We have computed the evolution of Super-AGB stars from the main sequence
and up to a few hundred thermal pulses, with special attention to the low metallicity cases
(Z = 1010; 105; 104 and 103). Our computations have been performed using time–
dependent mixing and new opacity tables that admit variations in the abundances of carbon
and oxygen. By following the evolution along the main central burning stages and the
early TP-SAGB, we resolve the upper mass limits for the formation of TP-SAGB stars and
determine the mass range at which the dredge-out phenomenon occurs. This phenomenon
involves the merger of a convective shell sustained by helium burning at the top of the
degenerate core with the hydrogen–rich convective envelope and the occurrence of a hydrogen
flash. The dredge–out allows elements synthesised through helium burning to be
transported to the stellar surfaces and therefore it can a ect the initial composition of the
TP-SAGB stars.Peer ReviewedPostprint (published version

Doherty, Carolyn L.

Gil Pons, Pilar

We have computed the evolution of Super-AGB stars from the main sequence

and up to a few hundred thermal pulses, with special attention to the low metallicity cases

(Z = 10\u10000010; 10\u1000005; 10\u1000004 and 10\u1000003). Our computations have been performed using time–

dependent mixing and new opacity tables that admit variations in the abundances of carbon

and oxygen. By following the evolution along the main central burning stages and the

early TP-SAGB, we resolve the upper mass limits for the formation of TP-SAGB stars and

determine the mass range at which the dredge-out phenomenon occurs. This phenomenon

involves the merger of a convective shell sustained by helium burning at the top of the

degenerate core with the hydrogen–rich convective envelope and the occurrence of a hydrogen

flash. The dredge–out allows elements synthesised through helium burning to be

transported to the stellar surfaces and therefore it can a ect the initial composition of the

TP-SAGB stars.Peer Reviewe

UPCommons

The upper-mass limit for the formation of super-agb stars and the dredge-out phenomenon

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Mem. S.A.It. Vol. 81, 974c© SAIt 2010 Memorie dellaThe upper mass limit for the formation ofTP{SAGB stars and the dredge{outphenomenonP. Gil–Pons1,2 and C. L. Doherty11 Universitat Politecnica de Catalunya – Department of Applied Physics, Campus BaixLlobregat, Building C3, 08860 Castellefels, Spain, e-mail: pilar@fa.upc.edu2 Centre for Stellar and Planetary Astrophysics, School of Mathematical Sciences, MonashUniversity, Victoria 3800, AustraliaAbstract. We have computed the evolution of Super-AGB stars from the main sequenceand up to a few hundred thermal pulses, with special attention to the low metallicity cases(Z = 10−10, 10−5, 10−4 and 10−3). Our computations have been performed using time–dependent mixing and new opacity tables that admit variations in the abundances of car-bon and oxygen. By following the evolution along the main central burning stages and theearly TP-SAGB, we resolve the upper mass limits for the formation of TP-SAGB stars anddetermine the mass range at which the dredge-out phenomenon occurs. This phenomenoninvolves the merger of a convective shell sustained by helium burning at the top of thedegenerate core with the hydrogen–rich convective envelope and the occurrence of a hy-drogen flash. The dredge–out allows elements synthesised through helium burning to betransported to the stellar surfaces and therefore it can affect the initial composition of theTP-SAGB stars.Key words. Stars: abundances – Stars: Population II – Stars: Population III1. IntroductionSuper-AGB stars develop central hydrogen andhelium burning and finally carbon burning ina degenerate core. They are the most mas-sive stars that evolve along the thermally puls-ing phase. As it has been shown by formerworks, Doherty et al. (2010), Siess (2007,2009), Gil–Pons et al. (2007), the mass rangefor the formation of Super-AGB stars dependson the initial metallicity and on the physics andnumerical details of the evolutionary codes, butit ranges approximately between 7 and 11 M.Send offprint requests to: P. Gil-PonsComputing the evolution of Super-AGBstars involves a considerable computational ef-fort, not only because carbon–burning in a se-ries of flashes must be followed, but also be-cause of the large number of thermal pulsesthat these stars go through –from hundredsor even thousands. They also pose an additi-nal challenge, as it is not clear that they al-ways end their lives as oxygen–neon whitedwarfs. Instead, the most massive of these ob-jects might end their lives as supernovae, andthe minimum initial mass value for Super–AGB stars to become supernovae is expectedto depend on their initial metallicity. To sum-Gil–Pons: Dredge–out 975marise, in spite of the effort that has alreadybeen made for their understanding, the con-tribution of Super–AGB stars to the chemicalevolution of the universe is still unknown.The present work considers the determina-tion of the upper mass limit for the formationof TP-SAGB stars as a function of the initialmetallicity. This involves the computation ofthe so–called dredge–out episode, in which re-gions processed by helium–burning are mixedwith the convective envelope of the stars attime scales much shorter than the turnovertimescale of the convective envelope.As we describe in the second section of thispaper our computations have been carried outusing the MONSTAR evolutionary code. In thethird section we describe the dredge-out phe-nomenon, determine its dependance on the ini-tial metallicity of the stars, and establish a re-lation between the initial mass of the stars andthe size of the degenerate cores they developafter carbon–burning. In the fourth section wedetermine the lower mass limit for the forma-tion of degenerate cores below MCh at the endof the carbon burning phase. In the fifth sectionwe compare the evolution of the surface metal-licities of Z = 10−5 stars of different masses, tosee the differences between a star that has un-dergone the dredge–out phenomenon and starsthat have undergone a standard second dredge–up. Finally in the last section we derive themain conclusions of our work.2. Brief description of the codeThe calculations presented in this work havebeen made using the MONSTAR code, thatis the Monash version of EVOLN -the MountStromlo Stellar Structure code. MONSTAR in-cludes only the isotopes that are relevant for thestructural evolution of stars, but its output canbe used to obtain the evolution of detailed nu-cleosynthesis -up to 116 isotopes from hydro-gen to iron, through the DPPNS45 code, alsodeveloped at Monash University. MONSTARhas been updated to include the new opacitytables (Rogers & Iglesias 1996) with variablecarbon and oxygen abundances, as well as themolecular opacities for the low temperaturecases (Ferguson et al. 2005). At higher densi-Fig. 1. Upper panel: Evolution of the luminosi-ties associated to hydrogen (LH), helium, (LHe)and carbon burning (LC). Lower panel: evo-lution of the convective shell and the convec-tive envelope. Both panels correspond to thelast stages of the carbon burning phase and thedredge-out process.ties and temperatures, the conductive opaci-ties used are from Potekhin (1999). Neutrinolosses are computed according to Itoh et al.(1996).Time–dependent mixing has been imple-mented in MONSTAR by Campbell (2007).The diffusion equation is solved using implicitfinite differences, as explained in Meynet et al.(2004). This treatment of mixing allows us tocompute the dredge-out because, as we will ex-plain later, this process involves evolutionarytime scales comparable to the time of the con-vective turnover for the convective envelope.3. The dredge-out as a function of theinitial metallicityThe dredge-out process was first described inthe literature by Ritossa et al. (1999). It oc-curs at the end of the carbon–burning phase ofSuper–AGB stars, and involves the advance in-wards of the hydrogen–rich convective enve-lope and the advance outwards of the convec-976 Gil–Pons: Dredge–outFig. 2. Energy generation rates due to hydro-gen burning (H , in solid lines) and heliumburning (He, in dotted lines) at the times spec-ified in Fig. 1. The shaded areas represent con-vection in a shell (CS) and in the hydrogen–rich envelope (CE).tive shell associated to helium burning. Whenthese zones merge, protons are ingested in re-gions of high density and temperature and,then, a hydrogen flash occurs. The ingestionof protons and the occurrence of the hydrogenflash take place in time scales that are of the or-der of, or shorter than, the convective turnovertimescale. Therefore, a time dependant mixingformalism is required in order to compute thisprocess.The characteristic time scales are an impor-tant difference between the dredge–out (DO)and a standard second dredge–up process(2DU), in which evolution takes place at char-acteristic timescales much longer than those ofconvective mixing and, therefore, the instantmixing approximation holds.The second important difference betweenthe 2DU and the DO is the composition of theregions that they affect. The 2DU mixes theconvective envelope with matter processed byhydrogen burning, whereas the DO is also ableto mix matter processed by helium burning.The third important difference is that, asa consequence of this mixing of protons intoFig. 3. Hydrogen (solid), helium (dotted) andcarbon abundances (dashed) at the differenttimes specified in Fig. 1. The shaded areas rep-resent convection in a shell (CS) and in thehydrogen–rich envelope (CE).very hot regions of the star, during the DOepisodes a hydrogen flash occurs, unlike thecases in which only standard 2DU processeshappen.Fig. 1 represents the evolution of luminos-ity and convection during the dredge-out phasefor our 9 M Z = 10−5 model star. The lowerpanel shows how the position of the base ofthe convective envelope (BCE) and of the innerconvective shell sustained by helium–burningin a shell (shaded regions) advance. We cansee at times a and b the coexistence of bothconvective zones. At time c the BCE advancesinwards and reaches the convective shells, en-riched in isotopes procesed by helium burning.This part of the evolution occurs in very shorttime scales –less than 1 year, and mixes pro-tons into interior regions that are at high den-sity and temperature. This causes the fast onsetof a flash in the hydrogen–burning shell –seetimes c and d.This burning shell reaches a peak luminos-ity above 106L and allows the expansion andcooling of the surrounding regions and, in par-ticular, of the helium–burning shell. Thereforehelium burning switches off, and hydrogen andGil–Pons: Dredge–out 977Fig. 4. Remnant core mass versus ZAMS massrelation for some of the computed models forthe solar metallicity cases (represented withopen squares), for the Z = 10−3 cases (solidsquares), for the Z = 10−4 cases (open trian-gles), for the Z = 10−5 cases (solid triangles)and for the Z = 10−10 cases (open circles).carbon burning remain the nuclear energy sup-pliers for the star during this phase of the evo-lution. Once the hydrogen flash is finished, hy-drogen burning still remains active and burnsin situ until the TP-SAGB phase starts.Figs. 2 and 3 represent partial mass profilesof the 9 M Z = 10−5 model star at the timeslabelled in Fig. 1. Fig. 2 shows the logarithmof the energy generation rates due to hydro-gen and helium burning. From panel a to panelc we can see that helium burning sustains theconvective shell –represented by the shaded re-gion above the mass point Mr = 1.30505M.At paneld d of Figs. 2 and 3 we can see that theBCE has advanced inwards to the helium–richregions.The ingestion of protons into high temper-ature and high density regions allows the onsetof hydrogen burning at the BCE, and the as-sociated expansion and cooling of the helium–burning shell causes a decrease in the helium–burning rates. Finally, at panel e of Figs. 2and 3 the BCE has reached the outermost partsof the carbon–oxygen shell that surrounds theoxygen–neon core.Fig. 5. Initial mass and metallicity for starsthat develop degenerate cores less massive thanMCh and undergo a standard second dredge–up episode (open squares); for stars that alsodevelop degenerate cores less massive thanMCh, but undergo a dredge–out process (blacksquares); and for stars that develop degeneratecores more massive than MCh (grey squares).4. The lower mass threshold for theformation of ONe cores below theChandrasekhar massWe have obtained the relation between the ini-tial mass of stars at different metallicities andthe masses of their remnant degenerate cores atthe end of carbon burning (Fig. 4).The solar metallicity models (opensquares) yield the lowest core masses, fol-lowed by the zero metallicity ones (opencircles). Z = 10−3 models (solid squares) yieldsomewhat more massive cores and finallyZ = 10−4 (open triangles) and Z = 10−5models (close triangles) tend to yield the mostmassive remnant cores. Anyway one can seein the figure that, for initial masses above8 M, the remnant core masses yield almostthe same values, independently of their initialmetallicity, except for the solar case.Stars that experience the dredge–out pro-cess are the most massive intermediate–massstars that can become oxygen–neon whitedwarfs, independently of their initial metallic-978 Gil–Pons: Dredge–outity (Mn−). Therefore, by computing this pro-cess, we are able to determine which stars willavoid a supernova explosion, at least before en-tering the TP-SAGB phase.As we can see in Fig. 5, solar metallic-ity stars can develop ONe cores below theChandrasekhar mass, from initial masses upto 10.7 M. Fig. 5 also shows the behaviourof Mn− with metallicity. Mn− decreases fromsolar metallicities down to Z=10−4 − 10−5values. This behaviour was also observed bySiess (2007). In our case Mn− decreasesfrom 10.7M for the solar metallicity down to9.3M for the Z = 10−4 case.5. Evolution of the surfacecomposition for the Z = 10−5 casesFig. 6 represents the time evolution of con-vection (left panels) and surface compositionsof carbon, nitrogen and oxygen (right panels)along carbon burning and the first tens of ther-mal pulses of the TP-SAGB phase for the Z =10−5 7.5, 8, 8.5 and 9 M models. On the rightpanels the carbon, nitrogen and oxygen surfaceabundances are represented with solid, dottedand dashed lines respectively.The 7.5, 8 and 8.5 M models undergoa normal second dredge–up process and the9 M model, as we have seen in Section 3of this work, undergoes a dredge–out episode.The 7.5 M model experiences a relativelymild second dredge–up and, because of the lowmetallicity, no first dredge–up at all. Thereforethe total surface metallicity remains low, of theorder of Z = 10−5, even along carbon burningand the TP-SAGB phase.The other models we have computed showan important increase in the surface metalabundance (two orders of magnitude with re-spect to the initial values) due to the seconddredge–up (or dredge–out) process. The mostmassive model, that is, the 9M case, showsa lower increase in surface metallicity, as thedredge–out process, even though it reaches re-gions of the star closer to the core, lasts a muchshorter time than a standard second dredge–up. The fact that metals in this case have tobe diluted in a larger hydrogen–rich envelopealso favours this result. We can also see, veryclearly, a decrease in carbon and oxygen and anincrease of nitrogen due to hot bottom burningalong the TP–SAGB.As a general trend, according to our com-putations, all the models up to MZAMS about8.5 M show a slow increase with mass ofthe surface abundances of C, N, O. Speciallyfor the Z = 10−4 cases, the carbon abundanceshows an increase of about 4 orders of mag-nitude with respect to the initial value and theoxygen abundance decreases significantly forinitial masses lower than about 7 M. We willthe develop this result further in a forthcomingwork (Gil–Pons & Doherty 2010, in prep.).6. ConclusionsWe have computed the evolution of the cen-tral burning stages and the first tens ofthermal pulses of the TP-(S)AGB phase ofintermediate–mass stars from 7M to 11M, ofmetallicities ranging from primordial to solarvalues. We have performed our calculations in-cluding time–dependent mixing. In particular,we have followed the dredge–out process, thatoccurs for all metallicities, in the most massivecases that develop degenerate cores below theChandrasekhar mass after carbon burning. Thedredge–out process is able to mix material pro-cessed by helium–burning with the hydrogen–rich convective envelope.We have obtained the upper initial masslimits for the formation of oxygen–neon coresbelow the Chandrasekhar mass, (Mn−), andshow its dependance on metallicity. Minimumvalues for Mn− are reached for metallicitiesabout Z = 10−5 − Z = 10−4.As pointed out by Tout & Eldridge (2004),Poelarends et al. (2006), Gil–Pons et al.(2007), or Siess (2007), the determinationof the fate of stars in the mass range wehave considered is a complex problem and,even though a star can develop a degeneratecore below the Chandrasekhar mass aftercarbon burning, depending on the core growthrates, the convection and mixing schemes andthe importance of the role of stellar windsduring the TP–ASAGB phase, such star mightbecome a supernova.Gil–Pons: Dredge–out 979Fig. 6. Evolution of convection (left panels) and surface composition (right panels) from the sec-ond dredge–up for the 7.5, 8.0 and 8.5 M models and including the dredge–out episode for the9.0 M model. On the right panels solid, dotted and discontinuous lines represent, respectively,the carbon, nitrogen and surface abundances. Carbon consistently appears to be the most abun-dant element for the 8, 8.5 and 9 M models after the second dredge–up or dredge–out process.ReferencesAngulo, C., et al. 1999, Nucl. Phys. A, 656, 3Campbell, S.W. 2007, PhD thesis, MonashUniversityCaughlan, G.R., & Fowler, W.A. 1988, At.Data Nucl. Data Tables, 40, 283Doherty, C.L., Siess, L., Lattanzio, J.C., & Gil–Pons, P. 2010, MNRAS 401, 143Ferguson, J.W., et al. 2005, ApJ 623, 585Gil–Pons, P., Gutie´rrez, J., Garcia-Berro, E.2007, A & A 464, 767Gil–Pons, P., Gutie´rrez, J., Garcia-Berro, E.2007, PoS, ”Supernovae: lights in the dark-ness” 013Gil–Pons, P., Doherty, C. L. 2010, in prep.Itoh, N., Hayashi, H., Nishikawa, A.,Kohyama, Y., 1996, ApJ 464, 943Meynet, G., Maeder, A., Mowlavi, N., 2004,A&A 416, 1023Poelarends, A. J. T., Izzard, R. G., Herwig, F.,Langer, N., Heger, A., 2006, MmSAI 77, 84Potekhin, A.Y., 1999, A&A 351, 787Rogers, F. J., Iglesias, C. A., 1996, AAS 28,915Ritossa, C., Garcia–Berro, E., & Iben, I.Jr.,(1999), Apj 515, 381Siess, L., A &A 476, 893Siess, L., A &A 497, 263Tout, C.A., & Eldridge, J.J., 2004, MmSAI 75,694

The upper-mass limit for the formation of super-agb stars and the dredge-out phenomenon

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