weremark
stance, the quiescent TP-AGB luminosity for Z =0:02 is
that models with masses up to M cover, by de(cid:12)nition,
up
about 20 % higher than for Z =0:001 (see Fig. 4).
the whole class of low- and intermediate-mass stars. In
other words, models with M > M (for whatever pre-
i up
dicted M ) would eventually meet the fate of supernova
up 5.1.3. Mass loss on the AGB
explosion.
Finally, a cautionary warning should be made in the The adopted prescription for mass loss on the AGB cru-
context of practical application of chemical yields. When cially in(cid:13)uences the predictions of stellar yields, as it af-
stellar yields from stars of di(cid:11)erent initial masses are to fectsthe totalnumberofthermalpulses(hencedredge-up
10 P. Marigo
Fig.4.Theoretical coremass-luminosityrelations. Thewell- Fig.5. Expected number of thermal pulses (and inter-pulse
knownIben&Truran(1988)relationisextrapolatedforsmall periods) as a function of the initial stellar mass for di(cid:11)erent
core masses and assuming a total mass of 1.5 M(cid:12). The pre- valuesof theinitial metallicity(see legendainFig. 6).Results
dicted e(cid:11)ect of the chemical composition of the envelope on ofthepresentwork(M2K)arecomparedwiththoseofRenzini
the luminosity is shown according to Boothroyd & Sackmann &Voli (1981; RV81).
(1988a).
These di(cid:14)culties have been overcome by later mass-
loss prescriptions { speci(cid:12)cally designed for AGB stars
episodes)su(cid:11)eredbyaTP-AGBstar,hencethegrowthof
(e.g.Bowen1988;Fleisheretal.1992;Vassiliadis&Wood
its core mass and AGB lifetime.
1993; Blo(cid:127)cker 1995) { which are all characterised by a
In this work we adopt the semi-empirical formalism more rapid increase of mass-loss rates during the AGB
presentedbyVassiliadis&Wood(1993)whocoupleresults evolution, then naturally leading to the development of
of pulsation theory with observations of variable AGB the superwind regime.
stars.InRV81theclassicalReimers’law(1975)isassumed The e(cid:11)ect of di(cid:11)erent laws for mass loss is signi(cid:12)cant
with the e(cid:14)ciency parameter (cid:17) set equal to 1/3 or 2/3. with respect to the expected number of thermal pulses
HG97aswellusetheReimers’law,butwith (cid:17) =5,which experienced on the TP-AGB evolution. As an example
they (cid:12)nd as the best value to ful(cid:12)l basic observational (see Fig. 5), we can notice that for a (5M(cid:12);Z = 0:02)
constraints (see Sects. 5.2.2 and 5.2.1). model our calculations yield N = 117(cid:0)153 (depending
p
To this regard the following remark should be made. on (cid:11)), whereas RV81 predict N = 8941 (1631) with the
p
As a matter of fact, the Reimers’ prescription was origi- e(cid:14)ciencyparameter(cid:17) =1=3((cid:17) =2=3).Ingeneral,itturns
nally designed to describe mass loss su(cid:11)ered by low-mass out that the largest di(cid:11)erences in the number of thermal
starsclimbing up the RGB,andit is usuallycalibratedin pulses show up for models with higher stellar masses (i.e.
viewofreproducingobservationsofstarsinthesubsequent Mi >(cid:24)2:5M(cid:12)), that are expected to experience the super-
horizontalbranchphaseof quiescentcoreHe-burning(see wind regime according to the the Vassiliadis & Wood’s
Sect. 2). prescription.
However, as already shown by RV81, the straightfor- Moreover, signi(cid:12)cantly di(cid:11)erent results are obtained
ward extension of the Reimers’ formula to the AGB evo- by RV81 and M2K as far as the TP-AGB duration is
lution does not suit important constraints. In fact, the concerned (see Fig. 6). First of all, we can notice that
Reimers’ prescription with (cid:17) <(cid:24) 1 cannot produce the our TP-AGB lifetimes present a pronounced trend with
\super-wind" mass-loss rates (M_ (cid:24) 10(cid:0)4 (cid:0) 10(cid:0)5 M(cid:12) the stellar mass, showing a maximum at around 2 { 2.5
yr(cid:0)1)measuredinstarsclosetotheAGB-tipluminosities, M(cid:12) (depending on metallicity). In particular, a drastic
and consequently it cannot account for the typical values drop of the TP-AGB duration is expected in the high-
of masses and radii of planetary nebulae at the observed est mass domain, i.e. for stars with HBB. In RV81 the
luminosities. mass-dependence is much less marked, and such a strong