AGB Stars: What Should Be Done ?

Home , Hayashi limit

View metadata, citation and similar papers at core.ac.uk brought to you by CORE

provided by CERN Document Server

C. A. Frost & J. C. Lattanzio

Department of Mathematics, Monash University, Australia

and

Institute of Astronomy, Cambridge University

Abstract: We provide an overview of the current theoretical picture of AGB stars, with particular

emphasis on the nucleosynthesis o ccurring in these stars, b oth in their deep interiors, asso ciated with

thermal pulses or ashes, and also during the phase of \hot b ottom burning". These pro cesses are

illustrated with some new results from hot b ottom burning calculations. Finally,we conclude with

recommendations ab out \what should b e done".

1 Intro duction

In the last twentyyears much research has b een dedicated to the understanding of Asymptotic Giant

Branch(AGB) stars. For particularly noteworthy reviews see Ib en and Renzini (1983), Lattanzio

(1989), Sackmann and Bo othroyd (1991) and Ib en (1991). Recent evidence for extensivenucleosyn-

thesis at the b ottom of their deep convectiveenvelop es (known as \Hot Bottom Burning", HBB)

together with extensive data from isotopic analysis of grains in meteorites is leading to a revolution in

the quantitative demands b eing placed on the mo dels. Further, the discovery that the C pocket is

burned under radiative conditions rather than in the intershell convective zone (see b elow for details)

demands that we re-examine the mo dels and their nucleosynthesis.

We b egin by giving a qualitative analysis of the evolution of stars of masses ' 1M and ' 5M

in Section 2. This illustrates the cases where we do, and do not, nd the \second dredge-up", and

intro duces the basic principles of the evolution of all stars which sp end some time on the AGB. These

vary from a minimum mass (probably a little under 1M ) to a maximum mass of M , which just

avoids core carb on ignition, and is ab out 9M (dep ending on comp osition).

Section 3 will outline the basic evolution during a thermal pulse, but quite brie y b ecause this is

well understo o d (or, rather, as well understo o d as it is likely to b e for the present!). As an illustration

of the nucleosynthesis which can o ccur during this stage, we will explicitly discuss the dredge-up of

12 13

C and the formation of Carb on stars. Section 4 will discuss the s-pro cess, whywe b elieve that Cis

the neutron source, and howwe b elieve the C is pro duced. Here we will also discuss the problem of

F pro duction. In Section 5 we will explain the observational motivation for considering HBB, and

its consequences for the comp osition of the star. Particular emphasis will b e placed on Li pro duction

and how HBB can prevent the formation of Carb on stars. Section 6 will intro duce meteorite grains as

an imp ortant source of abundance information, which is driving mo dels to a higher level of precision.

Finally, in Section 7, we will discuss the immediate future: \what should b e done?".

\Stellar Evolution : What Should Be Done"; 32 Liege Int. Astroph. Coll., 1995

Wenow give a qualitativeoverview of the evolution of stars of masses 1M and 5M , with emphasis

on the mechanisms and phenomenology of the structural and evolutionary changes. In this section we

consider only the evolution up to the b eginning of thermal pulses on the AGB (the \TP-AGB").

2.1 Basic Evolution at 1M

We make the usual assumption that a star reaches the zero-age main sequence with a homogeneous

chemical comp osition (for an alternativeevolutionary scenario see Lattanzio 1984). Figure 1 shows a

schematic HR diagram for this star. Core H-burning o ccurs radiatively, and the central temp erature

and density grow in resp onse to the increasing molecular weight (p oints 1{3). At central H exhaustion

(p oint 4) the H pro le is as shown in inset (a) in Figure 1. The star now leaves the main sequence

and crosses the Hertzsprung Gap (p oints 5{7), while the central He core b ecomes electron degenerate

and the nuclear burning is established in a shell surrounding this core. Inset (b) shows the advance of

the H-shell during this evolution. Simultaneously, the star is expanding and the outer layers b ecome

convective. As the star reaches the Hayashi limit ( p oint 7), convection extends quite deeply inward

(in mass) from the surface, and the star ascends the ( rst) giant branch. The convectiveenvelop e

p enetrates into the region where partial H-burning has o ccurred earlier in the evolution, as shown in

inset (c) of Figure 1. This material is still mostly H, but with added He together with the pro ducts

14 13

of CN cycling, primarily N and C. These are now mixed to the surface (p oint 8) and this phase

is known as the \ rst dredge-up". The most imp ortant surface abundance changes are an increase

4 14

in the He mass fraction by ab out 0.03 (for masses less than ab out 4M ), while N increases at the

12 12 13

exp ense of Cby around 30%, and the numb er ratio C/ C drops from its initial value of 90 to

lie b etween 18 and 26 (Charb onnel 1994).

As the star ascends the giant branch the He-core continues to contract and heat. Neutrino energy

losses from the centre cause the temp erature maximum to move outward, as shown in inset (d) of

Figure 1. Eventually triple alpha reactions are ignited at this p oint of maximum temp erature, but with

a degenerate equation of state. The temp erature and density are decoupled: the resulting ignition is

violent, and is referred to as the \core helium ash" (p oint 9: see for example Deupree 1984). Following

this the star quickly moves to the Horizontal Branch where it burns He gently in a convective core, and

H in a shell (which provides most of the luminosity). This corresp onds to p oints 10{13 in Figure 1.

12 16 12 16

Helium burning increases the mass fraction of C and O (the latter through C( ; ) O) and

the outer regions of the convective core b ecome stable to the Schwarzschild convection criterion but

unstable to that of Ledoux: a situation referred to as \semiconvection" (space prohibits a discussion

of this phenomenon, but an excellentphysical description is contained in Castellani et al. 1971a,b).

The semiconvection causes the comp osition pro le to adjust itself to pro duce convective neutrality,

with the resulting pro les as shown in inset (e) of Figure 1.

Following He exhaustion (p oint 14) the star ascends the giant branch for the second time, and

12 16

this is known as the Asymptotic Giant Branch, or AGB, phase. The nal prop ortions of C and O

4 12 16

in the He-exhausted core dep end on the uncertain rate for the C( ; ) O reaction (see Arnould

1995). The core now b ecomes electron degenerate, and the star's energy output is provided by the

He-burning shell (which lies immediately ab ove the C-O core) and the H-burning shell. Ab ove b oth

is the deep convectiveenvelop e. This structure is shown in inset (f ) in Figure 1. We will later see that

the He-shell is thermally unstable, as witnessed by the recurring \thermal pulses". Thus the AGB is

divided into two regions: the early-AGB, prior to (and at lower luminosities than) the rst thermal

pulse, and the thermally-pulsing AGB (TP-AGB) b eyond this. We will return to this in section 3.

2.2 Basic Evolution at 5M

A more massive star, sayof 5M , b egins its life very similarly to the lower mass star discussed

ab ove. The main initial di erence is that the higher temp erature in the core causes CNO cycling to log(T) He core CO

core envelope convective envelope convective

He shell H shell inset (d) H shell Beyond point 15 is the inset (f) Thermally pulsing AGB

inset (e) First Thermal 9 = Core He Flash 10 Pulse = 15

1011 12 13 14 convection 11

Beyond point 14 the 8 12 Early AGB begins 10 11 12 13 14

Core He H abundance 13 exhaustion

H abundance = 14 He abundance log(L) 14 78 mass fraction 13 inset (c) 12 11 10 mass fraction 8 = First Dredge-Up

1 7 6 5 2

4 = core H 3 exhaustion 3 4 H abundance H abundance 2 5 4 6 7 inset (b) 1 = ZAMS inset (a) mass fraction mass fraction

log(Te )

Figure 1: Schematic of evolution at 1M .

convective core to develop. As H is burned into He the opacity (due mainly to electron scattering,

and hence prop ortional to the H content) decreases and the extent of the convective core decreases

with time. This corresp onds to p oints 1{4 in Figure 2. Following core H exhaustion there is a phase of

shell burning as the star crosses the Hertzsprung Gap (p oints 5{7 and inset (b)), and then ascends the

( rst) giant branch. Again the inward p enetration of the convectiveenvelop e (p oint 8) reaches regions

where there has b een partial H-burning earlier in the evolution, and thus these pro ducts (primarily

13 14 12

C and N, pro duced at the cost of C) are mixed to the surface in the rst dredge-up, just as seen

at lower masses, and sketched in inset (c) of Figure 2.

For these more massive stars the ignition of He o ccurs in the centre and under non-degenerate

conditions, and the star settles down to a p erio d of quiescent He-burning in a convective core,

together with H-burning in a shell (see inset (d) in Figure 2). The comp etition b etween these two

energy sources determines the o ccurrence and extent of the subsequent blueward excursion in the HR

diagram (e.g. Lauterb orn et al. 1971), when the star crosses the instability strip and is observed as a

Cepheid variable (p oints 10{14). Following core He exhaustion the structural re-adjustment to shell

He burning results in a strong expansion, and the H-shell is extinguished as the star b egins its ascent

of the AGB. With this entropy barrier removed, the inner edge of the convectiveenvelop e is free to

p enetrate the erstwhile H-shell. Thus the pro ducts of complete H-burning are mixed to the surface in

what is called the \second dredge-up" (p oint 15). This again alters the surface comp ositions of He,

12 13 14

C, C and N, and actually reduces the mass of the H-exhausted core, b ecause in the pro cess of

mixing He outward we also mix H inward (see inset (e) in Figure 2). Note that there is a critical mass

(of ab out 4M , but dep endent on comp osition) b elow which the second dredge-up do es not o ccur.

Following dredge-up the H-shell is re-ignited and the rst thermal pulse o ccurs so on after: the star has

reached the thermally-pulsing AGB, or TP-AGB. Note that at this stage the structure is qualitatively

similar for all masses.

3 Thermal Pulses on the AGB: Making Carb on Stars

This phase has b een reviewed extensively, and we present here only a very brief summary (for further

details, see Ib en and Renzini 1983, Lattanzio 1989, Sackmann and Bo othroyd 1991, and Ib en 1991).

The He-burning shell is thermally unstable (e.g. Schwarzschild and Harm 1965, Sackmann 1977,

Sugimoto and Fujimoto 1978), and exp eriences p erio dic outbursts called \shell ashes" or \thermal

pulses". The four phases of such a thermal pulse are: (a) the o phase, where the structure is

basically that of an early-AGB star. During this phase almost all of the surface luminosity is provided

4 5

by the H-shell. This phase lasts for 10 to 10 years, dep ending on the core-mass; (b) the \on"

4 8

phase, when the He-shell burns very strongly, pro ducing luminosities up to 10 L . The energy

dep osited by these He-burning reactions is to o much for radiation to carry, and a convective shell

develops, which extends from the He-shell almost to the H-shell. This convective zone is comprised

4 12

mostly of He (ab out 75%) and C (ab out 22%), and lasts for ab out 200 years; (c) the \p ower

down" phase, where the He-shell b egins to die down, and the intershell convection is shut-o . The

previously released energy drives a substantial expansion, pushing the H-shell to suchlow temp eratures

and densities that it is extinguished (or very nearly so); and (d) the \dredge-up" phase, where the

convectiveenvelop e, in resp onse to the co oling of the outer layers, extends inward and, in later

pulses, b eyond the H/He interface (whichwas previously the H-shell) and can even p enetrate the

12 4

erstwhile ash-driven convective zone. This results in the C whichwas pro duced by the He-shell,

and mixed outward by the ash-driven convection, now b eing mixed to the surface by the envelop e

convection. This is the \third dredge-up", and it qualitatively (and almost quantitatively) accounts for

the o ccurrence of Carb on stars at higher luminosities on the AGB. Figure 3 shows these four phases

during one pulse (top) and during two consecutive pulses (b ottom). From this gure we see the

de nition of the so-called \dredge-up parameter", . This is de ned as =M =M where

dr edg e H

M is the amount of mass dredged-up by the convectiveenvelop e, and M is the amount

dr edg e H

. M 5 at olution ev of hematic Sc 2: Figure

log(L)

H abundance H abundance

3 2 1 He abundance 13 12 11 10 mass fraction 4 ZAMS =1 14 mass fraction 01 213 12 11 10 10 11 inset (a) 213 12 inset (d) 2 14 14 5 3

11 H abundance He abundance 4 =CoreHexhaustion 12 unchanged 13 after 6 mass fraction log(T Core He exhaustion = before e 10 7 inset (e) ) 14 8 =FirstDredge-Up TP-AGB 9 =CoreHeignition

H abundance 15 =Second Dredge-Up inset (b) 4 mass fraction 5 6 He shell 7 H shell H abundance CO core 7 mass fraction

8 8 convective inset (f)

convection envelope inset (c)

calculations show that ' 0:3 (at least for lower masses, although we nd 0:9 for M 6M ).

Also shown in the b ottom panel is the variation of the total radiated luminosity and the twonuclear

energy sources (i.e. the luminosities from H and He burning) during a pulse cycle.

4 Interior Nucleosynthesis on the AGB

4.1 C and the s-pro cess

It is nowwell established observationally that manyAGB stars showanoverabundance of the s-

pro cess elements. This is easily understo o d within the picture given ab ove. It was initially envisaged

(e.g. Ib en 1975a) that the H-shell, which burns primarily by the CNO cycles, would leave b ehind

14 14

signi cant amounts of N. During the next ash cycle this N is mixed downward to regions where

the temp erature is higher (the exact value dep ending mainly on the star's core mass) and then the

sequence of reactions

14 18 + 18 22

N( ; ) F( ) O( ; ) Ne

22 25

o ccurs. If the core mass is greater than ab out 0:9M then this is followed by Ne( ; n) Mg which

releases neutrons that are then captured by many sp ecies, including Fe and its progeny, pro ducing a

distribution of s-pro cess elements which is close to that seen in the solar system (Ib en 1975b, Truran

and Ib en 1977).

Various observations (see Smith et al. 1987) indicate that the s-pro cess enriched stars have masses

1 3M , which means they have smaller cores and consequently co oler intershell convection zones.

Thus the Ne source would never b e activated (or, at least, not at a sucient rate to provide enough

neutrons for the observed s-pro cessing to o ccur). Hence it app ears that Ne is not the neutron

13 16

source, and we are forced to nd another. One rather obvious source is C( ; n) O, which ignites at

muchlower temp eratures. The problem here is to pro duce enough Ctoprovide sucient neutrons.

The obvious source is CN cycling in the H-shell, but this leaves b ehind only very small amounts of

13 13 2

C: X ( C) 10 X (CNO).

Sackmann (1980) and Ib en (1982) discussed the p ossibility of p ost-pulse expansion causing the

carb on rich region to b e exp osed to very low temp eratures, with a consequent increase in the opacity

due to Carb on recombination, and p ossibly leading to some mixing. Ib en and Renzini (1982a) indeed

showed that following a pulse the b ottom of the convectiveenvelop e can b ecome semiconvective. This

results in the di usion of some protons downward b eyond the formal maximum inward extent of the

convectiveenvelop e during the third dredge-up phase. This is shown schematically in Figure 4. The

protons which are dep osited by this semiconvection are in a region comprising ab out 75% He and

12 13 14

22% C, so when the H-shell is re-ignited they are burned into C (and N). In this scenario, which

13 13

we shall call the \classical C scenario", when the next thermal pulse o ccurs the C is engulfed

by the ash-driven convection, and then in this He-richenvironment neutrons are released by the

13 16 56

C( ;n) O. These neutrons are then captured by Fe and its progeny to pro duce the observed

s-pro cess elements (see Ib en and Renzini 1982b, Gallino et al. 1988).

This scenario has many attractive features, but it has always had some problems (Lattanzio 1989),

the most serious of which is that not all calculations repro duce this semiconvective mixing. Of course,

a small amountofoversho ot inwards could pro duce the same results, as could almost any form of

mixing which will distribute some H b elow the convectiveenvelop e and into the previously ash-driven

convective zone. In anyevent, to calculate the e ects of this prop osed mixing, it has b een common to

arti cially add a C pro le just b efore a pulse. This is how subsequentnucleosynthesis was calculated

in the classical scenario.

Note that it is incorrect to refer to this as \undersho ot". Oversho ot refers to the mixing beyond the formal

convective b oundary, and undersho ot would mean that the mixing ended before reaching the normal b oundary.

Thus the phenomenon of oversho oting in the inward direction is quite distinct from undersho ot. owe ``On'' Down'' ``Dredge-Up'' ``Off''

Convective Envelope mass

H shell H shell Re-ignition of H shell

Flash-driven Convective Pocket

time Figure 3 (a). One thermal pulse.

Convective Envelope

∆ M ∆ dredge MH mass

Flash-Driven Convective Pocket

Helium Luminosity Hydrogen Luminosity Surface Luminosity log(L)

time

Figure 3 (b). Two consecutive thermal pulses

Figure 3: Details of interior evolution during one thermal pulse (top) and for two consecutive pulses (b ottom). Convective Envelope Convective Envelope

protons mixed downward by semiconvection 12 13 +13 C (p, γ ) NC( β ν )

mass 13 16 C( α, n ) O

13 ingestion of C

flash driven convective pocket

time

Figure 4: Schematic of the \classical" scenario describing how C acts as a neutron source in

low mass AGB stars.

A mo di cation to this scenario app ears to have b een found by Straniero et al. (1995a,b) who

discovered that any C present will burn under radiative conditions during the interpulse phase. They

observed this to happ en in their calculation of a 3M mo del with Z =0:02. The temp erature of the

intershell region is usually lower during the interpulse phase than when this zone b ecomes convective

during the next pulse. But it do es increase during the interpulse phase, reaching values of T 90

just b efore the later pulses. With an interpulse p erio d of ab out 50,000 years there is plenty of time

for the C to b e consumed by alpha captures b etween pulses and hence under radiative conditions.

13 16 13 16

Thus all the C is burned into O b efore the next pulse, by the same C( ;n) O reaction as in

the classical scenario. But now this o ccurs at lower temp eratures, and with the release of neutrons in

7 9

situ , so that the neutron density remains very low, with n at most a few 10 , compared with 10

in the classical picture. It now app ears that an asymptotic distribution of s-elements is achieved after

fewer pulses (ab out 5, see Gallino and Arlandini 1995) than in the classical scenario. The resulting

s-element distribution lo oks similar to that in the classical scenario only for the heavier elements, with

signi cant di erences app earing for the isotop es with A<90. For further details refer to Gallino and

Arlandini (1995).

It is worth noting, nally, that the radiative burning of C has b een con rmed byMowlavi et al.

(1995) and in unpublished calculations by the authors.

4.2 The Pro duction of F

19 16 12 16

Jorissen et al. (1992) discovered that the F/ O ratio in AGB stars increases with the C/ O ratio

implicates thermal pulses in the origin of this F. Little theoretical work has b een done at this

stage. The pap er by Jorissen et al. investigated many p ossible scenarios, and this was followed by

Forestini et al. (1992) who investigated the most promising scenario in more detail. This is shown in

13 13 16

Figure 5. Here, some C pro duces neutrons via the C( ;n) O reaction discussed ab ove, and some

14 14

of these neutrons are captured by N to pro duce C and protons. These protons, plus p ossibly some

26 26 18 18 15 19

from Al(n,p) Mg, are then captured by O and the sequence O(p; ) N( ; ) F pro duces the

observed F, which is then dredged to the surface in the usual way following the pulse. For all except

19 13

those stars with the highest abundances of F it app ears that the amountof C left from the CN

cycling H-shell is sucient. This may b e imp ortant in view of the fact that Cisnow b elieved to burn 13 C pocket from previous semiconvective phase This makes neutrons...which... at last pulse... release protons via this...

mass 13 16 C ( α, n ) O 14 14 (and maybe this...) N ( n, p ) C ( 26 26 ) Al (n,p) Mg and finally 19 18 15 19 produces F O (p, α ) N (α, γ) F 13 Ingestion of C

time

Figure 5: Schematic of the F pro duction mechanism as envisaged by Jorissen et al. (1992)

and Forestini et al. (1992)

between pulses, and may indicate that small overabundances of F are easily explained without the

extra C provided by the semiconvection of Ib en and Renzini (1982a,b). Yet for those stars showing

more enhanced Fwemay need to invoke some extra-mixing (semiconvection, oversho ot, di usion,

or whatever) to distribute some H into the carb on-richintershell region.

Recent mo dels byMowlavi et al. (1995) show that the scenario describ ed ab ove can work only for

the rst few pulses (for low masses). After that the high temp erature in the intershell destroys F via

19 16 18 22

F(p; ) O. Furthermore, with the new (and much higher) rate for the O( ; ) Ne reaction, the

survival of sucient O is not assured. To complicate matters further, during these thermal pulses

the lifetime of (neutrons and) protons can actually decrease b elow the convective timescale, so that the

usual homogeneous mixing approximation breaks down and one must include some time-dep endent

mixing algorithm, such as the di usion approximation or p erhaps something else (e.g. Cannon et al.

1995). Clearly wehave not yet heard the last word ab out F and muchwork still needs to b e done

to clarify the situation.

4.3 Pro ducing heavier elements

Stellar evolutionary calculations include all nuclear reactions necessary to calculate the energy pro duc-

tion in stellar mo dels. They usually ignore the many other reactions which are energetically negligible.

However, with improved observations and the emerging science of isotopic analysis in meteorites (see

b elow), it is now necessary to include many other sp ecies if we wish to make a detailed comparison

with real AGB stars. Calculations including sp ecies b eyond the CNO group are just b ecoming avail-

able now (but have b een available for massive stars for quite some time), and although we will deal

with this in more detail b elow, the case of Al has b een considered in the literature and is worthyof

particular attention at this p oint.

The b eta decayof Al pro duces 1.8 Mev -rays (see Schonfelder and Varendor 1991). These can

b e analysed to determine the approximate amountof Al present in the galaxy, with current estimates

26 6

giving 3 5M (Clayton and Leising 1987). Since Al has a half-life of 10 years, this means

Al ejected into the Galaxy every (Prantzos 1995). Many sources have b een there is ab out 2M of

26 26

p ostulated for this Al, and the analysis by Prantzos shows that the distribution of Al follows the 74Li ( p,α) He = PPII - 3He (α,γ) 7Be (β ,ν) 7Li 8

7Be ( p,γ) BBe(β+ ν) 8(α)4He = PPIII

Figure 6: The Cameron-Fowler Beryllium Transp ort Mechanism.

spiral structure of the galaxy,thus implying that it is asso ciated with massive stars. This is consistent

with pro duction by massiveAGB stars as well as Typ e I I sup ernovae and Wolf-Rayet stars.

Restricting our attention to AGB stars, there are two proven sites of formation of Al; these are

the H-shell itself, and the b ottom of the convectiveenvelop e. The latter will b e discussed b elowin

the section on HBB, but it is imp ortant to note that the H-shell pro duces some Al via the Mg-Al

25 26

cycle by transforming any initial Mg into Al. This was investigated byForestini et al. (1991), who

found that small amounts of Al can b e made and then dredged to the surface (although they had to

force the dredge-up, which do es not o ccur in their mo dels). More recently,Guelin et al. (1995) have

observed IRC+10216 for Mg and Al isotop es. They also present mo dels of AGB stars with HBB, and

we defer a discussion of these mo dels until Section 6.2

5 Hot Bottom Burning in AGB Stars

It has b een known for some time that it was theoretically p ossible for the convectiveenvelop e of a star

to reach so close to the H burning shell that some nuclear pro cessing could o ccur at the b ottom of the

envelop e. Cameron and Fowler (1971) suggested a mechanism for the pro duction of Li which required

HBB. In this picture, the He left in the star from earlier H-burning can capture an alpha particle at

7 7

the base of the convectiveenvelop e to form Be. If this Be remains exp osed to high temp eratures then

it can capture a proton, and go on to complete the PPI I I sequence (see Figure 6). Alternatively, if the

7 7 7

Be decays into Li then the Li can capture a proton to complete the PPI I sequence. If, however, we

7 7

are to makemuch Li without completing the PP chains, then the Be must b e moved away from the

7 7

hot region so that it can decayinto Li. This Li is also very fragile, and must sp end most of its time

in co ol regions or it will b e destroyed by the PPI I chain. Clearly a convectiveenvelop e with a thin,

hot base, can ful ll these criteria, and this is exactly what was prop osed by Cameron and Fowler.

Indeed, there were some calculations carried out in the 70s by Sackmann et al. (1974) and Scalo et

al. (1975), but with no observational motivation the mo dels were not further studied until recently.

5.1 Observational Motivation

Perhaps the rst serious consideration of the p ossibility of HBB was in the pap er byWood et al.

(1983), lo oked at the very brightest AGB stars in the Magellanic Clouds and found that they were not

Carb on stars. In this picture the brightest stars would have exp erienced many thermal pulses, and

hence dredge-up episo des, as they ascended the AGB. So how could the brightest not have dredged

enough C to b ecome Carb on stars? Wood et al. suggested that HBB was resp onsible: with a

suciently hot envelop e some CN cycling could o ccur, and conceivably pro cess the added Cinto

N (predominantly).

Later, Smith and Lamb ert (1990) checked these stars for Li, an exp ected by-pro duct of HBB

via the Cameron-Fowler mechanism mentioned ab ove. They found that all of these brightAGB M-

stars showed extremely strong Li lines .At ab out the same time there app eared some calculations

The suggestion that p erhaps these are sup ergiants rather than AGB stars is easily refuted, b ecause they

show excesses of s-pro cess elements (Smith and Lamb ert 1986) whichwehave seen are also pro duced by thermal

pulses on the AGB.

Figure 7: Temp erature at the base of the convectiveenvelop e during the rst few pulses of a

6M mo del with Z =0:02.

which indicated that the correct conditions did o ccur in some stars (see, for example, Blocker and

Schonb erner 1991; Lattanzio 1992). In mo dels of relatively large masses, ab ove 5M , the convective

envelop e was seen to reachinto the top of the H-burning shell, and hence the material in the envelop e

was exp osed to very high temp eratures, reaching up toward T = 100! An example, for a 6M mo del

with Z =0:02 is shown in Figure 7. (This mo del will b e used throughout the rest of this pap er to

illustrate the various topics we discuss.) Note that the temp erature rises rapidly at rst, as the pulses

reach \full amplitude", after which the growth is slowed somewhat. However, we see that even after 18

pulses the p eak temp erature during the interpulse phase is still growing, and is already ab ove T = 80.

5.2 The Pro duction of Lithium

Although there were early calculations of HBB and p ossible Li pro duction (Sackmann et al. 1974,

and Scalo et al. 1975) the calculations of Bo othroyd and Sackmann (1992a) showed quantitatively

that such a scenario can work in the required stars. The p eak abundances of Li found by the mo dels

7 3

agreed very well with the observations, showing log ( Li ) ' 4:5 . After rapidly reaching the p eak,

however, the Li is destroyed as it is rep eatedly cycled through the hot b ottom of the convective

envelop e. Also, the initial He supply is nite, and once it is used there is no more to form the

required Be. This b ehaviour is shown in Figure 8 for the 6M mo del discussed ab ove. These two

e ects combine to limit the lifetime of the so-called \sup er-Li-rich giants", so that they only app ear

in a small range of M '6:2to6:8. This predicted range of luminosities agrees well with the

bol

observations for the Magellanic Clouds which showed Li-rich stars con ned to a range M '6to

bol

7 (Smith and Lamb ert 1989, 1990).

Akey ingredient in these calculations is the inclusion of some time-dep endent mixing algorithm.

Bo othroyd and Sackmann (and earlier authors) have used the di usion equation to calculate the

log (E) = log (n(E)=n(H) ) + 12 where n(E) is the numb er abundance of element E and n(H) is the number

abundance of hydrogen.

7 7

Figure 9: Be and Li abundances in the en-

7 3

Figure 8: Surface Li and He abundances in

velop e of the 6M mo del discussed in the

the 6M mo del discussed in the text.

text. The hatched region denotes convection.

7 7

distribution of Be and Li in the convective regions. (They also quite nicely illustrated that the

instantaneous mixing assumption is incorrect for these sp ecies, and results in a decrease of Li rather

than an increase.) In the calculations of Cannon et al. (1995) a slightly di erent algorithm was

used, which allows for di erent comp ositions in the upward and downward moving streams, and

some horizontal di usion at a given level. This reduces to the di usion approximation in the case

of in nitely quick horizontal di usion b etween the two streams, but it do es allow us to calculate the

di erent comp ositions in the upward stream, which has just b een exp osed to high temp eratures, and

the downward stream, which has b een through the entire envelop e and is now returning to the high

temp erature regions. The e ect of this can b e seen in Figure 9, where the same algorithm as Cannon

et al. is applied to the 6M mo del with Z =0:02. The dashed lines represent the upward moving

stream, whichisricher in Be (having b een pro duced at the b ottom of the envelop e) and p o orer in

Li (which has just b een destroyed at the b ottom of the envelop e by the conclusion of the PPI I chain).

7 7

The solid line shows the downward stream, whichisricher in Li and p o orer in Be (due to the decay

7 7

of the Be into Li in the outer, co oler parts of the envelop e).

5.3 Preventing Carb on Star Formation

The original motivation for HBB byWood et al. (1983) was that it may pro cess sucient C for

the formation of a Carb on star to b e avoided, despite the exp ected large amounts of C dredged to

the surface. This was quantitatively shown to o ccur by Bo othroyd, et al. (1993). They found that

HBB b egun at M ' 5M for Z =0:001. Mo dels of 4M b ecame Carb on stars quite easily, but 5M

mo dels of this comp osition just failed to b ecome Carb on stars due to the CN cycling at the b ottom

of the envelop e. This is able to destroy all the C added by each pulse. In fact, the envelop e quickly

b ottom of the envelop e suciently often during the interpulse phase that equilibrium abundances of

12 13 14

C and C result. There is also, of course, some pro cessing into N, but the key result is that HBB

prevents the formation of Carb on stars for relatively massiveAGB stars.

The comp osition dep endence of their results is very interesting. For Z =0:001 there is negligible

CN cycling by HBB at 4M , which indeed b ecomes a Carb on star. However HBB in the 5M mo del

prevents it from b ecoming a Carb on star. At6M the HBB is so ecient that from the rst pulse

the C/O ratio declines, and N/O rises dramatically,even exceeding unity. The b ehaviour at Z =0:02

is similar. There is minimal dredge-up seen at 4M , re ecting the well-known phenomenon that

dredge-up is more easily obtained at lower metallicities. And where there is dredge-up, the increase

in C/O is slower due to the higher O abundance initially present. HBB b egins at ab out 5M again,

12 13

but it mainly a ects the C/ C abundance, with a negligible change in the C/O ratio. In fact, the

12 13

C/ C do es not even reach equilibrium b efore mass-loss has removed the entire envelop e. The 5M

mo del shows very substantial HBB, as did the same mass at Z =0:001. Similar results are found

for the 6M case discussed in this pap er, and the ratios of these surface abundances are shown in

Figure 10.

Before leaving this sub ject, we mention brie y some problems asso ciated with synthetic evolu-

tionary calculations. In these, one parametrises the results of detailed evolutionary calculations (e.g.

Ib en 1981, Renzini and Voli 1981, Gro enewegen and de Jong 1993, Marigo et al. 1995a,b) and then

constructs stellar p opulations for comparison with observations. Such calculations have led some to

min 12

conclude that M , the minimum core-mass for dredge-up of C, is closer to 0:58M than the values

of 0:65M obtained in detailed evolutionary calculations. Also, they conclude that the dredge-up

parameter, =M =M (see Figure 3b), is closer to 0.6 than the value of 0.3 returned by

dr edg e H

evolutionary calculations. Wewarn here against a literal interpretation of these results: b oth and

min

M are functions of comp osition, mass, and mass-loss history (and mass-loss is not prop erly un-

dersto o d at present). However, there is another problem asso ciated with the input for these mo dels.

At presentwe do not know when HBB ceases, or when dredge-up ceases. Both of these require a

reasonably massiveenvelop e mass, but with almost any combination of core-mass and envelop e mass

p ossible, due to di ering mass loss formulae, it is almost imp ossible to determine when these e ects

cease. The predictivepower of these mo dels is weakened by their dep endence on which assumptions

are made here.

5.4 Core-Mass Luminosity Relation

Finally, another consequence of HBB is that it results in departure from the well established core-

mass|luminosity relation, whichwas discovered byPaczynski (1970a,b), and relates the maximum

pre- ash surface luminosity to the mass of the H-exhausted core. Although the original relation as

quoted byPaczynski was indep endent of comp osition, numerous authors have re ned his calculations

and now the most accurate relations include the e ects of comp osition. It is the utility of this equation

which stands at the base of all the synthetic calculations, discussed ab ove.

However, Blocker and Schonb erner (1991) showed that once HBB b egins the stars no longer ob ey

this relation. They followed a di erent relation with a gradient at least a factor of 10 steep er. This

were con rmed by Bo othroyd and Sackmann (1992) and Lattanzio (1992). Blocker and Schonb erner

found that the reason for departure from the erstwhile relation was that a very deep convective

envelop e do es not allow for a radiative zone which decouples the envelop e from the H-shell. There

are twoobvious consequences of this discovery. Firstly, new synthetic evolutionary calculations will

have to include this e ect. Although the duration may b e short-lived, it can generate very high

luminosities, and since mass-loss is tied to the luminosity, the mass loss increases also. Of course,

as the envelop e mass decreases, the HBB will eventually cease, and the mo del will then return to

We do not discuss the thorny issue of mass-loss in this pap er. For a discussion particularly relevanttoAGB

stars see Blocker (1995).

assumed maximum luminosity on the AGB will b e incorrect. It was assumed that once the core-mass

reached the Chandrasekhar limit, then the core would collapse and the star would leave the AGB as

a sup ernova. So inserting this core-mass into the core-mass|luminosity relation yields a maximum

luminosity for stars on the AGB. This is no longer correct, which means that observational surveys

mayhave missed the brightest AGB stars !

We defer the discussion of HBB and oxygen ratios to Section 6.2.

6 Constraints on Nucleosynthesis from Meteorite Grains

In recentyears wehave seen the advent of a new source of information ab out the comp osition of

stellar material. This has b een provided by measurements of isotopic and elemental abundances in in

meteorites. A signi cant advantage of these measurements is that they can provide information ab out

many elements for each grain, and since each grain has condensed in the out ow from a single star,

we obtain much comp ositional information from a single stellar source. A further advantage is that

abundances can b e found for sp ecies which are simply not visible in sp ectra. The disadvantage is that

we do not know a priori which kind of star pro duced which grain. Although a young eld (the rst

grain isolation o ccurred in 1987 ! see Lewis et al. 1987) there is far to o much literature to b e reviewed

here. We will just try to givea avour for the kinds of constraints which the measurements place

on the mo dels, and then discuss some of the recent mo dels which attempt to address the problems.

Further information is found in Anders and Zinner (1993), Ott (1993) and the many pap ers in Section

V of the 1994 Nuclei in the Cosmos I I I meeting, edited by Busso, Gallino and Raiteri.

The grains of interest to us come from carb onaceous chondrites, and are called \exotic" by me-

teoriticists, b ecause of their isotopic anomalies compared to the solar system abundance distribution.

These are the silicon carbide (SiC) grains and the oxide grains, esp ecially corundum (Al O ). The

2 3

other main category, the graphite grains, are probably formed mainly in very massive stars, as dis-

cussed byTravaglio and Gallino (1995). Hence we do not discuss them here.

6.1 SiC Grains: Carb on and Nitrogen abundances

Because the SiC grains must form in a carb on-richenvironment it is b elieved that these grains origi-

12 13

nated in the envelop es of Carb on stars. Further evidence comes from the distribution of C/ C ratios

in the grains, which is similar to that seen in Carb on stars, and the fact that SiC is observed in the

sp ectra of the dustyenvelop es of many Carb on stars.

Basically, the abundances of the carb on and nitrogen isotop es in these grains agree quite well

12 13

with predictions from stellar mo dels. Nevertheless, there are some grains showing C/ C ratios less

than the value exp ected from rst dredge-up ( 20), even going as low as 2 or 3, appropriate to CN

14 15

equilibrium. Yet these grains do not show N/ N ratios exp ected from CN burning: they show ratios

which are up to a factor of ten lower than exp ected from rst dredge-up (e.g. El Eid 1994), and if

12 13

CN cycling is to reduce the C/ C ratios to the equilibrium values, then these grains should b e even

14 12 13

richer in N. Wehave seen that HBB can pro duce C/ C ratios appropriate to equilibrium CN

14 15

cycling, but these mo dels fail to account for the low N/ N ratios (e.g. Sackmann and Bo othroyd

1992, Bo othroyd et al. 1994). Further, HBB is exp ected to prevent the formation of Carb on stars by

12 13 14

cycling the Cinto C and N, so how could SiC grains form in this environment? Is it p ossible that

12 13 28;29;30

the J-stars could b e the sources of these SiC grains with low C/ C ratios? And the Si isotop es

themselves are not seen in the ratios exp ected for neutron captures in the intershell zone of thermally

pulsing AGB stars, and seem to indicate a spread of Si abundances in the initial comp osition. Much

more quantitativework needs to b e done on stellar mo dels to explain all the data from these grains.

There is always a disadvantage:::

Figure 10: Variation of surface ratios in the

26 27

Figure 11: The increase of log ( Al/ Al)

envelop e of the 6M mo del discussed in the

during the thermally pulsing evolution of the

text. Note that the curve lab elled c12/c13 is

6M mo del discussed in the text.

12 13

actually log( C/ C).

6.2 Corundum Grains: Oxygen and Aluminium abundances

The most studied of the various oxide grain is corundum, Al O . The interest in these is due to their

2 3

oxygen and aluminium isotopic ratios, which show evidence of the three dredge-up episo des, together

with HBB.

Nittler et al. (1994, 1995) divide these grains into 4 groups, according to their oxygen isotopic

18 16 17 16

ratios. The largest is Group 1, which shows O/ O and O/ O ratios that are consistent with the

18 16

rst and second dredge-up: namely that O/ O is reduced by a mo dest amount (less than a factor

17 16

of two), while the O/ O ratio increases by a factor of up to twenty, compared to the initial values

18 16 17 16

of O/ O' 0:002 and O/ O ' 0:00038. It app ears that a satisfactory explanation of all these

grains requires us to consider stars of varying initial masses and a spread in the initial oxygen isotopic

ratios, as discussed by Bo othroyd et al. (1994).

The e ect of HBB has b een calculated by Bo othroyd et al. (1995). Initially there is a rapid

18 17

destruction of the O in the envelop e, with a slower increase in the O as the temp erature at the

base of the convectiveenvelop e increases with the subsequent pulses. This would app ear to explain

18 16

many of the Group 2 grains, whichhavemuchlower O/ O ratios, and which simply cannot result

from the rst or second dredge-up episo des. Nevertheless, there are some Group 2 grains that could

only b e explained by HBB if the lowest mass for HBB is substantially lower than is found in detailed

mo dels. For these, Bo othroyd et al. (1995) suggested that some deep mixing could b e the explanation,

a phenomenon they called \co ol b ottom burning", and which is discussed b elow. The Group 3 grains

17 16

are a separate problem, showing O/ O less than solar. No satisfactory stellar site has b een found

for these grains yet, and they are likely not from AGB stars. The newly identi ed (Nittler et al. 1995)

18 17

Group 4 grains show enhancements of b oth O and O. These could b e due to AGB stars, as early

thermal pulses can pro duce large amounts of O, and if the stellar mass is less than ab out 5M , there

is no HBB to destroy it. But the origin of these grains is still unclear at present.

ple, many of the oxide grains of Nittler et al. (1995) have b een analysed for Al-Mg and show excesses

26 25 24 26

of Mg but have normal Mg/ Mg. This indicates that live Al has decayed in situ to pro duce the

26 26 27

Mg. The inferred initial Al/ Al ratios are as large as 0.016. In Figure 11 we show the variation in

this ratio for our 6M mo del discussed earlier. The second dredge-up raises the ratio from essentially

zero to 10 , and once HBB b egins the ratio climbs steadily, with no sign of levelling o when

24 25

the calculations were terminated. It still shows normal ratios of Mg/ Mg, as required. We should

26 27

note that the largest values for Al/ Al which can b e obtained by dredging-up the pro ducts of the

Mg-Al cycle from the H-shell are 2 10 (Forestini et al. 1991). It app ears that the 6M mo del

16 18 6

presented here would give rise to extreme Group 2 grains, with the currentvalues of O/ O 10

16 17

and O/ O ' 100. Note that these values agree well with the 5M mo dels of Guelin et al. (1995),

as well as their observations of IRC+10216.

There is also a wealth of data available for other sp ecies, such as Ti, Xe, etc (see, for example,

Gallino et al. 1994) but this will not b e addressed here, except to remind us that we ignore this new

source of highly accurate and wonderful data at our p eril.

6.3 Co ol Bottom Burning

We mentioned ab ove that some of the Group 2 corundum grains seem to imply that HBB o ccurs in

masses which are to o small to b e consistent with the extant mo dels. A p ossible solution to this was

prop osed by Bo othroyd et al. (1995) and followed up byWasserburg et al. (1995). In this mo del there

is some extra mixing from the b ottom of the convectiveenvelop e down toward the H-shell. This is

18 16

called \Co ol Bottom Burning", and seems to pro duce the lowvalues of O/ O required by the grains

(and also many observations of Carb on stars, which also show similar isotopic ratios). Wasserburg et

al. (1995) showed that the isotopic ratios dep end critically on the temp erature (of course!) to which

the material is mixed, but there was very little dep endence on the rate of mixing. For b est results the

mixing reaches down to log T ' 0:17 from the base of the H-shell on the AGB.

Note that Charb onnel (1994) has suggested a similar mechanism to explain the anomalously low

12 13

C/ C ratios for low mass stars, when compared to the predictions from rst dredge-up calculations.

Wasserburg et al. (1995) found that an identical mixing on the rst giant branch, with the same

12 13

log T , pro duced C/ C ratios in the required range. Further studies are needed.

7 The Future: What Should Be Done ?

So, after that lengthyintro duction, we come to the main topic of this review! We will break this into

two subsections.

7.1 Evolution

There remain many uncertainties in mo deling of AGB stars. First and foremost is the lackofagood

theory of convection (still). For AGB stars the thing whichwe most need is an accurate way to deter-

mine the b oundaries of the various convective zones, and any asso ciated oversho ot. Note that changes

in the assumptions one uses to treat convection can make large di erences in the amount of dredge-up

obtained (Frost 1995). Various authors may use di erentways of treating a discontinuityin r =r

rad ad

at the edge of a convective zone. These may all b e physically motivated, and phenomenologically

reasonable, yet yield di erent results.

Sometimes during dredge-up we can obtain convergence problems. If one iterates on the physical

variables until converged, and then mixes in the convective zone, one has a mo del whichisinternally

inconsistent: the comp osition used for convergence is not that which resulted from the implied mixing.

Alternatively, one could alternate iterations on the physical variables with mixing over the current

convective zone. (This is what we do.) When this works, one has an internally consistent mo del.

extent, the amount of dredge-up obtained dep ends on how these problems are handled (see Frost

1995). Of course, there are various other schemes, such as mixing rst and then iterating (Sweigart

1995). In short, these di erences in treatment of details in the convection, as well as treatmentof

convective b oundaries, can explain the di erences in the size of the dredge-up parameter found by

various authors.

Probably related to this is the exp ected (but rarely seen) semiconvective mixing of H down b eyond

the formal convective b oundary during dredge-up. It is this which pro duces the (apparently) required

C pocket resp onsible for the neutrons that enable the s-pro cessing to o ccur on the AGB. We need

to knowhow this p o cket is formed, and its size. All of this seems to require a greater knowledge of

convection and mixing (again, esp ecially at b oundaries, and probably involving semiconvection) than

wehave at present.

Another convection problem is that we need to knowhow the dredge-up varies with mass, com-

p osition and mass-loss history.Yet, as outlined ab ove, we cannot even agree on how to calculate it,

let alone embark on a computing job of such magnitude (Renzini 1989).

7.2 Nucleosynthesis

With suchawealth of data nowavailable, b oth from stars and meteorite grains, it has b ecome clear

that for quantitative comparisons wemust use co des which contain many more nuclear sp ecies than

are usually included in evolutionary calculations. It is now relatively common to see calculations now

including 20 to 40 sp ecies, and our nucleosynthesis calculations rep orted in this pap er for a 6M

mo del use a network of 74 sp ecies and some 506 reactions. It seems that calculations of this size are

now the minimum we need for comparison with the avalanche of data coming our way.

Of course, all calculations of nucleosynthesis are only as accurate as the rates used. Some of the

most imp ortant rates for these calculations (e.g. the Ne-Na and Mg-Al cycles) are not very well known

yet, as reviewed by Arnould (1995). These data are required urgently.

The consequences of the radiative burning of C need to b e investigated. How do es this a ect the

s-pro cessing? How will it a ect other nucleosynthesis? Indeed, how do es the C pocket come into

existence?

It also app ears that we can no longer assume that all mixing o ccurs instantaneously.Wehave

seen that this assumption must b e removed to pro duce the Li-rich stars. A similar situation is likely

to exist for some sp ecies in the intershell convective zone. Although this time-dep endent mixing is

likely to have little e ect on the stellar structure (as most of the reactions involved are energetically

negligible), it maywell b e crucial for accurate calculations of the nucleosynthesis. In lieu of a suitable

theory of time-dep endent convective mixing, wemust use the di usion equation (e.g. Bo othroyd et

al. 1995) or some variant (Cannon et al. 1995, Wasserburg et al. 1995).

Related to this is the p ostulated \co ol b ottom burning", where material burns while moving

(slowly) through radiative zones. This should b e investigated in twoways: rstly phenomenologically,

to see if it can account for the observed abundances, and secondly from a purely physical view, so

that the mechanism which drives the mixing can b e understo o d!

8 Conclusion

We hop e wehave conveyed some of the excitement, and frustration, of AGB stellar mo deling. We

are on the verge of a new level of quantitative understanding, pro duced by accurate observations and

meteoritic measurements, whichhave spurred the theorists to include more and more sp ecies and

even try to calculate time-dep endent mixing. Almost all of the areas we listed for future research are

indeed b eing investigated byvarious workers at present, but the most serious problem remains that

of determining convective b oundaries under the complex conditions found in these stars. The extant

hydro dynamical studies of convection (e.g. Nordlund 1995, Zahn 1995) cannot cover the dynamical

context. Sadly,we see no reason for optimism in this area in the near future.

But we cannot end on a sad note. Wehave made enormous strides in the last few years, and we

nowhave a new source of information concerning abundances. The next few years should b e exciting.

Acknowledgments

This researchwas supp orted in part by the Australian Research Council. CAF wishes to acknowledge

the assistance of an Australian Post-Graduate Award, and the British Council for travel funds to visit

the Institute of Astronomy, Cambridge, where this work was initiated.

References

Anders, E., and Zinner, E.: 1993, Meteoritics , 28, 490.

Arnould, M.: 1995, this volume.

Blocker, T.: 1995, A. & A., in press.

Blocker, T., and Schonb erner, D.: 1991, A. & A., 244, L43.

Bo othroyd, A. I. and Sackmann, I.-J.: 1992, Ap. J. Lett., 393, L21.

Bo othroyd, A. I. et al.: 1993, Ap. J., 416, 762.

Bo othroyd, A. I. et al.: 1994, Ap. J. Lett., 430, L77.

Bo othroyd, A. I. et al.: 1995, Ap. J. Lett., 442, L21.

Cameron, A. G. W., and Fowler, W. A.: 1971, Ap. J., 164, 111.

Cannon, R. C., et al.: 1995, in Nuclei in the Cosmos I I I, Eds. M. Busso, R. Gallino, C .M.

Raiteri, (AIP: New York), p. 469.

Castellani, V., et al.: 1971a, Astr. Sp. Sci ., 10, 340.

Castellani, V., et al.: 1971b, Astr. Sp. Sci., 10, 355.

Charb onnel, C.: 1994, A. & A., 282, 811.

Clayton, D. D., and Leising, M.: 1987, Phys. Rep., 144,1.

Deupree, R. G.: 1984, Ap. J., 287, 268.

El Eid, M.: 1994, A. & A., 285, 915.

Forestini, M., et al.: 1991, A. & A., 252, 597.

Forestini, M., et al.: 1992, A. & A., 261, 157.

Frost, C. A.: 1995, Monash UniversityInternal Rep ort.

Gallino, R., and Arlandini, C.: 1995, this volume.

Gallino, R., et al.: 1988, Ap. J. Lett., 334, L45.

Gallino, R., et al.: 1994, Ap. J. , 430 ,858 .

Gro enewegen, M. A. T., and de Jong, T,: 1993, A. & A., 267, 410.

Guelin, M., et al.: 1995, preprint.

Ib en, I., Jr.: 1975a, Ap. J., 196, 525.

Ib en, I., Jr.: 1975b, Ap. J., 196, 549.

Ib en, I., Jr.: 1981, Ap. J., 246, 278.

Ib en, I., Jr.: 1982, Ap. J., 260, 821.

Ib en, I., Jr.: 1991, in Evolution of Stars: The Photospheric Abundance Connection, p. 257.

Ib en, I., Jr., and Renzini, A.: 1982a, Ap. J., 259, L79.

Ib en, I., Jr., and Renzini, A.: 1982b, Ap. J., 259, L79.

Ib en, I., Jr., and Renzini, A.: 1983, A. R. A. & A., 21, 271.

Jorissen, A, et al.: 1992, A. & A., 261, 164.

Lattanzio, J. C.: 1984, MNRAS , 207, 309.

Zuckerman, CUP, p. 161.

Lattanzio, J. C.: 1992, Pro c. Astron. So c. Aust., 10, No. 2., 120.

Lauterb orn, D., et al.: 1971, A.&A.,10, 97.

Lewis, R. S., et al.: 1987, Nature , 326, 160.

Marigo, P., and Chiosi, C.: 1995a, this volume.

Marigo, P., and Chiosi, C.: 1995b, A. & A. , submitted.

Mowlavi, N., et al.: 1995, this volume.

Nittler, L. R., et al.: 1994, Nature , 370, 443.

Nittler, L. R., et al.: 1995, in Nuclei in the Cosmos I I I , Eds. M. Busso, R. Gallino, C. Raiteri,

AIP, p. 585.

Nordlund, A.: 1995, this volume.

Ott, U: 1993, Nature , 364, 25.

Paczynski, B.: 1970a, Acta Astron., 20, 47.

Paczynski, B.: 1970b, Acta Astron., 20, 287.

Prantzos, N.: 1995, in Nuclei in the Cosmos I I I, Eds. M. Busso, R. Gallino, C .M. Raiteri,

(AIP: New York), p. 553.

Renzini, A.: 1989, in Evolution of Peculiar Red Giants , Eds. H. R. Johnson and B. Zuckerman,

CUP, p 413 .

Renzini, A., and Voli, M.: 1981, A. & A., 94, 175.

Sackmann, I.-J.: 1977, Ap. J., 212, 159.

Sackmann, I.-J.: 1980, Ap. J. Lett., 241, L37.

Sackmann, I.-J., and Bo othroyd, A. I.: 1991, in Evolution of Stars: The Photospheric Abun-

dance Connection, p. 275

Sackmann, I.-J., and Bo othroyd, A. I.: 1992, Ap. J. Lett.,.

Sackmann, I.-J., et al.: 1974, Ap. J., 187, 555.

Scalo, J. M., et al.: 1975,Ap. J., 196, 809.

Schoenfelder, V., and Varendor , M.: 1991, in Gamma-Ray Line Astrophysics , Eds. Ph. Durou-

choux and N. Prantzos.

Schwarzschild, M., and Harm, R.: 1965,Ap. J., 142, 855.

Smith, V. V., and Lamb ert, D. L.: 1986, Ap. J. , 311, 843.

Smith, V. V., and Lamb ert, D. L.: 1989, Ap. J., 311, 843.

Smith, V. V., and Lamb ert, D. L.: 1990, Ap. J. Lett., 361, L69.

Smith, V. V., et al.: 1987, Ap. J., 320, 862.

Straniero, et al.: 1995a, in Nuclei in the Cosmos I I I, Eds. M. Busso, R. Gallino, C .M. Raiteri,

(AIP: New York), p. 407.

Straniero, O. et al.: 1995b, Ap. J. Lett., 440, L85.

Sugimoto, A., and Fujimoto, M. Y.: 1978, Pub. Astron. So c. Japan, 30, 467.

Sweigart, A. V.: 1995, p ersonal communication.

Travaglio, C., and Gallino, R.: 1995, this volume.

Truran, J. W., and Ib en, I., Jr.: 1977, Ap. J., 216, 797.

Wasserburg, G. J., et al.: 1995, Ap. J. Lett., 447, 37L.

Wood, P. R., et al.: 1983, Ap. J., 272, 99.

Zahn, J. P.: 1995, this volume.