Quo vadis Themes for this talk stellar 1.Stellar evolution: present state 2.The multi-dimensional star evolution 3.Application of stellar evolution

Falk Herwig University of Victoria

Beautiful British Coloumbia 1

Wednesday, March 31, 2010 Extra-mixing aka “cool-bottom processing”

Several observations on the AGB Proposed scenarios include as well as on the RGB indicate “Enhanced Extra Mixing in Low-Mass Red that a certain amount of mixing • Giants: Lithium Production and Thermal between the bottom of the giant Stability” Denissenkov & Herwig (2004) convection envelope and the H- magnetic fields: “Can Extra Mixing in RGB and burning shell is needed, e.g. • AGB Stars Be Attributed to Magnetic Mechanisms?” Busso etal (2007) large [N/Fe] in C-rich extremely • “Magneto-Thermohaline Mixing in Red metal poor stars • Giants” Denissenkov etal (2009) lower 12C/13C on the AGB then • followed finally by “Is Extra Mixing Really expected from standard models • Needed in Asymptotic Giant Branch Stars?” abundance correlations with L in • Karakas etal (2010) [best reproduction of RGB GC stars, e.g. C/N observations with enhanced 16O intershell Li enhancements in RGB GC • abundance] stars

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Wednesday, March 31, 2010 REPORTS all of these ideas are sufficient to explain the 13. S. P. Littlefair, V. S. Dhillon, S. B. Howell, D. R. Ciardi, 30. M. Politano, Astrophys. J. 604, 817 (2004). discrepancy between the observed and predicted Mon. Not. R. Astron. Soc. 313, 117 (2000). 31. D. Grether, C. H. Lineweaver, Astrophys. J. 640, 1051 14. R. E. Mennickent, M. P. Diaz, Mon. Not. R. Astron. Soc. (2006). mass and radius presented here. 336, 767 (2002). 32. D. M. Townsley, L. Bildsten, Astrophys. J. 596, L227 (2003). 15. S. Araujo-Betancor et al., Astron. Astrophys. 430, 629 33. V. Renvoizé, I. Baraffe, U. Kolb, H. Ritter, Astron. Astrophys. References and Notes (2005). 389, 485 (2002). 1. A. Duquennoy, M. Mayor, Astron. Astrophys. 248, 485 16. A. R. King, K. Schenker, Astron. Soc. Pac. Conf. Proc. 261, 34. I. Baraffe, U. Kolb, Mon. Not. R. Astron. Soc. 318, 354 (1991). 233 (2002). (2000). 2. S. D. Barthelmy et al., Nature 438, 994 (2005). 17. R. E. Taam, H. C. Spruit, Astrophys. J. 561, 329 (2001). 35. D. Saumon, G. Chabrier, H. M. van Horn, Astrophys. J. 3. L. Yungelson, M. Livio, Astrophys. J. 497, 168 (1998). 18. U. Kolb, I. Baraffe, Mon. Not. R. Astron. Soc. 309, 1034 Suppl. Ser. 99, 713 (1995). 4. B. Willems, U. Kolb, E. L. Sandquist, R. E. Taam, (1999). 36. We thank U. Kolb and I. Baraffe for productive G. Dubus, Astrophys. J. 635, 1263 (2005). 19. P. Szkody et al., Astron. J. 123, 430 (2002). discussions. S.P.L., C.A.W., and J.S. are supported by 5. B. Paczynski, R. Sienkiewicz, Astrophys. J. 248, L27 20. P. Szkody et al., Astron. J. 126, 1499 (2003). the Particle Physics and Astronomy Research Council (1981). 21.REPORTS P. Szkody et al., Astron. J. 128, 1882 (2004). (PPARC). T.R.M. acknowledges the support of a PPARC 6. S. B. Howell, S. Rappaport, M. Politano, Mon. Not. R. 22. P. Szkody et al., Astron. J. 129, 2386 (2005). Senior Research Fellowship. B.T.G. acknowledges the Astron. Soc. 287, 929 (1997). 23. P.all Szkody of theseet al. ideas, Astron. are sufficient J. 131, 973 to (2006). explain the 13. S. P. Littlefair,support V. S. Dhillon, of a S. PPARC B. Howell, advanced D. R. Ciardi, fellowship.30. M. Ultracam Politano, Astrophys. is J. 604, 817 (2004). 7. U. Kolb, Astron. Astrophys. 271, 149 (1993). 24. K.discrepancy Horne, T. R. between Marsh, theF. H. observed Cheng, and I. Hubeny, predicted T. Lanz, Mon. Not. R.supported Astron. Soc. 313 by, PPARC. 117 (2000). 31. D. Grether, C. H. Lineweaver, Astrophys. J. 640, 1051 14. R. E. Mennickent, M. P. Diaz, Mon. Not. R. Astron. Soc. (2006). 8. S. P. Littlefair, V. S. Dhillon, E. L. Martín, Mon. Not. R. Astrophys.mass and J. radius426, presented 294 (1994). here. 336, 767 (2002). 32. D. M. Townsley, L. Bildsten, Astrophys. J. 596, L227 (2003). Astron. Soc. 340, 264 (2003). 25. J. Wood et al., Mon. Not. R. Astron. Soc. 219, 629 (1986).15. S. Araujo-Betancor et al., Astron. Astrophys. 430, 629 33. V. Renvoizé, I. Baraffe, U. Kolb, H. Ritter, Astron. Astrophys. 9. R. E. Mennickent, M. P. Diaz, C. Tappert, Mon. Not. R. 26. J. SouthworthReferenceset and al., NotesMon. Not. R. Astron. Soc., in press;(2005).Supporting Online Material 389, 485 (2002). 1. A. Duquennoy, M. Mayor, Astron. Astrophys. 248, 485 16. A. R. King, K. Schenker, Astron. Soc. Pac. Conf. Proc. 261, 34. I. Baraffe, U. Kolb, Mon. Not. R. Astron. Soc. 318, 354 Astron. Soc. 347, 1180 (2004). available at http://xxx.lanl.gov/abs/astro-ph/0609196. www.sciencemag.org/cgi/content/full/314/5805/1578/DC1 (1991). 233 (2002).Materials and Methods (2000). 10. K. Beuermann, P. Wheatley, G. Ramsay, F. Euchner, 27. G. Chabrier,2. S. D. Barthelmy I. Baraffe,et al., NatureAstron.438 Astrophys., 994 (2005).327, 103917. R. E. Taam, H. C. Spruit, Astrophys. J. 561, 329 (2001). 35. D. Saumon, G. Chabrier, H. M. van Horn, Astrophys. J. B. T. Ga¨nsicke, Astron. Astrophys. 354, 49 (2000). (1997).3. L. Yungelson, M. Livio, Astrophys. J. 497, 168 (1998). 18. U. Kolb,SOM I. Baraffe, Text Mon. Not. R. Astron. Soc. 309, 1034 Suppl. Ser. 99, 713 (1995). 4. B. Willems, U. Kolb, E. L. Sandquist, R. E. Taam, (1999).References 36. We thank U. Kolb and I. Baraffe for productive 11. V. S. Dhillon et al., Mon. Not. R. Astron. Soc. 314, 826 28. L. Bildsten,G. Dubus, D.Astrophys. Chakrabarty, J. 635,Astrophys. 1263 (2005). J. 557, 292 (2001).19. P. Szkody et al., Astron. J. 123, 430 (2002). discussions. S.P.L., C.A.W., and J.S. are supported by (2000). 29. P. F.5. L. B. Maxted, Paczynski, R. R.Napiwotzki, Sienkiewicz, Astrophys. P. D. Dobbie, J. 248, L27 M. R. Burleigh,20. P. Szkody2 Augustet al., Astron. 2006; J. 126 accepted, 1499 (2003). 25 September 2006the Particle Physics and Astronomy Research Council 12. S. B. Howell, D. R. Ciardi, Astrophys. J. 550, L57 (2001). Nature(1981).442, 543 (2006). 21. P. Szkody10.1126/science.1133333et al., Astron. J. 128, 1882 (2004). (PPARC). T.R.M. acknowledges the support of a PPARC 6. S. B. Howell, S. Rappaport, M. Politano, Mon. Not. R. 22. P. Szkody et al., Astron. J. 129, 2386 (2005). Senior Research Fellowship. B.T.G. acknowledges the Astron. Soc. 287, 929 (1997). 23. P. Szkody et al., Astron. J. 131, 973 (2006). support of a PPARC advanced fellowship. Ultracam is 7. U. Kolb, Astron. Astrophys. 271, 149 (1993). 24. K. Horne, T. R. Marsh, F. H. Cheng, I. Hubeny, T. Lanz, supported by PPARC. 8. S. P. Littlefair, V. S. Dhillon, E. L. Martín, Mon. Not. R. Astrophys. J. 426, 294 (1994). Astron. Soc. 340, 264 (2003). 25. J. Woodburninget al., Mon. Not. shell, R. Astron. advances Soc. 219, 629 (1986). outward. During the 3 9. R. E. Mennickent, M. P. Diaz, C. Tappert, Mon. Not. R. 26. J. Southworth et al., Mon. Not. R. Astron. Soc., in press; Supporting Online Material Astron. Soc. 347, 1180 (2004). availablegrowing at http://xxx.lanl.gov/abs/astro-ph/0609196. phase, the SCZ dredgeswww.sciencemag.org/cgi/content/full/314/5805/1578/DC1 up and homog- Deep Mixing of He: Reconciling10. K. Beuermann, P. Wheatley, G. Ramsay, F. Euchner, Big27. G. Chabrier,enizes I. Baraffe, materialAstron. Astrophys. that, at327 the, 1039 earlierMaterials MS phase, and Methods was B. T. Ga¨nsicke, Astron. Astrophys. 354, 49 (2000). (1997). SOM Text References 11. V. S. Dhillon et al., Mon. Not. R. Astron. Soc. 314, 826 28. L. Bildsten,processed D. Chakrabarty, byAstrophys. nuclear J. 557 reactions, 292 (2001). in the interior. on February 5, 2010 Bang and Stellar Nucleosynthesis(2000). 29. P. F. L. Maxted,Along R. Napiwotzki, the P. MS, D. Dobbie, stars M. R. Burleigh,burn hydrogen2 August 2006; in accepted their 25 September 2006 12. S. B. Howell, D. R. Ciardi, Astrophys. J. 550, L57 (2001). Nature 442, 543 (2006). 10.1126/science.1133333 cores by a combination of the proton-protonREPORTS (pp) Peter P. Eggleton,1* David S. P. Dearborn,2 John C. Lattanzio3 chain (in which four protons unite to form a 4He burning shell,Fig. advances 4. A color-coded outward. During plot the ofm on a 3 nucleus) and the CNO tri-cyclegrowing (in which phase, the the SCZ dredges up and homog- Low-mass stars, ~1 to 2 solar masses, near the Main SequenceDeep are efficient Mixing at producing of theHe: helium Reconcilingsame process is catalyzed Big by carbon,enizes material nitrogen,cross-section that, at the earlier through MS phase, the was initial 3D 3 isotope He, which they mix into the convective envelope on the giant branch and should distribute and oxygen). The former is the moreprocessed importantmodel. by nuclear The reactions shell in the where interior. the m in- on February 5, 2010 Bang and Stellar Nucleosynthesis Along the MS, stars burn hydrogen in their into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile in low-mass stars, ≤1 M⊙, and the latterversion in more occurs is the yellow region 3 cores by a combination of the proton-proton (pp) the low observed cosmic abundance of He with the predictionsPeter P. Eggleton, of both1* David stellar S. P.and Dearborn, Big Bang2 John C. Lattanziomassive3 stars. However, even inchain the (inmore whichsandwiched mas-REPORTS four protons between unite to form a yellow-green a 4He nucleus) and the CNO tri-cycle (in which the nucleosynthesis. Here we find, by modeling a red giant with a fully three-dimensional sive stars there is still a shell, somewhatand outside a darker green.www.sciencemag.org The inversion is 3 hydrodynamicenough that code the andHe a produced full nucleosynthetic is convected network, into (Pop thatLow-mass mixing I)] stars, like arises ~1 the to Sun 2 insolar throughoutthe masses, supposedly near the the Main earlier stable Sequence partthe are maininversion efficient energy-producing at producing in the m thegradient. helium region, Thesame where inversion processat the a is radius catalyzedpp is tiny of by ~5 carbon,× 10 nitrogen,7 m. The base isotope 3He, which they mix into the convective envelope3 on the giant branch and should distribute and oxygen). The former is the more important and radiativethe center zone of the between star and the burnt hydrogen-burning there. In stars of shellof and Galactic the base history of the in determining convective envelope. the He abun-chain(Fig. partially 3): It operates,is in about burning the fourth H to decimal3ofHe the but place. SCZ is at ~2 × 109 m, well 3 into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile in low-mass stars, ≤1 M⊙, and the latter in more This mixinglower mass, is due however, to Rayleigh-TaylorHe accumulates instability (1) in within a dance athe zone low of observed just the above interstellar cosmic the abundance hydrogen-burning medium. of 3He The with process the predictions isnot beyond. ofOur both three-dimensional stellar and Big Bang (3D) modeling,massive stars.outside however, However, the even frame, in the and more the mas- surface 10 shell,broad where zone a nuclear outside reaction the main lowers energy-producing the mean molecularlargelynucleosynthesis. weight independent slightly. Here we offind, Thus, mass by we modeling provided are able a red it to giant is fairly with a fullyBecauseshows three-dimensional the the inversion pp chain to is be lesssive hydrodynamically sensitivestarsof there the is tostill star a shell, is at somewhat ~2 × 10 outsidem. www.sciencemag.org region (Fig. 2A).33He is enriched above its low:hydrodynamic 1 to 2 M code andfor a Pop full nucleosynthetic I and 0.8 to network, 1.6 M thatfor mixingunstable, arises in the as supposedly we should stable expectthe main from energy-producing the classic region, where the pp remove the threat that He production in low-mass starsand poses radiative to zonethe⊙ Bigbetween Bang the hydrogen-burningnucleosynthesis shell⊙ andtemperature the base of the than convective the CNO envelope. cycle,chain cores partially of low- operates, burning H to 3He but 3 −4 of He.assumed initial value [2 × 10 by mass (2), the PopThis mixing II. is due to Rayleigh-Taylor instability within a zonemass justRayleigh-Taylor stars above are the freehydrogen-burning of instability. convection,not but beyond. convectiveREPORTS same as its surface value in this plot] in a broad shell,Once where the a nuclear SCZhas reaction reached lowers its the deepest mean molecular extent,cores weightdevelop slightly.At a Thus, stage in higher-mass we (Fig. are able 3) to when stars because theBecause SCZ theCNO has pp just chain is less sensitive to 3 remove the threat that 3He production in low-mass stars poses to the Big Bang nucleosynthesis temperature than the CNO cycle, cores of low-

enough that the He produced is convected into (Pop I)] like the Sun throughout the earlier part inversion in the m gradient. The inversion is tiny Downloaded from peakhe standard extending evolution over nearly of a low-mass half the mass star (asvectionpart3 zone way (SCZ) up from penetrates the base deeply of the RGB,into the it star, retreats,energybegun production to retreat, is there too is temperature no bump in 1/ sensitivem, but just a of He. 3 mass stars are free of convection, but convective the centerwell(Fig. as of 1) about the takes star half it and from the burnt radius) a short-lived there. of In the stars pre star.– of Thebutof the Galacticand SCZ it can is history forced be expected in to determining retreat to leave again the behind as theHe fuel- aabun- regionfor(Fig.slight radiation 3): distortion It is to in stably about at about transport the 0.286 fourthM the decimal⊙. energy. This place. is be- 3 3 3 3 cores develop in higher-mass stars because CNO lowermaximum mass, however,He abundanceHe accumulates in this peak (1) is in larger a danceof ofuniformhe the standard interstellar composition evolution medium. of a low-mass with TheHe star process enhancedvection is zoneOur (SCZ)cause three-dimensional penetrates the He deeply consumption into the (3D) star, modeling, isenergy taking production place however, is in too a temperature sensitive Downloaded from TMain-Sequence (PMS) state, in which it exhausted core, surrounded by a thin, hot nuclear- Above ~2 M⊙ this convective core is large contractsbroadthan zone and the outside initial heats valueup the but main by has a energy-producingfactor not yet of become ~18. largely(Fig. independent(Fig. 2B). 1) This takes region it of from mass a is short-lived provided stable topre it– convection isbut fairly the SCZshows isregion forced to the where retreat inversion again there as is the still to fuel- be a substantialfor hydrodynamically radiationm gradient to stably transport the energy. region (Fig.On the 2A). lower3He part is of the enriched RGB (Fig. above 1), a its largelow:accordingT 1 toMain-Sequence 2 M tofor the Popusual (PMS) Icriterion and state, 0.8 in which to that 1.6 ittheMexhausted temper-for core,unstable,left surrounded over as from by we a thin, earlier should hot nuclear- history. expectAbove As from the ~2 the H-burningM⊙ classicthis convective core is large hot enough to burn its nuclear fuel, to the long- ⊙ ⊙ Fig. 1. Evolution of a low-mass Pop I −4 contracts and heats up but has not yet become 3 Fig. 5. The development with time of a contour livedassumedSCZ MS initial statedevelops, valuein which which [2 × slow,10 mixesby steady and mass homogenizes nuclear (2), the Popaturehot II. enough gradient to burn shouldits nuclear be fuel, subadiabatic to the long- and is Rayleigh-Taylorshellstar moves in a out luminosity-temperature instability. (in mass), though,Fig. 1. the dia-EvolutionHe- of a low-mass Pop I 3 surface of mean molecular weight near the reactionssamethe as itsouter keep surface ~0.7 the star valueM⊙ in(Fig. in thermal this 2B). plot] equilibrium. The in surface a broad He quiteOncelived MS the extensive state SCZ in has which in reached radius, slow, steady its although deepest nuclear extent,small in burningAtgram. a stage shell The preceding(Fig. model 3) was when it moves computed the into SCZstar ain in region has 1D, a luminosity-temperature just of dia- reactions keep the star in thermal equilibrium. 1 4 gram. The model was computed in 1D, Afterpeakabundance several extending gigayears is over raised nearly (but from depending halfthe initial the strongly mass value (as of 2 ×partmass. way up The from H-burning the base front of the moves RGB, outward it retreats, into begunmorethat to uniform retreat, is, spherical thereH/ He is no ratio, symmetry bump so in the 1/ wasm peak, but as-in just 1/ am peak in the blue curve of Fig. 3. The contour −4 −3 After several gigayears (but depending strongly that is, spherical symmetry was as- dimples, and begins to break up, on a time onwell mass),10 as aboutto the ~1.6 nuclear half× 10 the fuel, radius) that is is,exhausted of by the a factor star. at and of The ~8. andtheon it mass),can stable be the expectedregion, nuclear fuel but to is preceding leave exhausted behind at the and a H-burning region slightbeginssumed, distortion to stand using at out. theabout By code the 0.286 time of (M20 the⊙,sumed,.21 leading This) with using is edge be- the code of (20, 21) with 3 REPORTS 3 3 nearmaximum theAs center,He the theabundance star star climbs becomes in the this cooler, RGB peak beyondis larger, larger theofregion uniformnear the proper center, composition the is star a narrow becomes with region, cooler,He larger, usually enhanced thought causeof theupdated the shellHe equation has consumption moved of tostate, is 0.29 taking opacity,Mupdated⊙, place there and equation in is a a of state, opacity, and scale of only ~2000 s. 3 nuclear reaction rates (22). Surface tem- andthan morepoint the initial luminous, (Fig. value 1) where and by it a starts thefactor SCZ to of climb ~18.penetrates the red most(Fig.unimportant,and 2B). more luminous, This in region which and it starts isthe stable toHe climb burns. to the convection red The reaction regionclearnuclear wherelocal maximum reaction there is still rates in 1/ am (substantial22, which). Surface persistsm gradient tem- indef- Fig.giant 4. A branch color-coded (RGB). Its outer plot layers of3 m becomeon3 a 4 perature is in kelvins, luminosity in solar giantOndeeply, branch the lower the (RGB). part SCZ of Itsis the diminished outer RGB layers (Fig. by 1), become (i) a large nuclearaccordingthatturbulent mainly to and the convective, consumes usual criterion and it this is surface thatHe ( thecon-He, temper- 2p) He, leftinitely overperature as from the is earlier H-burning in kelvins, history. shell luminosity As advances theunits.from inH-burning solar and center the to photosphere, we economized on bulent and has the effect of diluting the inverse turbulentSCZburning develops, and below convective, which its base,mixes and in andthis a zone surfacehomogenizes that con- marchescross-sectionaturewhich gradient is an through should unusual be the reaction subadiabatic initial in 3D stellar and terms is shellconvectiveunits. moves envelope out (in retreats.mass), though,mesh the 3 pointsHe- by considering only the region be- molecular-weight gradient, but it cannot elimi- model makes this very likely. Although the m outward, and (ii) stellar-wind mass loss3 from because1Institute of it Geophysics lowers and the Planetary mean Physics, molecular Lawrence weight: two At a point somewhat beyond this in the evo- the outer ~0.7 M⊙ (Fig. 2B). The surface He model.quite extensive The shell in where radius, thealthoughm in- small in burning shell preceding it moves intolow a region the SCZ.of It is important for numerical pur- nate it. As the turbulent region entrains more of inversion that we find is somewhat above the its surface. The evidence for the latter is that nucleiLivermore become National Laboratory, three nuclei, 7000 East and Avenue, the mean mass lution of our 1D1 star4 (Fig. 1), we mapped the 1D 1abundanceInstitute of Geophysics is raised and from Planetary the initial Physics, value Lawrence of 2 × versionmass.Livermore, The occurs CA H-burning 94551, is USA. the2Physics front yellow and moves Applied region Technol- outward into more uniform H/ He ratio, so the peakposes in that 1/m the 1D and 3D codes use exactly the the normally stable region outside it, yet below main part of the H-burning shell, it is not far −4 the next long-lived−3 stage after the RGB is the perogies nucleus Division, Lawrence decreases Livermore from National 3 Laboratory,to 2. Because the model onto a 3D model and used the hydro- 3 Livermore10 to ~1.6 National× 10 Laboratory,, that is, by 7000 a factor East ofAvenue, ~8. the7000 stable East Avenue, region, Livermore, but CA preceding 94551, USA. Centre the H-burningfor begins to stand out. By the time the leadingsame approximations edge for physical processes, for the normal convective envelope, it brings in fresh above, and we can expect some modest process- on February 5, 2010 2 sandwiched between a yellow-green Livermore,horizontal CA 94551, branch USA. (HB),Physics and and Applied HB stars Technol- appear to molecularStellar and Planetary weight Astrophysics, (m) is the Monash mean University, mass per nu- dynamic code “Djehuty” developed at Lawrence 3 12 13 14 As the star climbs the RGB beyond the region proper is a narrow region, usually thought of the shell has moved to 0.29 M⊙, there is a Australia. example, equation of state, nuclear reaction He, which burns at the base of this mixing re- ing of C to C and N. According to (15), it ogies Division,have masses Lawrence that Livermore are typically National 0.5 Laboratory, to 0.6 M⊙and, cleus, a darker but including green. The also3 inversion the much largeris abun- Livermore National Laboratory (10–12). [The point (Fig. 1) where the SCZ penetrates3 most unimportant,*To whom correspondence in1 which4 should the7 beHe addressed. burns. E-mail: The reaction clear local maximum in 1/m, which persists indef- 7000 Eastsubstantially Avenue, Livermore, less CAthan 94551, the USA. massesCentre of for stars dances of H and He that3 are already3 there4 and code is described most fully in (12).]rates, Although and opacities. gion, thus sustaining the inverse molecular- appears to be necessary for some extra mixing to deeply, the SCZ is diminished by (i) nuclear atthat [email protected] radius mainly of consumes ~5 × 10 itm. is He The ( baseHe, 2p) He, initely as the H-burning shell advances and the Stellar and Planetary Astrophysics, Monash University, 9 The location of the starting model of the 3D weight gradient. Ultimately this turbulent region take place beyond the point on the RGB where the capable of evolving to the RGB in less than a not taking part in this reaction, this leads to a small Djehuty is designed to deal with an entire star, on February 5, 2010 Australia.burning below its base, in a zone that marches ofwhich the SCZ is an is unusual at ~2 × reaction10 m, in wellstellar terms convective envelope retreats. Hubble time (3, 4). Process (ii) leads to enrich- calculation is shown in Fig. 1. If we had been will extend to unite with the normally convective SCZ has penetrated most deeply; that is exactly outward, and (ii) stellar-wind mass loss from 1580because it lowers the mean molecular8 DECEMBER weight: 2006 two VOLAt 314 a pointSCIENCE somewhatwww.sciencemag.org beyond this in the evo- *To whomment correspondence of the interstellar should be medium addressed. (ISM) E-mail: in 3Heoutside the frame, and the surface clear before starting the 3D calculation that the envelope, so that the considerable reservoir of the point where our mechanism should start to [email protected] surface. The evidence for the latter is that nucleiFig. become 3. The three profile nuclei, of reciprocal10 and the mean mass lution of our 1D star (Fig. 1), we mapped the 1D (5–7). of the star is at ~2 × 10 m. 1/m bump was going to cause mixing, we would 3He there will also be depleted. If its speed of operate. In (15–18) it was suggested that rotation the next long-lived stage after the3 RGB is the 5permolecular nucleus decreases weight (1/ fromm), as 3 a to func- 2. Because the model onto a 3D model and used the hydro- Yet the ISM’s abundance of He, at ~5 × 10− horizontal branch (HB), and HB stars appear to moleculartion of mass weight in solar (m) is units, the meanat three mass per nu- dynamic code “Djehuty” developed athave Lawrence started further down, at the point where the ~500 m/s is maintained, the time for processed in the region between the SCZ and the hydrogen- 1580 by mass, is little different from that8 DECEMBER predicted by 2006successive VOL times 314 (red,SCIENCE then greenwww.sciencemag.org bump first presents itself, which is just above the material to reach the classically unstable SCZ burning shell might be responsible for the required have masses that are typically 0.5 to 0.6 M⊙, cleus, but including also the much larger abun- Livermore National Laboratory (10–12). [The Big Bang nucleosynthesis. This is a major prob- 2 million1 years4 later, then blue substantially less than the masses of stars dances of H and He that are already there and code is described most fully in (12).]point Although labeled “deepest penetration of convec- is only about 1 month, whereas the time for the mixing. We do not dispute the possible importance www.sciencemag.org lem (8, 9): Either the Big Bang value is too high, 2 million years later still).

tion.” It has become on February 5, 2010 clear that our unexpected H-burning shell to burn through the ~0.02 M of rotation; however, we emphasize that the mech- capableor the of evolution evolving of to low-mass the RGB stars in less is wrong. than a not taking part in this reaction, this leads to a small Djehuty is designed to deal with an entire star, ⊙ Hubble time (3, 4). Process (ii) leads to enrich- mixing will begin around here, and in practice layer is more than 106 years. anism we have discovered is not ad hoc but simply Here, we identify a mechanism by which www.sciencemag.org 3 ment of the interstellar medium (ISM) in 3He3 we expect that almost all of the He in the SCZ The above argument establishes that the arises naturally when the modeling is done in 3D. low-mass stars destroy (on the RGB) the HeFig. 3. The profile of reciprocal (5–7). that they produced during their MS evolution.molecular weight (1/m), as a func- will have been consumed by the time the model mixing in the SCZ is extended below the clas- This mixing occurs regardless of possible varia- Yet the ISM’s abundance of 3He, at ~5 × 10−5 Although we illustrate this with a star like thetion of mass in solar units, at three reaches the point where our 3DFig. calculation 5. The developmentsical convective with limit time and of that a it contour is very fast com- bles like rotation and magnetic fields. It seems by mass,Sun, is regarding little different both from mass that and predicted initial by com-successive times (red, then green started. Because 3D modeling is very expensive pared with the nuclear time scales of either the possible to us that different rates of rotation might surface of mean molecular weight near3 the Big Bangposition, nucleosynthesis. we emphasize This that is exactly a major the prob- same2 million years later, then blue of computer time, we have chosen not to redo the hydrogen-burning shell or the He-burning re- vary the efficiency of our process, and we intend lem (8, 9): Either the Big Bang value is too high, peak in the blue curve of Fig. 3. The contour applies to low-mass, metal-poor stars [Popula-2 million years later still). calculation for an earlier starting point. Figure 4 action. We estimate from the nuclear-burning to investigate models with rotation in the future. Downloaded from or thetion evolution II (Pop of II)], low-mass which stars may is have wrong. been more is a cross-section of the starting modeldimples, for the 3D andrates begins that to as the break hydrogen up, on shell a burns time outwards Correlations between abundance excesses Downloaded from

Here, we identify a mechanism by which www.sciencemag.org important than metal-rich stars [Population I run and shows the m inversion as a ringscale well of out- only ~2000the 3He s. will be destroyed in 16 times as much3 and deficits of various elements and isotopes in low-mass stars destroy (on the RGB) the 3He that they produced during their MS evolution. side the burning shell. mass as the hydrogen shell burns through. the low-mass evolved stars of globular clusters Although we illustrate this with a star like the from center to photosphere, we economized on bulent and has the effectAfter of diluting the early the development inverse of the initially We believe that the extra mixing that we have have been reported in (13). Although it is hard to Sun, regarding both mass and initialWednesday, com- March 31, 2010 spherical shell on which 1/m has a constant value seen gives a satisfactoryanswer to the problem of distinguish star-to-star variations that may be mesh points by considering only the region be- molecular-weight gradient, but it cannot elimi- model makes this very likely.3 Although the m position, we emphasize that exactly the same low the SCZ. It is important for numerical pur- nate it. As the turbulentnear region its peak entrains (Fig. 5), more the surface of hasinversion begun to thatmatching we find the is somewhatHe abundance above of Big the Bang nu- due to evolution from those that may be due to applies to low-mass, metal-poor stars [Popula- dimple after only ~800 s, and by 2118 s the dim- cleosynthesis. Although low-mass stars do in- primordial variation, we expect our mechanism poses that the 1D and 3D codes use exactly the the normally stable region outside it, yet below main part of the H-burning shell, it is not far3 tion II (Pop II)], which may have been more pling is very marked and the surface has begun to deed produce considerable amounts of He on the to lead to substantial evolutionary variations. on February 5, 2010 important than metal-rich stars [Population I same approximations for physical processes, for the normal convectivetear. envelope, Some points it brings haveDownloaded from in moved fresh ~2%above, radially, and that weMS, can this expect will all some be destroyed modest by process- the substantially Our investigation demonstrates particularly 3 12 13 14 example, equation of state, nuclear reaction He, which burns atis, the ~10 base6 m, of indicating this mixing velocities re- of ~500ing m/s.of TheC to deeperC and mixingN. that According we now expect to (15 on), it the RGB. clearly the virtue of attempting to model in 3D, rates, and opacities. gion, thus sustainingmean the velocity inverse decreases molecular- slightly inappears the passage to be necessaryOur deeper for some mixing extra can mixing also be to relevant to where the motion evolved naturally and to a The location of the starting model of the 3D weight gradient. Ultimatelyfrom the this second turbulent to the region fourth panel.take place Other beyondfurther the problems. point on According the RGB towhere the classical the mod- magnitude that was unexpected. calculation is shown in Fig. 1. If we had been will extend to unite withsphericalthe normally shells, well convective away from theSCZ inversion has on penetratedels of RGB most stars, deeply; there isthat no isfurther exactly modification either side, show no such dimpling, at least until to the composition in an RGB convective enve- References and Notes clear before starting the 3D calculation that the envelope, so that the considerable reservoir of the point where our mechanism should start to 1. I. Iben Jr., Astrophys. J. 147, 624 (1967). the influence of the inversion has spread to them. lope after it has reached its maximum extent early 3 1/m bump was going to cause mixing, we would 3He there will also be depleted. If its speed of operate. In (15–18) it was suggested that rotation 2. The initial value for He that we assumed is somewhat higher A movie of which Fig. 5 is four frames is given as on the RGB. Yet observations persistently suggest than the mass-fraction (~5 × 10−5) implied by (19). This is have started further down, at the point where the ~500 m/s is maintained,Movie the S1 time in the for Supporting processed Onlinein Material. the region betweenthat the ratios the SCZ13C/12 andC and the14 hydrogen-N/12C both increase partly because we assume that primordial deuterium, of 3 Fig. 2. (A) Profiles of the abundances of certainbump nuclei first in a presents star that has itself,(surface) which abundance. is just above (B) The the samematerial star later, to when reach the SCZthe reaches classicallyThe velocity its unstable we see is roughly SCZ consistentburning with shell mightappreciably be responsible as one goes for up the the required RGB (13, 14). comparable abundance, is wholly burnt into He before the 1 3 2 computation starts. However, the important point is that the evolved to roughly the end of the MS (Fig. 1) (T ~ 5000 K; L ~2L⊙). H is maximum inward extent (Fig. 1). The He peak has been homogenizedthe expectation to a that it should be v ~ glDm/m, Both these ratios can be expected to increase 3 point labeled “deepest penetration of convec- is only about 1 month, whereas the time for the mixing. Wedo not dispute the possible importance www.sciencemag.org orange, 4He is red, 16O is blue, 12C is black, 14N is green, and 3He is yellow. factor of 8 larger than its initial value. The inert, H-depleted core is about great bulk of the He in the RG phase is what was synthesized 3 tion.” It has become clear that our unexpected H-burning shell to burnwhere throughg is the the local ~0.02 gravityM and lofis rotation; the local however,only if wethe materialemphasize in the that envelope the mech- is somehow from ordinary hydrogen during the MS phase, not what was He shows a major peak where the abundance reaches ~18 times the initial 0.27 M⊙. ⊙ mixing will begin around here, and in practice layer is more than 10pressure6 years. scale height. The motionanism appears we tur- havebeing discovered processed is not near ad the hoc H-burning but simply shell. Our there initially. The enrichment factor of 8 that we mention we expect that almost all of the 3He in the SCZ The above argument establishes that the arises naturally when the modeling is done in 3D. www.sciencemag.org SCIENCE VOL 314 8 DECEMBER 2006 1581 will have been consumed by the time the model mixing in the1582 SCZ is extended below the clas- This8 DECEMBER mixing occurs 2006 regardless VOL 314 of possibleSCIENCE varia-www.sciencemag.org reaches the point where our 3D calculation sical convective limit and that it is very fast com- bles like rotation and magnetic fields. It seems Fig. 2. (A) Profiles of the abundances of certain nucleistarted. in a Because star that has 3D modeling(surface) abundance. is very expensive (B) The samepared star later, with when the the nuclear SCZ reaches time its scales of either the possible to us that different rates of rotation might 1 3 evolved to roughly the end of the MS (Fig. 1) (T ~ 5000of computer K; L ~2L⊙ time,). H is we havemaximum chosen inward not extent to redo (Fig. the1). The hydrogen-burningHe peak has been homogenized shell or to the a 3He-burning re- vary the efficiency of our process, and we intend orange, 4He is red, 16O is blue, 12C is black, 14N is green, and 3He is yellow. factor of 8 larger than its initial value. The inert, H-depleted core is about

3 Downloaded from He shows a major peak where the abundance reachescalculation ~18 times forthe initial an earlier0.27 startingM⊙. point. Figure 4 action. We estimate from the nuclear-burning to investigate models with rotation in the future. is a cross-section of the starting model for the 3D rates that as the hydrogen shell burns outwards Correlations between abundance excesses run and shows the m inversion as a ring well out- the 3He will be destroyed in 16 times as much and deficits of various elements and isotopes in www.sciencemag.org SCIENCE VOL 314 8 DECEMBER 2006 1581 side the burning shell. mass as the hydrogen shell burns through. the low-mass evolved stars of globular clusters After the early development of the initially We believe that the extra mixing that we have have been reported in (13). Although it is hard to spherical shell on which 1/m has a constant value seen gives a satisfactoryanswer to the problem of distinguish star-to-star variations that may be near its peak (Fig. 5), the surface has begun to matching the 3He abundance of Big Bang nu- due to evolution from those that may be due to dimple after only ~800 s, and by 2118 s the dim- cleosynthesis. Although low-mass stars do in- primordial variation, we expect our mechanism pling is very marked and the surface has begun to deed produce considerable amounts of3He on the to lead to substantial evolutionary variations. tear. Some points have moved ~2% radially, that MS, this will all be destroyed by the substantially Our investigation demonstrates particularly is, ~106 m, indicating velocities of ~500 m/s. The deeper mixing that we now expect on the RGB. clearly the virtue of attempting to model in 3D, mean velocity decreases slightly in the passage Our deeper mixing can also be relevant to where the motion evolved naturally and to a from the second to the fourth panel. Other further problems. According to the classical mod- magnitude that was unexpected. spherical shells, well away from the inversion on els of RGB stars, there is no further modification either side, show no such dimpling, at least until to the composition in an RGB convective enve- References and Notes 1. I. Iben Jr., Astrophys. J. 147, 624 (1967). the influence of the inversion has spread to them. lope after it has reached its maximum extent early 2. The initial value for 3He that we assumed is somewhat higher A movie of which Fig. 5 is four frames is given as on the RGB. Yet observations persistently suggest than the mass-fraction (~5 × 10−5) implied by (19). This is Movie S1 in the Supporting Online Material. that the ratios 13C/12C and 14N/12C both increase partly because we assume that primordial deuterium, of The velocity we see is roughly consistent with appreciably as one goes up the RGB (13, 14). comparable abundance, is wholly burnt into 3He before the the expectation that it should be v2 ~ glDm/m, Both these ratios can be expected to increase computation starts. However, the important point is that the great bulk of the 3He in the RG phase is what was synthesized where g is the local gravity and l is the local only if the material in the envelope is somehow from ordinary hydrogen during the MS phase, not what was pressure scale height. The motion appears tur- being processed near the H-burning shell. Our there initially. The enrichment factor of 8 that we mention

1582 8 DECEMBER 2006 VOL 314 SCIENCE www.sciencemag.org A&A 467, L15–L18 (2007) Astronomy DOI: 10.1051/0004-6361:20077274 & c ESO 2007 ! Astrophysics L   E

Thermohaline mixing: a physical mechanism governing the photospheric composition of low-mass giants

C. Charbonnel1,2 and J.-P. Zahn3

1 Geneva Observatory, University of Geneva, chemin des Maillettes 51, 1290 Sauverny, Switzerland e-mail: [email protected] 2 Laboratoire d’Astrophysique de Toulouse et Tarbes, CNRS UMR 5572, Université Paul Sabatier Toulouse 3, 14 Av. E. Belin, 31400 Toulouse, France 3 LUTH, CNRS UMR 8102, Observatoire de Paris, 92195 Meudon, France e-mail: [email protected] Received 9 February 2007 / Accepted 12 March 2007 ABSTRACT

Aims. Numerous spectroscopic observations provide compelling evidence for a non-canonical mixing process that modifies the surface abundances of Li, C and N of low-mass red giants when they reach the bump in the luminosity function. Eggleton and collaborators have proposed that a molecular weight inversion created by the 3He(3He, 2p)4He reaction may be at the origin of this mixing, and relate it to the Rayleigh-Taylor instability. We argue that one is actually dealing with a double diffusive instability referred to as thermohaline convection and we discuss its influence on the red giant branch. Methods. We compute stellar models of various initial metallicities that include thermohaline mixing, which is treated as a diffusive process based on the prescription given originally by Ulrich for the turbulent diffusivity produced by the thermohaline instability in stellar radiation zones. Results. Thermohaline mixing simultaneously accounts for the observed behaviour of the carbon isotopic ratio and of the abundances of Li, C and N in the upper part of the red giant branch. It significantly reduces the 3He production with respect to canonical evolution models as required by measurements of 3He/H in galactic HII regions. Conclusions. Thermohaline mixing is a fundamental physical process that must be included in stellar evolution modeling. Key words. instabilities – stars: abundances – stars: interiors – hydrodynamics

1. Introduction Shetrone 2003; Recio-Blanco & De Laverny 2007) that also modifies the abundances of lithium, carbon and nitrogen (e.g., 4 During the first dredge-up (1dup; Iben 1965), the surface com- 1 Gratton et al. 2000). This non-canonical process appears to be position of low-mass red giant stars is modified due to dilution universal as it affects at least 95% of the low-mass stars, whether Wednesday, Marchof the 31, external 2010 convective stellar layers with hydrogen-processed they belong to the field, to open, or globular clusters (Charbonnel material. The lithium and the carbon abundances as well as the & Do Nascimento 1998). This high number satisfies the galactic carbon isotopic ratio decline, while the helium 3 and nitrogen requirements for the evolution of the 3He abundance (Tosi 1998; abundances increase. The amplitude of these variations depends Palla et al. 2000; Romano et al. 2003), since the mechanism re- on the stellar mass and metallicity. This picture is nicely sup- sponsible for the low values of 12C/13C is also expected to lead ported by observations. to the destruction of 3He by a large factor in the bulk of the en- After the 1dup the stellar convective envelope retreats (in velope material, as initialy suggested by Rood et al. (1984; see mass) ahead of the advancing hydrogen-burning shell (HBS) also Charbonnel 1995; Hogan 1995; Weiss et al. 1996). that surrounds the degenerate helium core, and no further At present, we have no firm physical model for the non- surface abundance variation is predicted by canonical stellar canonical RGB mixing. Parametrized approaches have been 2 evolution theory on the RGB. However, spectroscopic ob- used to reproduce individual observations with the diffusive ve- servations clearly point out that some non-canonical mixing locity treated as a free parameter (i.e. Boothroyd & Sackmann connects the convective envelope with the HBS and further 1999; Weiss et al. 2000). On the other hand, rotation-induced modifies the surface composition of low-mass giants as soon as mixing has been investigated thoroughly (see references in they reach the bump in the luminosity function. The sudden drop Charbonnel & Palacios 2004). It turns out however that merid- 12 13 of the carbon isotopic ratio C/ C provides the most pertinent ional circulation and shear turbulence alone do not produce clue to this mechanism (Gilroy 1989; Gilroy & Brown 1991; enough mixing to account for the surface abundance variations Charbonnel 1994; Charbonnel et al. 1998; Gratton et al. 2000; as required by the observations (Palacios et al. 2006).

1 I.e., stars with initial masses below 2–2.5 M that evolve along the Red Giant Branch (RGB) to high luminosities∼ until# helium is ignited in 2. Mixing due to thermohaline convection their core under degenerate conditions. 2 By this we refer to the modelling of non-rotating, non-magnetic Recently Eggleton et al. (2006, 2007) identified a possible cause stars, where convection is the only transport process considered. for such non-canonical mixing, namely the molecular weight

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20077274 1972ApJ...172..165U Wednesday, March 31, 2010

1972ApJ...172..165U 5 The Astrophysical Journal, 677:581Y592, 2008 April 10 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

COMPULSORY DEEP MIXING OF 3He AND CNO ISOTOPES IN THE ENVELOPES OF LOW-MASS RED GIANTS Peter P. Eggleton and David S. P. Dearborn Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551; [email protected], [email protected] and John C. Lattanzio Monash University, Mathematics Department, Clayton, Victoria 3168, Australia; [email protected] Received 2007 January 17; accepted 2007 December 20

ABSTRACT Three-dimensional stellar modeling has enabled us to identify a deep-mixing mechanism that must operate in all low-mass giants. This mixing process is not optional, and is driven by a molecular weight inversion created by the 3He(3He,2p)4He reaction. In this paper we characterize the behavior of this mixing, and study its impact on the envelope abundances. It not only eliminates the problem of 3 He overproduction, reconciling stellar and big bang nucleosynthesis with observations, but solves the discrepancy between observed and calculated CNO isotope ratios in low-mass giants, a problem of more than three decades standing. This mixing mechanism, which we call ‘‘" mixing,’’ operates rapidly (relative to the nuclear timescale of overall evolution, 108 yr) once the hydrogen-burning shell approaches the material homogenized by the surface convection zone. In agreement with observations, Population I stars between 0.8 and 2.0 M develop 12C/13Cratiosof 14:5 1:5, while Population II stars process the carbon to ratios of 4:0 0:5. In stars less than 1.25 M , this mechanismÆ also destroys 90%Y95% of the 3He produced on the main sequence.Æ

Subject headinggs: hydrodynamics — stars: abundances — stars: chemically peculiar — stars: evolution — stars: interiors — stars: Population II

1. INTRODUCTION as rotation and magnetic fields. We would also like to emphasize the value of three-dimensional (3D) modeling. It was only by In a previous paper (Dearborn et al. 2006, hereafter Paper I) using a fully 3D (hydrodynamic) model that this mixing was we used a fully three-dimensional code Djehuty, developed in the noticed. It is due to a very slight effect, a -inversion that amounts6 Lawrence Livermore National Laboratory, to investigate the onset " to less than one part in 104, and yet it is quite obvious in a 3D sim- of the helium flash in a low-mass red giant. While convective ulation. One can in fact see the inversion in 1D models (although Wednesday,motion March due 31, 2010 to the helium flash was seen to occur in much the same we are not aware that anyone has actually commented on it), but region as predicted by one-dimensional (spherically symmetric, in1D models mixing only occurs if the code developer tells the hydrostatic) models, we noticed some minor motion, apparently code to include it. also of a turbulent convective character, in an unexpected region: a region above but not far above the hydrogen-burning shell, and Three-dimensional simulations are expensive of computer time. Our philosophy in using D has been that 3D simu- well below the base of the conventional surface convection zone. jehuty lations spanning a short period of time may allow us insight into This is visible in Figure 14 of Paper I. On subsequent close in- spection, we found that this additional motion was due to a very complex hydrodynamic and hydromagnetic phenomena, which will then enable us to improve the quality of simplistic 1D models. small molecular weight inversion, which developed into a dynam- We follow this principle here. We introduce into our 1D code a ical instability that we identified as a Rayleigh-Taylor instability convective mixing coefficient that depends on the -gradient, (Eggleton et al. 2006, 2007, hereafter Papers II and III). This " but only if the -gradient is in the sense that it is destabilizing. inversion was due to the burning of 3He, of which quite a high " This is in addition to the mixing coefficient that is due to ordinary concentration is left by the retreating surface convection zone. convective instability, which depends (crudely speaking) on the In Papers II and III we showed why such an inversion is ex- entropy gradient, but also only if this gradient has the sign which pected to arise, once the surface convection zone, having reached is destabilizing. its deepest extent (the first dredge-up, or FDU), begins to retreat. In 2 we discuss the significance of possible mixing for abun- Furthermore, we suggested that this motion should grow in extent, dancex measurements on the giant branch. In 3 we discuss our so that it reaches upward from the zone where the "-inversion is new mixing mechanism in more detail. Inx 4 we describe a maximal (which is also the zone where 3He-burning is maximal) " 1D code which incorporates a simple model ofx our mixing. In to the base of the normal surface convection zone. It should lead to " 5 and 6 we discuss the sensitivity of this model to some input the destruction of most ( 90%) of the 3He in the surface layers, parametersxx that we estimate. In 7Y12 we present our results and it should simultaneously allow for some processing of 12C to and conclusions. xx 13C. Thus, at the surface of the star 3He should be progressively depleted, and 13C progressively enhanced, beyond the values ex- 2. THE IMPORTANCE OF MIXING pected from conventional 1D models. ON THE GIANT BRANCH In this paper we consider further the effect of our additional mixing, which we refer to as ‘‘" mixing.’’ We would like to em- There is a long history of observing the carbon, nitrogen, and phasize that this mixing can explain in a natural way the observed oxygen (CNO) isotope ratios in red giants (Lambert & Dearborn abundances that have hitherto been attributed to mechanisms such 1972; Day et al. 1974; Dearborn et al. 1975, 1976; Tomkin et al. 581 Mass loss and opacities in AGB stars

An important new ingredient for Routinely employed now, e.g.: AGB stellar evolution are new low-T • ”New asymptotic giant branch models for a opacities and - ideally matching - range of metallicities” Weiss & Ferguson, mass loss rates, e.g. from A&A, 2009. hydrodynamic wind models (see • “Evolution and chemical yields of AGB Susanne Hoefner’s presentation for stars: effects of low-temperature opacities” details). Ventura & Marigo, MN, 2009. • “Molecular Opacities for Low-Mass Metal- Goal: correctly and predictively poor AGB Stars Undergoing the Third describe the loss of the envelope Dredge-up” Cristallo etal, ApJ, 2007. when the star becomes C-rich • “Low temperature Rosseland opacities with through 3rd dredge-up, and the varied abundances of carbon and nitrogen” surface temperature evolution. Lederer & Aringer, A&A 2009. • “Asymptotic Giant Branch evolution at varying surface C/O ratio: effects of changes in molecular opacities” Marigo, A&A, 2002.

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Wednesday, March 31, 2010 4 L. Mattsson et al.: Effects of Carbon-excess Dependent Mass Loss and Molecular Opacities

4 L. Mattsson et al.: Effects of Carbon-excess Dependent Mass Loss and Molecular Opacities

L. Mattsson et al.: Effects of Carbon-excess Dependent Mass Loss and Molecular Opacities 3

Within less than 200 Myr from the onset of the superwind, half of the stellar mass is lost in case D (see Fig. 2, lower right panel). We note that the AGB will probably be terminated even before the next thermal pulse. Hence the model star experiences only a few thermal pulses as C-star. We note also that in the beginning of the C-rich phase the mass-loss rate drops signifi- cantly, but then rapidly evolves into a superwind. In case B the superwind has not yet been reached after five thermal pulses, which is due to a combination of a slower decrease in effective temperature and a steep dependence of mass loss on temperature according to Mattsson et al. (2009). The origin of the superwind in the model is due to the combination of low effective tempera- tures and a carbon-excess dependent mass-loss rate. The relatively rapid decline in temperature (again, see Fig. 2) causes the star to move more or less horizontally to the right in the HR-diagram (Fig. 1) in all cases except C. Weiss & Ferguson (2009) obtained a similar migration to the right using the GARSTEC code (described in Weiss & Schlattl 2008) with Astronomy & Astrophysics manuscript no. evol c ESO 2009 the mass-loss formula by Wachter! et al. (2002) and the opacities MarchFig. 22, 1. 2009Luminosity-temperature diagram (cf. HR-diagram) for Model A-D. All tracks are plotted starting from theMass ZAHB. loss ofand Marigo (2002). opacities In their model, no superwind in developsAGB as in stars our case D, but as mass is eventually lost, the star will start to ex- LMattson,   E Herwig,Hoefner,pand rapidly. In case C, which Wahlin, is similar to the Lederer, models by Weiss Paxton compare the results obtained using the new opacities and mass- & Ferguson (2009), this point has not yet been reached. loss prescription, described in the previous section, with a track As previously argued by Mattsson (2008),ε ˜C, i.e., the abun- mass loss vs. age Effectscomputed using of Carbon-excess the opacities by Alexander Dependent & Ferguson (1994) Massdance Loss of carbon and available Molecular for dust formation, is a more decisive and the mass-loss formula by Bl¨ocker (1995). The following for Opacities on Models of C-starquantity Evolution than the C/O-ratio for the onset of strong dust-driven cases are considered: mass loss. As shown in Fig. 2 (middle panels),ε ˜C continues L. Mattsson1!, F. Herwig2, S. H¨ofner1, R. Wahlin1, M. Ledererto grow3, and with B. Paxtonevery thermal4 pulse, while C/O levels out due to A Mass loss according to Bl¨ocker for both M-star phase and the increasing dredge-up of oxygen. Since the mass-loss rate de- C-star phase. Low-temperature opacities by Alexander & 1 pend steeply onε ˜ in case B and D (see ? for further details), Dept.Ferguson Physics and (1994) Astronomy, without Div. ofdependence Astronomy and on Space the carbon Physics, Uppsala excess. University, Box 515, SE-751 20C Uppsala, Sweden 2 Dept. Physics and Astronomy, University of Victoria, PO Box 3055, STN CSC, Victoriawe BC have V8W a 3P6, run-away Canada process: with each thermal pulse more car- 3 BDept. Mass of Astronomy, loss according University to of Bl¨ Vienna,ocker T¨ forurkenschanzstrasse M-star phase 17, and A-1180, accord- Vienna,bon Austria is dredged up, which increases the carbon excess and hence 4 Kavliing Institute to Mattsson for Theoretical et al. Physics, (2009) University for the of C-star California, phase, Santa and Barbara, low- CA 93106,also theUSA mass-loss rate, that in turn limits the number of thermal temperature opacities as in A. Received date; accepted date pulses by terminating the AGB. C Mass loss as in A, but the new low-temperature opacities as described in Sect. 2.3. ABSTRACT D Mass loss as in B and low-temperature opacities as in C, i.e., “forward- We present models of stellar evolution for a 2M -star of initial metallicity Z = 0.01 (scaled solar), with focus on the carbon-star (C-star)the phase new in opacities particular, and the eff theects new of increasing mass-loss" carbon prescription excess on mass imple- loss and molecular4. Conclusions opacities. We employ a new, state- of-the-artmented theoretical simultaneously. mass-lossL. prescription Mattsson for dust-driven et al.: E winds,ffects which of Carbon-excess takes the effects of the Dependent carbon excessmodeling” into Mass account, Loss and and we Molecular Opacities 3 implement a set of composition-dependent molecular opacities, which incorporates theWe changes have due found to the that evolution including of the carbon the dependence on the carbon ex- excess.We note We that find that introducing the development the new of the composition-dependent carbon excess is controlling opac- much of thecess carbon-star of opacities evolution.superwind?!! and A very mass pronounced loss during the C-star phase, may superwindities, as forms in case and the C termination and D, leads of the AGB to significantly happens soon after lower the star eff becomesec- have carbon very rich, insignificant fact, after only effects a few on thermal the evolution. The new opacities pulses. The superwind develops as a consequence of the carbon-excess dependence included in the newWithin mass-loss prescription less than in 200 Myr from the onset of the superwind, combinationtive temperatures with the lower compared effective temperature to case (which A andfavours B mass (see loss) Fig. obtained 2). withleads the new to opacities.lowerhalf e offf Theective the superwind stellar temperatures, does mass not which is lost is in consistent case D with (see Fig. 2, lower right ariseThis immediately, is consistent since with the star previous has to become results suffi (see,ciently e.g., carbon-rich Marigo and, 2002, at the sameother time, studies have a low (Marigo enough temperature. 2002, Marigo The 2007), and the new mass- 8 5 mass-loss rate grows from M˙ 102 − up to M˙ 10− , while the carbon excess grows by a factor of fourpanel). and the temperature We note drops that by the AGB will probably be terminated even Weiss & Ferguson 2009)∼ . The C/∼O-ratio is also showing a loss prescription/code by Mattsson et al. (2009) in combination closeslightly to 1000 slower K. We increase, conclude that compared this is the probable to the tracksexplanation with for Alexander the origin of the C-starwith superwind. thesebefore opacities the lead next to the thermal formation pulse. of a very Hence pronounced the model star experiences Key& Ferguson words. Stars: (1994) AGB andopacities, post-AGB but – Stars: the di atmospheresfference is– Stars: not significant. carbon – Stars: masssuperwind, loss – Hydrodynamicsonly due to a which few – Radiative thermal the transfer number pulses of thermal as C-star. pulses and We as- note also that in the The overall luminosity evolution is similar for all four cases. sociated dredge-upbeginning events of the is very C-rich limited.Fig. phase The 2. nucleosynthetic theEvolution mass-loss on the rate TP-AGB, drops starting signifi- at the peak of the first thermal pulse. Top panels: luminosity (left) and effective temperature(right). Regarding the mass-loss evolution, we see a dramatic yields are thus probably lower comparedMiddle to many panels: previous C mod-/O-ratio (left) and carbon excess (right). Lower panels: mass-loss rate (left) and current stellar mass (right). 1. Introduction ment is important, since forcantly, C-stars, the but duration then of rapidly the AGB evolves into a superwind. In case B the change. In case D, a very pronounced superwind developsphase and as the the numberels of of C-star thermal evolution, pulses is almost but this solely needs deter- to be verified. Stellarcarbon evolution excess models increases. contain In uncertainties fact, the mass-loss due to input ratemined becomes by the so mass-lossOur rate. stellar Thesuperwind evolution evolution of has the sequence internal not struc-yet with beenab initio reachedinput physics after five thermal pulses, physicshigh that, that for thepractical average reasons, time need step to drops be prescribed three orders rather ofture magnitude also depends onis thereproducing mass-losswhich (Bl¨ theocker is superwind due 1995), to which a quantitatively combination in turn References in the of amounta slower ob- decrease in effective Cox J.P. & Giuli R.T., 1968, ”Principles of Stellar Structure”, New York, Gordon than computed simultaneously. Mass-loss on the AGB is a affects the fundamental stellar parameters. Since the5 mass-loss4 2 and appears to continue to drop. We have therefore not contin- served masstemperature loss (M˙ = 10 and− a10 steep− M dependenceyr− ). Extrapolating of mass the loss on temperature & Breach. process that is of great importance for stellar evolution mod- rate depends on these stellar parameters, there will− be a feed-" Alexander D.R. & Ferguson J.W., 1994, ApJ, 437, 897 els, butued is any usually of the implemented tracks beyond by some a few simple thermal empirical, pulses in the C-star mass loss to the end of the end of the AGB (by looking at the Ferguson J.W., Alexander D.R., Allard F., et al., 2005, ApJ, 623, 585 regime, since the drop in the time step needs to be investigatedback, which means that theaccording mass-loss prescription to Mattsson put into et a Bl¨ al.ocker (2009). T., 1995, The A&A, origin 297, of 727 the superwind semi-empirical or theoretical formula. The mass loss of AGB stellar evolution modelremaining is critical. mass In in particular, case D) since will the bring mass- us up to the observed level Herwig, F., 2000, A&A, 360, 952 in the model5 is2 due to theBowen combination G.H., 1988, of ApJ, low 329, effective 299 tempera- starsmore is thought in detail to be and driven the by numerics radiation of pressure the code on dust- may needloss rate modifi- is foundof to a increase few times significantly 10− M withyr− the. The carbon mass-loss ex- rate in the beginning " grainscation. in the outer The stellar time step atmospheres. drops significantly Various mass-loss in case for- Bcess as well, (Mattsson as etof al. 2008),the C-star eachtures thermal phase and drops pulse a carbon-excess and to acorrespond- very low level dependent (see Fig.2, mass-loss lower rate. mulaesoon/recipes as have a strong been used wind previously, begins to e.g., develop, a scaled Reimers-although noing such dredge-up pro- eventleft will panel), take a but C-star then closer rises to over the terminationroughly three orders of magnitude, law (Reimers 1975) was used by van den Hoek & Groenewegen of the AGB. This will lead to a mechanismThe8 relatively that is limiting5 rapid the decline in temperature (again, see Fig. nounced superwind as in case D seems to be developing at this from M˙ 10− up to M˙ 10− , while the carbon excess grows total (1997), while Karakas & Lattanzio (2007) used the formula by amount of carbon and other∼2) nucleosynthesis causes the products∼ star of AGBto move more or less horizontally to the Vassiliadisstage, & which Wood (1993), one can and expect Herwig due (2002; to the 2004) higher used e theffective tempera- by a factor of four. ture of the star (an effect of the opacities). stars, most notably the s-processright elements, in the that HR-diagram can be expelled (Fig. 1) in all cases except C. Weiss & theoretical prescription by Bl¨ocker (1995), derived from early by a carbon star. mass vs. wind models by Bowen (1988). Recently, Weiss & Ferguson The implementation of opacitiesFerguson that depend (2009) on the obtained chemi- a similar migration to the right using 2 Note that Rosseland mean opacities are used. Since the diffusion Acknowledgements. MTL has been supported by the Austrian Academy of (2009) made use of the theoretical formula by Wachter et al. cal composition of the star (which changes as the star evolves) Sciences (DOCthe programme) GARSTEC and acknowledges code (described funding by the in Austrian Weiss Science & Schlattl 2008) with age (2002),approximation which is probably does more not apply realistic. to the surface layers, it is unclearcan aff howect the structure and surface temperature significantly. Mattssoneffective et temperature al. (2009) have is aff recentlyected quantitatively. made an effort to de- Fund FWF (projectthe mass-loss P-18171). formula by Wachter et al. (2002) and the opacities Fig. 1. Luminosity-temperature diagram (cf. HR-diagram)Marigo (2002) for and Model Marigo & Girardi (2007) have shown that us- termine how the mass loss of carbon-rich AGB stars (C-stars) ing composition-dependent opacitiesof Marigo leads to an (2002). improvement In their of model, no superwind develops as in A-D.depends All on tracks stellar are parameters, plotted using starting a state-of-the-art from the ZAHB. wind the agreement between models and observations (e.g., colours, 8 model including time-dependent dust formation and frequency- initial-final mass relation, C-starour luminosity case D, functions but as massetc.) but is eventually lost, the star will start to ex- dependent radiative transfer. That work has provided a new also to significantly lower effpandective temperatures, rapidly. In compared case C, to which is similar to the models by Weiss mass-loss prescription, which includes steep dependences on earlier work. Since the mass-loss rate depends steeply on the ef- 1 compareFig.theWednesday, carbon 2. Evolution excess the March results, and e on31,ffective obtained the2010 temperature, TP-AGB, using as starting wellthe as new mass- at opacities thefective peak temperature, of and the mass- first i.e., sincethermal& dust Ferguson formation pulse. Top is (2009), inhibited panels: by this too luminosity point has (left) not yet and been effective reached. temperature(right). lossMiddleloss thresholdsprescription, panels: (see C also/O-ratio described Mattsson (left) et al. in 2007). and the carbon previous This improve- excess section,high (right). temperatures with Lower a track in panels: the atmosphere, mass-lossAs a previously lower rate effective (left) arguedtemper- and current by Mattsson stellar mass (2008), (right).ε ˜ , i.e., the abun- ature will affect mass loss favourably. Hence, in order to get a C computedSend offprint requests using to: the Lars Mattssonopacities by Alexander &correct Ferguson picture (1994) of the mass-lossdance and late of stages carbon of C-star available evo- for dust formation, is a more decisive and! e-mail: the [email protected] formula by Bl¨ocker (1995). The following for 1 quantity than the C/O-ratio for the onset of strong dust-driven ReferencesCarbon excess is here defined asε ˜C εC εO. Cox J.P. & Giuli R.T., 1968, ”Principles of Stellar Structure”, New York, Gordon cases are considered: ≡ − mass loss. As shown in Fig. 2 (middle panels),ε ˜C continues to grow& with Breach. every thermal pulse, while C/O levels out due to AAlexander Mass loss D.R. & according Ferguson J.W., to Bl¨ 1994,ocker ApJ, for 437, both 897 M-star phase and Ferguson J.W., Alexander D.R., Allard F., et al., 2005, ApJ, 623, 585 Bl¨ocker T., 1995, A&A, 297, 727 the increasing dredge-up of oxygen. Since the mass-loss rate de- C-star phase. Low-temperature opacities by Alexander & Herwig, F., 2000, A&A, 360, 952 Bowen G.H., 1988, ApJ, 329, 299 pend steeply onε ˜C in case B and D (see ? for further details), Ferguson (1994) without dependence on the carbon excess. we have a run-away process: with each thermal pulse more car- B Mass loss according to Bl¨ocker for M-star phase and accord- bon is dredged up, which increases the carbon excess and hence ing to Mattsson et al. (2009) for the C-star phase, and low- also the mass-loss rate, that in turn limits the number of thermal temperature opacities as in A. pulses by terminating the AGB. C Mass loss as in A, but the new low-temperature opacities as described in Sect. 2.3. D Mass loss as in B and low-temperature opacities as in C, i.e., the new opacities and the new mass-loss prescription imple- 4. Conclusions mented simultaneously. We have found that including the dependence on the carbon ex- We note that introducing the new composition-dependent opac- cess of opacities and mass loss during the C-star phase, may ities, as in case C and D, leads to significantly lower effec- have very significant effects on the evolution. The new opacities tive temperatures compared to case A and B (see Fig. 2). leads to lower effective temperatures, which is consistent with This is consistent with previous results (see, e.g., Marigo 2002, other studies (Marigo 2002, Marigo 2007), and the new mass- Weiss & Ferguson 2009)2. The C/O-ratio is also showing a loss prescription/code by Mattsson et al. (2009) in combination slightly slower increase, compared to the tracks with Alexander with these opacities lead to the formation of a very pronounced & Ferguson (1994) opacities, but the difference is not significant. superwind, due to which the number of thermal pulses and as- The overall luminosity evolution is similar for all four cases. sociated dredge-up events is very limited. The nucleosynthetic Regarding the mass-loss evolution, we see a dramatic yields are thus probably lower compared to many previous mod- change. In case D, a very pronounced superwind develops as the els of C-star evolution, but this needs to be verified. carbon excess increases. In fact, the mass-loss rate becomes so Our stellar evolution sequence with ab initio input physics high that the average time step drops three orders of magnitude is reproducing the superwind quantitatively in the amount ob- 5 4 2 and appears to continue to drop. We have therefore not contin- served mass loss (M˙ = 10− 10− M yr− ). Extrapolating the ued any of the tracks beyond a few thermal pulses in the C-star mass loss to the end of the end− of the" AGB (by looking at the regime, since the drop in the time step needs to be investigated remaining mass in case D) will bring us up to the observed level 5 2 more in detail and the numerics of the code may need modifi- of a few times 10− M yr− . The mass-loss rate in the beginning cation. The time step drops significantly in case B as well, as of the C-star phase drops" to a very low level (see Fig. 2, lower soon as a strong wind begins to develop, although no such pro- left panel), but then rises over roughly three orders of magnitude, 8 5 nounced superwind as in case D seems to be developing at this from M˙ 10− up to M˙ 10− , while the carbon excess grows stage, which one can expect due to the higher effective tempera- by a factor∼ of four. ∼ ture of the star (an effect of the opacities).

2 Note that Rosseland mean opacities are used. Since the diffusion Acknowledgements. MTL has been supported by the Austrian Academy of approximation does not apply to the surface layers, it is unclear how the Sciences (DOC programme) and acknowledges funding by the Austrian Science effective temperature is affected quantitatively. Fund FWF (project P-18171). Rotation and magnetic4 fields Suijs et al.: White dwarf spins

lar momentum transport has been shown by Zahn et al. (2007) to be more complex than in the picture of Spruit (2002). Also, • Rotation in 1D stellar evolution, Yoon et al. (2008) find strong poloidal fields may be generated by convective cores, and suggest that their influence on angu- e.g. Maeder & Meynet, Heger etal, lar momentum transport may be comparable to that of the fields Langer etal. suggested by Spruit. • plus magnetic fields, e.g. Taylor & Spruit dynamo, questioned by 5. Conclusions Zahn etal (2007) While nature may be more complex, it is worthwhile to attempt to understand the spins of compact stellar remnants with a sin- gle theoretical approach for all initial masses. We showed above that angular momentum transport through rotationally induced Compare to observations in late magnetic fields according to Spruit (2002) provides a major im- phases: provement of the predicted spins of white dwarfs and neutron stars. Magnetic angular momentum transport appears also the • Rotation rates of neutron stars most promissing candidate to bridge the still existing gap be- and white dwarfs tween observed and predicted white dwarf spins at low mass (see Fig. 5). Fig. 5. Average core specific angular momentum of our initial • Implications from nucleosynthesis, If internal magnetic torques in their progenitors are indeed and final models (cf. Table 1 and Fig.Suijs 4), versus etal initial (2008) stellar resopnsible for the slow rotation of compact stars in the Milky e.g. s-process in TP-AGB stars mass (full drawn lines). Points for 15 M stars computed with ! Way, then there may be little room for an important role of angu- the same physics from Heger et al. (2005) have been added. The (Herwig etal 2003) lar momentum in their formation process, at least in single stars. upper line corresponds to the initial models. Filled triangles cor- This may have implications for understanding the progenitors responds to the final models of the non-magnetic sequences, and and the formation meachanism of magnetars (Sawai et al. 2008) filled squares to the final models of the magnetic sequences. The and long gamma-ray bursts (Woosley and Bloom 2006). “Seismic evidencedashed for horizontal the loss line of indicates stellar the angular spectroscopic upper limit on momentum beforethe white the dwarf white-dwarf spins obtained stage” by Berger et al. (2005). Star sym- Acknowledgements. AH performed this work under the auspices of the National bols represent astroseismic measurements from ZZ Ceti stars Nuclear Security Administration of the U.S. Department of Energy at Los Charpinet, S.; Fontaine,(Bradley 1998, G.; 2001; Brassard, Dolez 2006; P., Nature, Handler 2001, 2009. Handler et al. Alamos National Laboratory under Contract No. DE-AC52-06NA25396, and 2002, Kepler et al. 1995, Kleinmann et al. 1998, Winget et al. was supported by the DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DE-FC02-01ER41176). 1994), where smaller symbols correspond to less certain mea- surements. The green hatched area is populated by magnetic white dwarfs (Ferrario & Wickramasinghe 2005; Brinkworth9 et References al. 2007). The three black open pentagons correspond to the youngest Galactic neutron stars (Heger et al. 2005), while the Berger, L., Koester, D., Napiwotzki, R., Reid, I. N., Zuckerman, B., 2005, Wednesday, March 31, 2010 A&A, 444, 565 green pentagon is thought to roughly correspond to magnetars Bradley, P. A., 1998, ApJS 116, 307 (Camilo et al. 2007), where the vertical dotted green line indi- Bradley, P. A., 2001, ApJ 552, 326 cates the possibility that magnetars are born with higher core Brinkworth, C.S., Burleigh, M.R., Marsh, T.R., 2007, in: 15th European angular momentum. Workshop on White Dwarfs, ASP Conference Series, Vol. 372, San Francisco, Ralf Napiwotzki and Matthew R. Burleigh, eds., p.183 Camilo, F., Ransom, S.M., Halpern, J.P., Reynolds, J., 2007, ApJ, 666, L93 Charbonnel, C., Talon, S., 2005, Science, 309, 2189 Dolez N., Vauclair, G., Kleinman, S. J., et al., 2006, A&A 446, 237 In the first case, one may speculate whether the situation in Eggenberger, P., Meynet, G., Maeder, A., 2005, A&A, 440, L9 Ferrario, L., Wickramasinghe, D. T., 2005, MNRAS, 356, 615 analogous to the neutron star case: for pulsars it is well known Hamada, T., Salpeter, E.E., 1961, ApJ, 134, 683 that they spin down with time. As the ZZ Ceti stars have a cool- Handler, G., 2001, MNRAS, 323, L43 ing age of about 109 yr, they might have lost angular momen- Handler, G., Romero-Colmenero, E., Montgomery, M. H., 2002, MNRAS, 335, tum on their cooling track. However, estimating the spin-down 399 − 1 1 Heger, A., Langer, N., & Woosley, S.E., 2000, A&A, 2000, ApJ, 528, 368 ˙ 2 4 time through a magnetic wind by τ1 = M (M/BR)(2GM/R) Heger, A., Woosley, S.E., & Spruit, H.C., 2005, ApJ, 626, 350 (Justham et al. 2006) would allow for a significant effect at most Justham, S.; Rappaport, S.; Podsiadlowski, P., 2006, MNRAS, 366, 1415 in strongly magnetic white dwarfs, and spin-down through elec- Kawaler S.D., 2004, in: IAU-Symp. No. 215 on “Stellar Rotation”, A. Maeder 3 2 2 4 and P. Eenens, eds, ASP, p. 561 tromagnetic radiation, with τ2 = Mc /(B Ω R ) is always in- significant. In the above expressions, M, R, Ω and B are white Herwig, F., Langer, N., Lugaro, M., 2003, ApJ, 593, 1056 Kepler, S.O., Giovannini, O., Wood, M.A., et al., 1995, ApJ 447, 874 dwarf mass, radius, surface magnetic field strength and spin fre- Kleinman, S. J.; Nather, R. E.; Winget, D. E., et al., 1998, ApJ 495, 424 quency. Langer, N., El Eid M.F., Fricke K.J., 1985, A&A, 145, 179 In the second case, perhaps an additional internal angular Langer, N., Heger, A., Wellstein, S., Woosley, S.E., 1999, A&A, 346, L37 momentum transport mechanism in white dwarf progenitors is Maeder, A., Meynet, G., 2000, ARAA, 38, 143 Maeder, A., Meynet, G., 2005, A&A, 440, 1041 required. While transport through gravity waves has been sug- Motz, L., 1952, ApJ, 115, 562 gested as such (Zahn et al. 1997), we point out that, for stars Ott, C. D.; Burrows, A.; Thompson, T. A.; Livne, E.; Walder, R., 2006, ApJS, above ∼ 1.3M!, the core spin-down is likely to occur during 164, 130 the post-main sequence evolution, since on the main sequence Palacios, A., Talon, S., Charbonnel, C., Forestini, M., 2003, A&A, 399, 603 Palacios, A., Charbonnel, C., Talon, S., Siess, L., 2006, A&A, 453, 261 these stars are still rapid rotators. It is unclear at present whether Petrovic, J., Langer, N., Yoon, S.-C., Heger, A., 2005, A&A, 435, 247 gravity waves can transport angular momentum through the shell Reimers, D., 1975, Mem. Soc. Liege, 8, 369 source in the giant stage. On the other hand, the magnetic angu- Sawai, H.; Kotake, K.; Yamada, S., 2008, ApJ, 672, 465 1064 HERWIG, LANGER, & LUGARO1066 Vol. HERWIG, 593 LANGER, & LUGARO Vol. 593 plateau between 0.741 and 0.746 M . This region contains exposure in the s-process layer is higher than in models that 5.3. Neutron Production for the s-Process in the !

¼ ,-./0 efficiency derived from convective core overshoot of main- # include all theAt species 0:0034 and the reactions He flash needed convection to study zone the has formed, sequence stars. The effective mass of the partial mixing zone s-process. Asand initial the¼ mass conditions layers covered we use bythe convection thermodynamic are spun up. At where the neutrons are efficiently released is confined within and abundancethis time profiles the from He flash the convectionstellar evolution zone reaches model at up to mass " the region where the proton abundance follows the end ofcoordinate the third dredge-up 0.745 M . phaseBetween after this the and TP. the following These profile 2 < log X < 3 (for an intershell 12C mass fraction of p profiles areat mapped 0:0037 to the the equidistant, He flash convection Lagrangian zone postpro- reaches its fullest À20%; GorielyÀ & Mowlavi 2000). According to this crite- ¼ ! cessing gridextent and up then to evolved 0.746 M according(just below to the the stellar location of the !'(%&) !'(%&)& !'(%&* !'(%&*& !'(%+ !'(%+!& !'(%+" rion the mass of the s-process layer computed with structure modelsH-burning at shell a series before of the times TP). throughout In addition, the the intershell 7 89 f 0:016 is only 10 6 M , which is much smaller than 1 5:; À interpulse phase.region is expanding because of the energy provided by the required¼ (see 2).  x We startHe the flash. simulation This leads with to the a reduction partially of mixed the angular H/12C velocity in Fig. 8.—Evolution of mixing coefficient due to rotationally induced However, one overshoot efficiency parameter will not the4 intershell. This effect is still present at  0:0087, until mixing during the interpulse phase; labels give interpulse phase zone of 10À M that has formed at the end of the third apply to all convective boundaries during all evolutionary  contraction resumes and the angular velocity¼ in the  t t0 =Dt, where the previous pulse, i.e., the maximum He-burning dredge-up phase as a result of time- and depth-dependent luminosity,¼ð À Þ has occurred at t ; the interpulse period is Dt 3 104 yr. Two phases. After Shaviv & Salpeter (1973) first considered the intershell region increases accordingly (profiles  0:0122– 0 ¼  hydrodynamic overshoot (top panel, Fig. 6). In this model¼ different mixing periods resulting from rotation occur in the partial mixing possibility of the convective overshoot, several studies have no mixing0.1706). takes place The during angular the velocity interpulse profiles phase. at later In the times show zone during the interpulse period (see text). used a very simple prescription in which convective mixing • Implications from nucleosynthesis, middle panelRotationagain of Figure the formation 6 the 13C ofand neutron a plateau source between has started 0.746 and 0.749 was treated instantaneously and overshoot was simply a M , where the H shell is now located,13 because of depositione.g. s-process in TP-AGB stars releasing neutrons, and up to 10% of the C abundance has In Table 2 we give the mixing properties in the partial matter of extending the instantaneously mixed region by been consumed.of H-shell In the ashes upper on part top of of the the partial core. mixing zone, some fraction of the pressure scale height. In this approxi- (Herwigmixing etal 2003) zone at three different times: an early phase soon where 14magneticN dominates,From the the evolution majority fields of of neutrons the angular are velocity absorbed in rotating mation main-sequence core overshoot should extend by 14 TP-AGB14 stars we can anticipate the following mixing prop- after the pulse, a phase just before the release of neutrons by the N(n, p) C reaction. This can be seen from the pro- 13 about 0.2Hp (see, e.g., Schaller et al. 1992 and references 14 erties. Efficient shear mixing will take place6 at 3 0.746 M starts, and a phase after the neutron source C is exhausted. file of C. The maximum neutron density is 5:7 10 cmÀ therein). Alongi et al. (1991) argued that overshoot of 0.7Hp after the formation of the large angular velocity gradient. below the envelope of red giant stars could align the location This gradientno formsrotation because two convective regions extend with rotation of luminosity bump with observations. The two-dimen- * to these mass coordinates from below and above in short ! sional radiation hydrodynamic simulations by Freytag et al. !) succession. The He flash convection first taps the reservoir =" (1996) have shown that the shallow surface convection zone !( of high angular momentum in the core. Then the convective =# of white dwarfs has exponential overshoot mixing according !' envelope establishes contact between the fast-rotating inter- =$ to an overshoot parameter of f 1:0, while the convection !& shell and the slow-rotating envelope. At this interface rota- =% zone simulation of A stars shows¼f 0:25. For the oxygen- !% tionally induced shear mixing will be most efficient in acting =& burning layer in presupernova models,¼ Asida & Arnett !$ on abundance gradients. The timescale to establish a partial =+ ,-../01-23456/7589:; < 12 7>55/?1>42@-;/,-.ABC D (2000) found perturbations of the stable layers reaching 1Hp !# )(mixing zone of hydrogen and C as needed for the forma- =( "# !/7589? by two-dimensional hydrodynamical computations by Correspondingly, two mixing periods during the inter- ,-.ABCF/,-.AG Deupree (2000), who showed that the core overshoot dis- !# pulse phase resulting from rotation can be distinguished, as =( !1; ! during the third¼ dredge-up phase. This has no major effect " *+$ log D 5 (in cgs units), but decreasing rapidly at a time- !'+ on the properties of the models, other than stretching the r  13 14 *+& scale of 1000 yr. However, after the TP the mass gradient !'% partial mixing zone and, consequently, the C and N pro- in the partial mixing zone increases steadily as the intershell files in that layer over a larger mass range. The peak neutron *+( layers contract and evolve toward a preflash structure. For !'# exposure and the s-process abundance distribution in the !term of! spherical harmonics nodes) presently achieved ing stars. They affect their surface velocities and chemical abun- in global numerical simulations. Giant Star. I. Three-dimensional Models of dances, and change their paths across the colour-magnitude dia- gram (Maeder & Meynet 2000b; Maeder 2009). They also mod- Turbulent Convection and Associated Mean ify the internal structure of stars in a way that we will soon be bulent motions in the vertical direction. This leads to a strongly able to test thanks to asteroseismology over a broader range of anisotropic“Secular turbulent hydrodynamic transport that is more processes efficient in the in hor- Flows” Brun & Palacios, 2009 evolutionary phases. izontal direction (along isobars) than in the vertical one. As a In this paper we present a set of diagnosis tools adapted to the result,rotating the horizontal stars” gradients Decressin of all scalar et fields al (temperature, (2009) analysis of stellar evolution with rotation, and use them to com- angular velocity. . . ) are much smaller than their vertical gradi- pare the efficiency of different transport processes. The present ents, which allows their expansion in a few spherical harmonics. study focuses on “type I rotational transport”, where magnetic This scale separation, both in space and in time, is illustrated in fields and waves are not accounted for, and where the angular Fig. 1. momentum and the nuclides are both transported exclusively by Considering the axisymmetric case, each scalar field is thus 11 meridional circulation and shear-induced turbulence. These di- written as the sum of its horizontal average on an isobar, and its agnosis and tools rely on a specific expansion of the equations associated fluctuation, which is expanded the Legendre polyno- Wednesday, March 31, 2010 for the transport of angular momentum, heat and chemicals that mials basis P#(cos θ), up to some maximum order #th. For sim- are briefly recalled in § 2. In § 3, we validate our method by plicity’s sake, we shall present here the results keeping a single applying our tools to two specific stellar models for which the scale # = 2, that is dominant. Let us note that there are circum- hydrodynamics has already been extensively studied in the liter- stances where we have to include many more components, for ature. Conclusions and perspectives are presented in § 4. instance when dealing with magnetic fields. The unresolved scales intervene in the turbulent transport, for which a prescription is applied that is derived, whenever pos- 2. Modelling the secular processes sible, from laboratory experiments or numerical simulations, and if not through phenomenological considerations. 2.1. Scale separation

To simulate in full detail the dynamical processes in a star, would 2.2. Linearization and expansion in spherical harmonics require to include length-scales and time-scales spanning many orders of magnitude. This is clearly not feasible, even with the Let us briefly recall how these expansions are performed in prac- most powerful computers. Either one chooses to describe what tice; for more details we refer the reader to Mathis & Zahn occurs on a dynamical time-scale, such as a convective turnover (2004) and Maeder (2009). We begin with the macroscopic ve- time, or one focuses on the long time evolution, as we shall here, locity field, which is split in 3 components: where the typical time is either the Kelvin-Helmholtz time or V = r sin θ Ω (r, θ) eϕ + r˙ er + M (r, θ) . (1) that characterizing the dominant nuclear reactions. The same U is true for the length-scales, at least in the vertical direction, 1 2 3 ! ! where we shall take the resolution which represents adequately Term 1 represents" the#$ azimuthal% "#$% velocity" field#$ associated% with the steepest gradients that develop during the evolution. the differential!!!!!!!!!!!!!! rotation.!!!!!!!!!!!!!! Term 2 corresponds!!!!! !!!!! to the radial The situation is somewhat different in the horizontal direc- Lagrangian velocity due to the structural readjustments of the tion – i.e. in latitude, since we consider here only the axisym- star during its evolution. Term 3 is the meridional circulation metric case. Stellar radiative zones are stably stratified regions, velocity field. ek where k = r, θ, ϕ are the unit vectors in the and the buoyancy, which is the restoring force, acts to inhibit tur- radial, latitudinal and azimuthal{ directions.} ! – 21 –

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Busso, M., Gallino, R., Lambert, D. L., Travaglio, C., & Smith, V. V. 2001, ApJ, 557, 802

Calder, A. C., Fryxell, B., Plewa, T., Rosner, R., Dursi, L. J., Weirs, V. G., Dupont, T., Robey, H. F., Kane, J. O., Remington, B. A., Drake, R. P., Dimonte, G., Zingale, M., Timmes, F. X., Olson, K., Ricker, P., MacNeice, P., & Tufo, H. M. 2002, ApJS, 143, 201 –3– Campbell, S. W. & Lattanzio, J. C. 2008, A&A, 490, 769

of highly exothermicStellar nuclear evolution reaction and the convectivein theCassisi, fluidearly S., flow Iben, timeUniverse I. J., scales & Tornambe, are of the A. same1998, ApJ,order. 496, 376

The ratio of the mixing time scale and the reactionColella, time scale P. & Woodward, is called the P. R.Damköhler 1984, Journal number: of Computational Physics, 54, 174

τDillmann,mix I., Heil, M., Käppeler, F., Plag, R., Rauscher, T., & Thielemann, F.-K. 2006, in American Institute Dα = . (1) τreact of Physics Conference Series, Vol. 819, Capture Gamma-Ray Spectroscopy and Related Topics, ed. A. Woehr & A. Aprahamian, 123–127 MLT is concerned with averaged properties both in time over many convective turn-overs and in space over the order of a pressure scale height. In the categoriesDimotakis, of Dimotakis P. E. 2005,(2005) Annu. diffusion Rev. Fluid coeffiecients Mech., 37, derived 329 from MLT may describe level-1 mixing (while mixing induced by rotation involves flow dynamics that Duerbeck, H. W., Liller, W., Sterken, C., Benetti, S., van Genderen, A. M., Arts, J., Kurk, J. D., Janson, M., are altered by mixing processes and labeled in this scheme asVoskes, level-2 T., mixing). Brogt, E., Therefore,Arentoft, T., time-dependent van der Meer, A., & Dijkstra, R. 2000, AJ, 119, 2360 mixing through• D aα diffusion <<1: fully algorithm mixed withburning, diffision MLT coefficients appropriate derived from MLT is appropriate for regimes with D 1.• D Theα ~1 difficulty : combustion of simulating regime, convective-reactive MLT and 1D spherical phases symmetry in present one-dimensionalassumption stellar α ! inappropriate evolution codes then appears as the inability of MLT (or any similar convection theory) to properly account • combustion in low- and zero-metallicity stars common, inlcuging both low- for the additionalmass dynamic and massive, effects introduced rotating and through non-rotating rapid and dynamicallystars relevant nuclear energy release in level-3 mixing associated with Damköhler numbers D 1. • examples of papers which have not observedα ≈ this physics requirement: e.g. Convective-reactiveHerwig etal episodes 1999, canHerwig be encountered 2001 plus ca. in numerous10-20 since phases then. of stellar evolution, including the He-shell flash• check of AGB our poster stars of and extremely arXiv:1002.2241 low metal content for details (e.g. Fujimoto et al. 2000; Iwamoto et al. 2004), the He-core flash in extremely low metallicity low-mass stars (e.g. Hollowell et al. 1990; Schlattl et al. 2002; Campbell & Lattanzio 2008), young white dwarfs of solar metallicity (e.g. Iben et al. 1983; Herwig et al. 1999; Lawlor & MacDonald 2003, and others), both rotating and non-rotating Pop III massive stars (Ekström et al. 2008) and more in general low metallicity massive stars (Woosley & Weaver 1995), the X-ray burst in accreting neutron stars (Woosley et al. 2004; Piro & Bildsten 2007), and accreting white dwarfs (Cassisi et al. 1998) that may be the progenitors of SN Ia. Convective-reactive events have12 been found in post-RGB stellar evolution models and associated with the horizontal branch anomalies in certain Wednesday,globular March 31, clusters 2010 (Brown et al. 2001; Miller Bertolami et al. 2008). Finally, again in AGB stars convective- reactive phases can be found in hot dredge-up (Herwig 2004; Goriely & Siess 2004; Woodward et al. 2008), a phenomenon that is associated with the treatment of convective boundaries, generally in more massive and lower metallicity AGB stars.

Although convective-reactive phases are quite common in stellar evolution, in particular in the early, low-metellicity Universe, we do not currently have a reliable and accurate way of simulating them. In this work we discuss the case of the He-shell flash with H-ingestion in a very-late (post-AGB) thermal pulse at solar metallicity. This situation is extremely similar to H-ingestion associated with the He-shell flash in AGB stars at extremely low metallicity. The one-dimensional, spherically-symmetric stellar evolution approxi- mation is not very realistic in this case, because both the entrainment of H into the He-shell flash convection zone as well as the subsequent convective transport, mixing and nuclear burning of hydrogen enriched fluid parcels are inherently a three-dimensional hydrodynamic process. The energy from the 12C(p,γ)13N reac- tions is released on the same time scale ( 5min for T =1.5 109 K) of the fluid flow of convection, and ∼ × this energy will add entropy to fluid elements and in turn feedback into the hydrodynamics (Herwig 2001). These highly coupled, multi-dimensional processes are approximated in one-dimensional spherically sym- metric stellar evolution codes through mixing-length theory complemented with a time-dependent mixing algorithm, in our code as a diffusion process in which the abundances are treated as isotropic on spheres. MESA: modules for experiments in stellar evolution A new, modern, modular, open, fast community stellar evolution code 0 Minit=1.00 Sound Speed Comparison — Age 0.000 (seconds) Zinit=0.02 M=1.00 1 ! ! ! ! 001 ! . Y =0.275 0 mesa ! Z =0.019 BP98 0 ! # 1 # PMS of Brown dwarfs, VLM

! 000 0 τ = 10 0.9 .

# 0 99.99% 0.8 # and LM stars 99.9% " ! 1 0.7 99% − " !

! # 90% 001

L 0.6 " ! . Minit=1.00 / # 0 50% M 0.5 ! tot ! − # " ! 3 0.4 10 Z =0.02 # init log L 2 0.3 " − Sound Speed Comparison — Age 0.000 (seconds) # " 002 .

0.2 30 0 M=1.00 "

# − 0.15 "

" 100 : (mesa - data) / data

0.12 ff 3 D Depletion

− ! 0.1 003 7 300 . " Li Depletion 0.09 0 001 − # ZAMS. 0 0.08 mesa 4 relative di 004 . − 3.8 3.7 3.6 3.5 3.4 0 BP98 − log Teff 005 . 0

000 τ = 10 − MS to WD. through He-core flash < 1day on my laptop

0 0.1 0.2 0.3 0.499.99%0.5 0.6 0.7 0.8 0.9 4 R/R 99.9% ! Internal Structure:99% M=0.549, initial Z=0.02 3 90% 001 9 . 0 .

!" Total mass 1 0 # $ 50% Mtot Burning > 50 ergs/gm/sec

2 − Burning > 1000 ergs/gm/sec 8

H boundary (X 0.0001) 9

∼ .

He boundary (Y 0.0001) 0 ∼ Surface luminosity H burning luminosity 7

He burning luminosity 8 1 % . &'( 0 ) Convective mixing 002 6 sun . 7 . 0 0 0 − 5 log L/L 6 . 0 ! : (mesa - data) / data ! -1 L / 4 M ff 5 / . 0 m log L 003 3

-2 . 4 4 0 . . 0 0 − 2 3 -3 3 . . 0 M0.80 0 M1.00 M1.25 1 2 .

-4 0 relative di

5 004 4.8 4.6 4.4 4.2 4 3.8 3.6 3.4 0 . 0 log T 1 eff . 0 − 1 1Msun internal − 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 13 evolution model number 005 . Wednesday, March0 31, 2010 − 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 R/R ! MESA: modules for experiments in stellar evolution A new, modern, modular, open, fast community stellar evolution code 4 low-/intermediate 7.0 3 6.0 mass evolution 5.0 4.5 4.0 massive star evolution 3.5 2 ! 3.0 L / 2.7 0 . 1000 km/sec infall ! 2.3 10

log L 2.0 Si end! 1 5

1.8 . !Si start

9 O end ! 1.5 ! Ne end and O start ! ! Ne start 0 Y =0.28 . C end 1.2 9 Z =0.02 ! 0 C start 1.0 5

. ! 8 He end 25Msun

0.8 ! He start 0 . 8

4.4 4.2 4.0 3.8 3.6 ! H end log Central Temperature (K) ! log T 5 eff . H start C-star 7 0 1 2 3 4 5 6 7 8 9 10 2 2 3 formation log Central Density (gr cm− ) 1.8 1.8

1.6 1.6 on the 0 . 1000 km/sec infall !

1.4 10 1.4 AGB 1.2 Si end !

5 ! 1.2 . Si start 9 sun O end 1 ! /M C/O 1 r ! m ! Ne end and O start

0.8 0 Ne start 15Msun . C end 0.8 9 ! 0.6 !C start

0.6 5 0.4 . ! 8 He end 0.4 MESA pax2010: M tar 0.2 ! s He start

CO ratio 0 .

0.2 0 8 0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 !H end age/yr log Central Temperature (K) 5 ! . H start 7

0 1 2 3 4 5 6 7 8 9 10 3 log Central Density (gr cm− ) 14

Wednesday, March 31, 2010 MESA: modules for experiments in stellar evolution A new, modern, modular, open, fast community stellar evolution code

15

Wednesday, March 31, 2010 MESA: modules for experiments in stellar evolution A new, modern, modular, open, fast community stellar evolution code 10

9

MESA acknowledgements: 8 HELM MESA was written from 7 T scratch by Bill Paxton Some features: 6 (KITP/UCSB) with major log • versatile compilation of 5 OPAL 100M support from Lars Bildsten EOS, allowing VLM stars, ! 4 1.0M as well as the following ! brown dwarfs, degenerate 0.1M individuals: 3 SCVH ! stars 0.01M !

9 6 3 0 3 6 9 − − − ★ Frank Timmes • full coupling of mixing, burning and structure operators log ρ ★ Lorne Nelson • both hydrodynamic and hydrostatic option ★ Pierre Lesaffre • range of networks, including those needed for massive star collapse ★ Falk Herwig • convection MLT (different versions), overshooting, Ledoux criterion, semi- ★ Aaron Dotter convection ★ Don VandenBerg • mass transfer, accretion, mass loss, binary stars (Roche Lobe overflow) ★ Steinn Sigurðsson • several atmosphere options, including atmosphere tables, e.g. from Phoenix ★ Raphael Hirschi code ★ Jon Tomshine • verified (as in code comparison with established research codes) for low ★ Ed Brown mass stars, the sun, advanced phases (AGB), massive stars, including nucleosynthesis predictions • passed Stellar Code Calibration (Achim Weiss etal) project test cases • individual module level verification for eos, kap, atm, mlt by running in DSEP code and EVOL code • diffusion/gravitational settling via Thoul et al. (1994); recently verified against VandenBergʼs code with diffusion treated according to Michaud & Proffit. • pulsation module (LAWE according to Jørgen Christensen-Dalsgaard's ADIPLS, 1997) • thermohaline mixing • compatible with NuGrid nucleosynthesis codes. 16

Wednesday, March 31, 2010 NuGrid: Nucleosynthesis for a wide range of (M,Z) A new, parallel, comprehensive nucleosynthesis code for large-scale post-processing computations

17

Wednesday, March 31, 2010 NuGrid: Nucleosynthesis for a wide range of (M,Z) Application examples

25Msun nucleosynthesisStellar evolution 7

Ne C C Initial massHe = 25 Msun, Zini=0.01H -burning 1

0 16O 4He 20 Ne H -1 12C -2 28Si -3

-4 56Fe X (mass fraction) -5

-6 88Sr Z=0.01, 25Msun

-7

0 2 4 6 8 10 12 14 mass coordinate

FIG. 3.— [Credit: NuGrid collaboration] Abundance profiles of 25M stellar evolution model during Ne burning (burning zones are indicated at the top of the frame) according to full nucleosynthesis post-processing of massive star! stellar evolution models (Fig. 7) using a new parallel post-processing nucleosynthesis code (PPN). The same code can be used for low-mass stars as well and will consider automatically all possible reactions. It uses a continuously updated compilation of nuclear data compilations.

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Wednesday, March 31, 2010 NuGrid: Nucleosynthesis for a wide range of (M,Z) Application examples 2.0Msun nucleosynthesis

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Wednesday, March 31, 2010 NuGrid: Nucleosynthesis for a wide range of (M,Z) Application examples 2.0Msun nucleosynthesis

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Wednesday, March 31, 2010 NuGrid: Nucleosynthesis for a wide range of (M,Z)

NuGrid acknowledgements:

★R. Hirschi, M. Bennett (Keele University, UK) ★F. Herwig, M. Pignatari, William Hillary, Debra Richman, Aaron Dotter (University of Victoria, BC, Canada) ★C. L. Fryer, G. Rockefeller, A. Hungerford, Aaron Courture (Los Alamos National Laboratory, NM, USA) ★F. X. Timmes, P. A. Young (Arizona State University) ★Claudia Travaglio (Observatory of Torino, INAF) ★Bill Paxton (KITP, UC Santa Barbara) ★JINA

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Wednesday, March 31, 2010 118 H.-G.Ludwig et al.: A calibration of the mixing-length for solar-type stars. I

2.5 0.462 0.269

0.395 0.206 3.0 0.208 0.221 0.215 0.214 0.210 0.295 0.163 0.138

3.5 0.519 0.373 0.220 0.176 0.126 0.528 0.373 0.127

logg 0.522

0.559 0.372 0.167 0.097 4.0

0.716 0.268 0.207 0.079 0.276

0.997 0.885 0.757 0.656 0.580 0.493 0.442 0.250 0.204 0.152 0.110 0.089 0.065 4.5 0.873 0.446 0.254 0.204 0.154 0.089 0.069 0.198 0.151 0.068 0.201 0.068 0.201 0.066

0.146 0.149 7000 6500 6000 5500 5000 4500 Teff [K]

9 Fig. 4. Entropy jumps in units of s0 = 10 erg/g/K. The entropy jump was calculated as difference between senv and the entropy at the photospheric entropy minimum. See Fig. 3 for further explanations.

2.5 1.70 Multi-dimensional stars 1.83 1.67 1.79 3.0 1.78 1.71 1.74 1.74 1.77 1.66 1.73 1.76

3.5 1.55 1.62 1.65 1.66 1.71 1.53 1.62 1.70

logg 1.54

1.50 1.58 1.62 1.73 Convection (vs. secular 4.0

1.44 1.60 1.60 1.73 instabilities) of the stellar 1.57

1.30 1.32 1.39 1.43 1.45 1.51 1.51 1.59 1.57 1.61 1.65 1.65 1.78 4.5 1.34 1.50 1.57 1.57 1.59 1.66 1.70 1.60 1.62 1.72 interiors: 1.58 1.72 1.59 1.75

1.60 αMLT is different in different 1.58 7000 6500 6000 5500 5000 4500 T [K] convection zones eff Fig. 5. αMLT for standard mixing-length theory (Bohm-Vitense¨ 1958) with Λ = αMLT HP (Λ: mixing-length, HP: local pressure scale height). i. “A calibration of the mixing- The presentation of the data is analogous to Fig. 3. length for solar-type stars based on hydrodynamical simulations”, Ludwig, Freytag & Steffen, A&A (1999) ii.“Abundances in intermediate- mass AGB stars undergoing third dredge-up and hot-bottom burning” McSaveney, J. A.; Wood, P. R.; Scholz, M.; Lattanzio, J. C.; Hinkle, K. H., MN (2007) αMLT ~ 2.3 - 2.6 iii.“Three-dimensional Simulations of Turbulent Compressible Convection”, Porter & Woodward (2000) αMLT ~ 2.68

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Wednesday, March 31, 2010 Multi-dimensional454 stars MEAKIN & ARNETT Vol. 667

Stellar interior simulations:

i. massive stars: 458 MEAKIN & ARNETT Vol. 667 Fig. 3.—Time sequence showing the onset of convection in the oxygen shell burning model. The first 200 s of the 2D model (ob.2d.c) is shown, including the initial “Turbulent convection transient and the settling down to a new quasiYsteady state. The light yellow line indicates the location of the convective boundary as defined in the 1D TYCHO stellar in stellar interiors” evolution model (Ledoux criterion), which was used as initial conditions for the simulation. assuming a full spherical geometry. The gravitational energy con- where the mass increment is dM 4r 2  and the integral is Meakin & Arnett (2007) tribution from material on the computational grid is calculated taken over the radial limits of the¼ grid. h i according to The total kinetic energy levels off in all of the models by t 300 s. The 2D models are characterized by a much larger overall GM r dM kinetic energy. The total kinetic energy settles down to a slow in- EG ðÞ dr; 13  r ð Þ crease as the oxygen shell evolves; this is true for both 2D and Z 3D. The radial profiles of the rms velocity fluctuations are presented in Figure 6 for the 2D and 3D models. The velocity fluctuation amplitudes in all of the 2D models are higher than the 3D model by a factor of 2. The 2D models also assume a significantly Fig. 9.—Velocity isocontours showing the development of the flow in the 3D core convectiondifferent model. radial The profile turbulent than convective the 3D flow model excites and internal a flow waves structure that radiate that into the overlying stably stratified layer. By the end of the time sequence shown the stableis dominated layer cavity is by filled large with convectiveresonant modes. vortices that span the depth of the convection zone. The signature of these large eddies is ap- structures and is more obviously turbulent. In both models the parentThe time-averaged in the horizontal convective velocity flow components, velocity for as well the 3D as model the fairly symmetric shape5 of the1 radial velocity profile within the convec- ii.“The core helium flash stably stratified regions are rife with internal waves excited by the is vc 2:8 ; 10 cm sÀ . The turnover time is tc 2ÁR/vc convection. 3tion:2 ; zone.105 s, The and velocity the simulation components spans in approximately the 3D model¼ reveal five con- an up- flowing and downflowing circulation with horizontal deflection The 3D convective flow attains a quasi-steady character after vective turnovers. The peak velocity fluctuation is v peak 2 ; revisited” Mocák etal 5 6 1  approximately 6 ; 10 s, or approximately two convective turn- 10takingcms placeÀ , corresponding in a fairly narrow to a peak layer Mach at the number convective of M boundaries.0:03, overs. The evolution of the internal, gravitational, and total kinetic andAlthough the maximum significant density fluctuations differences within exist betweenthe convective 2D and flow 3D A&A (2009) energy components on the computational grid for the 2D and aremodels,0.02%, the 2D which models is of are order foundM 2 toas be expected in good for agreement low Mach with 3D models is presented in Figure 11 and is calculated in the same numbereach other thermal to the convection extent that (Gough the statistics 1969). The have time-averaged converged, con- which 6 1 way as for the oxygen-burning model. In both the 2D and 3D vectiveare calculated flow velocity over in the the time 2D periodmodel ist vc 3001;:3450; 10s.cm The sÀ time, 2½ Š 4 models, the total kinetic energy fluctuates in times with excursions andperiod the forconvective calculating turnover statistics time was for this limited model by isthetc model7 ; 10 ob.2d.C,s. 6  from the mean as large as EK /EK 0:4 in 3D and EK /EK Thewhich simulation was only spans run as 1:5 far; as10t s, which450 s. isThe21 agreement convective among turn- the 0:6 in 2D. The kinetic energy in the 2D model grows on a slightly overs.2D models The peak shows velocity that the fluctuation outer boundary in the 2D condition model is compa- (tested by 6 6 1 longer timescale and achieves a steady character after 10 s, at rablemodel to ob.2d.e) that in the and 3D the simulation, grid resolution with v (testedpeak by2 ; model10 cm ob.2d.C) sÀ , which time the kinetic energy growth rate tapers off. The total en- andare notthe playingpeak density a decisive fluctuation role in is determining a little more the than overall twice23 structure that ergy is conserved to better than 0.2% for both the 2D and 3D foundof the in flow, the 3Dat least model, in these0.05%. preliminary The turnover tests. timesThe agreement and con- in   flows by the end of the calculation. vectiveoverall velocity velocity scales amplitude are summarized in the upper in Table stable 3. layer in model The rms velocity fluctuations are presented in Figure 12 for Wednesday, March 31, 2010 5.2.ob.2d.eThe indicatesStable Layer that Dynamics the stable O layerverlyin velocityg the Con amplitudesvective Core are not the 2D and 3D models. The resultant flows in both the 2D and 3D strongly affected by the details of the modes that are excited in that models are similar to that found for the oxygen shell burning region.As in the This oxygen gives shell credence burning to the model, analysis the stably in Meakin stratified & lay- Arnett model. The velocity amplitudes are higher in 2D by a factor of ers(2007), in the which core convection assumes that models the stable are characterized layer velocity by amplitudes velocity Fig. 4.—Time evolution of the 3D oxygen shell burning model. Top: Mag- 5 (see axis scale in Figure 12), and the flows are dominated by fluctuationsare determined throughout. by the dynamical Similar to balance shell burning, between the the 2D convective stable nitudelarge ofthe eddies oxygen spanning abundance the gradient depth is ofshown the and convective illustrates the region. migration The of layer velocity amplitudes are larger and have a smaller radial- the convective boundaries into the surrounding stable layers. Interfacial oscil- ram pressure and the wave-induced fluctuations. horizontal deflection of matter is also found to occur in a much9 to-horizontal component ratio vr/v !/N compared to the lations are also apparent in the upper convective boundary layer (r 0:85 ; 10 The convective turnover times tc ? 2ÁR/vconv for the 2D mod- cm),narrower and internal region wave in motions the 3D can model. be seen The quite hard-wall clearly in the lower upper boundarystable layer. 3D flow. The dependence of the wave¼ spectrum on dimension- els are all of order tc 40 s, and they span between 10 and 55 Bottomof the: Kinetic 3D model energy is density characterized is shown and by illustrates an even the narrower intermittent horizontal nature of ality seen in our suite of models suggests that one should be convective turnovers. The turnover time for the 3D model is theflow, convective probably motions. due The tothe upwelling absence chimney-like of a stable features layer in that the convective can host cautious when drawing conclusions from 2D simulations of t 100 s, and the model spans approximately eight convective regionthe arehorizontal seen to excite flows internal associated wave trains with in theg-modes. stable layers, which propagate wave-turbulencec interactions, particularly when the turbulence away from the boundaries of the convection zones. See also Fig. 25. turnovers.

Fig. 10.—Velocity magnitude for the core convection model at t 106 s: a slice through the 3D model (left) and the 2D model (right). The topology of the convective flow is significantly different between 2D and 3D models: the 3D convective¼ flow is dominated by small plumes and eddies, while the 2D flow is much more laminar and dominated by large vortical eddies that span the depth of the layer. The wave motions in the stable layer have similar morphology in 2D and 3D, but the velocity amplitudes are much larger in 2D. The computational domains have been tiled once in angle for presentation. 2D entropy fluctuations (2400x800), realistic heating rate Multi-dimensional stars Courant time scale at this resolution: ~3*10-3sec -> 1.6M cycles

He-shell flash convection

i. 2D and 3D plane- parallel box-in-a-star (Herwig etal 2006)

quantify “overshooting” - develop models for 1D stellar evolution (cf. Karakas etal 2010.)

24 k-! diagrams for various heights of benchmark run lc0gg Wednesday, March 31, 2010 Multi-dimensional stars Next generation He-shell abundance of H-rich material entrained from above flash convection into convection zone at ~20ks

i. 3D 4π star-in-a-box simulations (e.g. Herwig etal 2010, poster outside) ii.compressible gas dynamics PPM code Paul Woodward (http:// www.lcse.umn.edu) iii.high accuracy PPB advection scheme iv.2 fluids, with individual, realistic material densities v.5763 cartesian grid, simulated time total 60ks vi.Ma ~ 0.03, 11Hp in conv. zone

http://www.lcse.umn.edu/index.php?c=movies 25

Wednesday, March 31, 2010 Multi-dimensional stars 1D mixing profiles 14 0

3D 4π star-in-a-box simulations 12 -1

10 -2 horizontal and vertical vrms 8 -3 20 18 6 -4 [mass fraction] log D [cgs] 16 H 4 D(t0) -5 14 D(t1) log X 12 2 XH(t0) -6 10 XH(t1) 8 0 -7 velocity / km/s 6 0.597 0.598 0.599 0.6 0.601 0.602 0.603 0.604

4 mr/Msun 2

0 10 15 20 25 30 radius / Mm

comparison 1D and 3D averaged profiles

26

Wednesday, March 31, 2010 Multi-dimensional stars

3D 4π star-in-a-box simulations

How expensive is it? 5763 for 60ks (several M cycles):

18*8*10*24 ~ 34,000 CPU hrs factor 2 up in resolution = factor 8 in effort: ~270,000 CPU hrs for 11523 another factor 2 up: 2.2M CPU hrs 3 another one up 17M CPU hrs (4608 , corresponding to ∆r=6km, ∆reff=3km )

How does this compare to availability? 256 cluster: 2.2M CPU hrs regional facilities: > dozen CPU hrs peta-scale computing now deployed: ~1,500 M CPU hrs

27

Wednesday, March 31, 2010 Applications of stellar evolution

• stellar populations • first stars/near-field cosmology • high-z Universe, especially AGB stars (e.g. how well can we describe C-star formation?) • grains, nucleosynthesis • SN progenitors

28

Wednesday, March 31, 2010 Adding another argument to the solar abundance puzzle:

VandenBerg etal. 2007 29

Wednesday, March 31, 2010 Applications of stellar evolution

Stellar evolution 5 first stars/near-field cosmology • (c) (a) R. Cayrel et al.: Abundances from C to Zn in extremely metal-poor giants 1131

ANRV352-AA46-08 ARI 15 July 2008 11:46

(d) Fig.1.0 11. [Cr/Mn] plotted vs. [Fe/H]. The symbols are the same as in Fig. 10. TheCS ratio 22892-052 Cr/ dataMn is almost constant and close to the solar 4 Fran¸coiset al.: First Stars VIII – Abundances of the neutron-capture elements SS r-process abundances SS s-process abundances value.0.5 Pt Os Pb (b) Ba 0 Dy Ir Nd Gd Er decreasingCe metallicity (McWilliam et al. 1995; Ryan et al. Yb –1996; 0.5 CarrettaSm et al. 2002). Hf log As shown in Fig. 10, the slope of [Cr/Fe] vs. [Fe/H] is –1.0 Eu Ho smaller thanLa that found by Carretta et al. (2002). Moreover, Pr Tb Au Lu – our1.5 precise measurementsTm show that [Cr/Fe] exhibits extremely Fig. 10. [Cr/Fe] and [Mn/Fe] plotted vs. [Fe/H]. For Mn the hyperfine small scatter (σ = 0.05 dex over the entireTh metallicity range; structure has been taken into account, and only the lines with an exci- – see2.0 Table 9). This scatter is no larger than expected from mea- tation potential larger than 2.2 have been used. When these lines are surement errors alone, indicating that anyU intrinsic scatter is too weak (open symbols) the abundance has been deduced from the –2.5 extremely50 small 60 and that70 the production 80 90 of Fe and Cr are very resonance lines and corrected for a systematic effect. Atomic number closely linked. Among all elements measured in extremely FIG. 1.— Examples of important observational results of first stars research over theFigure past 10 decade: by University of Keele on 10/16/08. For personal use only. Comparisonmetal of CS 22892-052 poor Z stars,56 abundances no with other Solar-system elements-(purple dashed follows line) and iron so closely. We Panel (a): Elements associated with nuclear production in massive stars show surprisingly little scatter as a≥ function of metallicity (Cayrel et al. 2004). By itself r-process-only (solid blue line) elemental abundance distributions. The CS 22892-052 data are from Sneden 30 this could either imply efficient mixing of the ejecta of the first supernova or a very uniformet al. (1996)discuss nuclear with revised production valuesthis for point Nd (Den process. Hartog further et al. 2003), in Ho Sect. (Lawler, Sneden 5.3). & Cowan 2004), Gd Panel (b): Elements around Sr, Y, Zr however show a large scatter, which is increasing(Den Hartog at lower et al. 2006), metallcities Sm (Lawler(François et al. 2006), and et Hf al. (Lawler 2007). et al. 2007).This The implies Solar-system that curves mixing are of ejecta can not have been extremely efficient and that these elements have a different nucleosyntheticfrom Simmerer etPresent al. (2004), origin as updated nucleosynthesiscompared by Cowan to et Cr, al. (2006). for example. These theories curves have It is been suggested do normalized not thatas yet they provide a clear and Zn are built during (complete or incomplete) explosivefollows: the s-process-only curve ( purple dashed line) to the CS 22892-052 Ba abundance and the originate from a different nucleosynthesis processes than the r process which hasAnnu. Rev. Astro. Astrophys. 2008.46:241-288. Downloaded from arjournals.annualreviews.org not yet clearly been identified (Lighter Element Primary Process, or LEPP, e.g., Wednesday, March 31, 2010 r-process-onlyexplanation (blue solid line) to the for CS 22892-052 this close Eu abundance. link between Fe and Cr, together with siliconPignatari burning et al. 2008, in and two reference diff therein),erent regionscf. top panel characterized Sect. 4. by the Panel (c): We now know that most of the stars with the extreme signatures in CNOrelative elementsthe Solar-system and observed heavyr-element elements abundance decrease have distribution in of fact scaled [Cr been to/ theFe] polluted overall with rare-earth from decreasing AGB abundance binary metallicity. peakcompanions temperature that are now of WD. the These shocked show extreme material variations (Woosley of overabundances & Weaver oflevel heavy in this elements, star. More as recent for example work (Sneden the et Lead al. 2003), (Pb) utilizing StarHE updated 0024-2523 experimental (Lucatello atomic 1995;et al. 2003).Arnett 1996; Chieffi & Limongi 2002; Umeda & Nomotodata to determineThis is more even accurate abundances, more puzzling has confirmed this since agreement. the We illustrate metallicity this in ([Fe/H]) of Panel (d): Meanwhile, the main r-process component between Ba and Pb in severalFigure r-process 10a, wheregiven rich westars compare XMP of the very observed star low abundances may metal content be for Ba considered and resemble heavier elements very as well in CS the the22892- solar ratio of the iron 2002).r-process contribution (e.g., Sneden et al. 2008). However, from galactic chemical evolution052 with s-process-only studies the and r-processr-process-only is not Solar-system typically elemental associated abundances. with FeIn both production cases, from massive stars (e.g., Travaglio et al. 2004, and reference therein). these elemental curves have been obtained as described above, based upon elemental and isotopic abundanceyield data in to the classical the volume model (Simmerer of et H al. 2004, gas Cowan swept et al. 2006). up Thebys-process the ejecta, which is curve clearlya priori does not fit independent the rest of the abundance of data. the It is obvious nucleosynthesis that the Solar-system r-process which takes place 4.5.1. Cr and Mn curve provides an excellent fit to all of the abundance data for the heaviest stable elements. Althoughin the CS 22892-052 exploding is very strongly SN enriched and in drivesr-process material, the [Cr it was/Fe] not clear ratio. at However, as first whether this star might be somehow anomalous. But extensive observations of other r-rich stars haveargued confirmed the by same Ryan scaled Solar-system et al. (1996) abundance pattern and for explored elements with Z further56 by Umeda The energy levels of manganese are affected by a considerable ≥ (see, e.g., Westin et al. 2000, Cowan et al. 2002, Hill et al. 2002, Johnson 2002, Johnson & Bolte splitting which de-saturates the lines. The maximum of this ef-2002b, Honda& Nomoto et al. 2004, Barklem (2002), et al. 2005, both Ivans et the al. 2006, amounts Frebel et al. 2007). of Wegas present swept up and the fect on the abundance determination, occurs for lines with anan updatedsupernova compilation of the yields abundancemay data for these be six correlatedr-rich stars in Table through 2. In several cases the energy of the

www.annualreviews.org Neutron-Capture Elements in the Early Galaxy 259 equivalent width close to 100 mA, a value wich corresponds explosion, which depends in• turn on the mass of the progenitor. to the equivalent widths of several lines measured on our spec- But the low scatter is surprising. Fig. 1. The abundancetra. ratios It is [Sr/Fe], thus important [Y/Fe], and to [Zr/Fe] consider as functi hyperfineons of [Fe/H]. structureBlack whenrectangles: presentThe study; relationred [Cr/Mn] vs. [Fe/H] shows practically no trend triangles; Honda et al.performing (2004); blue abundance rectangles: Johnson analysis. & Bolte The (2002); hfs constantsgreen crosses have: selected been resultswith from metallicity earlier lit- in the range 4.0 < [Fe/H] < 2.5 (Fig. 11). erature (see references listed in text). CS 31082-001 (Paper I) is shown by a magenta star. − − taken from Kurucz & Bell (1995). Moreover, six manganese However at low metallicity the manganese abundance is de- lines are generally visible in our spectra but three of them be- duced from the resonance lines and a correction of 0.4 dex is 4.1.1. Strontium long to the resonance triplet (a6S z6P0) at 403 nm. The abun- empirically applied. An NLTE 3D analysis of these lines would − be necessary to be sure that no significant slope is found, but dance of Mn deduced from this tripletStrontium is systematically is a key element lower for probing the early chemi- ( 0.4 dex) than the abundance deducedcal evolution from of the the Galaxy, other because man- itsit resonance seems that lines the are ratio Cr/Mn is close to the solar value in the ganese− lines, and thus has not beenstrong taken and can into be account measured ineven the in starsmost with metal-poor metallicities stars, although Mn is an odd-Z element and Cr as low as [Fe/H] = 4.0. For most of our stars, only the − mean. (The difference can be dueresonance to NLTE lines effects, at 4077.719 to a badA˚ and es- 4215.519an even-A˚ areZ visibleelement. in timation of the g f values of the linesour spectra. of this multiplet, or both). However, for the five most metal-poor stars only the resonance We adopt the gf values from Sneden4.5.2. et Co,al. (1996) Ni, and Zn triplet was detected. In this caseand the confirm abundance the large deduced underabundance from of Sr in EMP stars these lines has been systematicallyreported corrected e.g. by by Honda 0.4 etdex al. and (2004). It has long been realized that the [Sr/Fe] ratio exhibitsFe, very Co, high Ni, disper- and Zn are produced mainly in complete explosive this corrected value is given in Tablesion for8. stars with [Fe/H] 2.8 (McWilliamSi burning. et al. 1995; The abundance trends of these elements are pre- ≤− Fig. 2. [Y/Sr] as a functionCr of and [Fe/H]. Mn Symbols are produced as in Fig. 1. mainlyRyan by et al. incomplete 1996), and explosivewe confirm thissented as well. in As Fig. typical 12. errors in the [Sr/Fe] ratio are no more than a few tenths silicon burning (Woosley & Weaverof a 1995; dex at Chieworst,ffi this& large Limongi spread (overMcWilliam 2 dex) cannot et al. (1995) found that [Co/Fe] increases with 2002; Umeda & Nomoto 2002).be The attributed observed to observational abundances errors; of see,decreasing e.g., Ryan et [Fe al./H]. We confirm this trend (Fig. 12), but the (1996). these elements have previously been shown to decrease with slope of the relation we obtain ( 0.13 dex per dex) is not as ∼ Applications of stellar evolution • high-z Universe, especially AGB stars (e.g. how well can we describe C-star formation?)

AGB Stars Have Huge Implications for Measuring Masses of High-z Galaxies Melbourne etal (2010) Marasont etal (2009) Tonini etal (2009)

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