Molecular opacities for low-mass metal-poor AGB stars undergoing the Third Dredge Up
aa r X i v : . [ a s t r o - ph ] J un Molecular opacities for low-mass metal-poor AGB starsundergoing the Third Dredge Up
S. Cristallo and O. Straniero
INAF-Osservatorio Astronomico di Collurania, 64100 Teramo, Italy
M. T. Lederer and B. Aringer
Institut f¨ur Astronomie, T¨urkenschanzstraße 17, A-1180 Wien, Austria
ABSTRACT
The concomitant overabundances of C, N and s-process elements are com-monly ascribed to the complex interplay of nucleosynthesis, mixing and massloss taking place in Asymptotic Giant Branch stars. At low metallicity, the en-hancement of C and/or N may be up to 1000 times larger than the original ironcontent and significantly affects the stellar structure and its evolution. For thisreason, the interpretation of the already available and still growing amount ofdata concerning C-rich metal-poor stars belonging to our Galaxy as well as todwarf spheroidal galaxies would require reliable AGB stellar models for low andvery low metallicities. In this paper we address the question of calculation anduse of appropriate opacity coefficients, which take into account the C enhance-ment caused by the third dredge up. A possible N enhancement, caused by thecool bottom process or by the engulfment of protons into the convective zonegenerated by a thermal pulse and the subsequent huge third dredge up, is alsoconsidered. Basing on up-to-date stellar models, we illustrate the changes inducedby the use of these opacity on the physical and chemical properties expected forthese stars.
Subject headings: stars: AGB and post-AGB — stars: atmospheres — stars:carbon — stars: evolution
1. Introduction
The modification of the surface composition of a star may be due to several processes.If the synthesis of nuclei occurs in stellar interiors, the products of nuclear reactions onlyappear at the surface when this chemically enriched material is moved from the deepest 2 –layers to the external zone. The most common deep-mixing processes are caused by convec-tive instabilities. Less studied, but not less important, are dynamical instabilities inducedby rotation or by magnetic forces (see e.g. Maeder & Meynet 2000). Minor surface chemi-cal alterations occur on a longer timescale, as those due to microscopic diffusion, levitationpowered by radiation pressure or other thermal instabilities (Kippenhahn & Weigert 1990,see also Piersanti et al. 2007, and references therein). The first systematic modification ofthe surface composition takes place at the base of the red giant branch, when the externalconvection penetrates the zone previously exposed to the H burning. This is the so called first dredge up (FDU). Later on, during the early Asymptotic Giant Branch, intermediatemass stars (4 < M/M ⊙ <
8) eventually experience a second dredge up . The main effect on thesurface composition of these two dredge-up episodes is the increase of the He abundance. Aredistribution of the CNO isotopes also occurs, namely isotopes with a slow proton capture(e.g. N) become more abundant, whereas those whose proton capture is fast are depleted(e.g. C). In any case, after the first and the second dredge up the global number of CNOisotopes is conserved. This is not the case of the
Third Dredge Up (TDU). Actually, TDUrefers to multiple dredge up episodes occurring during the late part of the AGB. In thesestars, recursive Thermal Pulses (TPs) are powered by violent He ignitions, which take placeat the base of the thin He-rich zone located between the CO core and the H-rich enve-lope (intershell). These violent He burning episodes cause the intershell to become instableagainst convection and therefore to mix the products of the 3- α burning throughout thisregion. Shortly after each thermal pulse, the H-burning dies down (owing to the expansioninitiated to counterbalance the excess of energy released by the 3- α reactions) and the ex-ternal convection may penetrate down to the H-exhausted region. Thus, the stellar envelopeis enriched with the ashes of the He burning, mainly C. This carbon dredge up is of greatimportance for the future AGB evolution. Indeed, the efficiency of the CNO cycle and thatof the radiative energy transfer are both depending on the carbon abundance in the envelope.During the AGB, owing to the carbon enhancement, the opacity increases and, in turn, thetemperature gradient becomes larger . In practice, since as a consequence of the C dredgeup the C/O becomes rapidly greater than 1, the effective temperature decreases, the stellarradius increases and the average mass loss rate increases, thus eroding at a faster rate theenvelope mass. On the other hand, the growth in mass of the H-exhausted core, which iscontrolled by the H burning, also depends on the amount of C (and N) in the envelope. Asshown by Straniero et al. (2003), changes of the core and the envelope masses affect all thefundamental properties of AGB stars, such as the thermal pulse strength or the total amountof mass that is dredged up. In the external convective zone of an AGB stars, the radiative flux significantly contributes to the overallenergy transport. > ⊙ ), an additional phenomenon should be con-sidered. In this stars, indeed, the temperature at the base of the convective envelope maybecome large enough (T > × K) for the activation of the CN cycle. In this case, theC excess in the envelope is partially converted into N. This process is known as
Hot BottomBurning (Sugimoto 1971; Iben 1973).In principle, a stellar evolution code should account for the variations of the envelopechemical composition. In practice, only variations of the main constituents are usually con-sidered. In particular, low temperature radiative opacity tables are available only for scaledsolar composition, so that only changes of H and He can be accounted for. Although the useof these tables substantially underestimates the radiative opacity of the cool atmosphere ofan evolved AGB star eventually enriched in C and N, they are commonly adopted by stellarmodelers, who are often left without any other alternative.Marigo (2002) made a first step towards a correct description of the abundance changesin the calculation of opacity coefficients, by estimating molecular concentrations throughdissociation equilibrium calculations. Although the results of this work definitely demon-strate the importance of a correct opacity treatment, its simplified approach suffers fromsome drawbacks, in particular the limited number of molecular species included.In this paper, we make a further step ahead. By interpolating on a grid of opacitytables properly computed by increasing the abundances of C and N with respect to thescaled solar value, we calculate new models for low mass AGB stars. We start with avery metal poor composition ([Fe/H] < -2), because the effect of the TDU is stronger in thiscase. Observational constraints for these models come from the so-called CEMP (CarbonEnhanced Metal Poor) stars, for which C/Fe ratios even larger than 10 have been observed.Actually, they are not AGB stars, but unevolved dwarfs belonging to wide binary systems,which have been polluted by the wind of an AGB companion (see e.g. Lucatello et al. 2005).The majority of these CEMP stars also show huge nitrogen enhancements. A slow deepcirculation, perhaps driven by rotation-induced instabilities or by the formation of magneticpipes connecting the base of the convective envelope to the region where the CN cycle takesplace, is generally considered responsible for the partial conversion of C into N in low massAGB stars. After Wasserburg et al. (1995) this phenomenon has been called Cool BottomProcess (CBP). However, nitrogen enhancements can also be produced in very metal poorstars by a peculiar thermal pulse occurring at the beginning of the TP-AGB phase, whenthe abundances of CNO isotopes in the envelope are particularly low. As firstly proposedby Hollowell et al. (1990) (see also Iwamoto et al. 2004 and Straniero et al. 2004), in sucha case the convective zone generated by this anomalous thermal pulse may extend up tothe base of the H-rich envelope. Protons, captured by convection, are rapidly mixed within 4 –the intershell, where the high temperature and the large C abundance induce a violent H-burning flash. For a short time, up to 10 erg/sec are released by the CN cycle. Thus, inthe intershell zone, a substantial amount of N (and C) is produced. Later on, after aparticularly deep TDU, the envelope is enriched with both C and N. If C/O >
1, a large Nabundance, in addition to the C enhancement, favors the formation of CN molecules, thusinducing a further increase of the radiative opacities in the cool atmospheres of AGB stars.In Section 2 we discuss in more detail the new opacity tables. New models for low massAGB stars undergoing the TDU are presented in Section 3, while in Section 4 we comparemodels with only carbon dredge up and models where both C and N are enhanced. A finaldiscussion follows.
2. Molecular opacities
In the cool layers (i. e. temperatures lower than about 4000 K) of the convective envelopeand of the atmosphere of late-type stars, molecules become the dominant opacity source. Be-side the local thermodynamic conditions, the concentration of the various molecular speciesbasically depends on the atomic abundances. In this respect, an important quantity is thecarbon to oxygen number ratio. Among the various molecular species involving C atoms,CO have indeed the larger dissociation energy, so that for C/O < ≃
1) and subsequently into carbon-rich objects (N stars withC/O > O are mostimportant in the oxygen-rich regime, while carbon-bearing molecules (e. g. C , CN, C H and C ) dominate the opacity for C/O > as well as the Opacity Project provided web tools to calculate Rosseland mean http://opacities.osc.edu/ . ). Below 10 K, the Rosselandmean tables presented by Alexander & Ferguson (1994), which are available for scaled solarcompositions only, are widely used.In order to improve our AGB models and to evaluate the effects of the chemical modifi-cations caused by the TDU and, eventually, by the CBP, we have calculated a grid of opacitytables by means of the COMA code from Aringer (2000), based on molecular data given inTab. 1. Atomic opacities have been derived from VALD (Kupka et al. 2000). We have gen-erated a set of tables for different mass fractions of hydrogen, helium, carbon and nitrogen.The abundances of all the other elements have been scaled with respect to the correspondingsolar values, namely X ∗ = X ⊙ × Z ∗ /Z ⊙ , where Z ∗ = 1 × − and X ∗ refer to the stellarmodel composition. As reference solar composition we adopt Anders & Grevesse (1989),with some exceptions (C and N from Allende Prieto et al. 2002, while O, Ne and Ar fromAsplund et al. 2004). In order to cover the large overabundances observed in CEMP stars,we calculate tables where C and N have been independently multiplied up to a factor of2000 (with intermediate enhancements of 10, 100 and 500), taking into account all the pos-sible combinations. Temperatures has been varied to cover the parameter space of the coolexternal layers of an AGB star (3 . < log T < . T = 4 .
05. Cubic interpolationsin log T and log R and linear interpolations in the mass fractions of H, C and N ensure asufficient accuracy in the evaluation of the opacity coefficients. We decide to first computeC- and N-enhanced opacity tables at Z = 1 × − because the effects induced by the carbondredged up in the envelope is maximized at low metallicity. However, we plan to prepare C-and N-enhanced tables covering a larger metallicity range and to collect them in a database.The differences between opacities calculated for scaled solar composition and opacitiescalculated by enhancing C and N are illustrated in Figs. 1 and 2. As shown in Fig. 1, anenhancement of carbon and nitrogen due to the third dredge up leads to a C- (and N-)rich mixture whose opacities are more than two orders of magnitude larger than the initialones over a wide range of temperature and density. In this Figure, we also compare ourinitial scaled solar opacity to the corresponding values from Alexander & Ferguson (1994).The overall agreement is quite good. The significant discrepancy at low temperature/highdensity is due to the inclusion of dust absorption in Alexander & Ferguson (1994). Eventhough the stellar models here considered never attain the physical conditions for dust grainformation in their atmospheres, we want to point out that, for the astrophysical scenario R = ρ × /T . − and then we enhance the mass fraction of C by afactor of 500 and the mass fraction of N by a factor of 10, thus attaining a total metallicityZ=8.5 × − (the same as in case A). In the oxygen-rich case A, H O and TiO dominatethe opacity at low temperatures. For high densities, the Rosseland mean is higher thanin the carbon-rich case B, whereas the opposite is true for lower densities. In this regioncarbon-bearing molecules are the dominant opacity source (see below and cf. Fig. 3). In theregion from log T ≃ T ≃ R ), atomic opacities significantlycontribute to the Rosseland mean. Consequently, case A comprises higher opacities in thisregion as more metals (apart from C and N) are present than in case B.The most important contributions in the Rosseland mean opacities of a C-rich mixtureare due to CN, C , C H , and C . These molecules contribute to the mean opacity indifferent regions of the parameter space (log T, log R ) (see Fig. 3). In particular, C H dominates the low temperature high density region, while C provides the main photonabsorbtion at low T and low R, but only for extreme C-rich mixture. At higher temperatures(3000 < T < , and the relativecontribution between these two molecules also depends on the amount of nitrogen. Notethat, at variance with solar metallicity, in metal poor stars, even considering the nitrogenenhancement resulting after the first dredge up, the CN molecules may contribute to theopacity only if primary nitrogen is added, as in the case of many CEMP stars.Finally, we have also investigated the influence of a moderate increase of the oxygenmass fraction. Compared to the effects of the carbon enhancement, this contribution wasfound to be negligible. For this reason, variations of the O abundance were not included intoour set of tables.
3. C-enhanced models
As outlined in the previous section, molecules are the dominant opacity source in therange 3.3 < logT < ≥
6. In that case, we didn’tallow for possible relative variations among these elements. Actually, the material that isdredged up by convection is mainly composed by freshly synthesized C, while other heavyelements, as iron, remain practically unchanged. Thus, such a global metallicity interpolationoverestimates the atomic iron contribution to the opacity, whereas underestimates the carbon(atomic and molecular) contribution. Since these different atomic and molecular opacitysources operates in distinct stellar layers, it is rather difficult to evaluate, a priori, how muchthe contributions from these two different sources of opacity may compensate each other.In this Section we compare stellar models with initial mass M =2 M ⊙ , initial heliumY=0.245 and initial metallicity Z =1 × − (or [Fe/H]=-2.17), as obtained under differentassumptions about opacity. To calculate the corresponding evolutionary sequences, we haveused the FRANEC stellar evolution code (the release described in Chieffi et al. 1998). Mix-ing and mass loss algorithms for the AGB phase are those described in Straniero et al. (2006).In particular, we derive the mass loss rate for AGB models basing on the observed corre-lation with the pulsational period (Sch¨oier & Olofsson 2001,Whitelock et al. 2003). Periodsare estimated from the P-M K relation proposed by Feast et al. (1989) .We discuss, in particular, three different models, namely:1. the Z-fixed model, where only variations of He/H are considered (the metallicity isalways maintained equal to the initial value);2. the
Z-int model, where variations of He/H and Z are considered, but the elementaldistribution of heavy elements is always maintained scaled solar; Bolometric corrections from Fluks et al. (1994) have been used.
CN-int model, which properly takes into account variations of He/H, C and, even-tually, N caused by the TDU. All the other elements are maintained to their initial(scaled solar) values.Let us remark that the three models have been computed with identical input physics,except the opacity coefficients, and that the three evolutionary sequences have been followedup to the last TDU episode.Fig. 4 clearly shows the huge difference in AGB evolution resulting from different opacitycalculations. The first direct consequence of the introduction of a growing envelope opac-ity in the
Z-int and
CN-int models is the evident drop of the effective temperature. Thetemperature gradient is indeed linearly dependent on the opacity coefficient. For a givenluminosity, this occurrence implies a larger radius as well as a larger mass loss rate. As aresult, the duration of the TP-AGB phase is significantly shortened. This effect is howeveroverestimated in the
Z-int model with respect to the more appropriate
CN-int model.A second important consequence of the different treatment of the low temperatureopacity concerns the chemical yields. The amount of mass that is dredged up after a thermalpulse ( δM T DU ) basically depends on the core mass and on the envelope mass and both ofthem are affected by a variation of the envelope opacity. The evolution of the three calculated δM T DU are illustrated in Fig. 5. They initially increase, because the core mass increases,reach a maximum and, then, decrease, because the mass loss erodes the envelope mass.However, since the growth of the mass loss is steeper in the
Z-int and
CN-int models, thetotal mass that is dredged up is lower than that found in the case of the
Z-fixed model. Asa result, models computed with larger opacity predict a smaller contribution to the galacticchemical evolution.Cristallo (2006) already noted that the overabundances of the heavy elements synthe-sized by the s process in the
Z-int model are generally too small compared to the availablespectroscopic determination for C- and s-rich metal poor stars belonging to the galactic halo.Such a discrepancy appears more severe, considered that these halo stars are not AGB starsundergoing the TDU, but less evolved objects, dwarfs or red giants, whose envelopes havebeen polluted by the wind of already evolved AGB companions. After the rapid accretionprocess, the C- and s- enriched material has been diluted by convection, in case of giantstars, or by secular processes, as microscopic diffusion or thermohaline mixing, in case ofdwarf stars (see e.g. Stancliffe et al. 2007). We concluded that the opacity is overestimatedin these models, causing a too large mass loss and a too short TP-AGB phase.A longer TP-AGB phase, with more dredge up episodes and, in turn, with larger finaloverabundances of the s-elements, are obtained in the case of the
Z-fixed model, but in 9 –this case the effective temperature, always greater than 4200 K (see the upper curve inFig. 4), would not match the observed temperatures of metal poor C(N) stars found in dwarfsspheroidal galaxies, typically ranging between 3500 and 4000 K (Dom´ınguez et al. 2004).An inspection of Fig. 5 shows that the
CN-int model, which undergoes 15 TDU episodes,represents an intermediate case between the
Z-int model (9 TDU) and the
Z-fixed model (48TDU). The total amount of mass that is dredged up is 3.8 × − M ⊙ , 9.7 × − M ⊙ and1.9 × − M ⊙ in the Z-int , CN-int and
Z-fixed model, respectively. Even if the
CN-int modelshows lower overabundances with respect the
Z-fixed model, the drop of its effective temper-ature caused by the C dredge up matches the low values found for metal poor C(N) starsin dwarf spheroidal galaxies. It appears, therefore, that the inconsistency between surfacetemperatures and s-process enhancement could be solved by using appropriate opacity coef-ficients. A detailed comparison between the prediction of our AGB models and the observedelemental overabundances in CEMP stars will be presented in a forthcoming paper.
4. C- and N-enhanced models
In massive AGB (M > ⊙ ) the temperature at the base of the convective envelope islarge enough to convert part of the C dredged up into N (the so called Hot Bottom Burning).This is not the case of low mass AGB, although some authors postulated the existence of aslow circulation, named Cool Bottom Process (CBP), capable to mix the material within thethin layer located between the H-burning shell and the cool base of the convective envelope(see Nollett et al. 2003, and references therein). While it is widely accepted that the CBPoperates during the RGB, mainly because low mass red giant stars show low values of the C/ C ratio (Gratton et al. 2000), its activation during the AGB still remains a matter ofdebate. Up to date, the origin of CBP has not been clearly identified, but the magnetic fieldcould play a relevant role for the activation of this process (Busso et al. 2006). If the CBPwould be at work in low mass AGB, it might be responsible for the conversion of C into N.Actually, many CEMP stars show large N enhancements. However, as already recalled, ahuge N enhancement might be also produced if the convective zone generated by a thermalpulse ingests protons from the top, a possibility early recognized by Hollowell et al. (1990),who claimed that this process should be rather common in very metal poor stars. We arepreparing a paper where we describe the evolution and the nucleosynthesis of these models.Preliminary results indicate that it exists a maximum mass for which such a peculiar thermalpulse takes place and that this limit increases as the metallicity decreases. In Fig. 6, theasterisk represents the initial input parameters of the models presented here.Our interest, in the context of this paper, is related to the possible consequences induced 10 –by the N enhancement on the properties of low-mass low-metallicity AGB stars. A firstindication about the difference between a C-rich and a CN-rich envelope can be deducedfrom Fig. 7. Here, starting from the physical structure of the
CN-int model after the 4 th and the 14 th pulse with TDU, we calculate, without a re-adjustment of the stellar structure,the opacity coefficients assuming that one half of the C has been converted into N. Theresulting percentage differences with respect to the original opacity of the
CN-int model(those calculated taking into account the C dredge up only) have been reported.The important differences found at low temperature are due to the absorbtion of the CNmolecules, whose contribution to the opacity is marginal in the
CN-int model. This effectis larger toward the end of the AGB phase, because the surface temperature drops down to3500 K (logT=3.55), where the CN contribution is maximum (see Fig. 3).In order to better characterize the influence of the N enhancement, four additionalAGB models have been computed, by introducing an extra-circulation below the base of theconvective envelope. As shown by Dom´ınguez et al. (2004), the most important parameterof the CBP is the maximum temperature at which the circulated material is exposed (T max ),while the actual rate of circulation is significantly less important. Then, in the four modelshere presented, the circulation rate is taken constant and fixed to 1/1000 of the averageturbulent velocity of the most internal layers within the convective envelope ( correspondingto v conv ∼ (20 ÷ · s − ), while the mass extension of the extra-circulation is varied sothat T max =30, 40, 50 and 60 × K in model
CN-int-30 , CN-int-40 , CN-int-50 and
CN-int-60 , respectively. The extra-circulation has been switched on at the beginning of the TP-AGBphase and it remains active only if the energy flux released by the H-burning is larger thanthat of the He-burning( i.e. during the interpulse phase).When T max ≥ × K, the larger opacity caused by the N production from CBPmakes the surface temperature lower with respect to the standard (i.e.
CN-int ) model (forT max = 30 × K no appreciable differences have been found). This implies a more efficientmass loss and a shorter TP-AGB phase. The
CN-int-40 model experience 12 TDU episodes,11 the
CN-int-50 model and 9 the
CN-int-60 model. The total masses that are dredged upare 7.6 × − M ⊙ , 6.6 × − M ⊙ and 6.3 × − M ⊙ , respectively.The envelope chemical composition is significantly affected by the introduction of theCBP, the surface nitrogen abundance being greatly enhanced with respect to the standardcase. In Fig. 8, we report the evolution of the [C/N] ratio versus the [C/Fe] ratio, in theusual spectroscopic notation, for the four models with CBP and the one without CBP.All these models start the pre-main sequence with scaled solar abundance ratios, namely[C/Fe]=0 and [C/N]=0, whose values drop down to -0.31 and -0.74, respectively, after the 11 –first dredge up. Then, the resulting saw-blade pattern of the various curves is due to thealternate action of the TDU and the CBP during the AGB phase. Indeed, [C/Fe] and [C/N]both increase after a TDU episode, whereas they decrease during interpulse periods, as aconsequence of the CBP. The deeper the CBP is, the lower the final [C/N] ratio is, spanninga range of about two order of magnitude (from [C/N] ∼ ∼ -0.5). Note thatthe [C/N] of the CEMP stars, for which this ratio has been derived, typically ranges between0 and 1 (Johnson et al. 2007).
5. Conclusions
In this paper we have discussed the use of appropriate opacity to describe the effects ofthe C enhancement caused by the third dredge up in low-mass-low-metallicity AGB stars.New opacity tables for chemical mixtures with different overabundances of C and N havebeen obtained by means of the COMA code (Aringer 2000). Then, stellar models with M =2 M ⊙ , Y=0.245 and Z =1 × − have been computed, varying the interpolation schemeon these tables. We have also discussed the consequence of the conversion of C into N, aseventually caused by the Cool Bottom Process operating in low mass AGB stars or by protoningestion in the first Thermal Pulse of very low metallicity AGB stars.Both the C dredge up and the conversion of C into N induce substantially affect themolecular contribution to the opacity for temperature lower than 4000 K. Larger opacitycoefficients imply cooler envelopes, larger mass loss rate and, in turn, shorter AGB lifetime.It also affects the variation of the surface composition and the global yields produced bylow mass AGB stars. The amount of mass that is dredged up is, indeed, influenced by thedifferent temporal variation of the envelope mass.We show that only models computed by adopting opacity that properly include theenhancements of C and, eventually, N can reproduce the photometric and spectroscopicproperties of their observational counterparts. In particular, the low effective temperature(3500 ∼ REFERENCES
Aaronson, M., & Mould, J.: 1985, ApJ, 290, 191.Alexander, D.R., & Ferguson, J.W.: 1994, ApJ, 437, 879.Allende Prieto, C., Lambert, D.L., Asplund, M.: 2002, ApJ, 573, 137.Alvarez, R., & Plez, B.: 1998, A&A, 330, 1109.Anders, E., & Grevesse, N.: 1989, Geochim. Cosmochim. Acta, 53, 197.Aringer, B.: 2000,
Ph.D. thesis , University of Vienna.Asplund, M., Grevesse, N., Sauval, A.J., Allende Prieto, C., Kiselman, D.: 2004, A&A, 417,751.Barber, R.J., Harris, G.J., Tennyson, J.: 2002, J. Chem. Phys., 117, 11239.Barber, R.J., Tennyson, J., Harris, G.J., and Tolchenov, R.N.: 2006, MNRAS, 368, 1087.Busso, M., Calandra, A., Nucci, M.C.: 2006, Mem. Soc. Astron. Italiana, 77, 798.Chieffi, A., Limongi, M., Straniero, O.: 1998, ApJ, 502, 737.Cristallo, S.: 2006, PASP, 118, 1360.Dom´ınguez, I., Abia, C., Straniero, O., Cristallo, S., Pavlenko, Ya.V.: 2004, A&A, 422, 1045.Feast, M.W., Glass, I.S., Whitelock, P.A., Catchpole, R.M.: 1989, MNRAS, 241, 375.Fluks, M.A., Plez, B., The, P.S., de Winter, D., Westerlund, B.E.,Gail, H.-P., & Sedlmayr, E.: 1988, A&A, 206, 153.Goorvitch, D., & Chackerian, Jr.C.: 1994, ApJS, 91, 483.Gratton, R., Sneden, C., Carretta, E., Bragaglia, A.: 2000, A&A, 354, 169.Gustafsson, B., Bell, R.A., Eriksson, K., Nordlund, A.: 1975, A&A, 42, 407.Harris, G.J., Tennyson, J., Kaminsky, B.M., Pavlenko, Y.V., Jones, H.R.A.: 2006, MNRAS,367, 400.H¨ofner, S., Gautschy-Loidl, R., Aringer, B., Jørgensen, U.G.: 2003, A&A, 399, 589.Hollowell, D., Iben, I.Jr., Fujimoto, M.Y.: 1990, AJ, 351, 245. 13 –Iben, I.: 1973, ApJ, 185, 209.Irwin, A.W.: 1988, A&AS, 74, 145.Iwamoto, N., Kajino, T., Mathews, G.J., Fujimoto, M.Y., Aoki, W.: 2004, ApJ, 602, 377.Johnson, J.A., Herwig, F., Beers, T.C., Christlieb, N.: astro-ph/0608666Jørgensen, U.G., Almlof, J., Siegbahn, P.E.M.: 1989, ApJ, 343, 554.Jørgensen, U.G.: 1997,
Molecules in Astrophysics: Probes and Processes
IAU Symp. 178,Ed. van Dishoeck, E.F., p. 441.Kippenhahn, R. & Weigert, A.: 1990,
Stellar Structure and evolution , Springer-Verlag, BerlinHeidelberg.Kupka, F.G., Ryabchikova, T.A., Piskunov, N.E., Stempels, H.C., Weiss, W.W.: 2000,BaltA, 9, 590.Langhoff, S.R., & Bauschlicher, C.W.: 1993, Chem. Phys. Lett., 211, 305.Lucatello, S., Tsangarides, S., Beers, T.C., Carretta, E., Gratton, R.G., Ryan, S.G.: 2005,ApJ, 625, 825.Maeder, A., & Meynet, G.: 2000, ARA&A, 38, 143.Marigo, P.: 2002, A&A, 387, 507.Nollett, K.M., Busso, M., Wasserburg, G.J.: 2003, ApJ, 582, 1036.Piersanti, L., Straniero, O., Cristallo, S.: 2007, A&A, 462, 1051.Querci, F., Querci, M., Tsuji, T.: 1974, A&A, 31, 265.Rossi, S.C.F., Maciel, W.J., Benevides-Soares, P.: 1985, A&A, 148, 93.Rothman, L.S. and 19 coauthors: 1998,
Journal of Quantitative Spectroscopy and RadiativeTransfer , 60, 665.Sauval, A.J., & Tatum, J.B.: 1984, ApJS, 56, 193.Sch¨oier, F.L., & Olofsson, H.: 2001, A&AS, 368, 969.Schwenke, D.W.: 1997, private communication. 14 –Schwenke, D.W.: 1998, in
Chemistry and Physics of Molecules and Grains in Space. FaradayDiscussions No. 109 , pp 321.Stancliffe, R.J., Glebbeek, E., Izzard, R.G., Pols, O.R.: 2007, A&A, 464, 57.Straniero, O., Dom´ınguez, I., Cristallo, S., Gallino, R.: 2003, PASA, 20, 389.Straniero, O., Cristallo, S., Gallino, R., Dom´ınguez, I.: 2004, Mem. Soc. Astron. Italiana,75, 665.Straniero, O., Gallino, R., Cristallo, S.: 2006, Nucl. Phys. A, 777, 311.Suda, T., Aikawa, M., Machida, M.N., Fujimoto, M.Y., Iben, I.Jr.: 2004, ApJ, 611, 476.Sugimoto, D.: 1971,
Prog. Theor. Phys. , 45, 761.Vidler, M., & Tennyson, J.: 2000, J. Chem. Phys., 113, 9766.Wasserburg, G.J., Boothroyd, A.I., Sackmann, I.-J.: 1995, ApJ, 447, 37.Whitelock, P.A., Feast, M.W., van Loon, J.Th., Zijlstra, A.A.: 2003, MNRAS, 342, 86.
This preprint was prepared with the AAS L A TEX macros v5.2.
15 –Table 1. Molecular Line DataMolecule Source of Thermodynamic Data Number of Lines Source of Line DataCO 1 131,859 6CH 2 229,134 7C O 3 27,988,952 11HCN/HNC 4 34,433,190 12OH 1 38,068 13VO 1 3,171,552 14CO H - opacity sampling 16C - opacity sampling 16Note. — Molecules entering the calculation of the Rosseland mean opacity. References forthermodynamic and line data as indexed in columns two and four are given below. Atomicline data are taken from VALD (Kupka et al. 2000).References. — (1) (Sauval & Tatum 1984); (2) (Rossi et al. 1985); (3)(Vidler & Tennyson 2000); (4) (Barber et al. 2002); (5) (Irwin 1988); (6)(Goorvitch & Chackerian 1994); (7) (Jørgensen 1997); (8) (Querci et al. 1974); (9)(Langhoff & Bauschlicher 1993); (10) (Schwenke 1998); (11) (Barber et al. 2006);(12) (Harris et al. 2006); (13) (Schwenke 1997); (14) (Alvarez & Plez 1998); (15)(Rothman et al. 1998); (16) (Jørgensen et al. 1989). 16 – κ Ross [cm /g] AF94: X=0.8, Y=0.1999, Z=0.0001COMA: X=0.8, Y=0.1999, Z=0.0001COMA: X( C) * 500, X( N) * 10, X=0.8, Y=0.1915, Z=0.0085log T [K]log R [g cm -3 (K/10 ) -3 ]log κ Ross [cm /g] Fig. 1.— Rosseland mean opacity as a function of log T and log R in a range representative forthe envelopes of AGB stars: dashed lines represent values for a chemical composition X=0.8,Y=0.1999, and Z=0.0001. As a comparison, the results of Alexander & Ferguson (1994),which are based on a different line data set, are shown (dotted lines); the strong discrepancyat low log T and high log R is due to grain opacity which is not included in our calculations.Enhancing the C (and N) mass fraction results in a significant increase of opacity (solidlines) in the cooler layers due to the favored formation of carbon-bearing molecules, especiallyCN and C H . 17 – κ Ross [cm /g] - - ++ AF94: solar metal composition, X=0.8, Y=0.1915, Z=0.0085 (case A)COMA: X( C) * 500, X( N) * 10, X=0.8, Y=0.1915, Z=0.0085 (case B)log T [K]log R [g cm -3 (K/10 ) -3 ]log κ Ross [cm /g] Fig. 2.— Comparison of the Rosseland mean opacity for two chemical mixtures with thesame overall metallicity Z=0.0085. Case A is a mixture with solar scaled metal abundances(dashed lines). For case B only the mass fractions of C and N have been enhancedstarting from a solar scaled mixture with Z=0.0001 (solid lines). The differences betweenthe two tables are indicated by contour lines at the base of the plot. The thick line, at whichin terms of opacity B = A, separates regions where B > A and B < A, marked with + and − signs, respectively (dotted lines are separated from each other by steps of 0.5 dex). Forcase A, H O and TiO dominate κ Ross at lower temperatures. At high densities, this leads toa higher mean opacity than in case B, whereas at low densities carbon-bearing molecules (cf.Fig. 3) cause an increase of the mean opacity of up to 2.5 dex compared to case A. Atomicopacities, relevant from log T ≃ T ≃ R ), are higher in caseA. 18 –Fig. 3.— Contribution of molecular species to the Rosseland mean opacity: the plots showdifferences (in orders of magnitudes) between the total opacity and calculations where par-ticular molecules (indicated in each panel) have been omitted. The extreme case of our grid(i. e. mass fraction of C and N enhanced by a factor of 2000) has been chosen as thebasis for these figures, as in this way the regions where certain molecules contribute can beindentified most clearly. 19 –Fig. 4.— We report, for the three models discussed in the text, the surface temperature vs.age. 20 –Fig. 5.— We report, for the three models discussed in the text, the dredged up material vs.core mass. 21 –Fig. 6.— In a metallicity-mass diagram, we report the line that separates models following astandard AGB evolution (upper region) from that ones suffering a proton ingestion episodeat the beginning of their AGB phase (lower region). The asterisk corresponds to the initialinput parameters of the models presented in this paper. 22 –Fig. 7.— Percentage differences of the opacity coefficients calculated in the physical structureof the
CN-int model after the 4 th TP with TDU (dashed line) and after the 14 thth