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Evolution of low- & intermed. mass stars Evolution of low- and intermediate mass stars Falk Herwig Dept. of Physics and Astronomy University of Victoria Evolution of low- & intermed. mass stars 2 thermohaline mixing mass loss and opacities rotation convection 13C-pocket • 12C combustion proton• Motivation Sagittarius Carina MW 2.0 a [Ba/Fe] 1.0 • understanding SFH and chemical evolution in dSph galaxies • constrain nucleosynthesis processes, e.g. Eu vs α-elements • near-field cosmologie: identify the building blocks of our galaxy 0 – 1.0 1.5 Annu. Rev. Astro. Astrophys. 2009.47:371-425. Downloaded from arjournals.annualreviews.org by UNIVERSITY OF VICTORIA on 05/25/10. For personal use only. b 1.0 [Eu/Fe] Evolution of low- & intermed. mass stars 3 Sculptor Fornax 0.5 0 – 47 – – 0.5 –2 Tolstoy etal 2009 (ARAA) [Fe/H] –1 0 Figure 13 Neutron-capture elements (a) Ba, and (b) Eu in the same four dSphs as in Figure 11 compared to the Milky Way. Sgr (orange: McWilliam & Smecker-Hane 2005; Monaco et al. 2005; Sbordone et al. 2007), Fnx (blue: Shetrone et al. 2003; Letarte 2007), Scl ( green: V. Hill & DART, in preparation; Shetrone et al. 2003; Geisler et al. 2005), and Carina ( purple: Shetrone et al. 2003; Koch et al. 2008a). Open symbols refer to single-slit spectroscopy measurements, whereas filled circles refer to multiobject spectroscopy. A representative error-bar for the latter is shown on the left-hand side of the picture. The small gray squares are a compilation of the Milky Way disk and halo star abundances, from Venn et al. (2004a). • abundances in extremely enriched very metal-poor stars • stellar archeology: find the nucleosynthetic signature of the first stars in the Universe Lucatello etal 2004 406 barium (Ba) or lanthanum (La). Among the few exceptions is europium (Eu), which is almost exclusively an r-process product. Figure 13 compares Ba and Eu abundances in four dSph galaxies and in the Milky Way. At first glance, the Eu evolution in dSph galaxies resembles that of their respective α-elements (see Figure 11), as expected for an r-process originating in massive stars. In the Milky Way, Ba and Y are dominated by the r-process for [Fe/H] ! −2.0 (e.g., Johnson & Bolte 2002, Simmerer et al. 2004), whereas the s-process dominates at higher metallicities (e.g., more than 80% of the solar Ba is of s-process origin). At early times (at [Fe/H] < −1), there seems to be little difference between the various dSphs and the Milky Way halo in Figure 13. However, there is a hint that at the lowest metallicities ([Fe/H] < −1.8), [Ba/Fe] increases in scatter and starts to turn down. This hint is confirmed in the plot in Section 4.2, which includes other dSphs, although from much smaller samples (Shetrone, Côté & Sargent 2001; Fulbright, Rich & Castro 2004; Aoki et al. 2009). In fact, this scatter and downturn of [Ba/Fe] is a well-known feature in the Milky Way halo (François et al. 2007; Barklem et al. 2005, and references therein), where it occurs at much lower metallicities ([Fe/H] < −3.0). So far we have extremely low number statistics for dSphs, and these results need to be confirmed in larger samples of low-metallicity stars. These low r-process values at higher [Fe/H] Tolstoy · · Hill Tosi Evolution of low- & intermed. mass stars how? 4 Multi-physics and multi-scale simulations: Multi-physics: • nuclear physics, nucleosynthesis • evolution of the star: atomic, plasma, hydro, EOS under extreme conditions • stellar explosion Multi-scale (e.g. time): Evolution time: 100 to 103yrs (log t/s = 7 … 11) Flash-burning (combustion) times: hours to days (log t/s = 3 … 5) Convective mixing/Nuclear reaction time: minutes (log t/s = 1 … 2) Sound crossing time: seconds (log t/s = 0 … 1) n-capture time scale: < seconds (log t/s < 0) How to respond? Combine different simulation approaches for different components ... Evolution of low- & intermed. mass stars how? 5 The three simulation components Stellar hydrodynamics Stellar evolution Nucleosynthesis Evolution of low- & intermed. mass stars 6 Stellar evolution: macroscopic/global evolution of stars Assumptions: • Spherical symmetry • Hydrostatic equilibrium (u=0) Complete evolution of intermediate mass star Conservation laws: mass momentum energy plus material properties: atomic, nuclear, thermodynamic physics. Evolution of low- & intermed. mass stars He-shell flashes in AGB stars 7 Adopted from Herwig, 2005, ARAA, 43. MESA: modules for experiments in stellar evolution 8 4 low-/intermediate mass evolution 3 MS to WD through Hecore flash 4 2 log L/Lsun 1 6.0 -1 10.0 -2 1.8 1.5 5 Y = 0.28 Z = 0.02 0 -4 M0.80 M1.00 M1.25 4.8 4.6 4.4 log Teff 1.2 1.0 0.8 4.0 3.8 3.6 log Teff 2 C-star formation on the AGB 2 1.8 1.8 1.6 1.6 1.4 1.4 1 1 stellar mass CO ratio 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 4.5e+06 0 age/yr 0.6 mr/Msun 1.2 1.2 O end ! Si ! start ! 4 3.8 3.6 ! 3.4 ! Ne end ! Ne start and O start C end ! C start ! He end ! 25Msun He start ! H end ! 7.5 4.2 H start 0 1 2 3 4 5 6 7 log Central Density (gr cm −3 8 9 10 ) massive star evolution 8 MH log LH log LHe 7 6 0.58 mr/Msun 4.4 4.2 Si end ! 5 0.56 4 0.54 3 0.52 2 0.5 0 1 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 4.5e+06 t/yrs log L/Lsun -3 2.0 1000 km/sec infall 9.5 2.3 9.0 2.7 8.5 3.0 8.0 2 4.0 3.5 1 log L/L! 5.0 4.5 0 log Central Temperature (K) 3 7.0 C/O Evolution of low- & intermed. mass stars A new, modern, modular, open, fast community stellar evolution code Paxton etal 2010, in prep. read the Manifesto before using!!! Evolution of low- & intermed. mass stars 9 Local 3D simulations of hydrodynamic processes on shorter time scales The fluid equations of motion Conservation laws: mass momentum energy Plus nuclear burn: Stellar interior convection: Hydrodynamics and Mixing of He-shell Flash Convection (Paul Woodward, LCSE, Minnesota) Evolution of low- & intermed. mass stars Extra-mixing aka “cool-bottom processing” 10 Several observations on the AGB as well as on the RGB indicate that a certain amount of mixing between the bottom of the giant convection envelope and the Hburning shell is needed, e.g. • large [N/Fe] in C-rich extremely metal poor stars • lower 12C/13C on the AGB then expected from standard models • abundance correlations with L in RGB GC stars, e.g. C/N • Li enhancements in RGB GC stars Proposed scenarios include • “Enhanced Extra Mixing in Low-Mass Red Giants: Lithium Production and Thermal Stability” Denissenkov & Herwig (2004) • magnetic fields: “Can Extra Mixing in RGB and AGB Stars Be Attributed to Magnetic Mechanisms?” Busso etal (2007) • “Magneto-Thermohaline Mixing in Red Giants” Denissenkov etal (2009) • followed finally by “Is Extra Mixing Really Needed in Asymptotic Giant Branch Stars?” Karakas etal (2010) [best reproduction of observations with enhanced 16O intershell abundance] shell, where a nuclear reaction lowers the mean molecular weight slightly. Thus, we are able to remove the threat that 3He production in low-mass stars poses to the Big Bang nucleosynthesis of 3He. T he standard evolution of a low-mass star (Fig. 1) takes it from a short-lived pre– Main-Sequence (PMS) state, in which it contracts and heats up but has not yet become hot enough to burn its nuclear fuel, to the longlived MS state in which slow, steady nuclear reactions keep the star in thermal equilibrium. After several gigayears (but depending strongly on mass), the nuclear fuel is exhausted at and near the center, the star becomes cooler, larger, and more luminous, and it starts to climb the red giant branch (RGB). Its outer layers become turbulent and convective, and this surface con- vection zone (SCZ) penetrates deeply into the star, but the SCZ is forced to retreat again as the fuelexhausted core, surrounded by a thin, hot nuclear- REPORTS Fig. 4. A color-coded plot of m on a cross-section through the initial 3D model. The shell where the m infrom center photosphere, economized on versiontooccurs is the yellowwe region sandwiched between a yellow-green mesh points by considering only the region be*To whom correspondence should beThe addressed. E-mail: is and a darker inversion low the SCZ. It isgreen. important for numerical [email protected] at a radius of ~5 × 107 m. The base poses that the 1D and 3D codes use exactly the of the SCZ is at ~2 × 109 m, well 1580 approximations for physical 8 DECEMBER 2006 VOLfor 314 same processes, outside the frame, and the surface example, of× state, of theequation star is at ~2 1010 m.nuclear reaction 11 1 Institute of Geophysics and Planetary Physics, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551, USA. 2Physics and Applied Technologies Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551, USA. 3Centre for Stellar and Planetary Astrophysics, Monash University, Australia. rates, and opacities. The location of the starting model of the 3D calculation is shown in Fig. 1. If we had been clear before starting the 3D calculation that the 1/m bump was going to cause mixing, we would have started further down, at the point where the bump first presents itself, which is just above the point labeled “deepest penetration of convection.” It has become clear that our unexpected mixing will begin around here, and in practice we expect that almost all of the 3He in the SCZ from center to photosphere, economized on will have been consumed by thewe time the model mesh points by considering only the region bereaches the point where our 3D calculation 2 August 2006; accepted 25 September 2006 10.1126/science.1133333 burning shell, advances outward. During the growing phase, the SCZ dredges up and homogenizes material that, at the earlier MS phase, was processed by nuclear reactions in the interior. Along the MS, stars burn hydrogen in their cores by a combination of the proton-proton (pp) chain (in which four protons unite to form a 4He nucleus) and the CNO tri-cycle (in which the same process is catalyzed by carbon, nitrogen, and oxygen). The former is the more important in low-mass stars, ≤1 M⊙, and the latter in more massive stars. However, even in the more massive stars there is still a shell, somewhat outside the main energy-producing region, where the pp chain partially operates, burning H to 3He but not beyond. Because the pp chain is less sensitive to temperature than the CNO cycle, cores of lowmass stars are free of convection, but convective cores develop in higher-mass stars because CNO energy production is too temperature sensitive for radiation to stably transport the energy. Above ~2 M⊙ this convective core is large Fig. 1. Evolution of a low-mass Pop I star in a luminosity-temperature diagram. The model was computed in 1D, that is, spherical symmetry was assumed, using the code of (20, 21) with updated equation of state, opacity, and nuclear reaction rates (22). Surface temperature is in kelvins, luminosity in solar units. Fig. 5. The development with time of a contour surface of mean molecular weight near the peak in the blue curve of Fig. 3. The contour dimples, and begins to break up, on a time scale of only ~2000 s. bulent and has the effect of diluting the inverse molecular-weight gradient, but it cannot elimi- model makes this very likely. Although the m nate it. As the turbulent region entrains more of inversion that we find is somewhat above the the normally stable region outside it, yet below main part of the H-burning shell, it is not far SCIENCE www.sciencemag.org the normal convective envelope, it brings in fresh above, and we can expect some modest process3 He, which burns at the base of this mixing re- ing of 12C to 13C and 14N. According to (15), it gion, thus sustaining the inverse molecular- appears to be necessary for some extra mixing to weight gradient. Ultimately this turbulent region take place beyond the point on the RGB where the will extend to unite with the normally convective SCZ has penetrated most deeply; that is exactly envelope, so that the considerable reservoir of the point where our mechanism should start to 3 He there will also be depleted. If its speed of operate. In (15–18) it was suggested that rotation ~500 m/s is maintained, the time for processed in the region between the SCZ and the hydrogenFig. 5. The development with be time of a contour material to reach the classically unstable SCZ burning shell might responsible for the required surface of mean molecular weight near the do not dispute thecontour possible importance is only about 1 month, whereas the time for peak the in mixing. the blueWe curve of Fig. 3. The H-burning shell to burn through the ~0.02 M ofand rotation; dimples, beginshowever, to break we up,emphasize on a timethat the mech⊙ 6 scale of anism only ~2000 s. discovered is not ad hoc but simply we have layer is more than 10 years. The above argument establishes that the arises naturally when the modeling is done in 3D. bulent effect diluting the inverse mixingandinhas thethe SCZ is of extended below the clas- This mixing occurs regardless of possible variamolecular-weight gradient, but it cannot elimi- model makes this very likely. Although the m sical convective limit and that it is very fast com- bles like rotation and magnetic fields. It seems aded from www.sciencemag.org on February 5, 2010 Evolution of low- & intermed. mass stars 3a Fig. Deep 4. A color-coded plot ofof m on Mixing He: Reconciling Big cross-section through the initial 3D Bang and Stellar model. The shell where the m in-Nucleosynthesis 2 version is 1the yellow region Peteroccurs P. Eggleton, * David S. P. Dearborn, John C. Lattanzio3 sandwiched between a yellow-green Low-mass stars, ~1 to 2 solar masses, near the Main Sequence are efficient at producing the helium 3 and aisotope darker green. inversion isenvelope on the giant branch and should distribute He, which they The mix into the convective into the Galaxy by way of 7envelope loss. This process is so efficient that it is difficult to reconcile at a radius of ~5 × 10 m. The base the low observed cosmic abundance of 3He with the predictions of both stellar and Big Bang a red giant with a fully three-dimensional m, well of thenucleosynthesis. SCZ is atHere ~2we×find,10by9 modeling hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable outside the frame, andthethe surface shell and the base of the convective envelope. and radiative zone between hydrogen-burning 10 mixing to Rayleigh-Taylor of theThisstar is isatdue~2 × 10 m.instability within a zone just above the hydrogen-burning References bruary 5, 2010 REPORTS 28. L. Bildsten, D. Chakrabarty, Astrophys. J. 557, 292 (2001). 29. P. F. L. Maxted, R. Napiwotzki, P. D. Dobbie, M. R. Burleigh, Nature 442, 543 (2006). Downloaded from www.sciencemag.org on February 5, 20 11. V. S. Dhillon et al., Mon. Not. R. Astron. Soc. 314, 826 (2000). 12. S. B. Howell, D. R. Ciardi, Astrophys. J. 550, L57 (2001). Astronomy & Astrophysics A&A 467, L15–L18 (2007) DOI: 10.1051/0004-6361:20077274 Evolution of low- & intermed. mass stars c ESO 2007 ! 12 L E Thermohaline mixing: a physical mechanism governing the photospheric composition of low-mass giants C. Charbonnel1,2 and J.-P. Zahn3 1 2 3 Geneva Observatory, University of Geneva, chemin des Maillettes 51, 1290 Sauverny, Switzerland e-mail: [email protected] Laboratoire d’Astrophysique de Toulouse et Tarbes, CNRS UMR 5572, Université Paul Sabatier Toulouse 3, 14 Av. E. Belin, 31400 Toulouse, France 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 3 He(3 He, 2p)4 He 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 3 He production with respect to canonical evolution models as required by measurements of 3 He/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 During the first dredge-up (1dup; Iben 1965), the surface composition of low-mass red giant stars1 is modified due to dilution Shetrone 2003; Recio-Blanco & De Laverny 2007) that also modifies the abundances of lithium, carbon and nitrogen (e.g., Gratton et al. 2000). This non-canonical process appears to be universal as it affects at least 95% of the low-mass stars, whether 13 Evolution of low- & intermed. mass stars 1972ApJ...1 1972ApJ...172.. 1. study the hydrodynamics of thermohaline mixing 2. apply results in stellar evolution and compare with observations Evolution of low- & intermed. mass stars NUMERICAL SIMULATIONS OF THERMOHALINE CONVECTION: IMPLICATIONS FOR EXTRA-MIXING IN LOW-MASS RGB STARS 14 Pavel A. Denissenkov – 29 – Department of Physics & Astronomy, University of Victoria, P.O. Box 3055, Victoria, B.C., V8W 3P6, Canada arXiv:1006.5481 [email protected] ABSTRACT Ocean Low-mass stars are known to experience extra-mixing in their radiative zones on the red-giant branch (RGB) above the bump luminosity. To find out if the 100 salt-fingering transport of chemical composition driven by 3 He burning is efficient enough to produce the RGB extra-mixing, we have done 2D numerical simulations of thermohaline convection for physical conditions corresponding to the RGB 200 case. We have found that the effective ratio of salt-finger’s length to its diameter aeff ! 0.5 is more than ten times smaller than the observationally constrained 300 finger aspect ratio aobs " 7. On the other hand, the thermohaline diffusion coefficient from the linear stability analysis with a = aobs turns out to describe the RGB extra-mixing at all metallicities so surprisingly well that it is tempting 400 to believe that it may represent the true mechanism. Given this discrepancy, we call for the necessity of performing 3D numerical simulations of thermohaline convection for the RGB case. 500 In ocean conditions longish finger structures establish with an aspect ratio (vertical to horizontal) of a few. Subject headings: stars: abundances — stars: evolution — stars: interiors 600 1. 700 Introduction A main sequence (MS) star with a mass M ! 1.5 M! , e.g. the Sun, gets its energy from thermonuclear fusion reactions of the pp-chains. When its core has run out of the 800 hydrogen fuel, the star leaves the MS and becomes a red giant branch (RGB) star. The red giant has a compact electron-degenerate helium core of the size of the Earth surrounded by 900 hydrogen burning shell (hereafter, HBS) that provides the star with the energy a narrow via a transformation of H into He in the CNO-cycle. The bulk of the red giant’s volume is 1000 100 200 300 400 500 600 700 800 900 1000 RGB: R =1700, " = 400 cm2/s, " 100 200 300 400 500 600 700 – 38 – 800 900 (3D simulations underway, no dramatic effect expected) 1000 100 200 300 400 500 600 700 800 900 1000 2 0.25 log10 [X(12C)/X(13C)] Application to stellar evolution and obs: 6 RGB: R =1700, " = 4x10 cm2/s, " =200 cm2/s (black) 1.5 • black lines: aspect! ration according to mol hydro 1 100 coloured lines: aspect ratios 5-7 best • fitting observations 200 0.5 1 15 In star conditions the ratio of thermal diffusivity to diffusivity of “salinity” is much greater PLUS the viscosity is much smaller: fingers are shredded, aspect ration < 1. mol ! 300 1.5 2 2.5 log10 (L/Lsun) a b 0 [C/Fe] Evolution of low- & intermed. mass stars =200 cm2/s (red) !0.25 !0.5 !0.75 3 3.5 !1 1 1.5 2 2.5 log10 (L/Lsun) 3 3.5 Evolution of low- & intermed. mass stars Mass loss and opacities in AGB stars 16 An important new ingredient for AGB stellar evolution are new low-T opacities and - ideally matching mass loss rates, e.g. from hydrodynamic wind models (see Susanne Hoefner’s presentation for details). Goal: correctly and predictively describe the loss of the envelope when the star becomes C-rich through 3rd dredge-up, and the surface temperature evolution. Routinely employed now, e.g.: • ”New asymptotic giant branch models for a range of metallicities” Weiss & Ferguson, A&A, 2009. • “Evolution and chemical yields of AGB stars: effects of low-temperature opacities” Ventura & Marigo, MN, 2009. • “Molecular Opacities for Low-Mass Metalpoor AGB Stars Undergoing the Third Dredge-up” Cristallo etal, ApJ, 2007. • “Low temperature Rosseland opacities with varied abundances of carbon and nitrogen” 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. 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 c ESO Astronomy & Astrophysics manuscript no. evol ! 2009 & Schlattl 2008) with the GARSTEC code (described in Weiss March 22, 2009 the mass-loss formula by Wachter et al. (2002) and the opacities Fig. 1. Luminosity-temperature diagram (cf. HR-diagram) for Model of Marigo (2002). In their model, no superwind develops as in A-D. All tracks are plotted starting from the ZAHB. our case D, but as mass is eventually lost, the star will start to exL E pand rapidly. In case C, which is similar to the models by Weiss 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 abunEffects of Carbon-excess Dependent Mass and Molecular computed using the opacities by Alexander & Ferguson (1994) danceLoss of carbon available for dust formation, is a more decisive and the mass-loss formula by Blöcker (1995). The following for quantity than the C/O-ratio for the onset of strong dust-driven Opacities on Models of C-star Evolution cases are considered: mass loss. As shown in Fig. 2 (middle panels), ε˜C continues 3 , and B. Paxton4 L. Mattsson1 ! , F. Herwig2 , S. Höfner1 , R. Wahlin1 , M. Lederer to grow with every thermal pulse, while C/O levels out due to A Mass loss according to Blöcker for both M-star phase and the increasing dredge-up of oxygen. Since the mass-loss rate de1 C-star phase. Low-temperature opacities by Alexander & Dept. Physics and Astronomy, Div. of Astronomy and Space Physics, Uppsala University, 515, SE-751 pend Box steeply on ε˜C20inUppsala, case BSweden and D (see ? for further details), 2 Dept. Physics(1994) and Astronomy, University of Victoria, PO Box 3055,excess. STN CSC, Victoria BC V8W 3P6, Canada Ferguson without dependence on the carbon weAustria have a run-away process: with each thermal pulse more car3 Astronomy, University of Vienna,for Türkenschanzstrasse 17, A-1180, Vienna, B4 Dept. Massof loss according to Blöcker M-star phase and accordis USA dredged up, which increases the carbon excess and hence Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CAbon 93106, 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 Received date; accepted date as in A. temperature opacities pulses by terminating the AGB. C Mass loss as in A, but the new low-temperature opacities as ABSTRACT described in Sect. 2.3. presentloss models of stellar for a 2M" -star of initial metallicity Z = 0.01 (scaled solar), with focus on the carbon-star DWeMass as in B andevolution low-temperature opacities as in C, i.e., (C-star) phase in particular, the effects of increasing carbon excess on mass loss and4. molecular opacities. We employ a new, stateConclusions the new opacities and the new mass-loss prescription impleof-the-art theoretical mass-loss prescription for dust-driven winds, which takes the effects of the carbon intoand account, and we L. Mattsson et al.: Effects of Carbon-excess Dependent Massexcess Loss Molecular Opacities 3 menteda simultaneously. implement set of composition-dependent molecular opacities, which incorporates the changes due to the evolution of the carbon We have found that including the dependence on the carbon exexcess. We find that the development of the carbon excess is controlling much of the carbon-star evolution. A very pronounced We note that introducing the new composition-dependent cess of rich, opacities andonly mass loss during the C-star phase, may superwind forms and the termination of the AGB happens soon after the opacstar becomes carbon in fact, after a few thermal Within less than 200 Myr from the onset of the superwind, pulses.asThe a consequence of the carbon-excess included in significant the new mass-loss prescription ities, insuperwind case C develops and D,asleads to significantly lower dependence effec- have very effects on the in evolution. The new opacities combination with the lower effective temperature (which favours mass loss) obtained with the of newthe opacities. The superwind does not in case D (see Fig. 2, lower right half stellar mass is lost tive temperatures compared to case A and B (see Fig. 2). leads to lower effective temperatures, which is consistent with arise immediately, since the star has to become sufficiently carbon-rich and, at the same time, have a low enough temperature. The −8 −5 panel). note that theMarigo AGB will probably terminated even This is consistent withṀprevious results e.g., 2002, other studies 2002, and the newbe massmass-loss rate grows from ∼ 10 up to Ṁ ∼ 10(see, , while the Marigo carbon excess grows by a factor of We four (Marigo and the temperature drops by 2007), close to&1000 K. We conclude this is C/O-ratio the probable explanation the originaof theloss C-star superwind. Weiss Ferguson 2009) 2that . The is also for showing prescription/code by Mattsson et al. (2009) in combination before the next thermal pulse. Hence the model star experiences slightly slower compared to the tracks with with these opacities lead topulses thetransfer formation of a very pronounced Key words. Stars:increase, AGB and post-AGB – Stars: atmospheres – Stars:Alexander carbon – Stars: mass loss –aHydrodynamics – Radiative only few thermal as ofC-star. We note also that in the & Ferguson (1994) opacities, but the difference is not significant. superwind, due to which the number thermal pulses andTP-AGB, asFig. 2. Evolution on the starting at the peak of the first thermal p beginning of theevents C-rich phase the mass-loss rate drops signifiThe overall luminosity evolution is similar for all four cases. sociated dredge-up is very limited. The nucleosynthetic Middle panels: C/O-ratio (left) and carbon excess (right). Lower panels: mass 1. Introduction is important, since C-stars, therapidly duration the AGBinto cantly, but then evolves a superwind. Regarding the mass-loss evolution, we see ament dramatic yields arefor thus probably lower of compared to many previous mod-In case B the phase and the number of thermal pulses is almost solely deterchange. In case D, acontain very pronounced develops as the els of C-star evolution, thisbeen needsreached to be verified. superwind has notbut yet after five thermal pulses, Stellar evolution models uncertaintiessuperwind due to input mined by the mass-loss rate. The evolution of the internal struccarbon increases. fact,to the mass-lossrather rate becomes so Our stellar evolution sequence with ab initio inputdecrease physics in effective physics that, excess for practical reasons,Inneed be prescribed is due(Blöcker to a combination of a slower ture also dependswhich on the mass-loss 1995), which in turn References Co that the average timeMass-loss step drops orders thanhigh computed simultaneously. on three the AGB is aof magnitude is reproducing the superwind quantitatively in the amount obaffects the fundamental stellar parameters. Since the mass-loss temperature and a steep dependence −2 of mass loss on temperature process is of to great importance for stellar evolution mod- not and that appears continue to drop. We have therefore ratecontindepends onserved these stellar be −4 aM feedmassparameters, loss ( Ṁ =there 10−5will − Alexander 10 ). Extrapolating the 1994, ApJ, 437, 897 & Ferguson J.W., " yrD.R. Fer els, ued but any is usually by asome empirical, according to Mattsson et al. (2009). The origin of the superwind of theimplemented tracks beyond few simple thermal pulses in back, the C-star which means that the mass-loss prescription put into a mass loss to the end of the end of the AGB (by looking at the Blöcker T., 1995, A&A, 297, 727 He semi-empirical or theoretical The mass loss of to AGB stellar evolutionremaining model ismodel critical. In particular, since the massregime, since the dropformula. in the time step needs be investigated in the is due to the combination of low effective temperamass in case D) will bring us up to the observed level Bowen G.H., 1988, ApJ, 329, 299 stars is thought to be driven by radiation pressure on dust- loss rate is found to increase significantly with the carbon ex−5 more in outer detailstellar and atmospheres. the numericsVarious of themass-loss code may modifi- of a few times M"pulse yr−2and . The mass-loss ratemass-loss in the beginning grains in the for-need tures and a 10 carbon-excess dependent rate. cess (Mattsson et al. 2008), each thermal correspondcation. The time step drops significantly in case B as well, as mulae/recipes have been used previously, e.g., a scaled Reimers- ing dredge-up event of the C-star phase drops to a very low level (see Fig. 2, lower will take a C-star closer to the termination The relatively decline in temperature (again, see Fig. as a1975) strong begins toHoek develop, although noofsuch pro- This law soon (Reimers waswind used by van den & Groenewegen leftwill panel), then risesrapid over the AGB. lead tobut a mechanism that isroughly limiting three the orders of magnitude, (1997), while Karakas & Lattanzio (2007) used thetoformula by amount −8 −5 of AGB nounced superwind as in case D seems be developing at this 2)andcauses the star more or less horizontally to the of carbon other nucleosynthesis products from Ṁ ∼ 10 up to Ṁ ∼to 10move , while the carbon excess grows Vassiliadis & Wood (1993), and Herwig (2002; 2004) used the most notably the s-process elements, that can be expelled stage, which one can expect due to the higher effectivestars, temperaa factor of four. right in the HR-diagram (Fig. 1) in all cases except C. Weiss & theoretical prescription by Blöcker (1995), derived from early by a carbon star.by ture of the star (an effect of the opacities). wind models by Bowen (1988). Recently, Weiss & Ferguson Mass loss and opacities in AGB stars Evolution of low- & intermed. mass stars Mattson, Herwig,Hoefner, Wahlin, Lederer, Paxton mass loss vs. age “forwardmodeling” superwind?!! Ferguson (2009) similar migration to the right using The implementation of opacities that obtained depend on theachemi(2009)2 made use of the theoretical formula by Wachter et al. cal composition of the star (which changes as the star evolves) Note that Rosseland opacities are used. Since the diffusion Acknowledgements. MTLcode has been supported byintheWeiss Austrian& Academy of 2008) with the GARSTEC (described Schlattl (2002), which is probably moremean realistic. can how affectthe the structure and surface temperature significantly. Sciences (DOC programme) and acknowledges funding by the Austrian Science approximation does not apply to the surface layers, it is unclear Mattsson et al. (2009) have recently made an effort to de- Marigo (2002) and the mass-loss formula by Wachter Marigo & Girardi (2007) have shown that us- et al. (2002) and the opacities Fund FWF (project P-18171). effective temperature affected quantitatively. Fig. 1. Luminosity-temperature (cf. HR-diagram) Model termine how the mass lossisofdiagram carbon-rich AGB stars (C-stars) for ing composition-dependent opacities leads toIn an improvement of no superwind develops as in of Marigo (2002). their model, A-D. All tracks areonplotted starting from ZAHB. wind the agreement between depends stellar parameters, using the a state-of-the-art models and observations (e.g., colours, caseC-star D, but as mass is eventually lost, the star will start to exmodel including time-dependent dust formation and frequency- initial-final massour relation, luminosity functions etc.) but dependent radiative transfer. That work has provided a new also to significantly lower effective In temperatures, to similar to the models by Weiss pand rapidly. case C, compared which is mass-loss prescription, which includes steep dependences on earlier work. Since the mass-loss rate depends steeply on the ef- 17 total mass vs. age 600 -400 -200 0 200 400 600 600 -400 -200 0 11.74 yrs 200 400 600 600 -400 -200 0 11.74 yrs 200 400 600 600 -400 -200 0 11.74 yrs 200 400 600 11.74 yrs Evolution of low- & intermed. mass stars Hydrodynamic simulations of AGB envelopes 18 Freytag & Hoefner (2008) density temperature velocity field grey intensity 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 600 -400 -200 0 200 400 600 12.06 yrs 12.37 yrs 12.06 yrs 12.37 yrs 12.06 yrs 12.37 yrs 12.06 yrs 12.37 yrs Fig. 1. Time sequence of five snapshots for model S (st28gm06n02). The model age in years is indicated on top of each frame. The axes are in solar radii. Shown from left to right are log density (color range from 10−13 to 2 × 10−7 g/cm3 ), log temperature (color range from 800 K to 50 000 K), velocity field (pseudo-streamlines of the velocity components within the image plane integrated over 5× 106 s) and grey intensity. Evolution of low- & intermed. mass stars 19 1. Formation and 2. evolution of the 13C-pocket Gravity waves (Denissenkov & Tout, 2002) Mixing processes for the radiative s-process (partial mixing of protons with 12C at the base of the convective envelope during/ after 3DUP) Rotation (Langer etal. 1999) Hydrodynamic overshooting (Herwig etal. 1997) Evolution of low- & intermed. mass stars Hydrodynamic simulations of AGB envelope convection focus on beneath-atmosphere, deeper layers 20 Woodward & Porter, LCSE, U Minnesota, http://www.lcse.umn.edu temperature fluctuation Evolution of low- & intermed. mass stars Rotation and magnetic fields 4 21 Suijs et al.: White • Rotation in 1D stellar evolution, e.g. Maeder & Meynet, Heger etal, Langer etal. • plus magnetic fields, e.g. Taylor & Spruit dynamo, questioned by Zahn etal (2007) Compare to observations in late phases: • Rotation rates of neutron stars and white dwarfs • Implications from nucleosynthesis, e.g. s-process in TP-AGB stars (Herwig etal 2003, Siess etal 2004) Fig. 5. Average core specific angular momentum of our initial etalinitial (2008) and final models (cf. Table 1 and Fig.Suijs 4), versus stellar mass (full drawn lines). Points for 15 M! stars computed with the same physics from Heger et al. (2005) have been added. The upper line corresponds to the initial models. Filled triangles corresponds to the final models of the non-magnetic sequences, and filled squares to the final models of the magnetic sequences. The “Seismic evidence forhorizontal the loss stellar dashed lineof indicates the angular spectroscopic upper limit on the white dwarf spins obtainedstage” by Berger et al. (2005). Star symmomentum before the white-dwarf bols represent astroseismic measurements from ZZ Ceti stars Charpinet, S.; Fontaine, G.; Brassard, P., 2009. (Bradley 1998, 2001; Dolez 2006; Nature, Handler 2001, Handler et al. 2002, Kepler et al. 1995, Kleinmann et al. 1998, Winget et al. 1994), where smaller symbols correspond to less certain measurements. The green hatched area is populated by magnetic white dwarfs (Ferrario & Wickramasinghe 2005; Brinkworth et al. 2007). The three black open pentagons correspond to the la to Y b la s 5 W to g th m p s m tw F re W la T a a A N A w C R zone of #10 M$ that has formed at the end of the third ! ¼ ðt & t0 Þ=Dt, where the previous pulse, i.e., the maximum He-burning contraction andofthe angular velocity in the dredge-up phaseresumes as a result timeand depth-dependent luminosity, has occurred at t0; the interpulse period is Dt ¼ 3 ' 104 yr. Two intershell region increases accordingly (profiles ! ¼ 0:0122– hydrodynamic overshoot (top panel, Fig. 6). In this model different mixing periods resulting from rotation occur in the partial mixing 0.1706). The angular velocity profiles at later times show zone during the interpulse period (see text). no mixing takes place during the interpulse phase. InImplications the from nucleosynthesis, againpanel the formation a plateau between 0.746 0.749 13C neutron source hasand started middle of Figure of 6 the the H and shellup is now located, of deposition M!, where e.g. in TP-AGB stars 13C abundance has s-process releasing neutrons, to 10% of thebecause In Table 2 we give the mixing properties in the partial of H-shell ashes of the core. been consumed. Inon thetop upper part of the partial mixing zone, (Herwig etal mixing 2003) zone at three different times: an early phase soon the evolution of the angular velocity rotating 14N dominates, the majority of neutrons are in absorbed whereFrom after the pulse, a phase just before the release of neutrons can anticipate the following mixing propp)14we C reaction. This can be seen from the probyTP-AGB the 14N(n,stars starts, and a phase after the neutron source 13C is exhausted. erties. Efficient shear mixing will take place at #0.746 M 14 "3 ! 6 file of C. The maximum neutron density is 5:7 % 10 cm after the formation of the large angular velocity gradient. This gradient because two convective regions extend no forms rotation with rotation to *these mass coordinates from below and above in short ! succession. The He flash convection first taps the reservoir !) =" of!(high angular momentum in the core. Then the convective =# envelope establishes contact between the fast-rotating inter!' =$ shell and the slow-rotating envelope. At this interface rota!& =% tionally induced shear mixing will be most efficient in acting !% =& on!$abundance gradients. The timescale to establish a partial =+ 12 < D mixing zone of hydrogen and C as needed for the forma!# =( !<!'!%) )( "# =13 E tion !" of the C pocket is limited to the time interval when the =) *+$(*' *+$(*& *+$(*% *+$(*$ *+$(*# !'(%&) !'(%&* !'(%+ !'(%+" envelope and the intershell are in contact, i.e., between the end * of the third dredge-up and the reignition of the H-shell. ! )' "$ = E This lasts 2000–3000 yr (Fig. 1). However, as can be !) period =" )& "% ? G ?6 G; seen 7, the steep angular velocity gradient remains !( in Figure =# )& "% = E at!'this mass coordinate after the formation of the partial =$ !& =% mixing zone, and shear mixing at this location will persist !% =& throughout the intershell period. !$ =+ Correspondingly, two mixing periods during the inter!# phase resulting from rotation can be distinguished, as =( !<!'$)# pulse !" =) shown by the temporal evolution of the mixing coefficient *+$(*' *+$(*& *+$(*% *+$(*$ *+$(*# !'(%&) !'(%&* !'(%+ !'(%+" presented in Figure 8. During the initial envelope-core con" tact)period at the end of the third dredge-up, a partial mix12 ing*+"zone of protons and C forms (top panel, Fig. 9). The !') mixing efficiency in Eulerian coordinates at this time is !'+ log*+$Dr # 5 (in cgs units), but decreasing rapidly at a timescale *+& of #1000 yr. However, after the TP the mass gradient !'% in the partial mixing zone increases steadily as the intershell *+( !'# layers contract and evolve toward a preflash structure. For !<!'+** assessing the effect on the abundance evolution, the * ! *+$(*' *+$(*&coefficient *+$(*% !'(%&) !'(%&* !'(%+ !'(%+" Lagrangian mixing should be *+$(*$ considered: *+$(*# ,1EF.A6 71895:; ! "2 dm 2 2 Fig. 9.—Same as Fig. 6 for the simulation at the 25th interpulse phase ¼ Drpartial ¼ ð4"#r Þ D ð6Þ Dm profiles Fig. 6.—Abundance in the mixing zone r ; at three times dr including rotation and no hydrodynamic overshoot. The middle panel during the seventh interpulse phase of the model with hydrodynamic over- • ,-.ABCF/,-.AG;C=) 7589:;>/7589?6;!" 7>55/?1>42@-;/,-.ABC ,-../01-23456/7589:; Rotation and magnetic fields =" ;H:21-;/HIJ-5:1H/"/A7K>1; C 6@A3156/@BC5.A1@/!/9,D-16!); Evolution of low- & intermed. mass stars utionary ered the ies have e mixing imply a gion by approxitend by ferences of 0.7Hp location o-dimentag et al. ion zone ccording nvection oxygenArnett hing 1Hp there is not the convecg as the thermal oundary. expect a pported ons by oot dismass. meter for nvective applied or effect hing the 14N proneutron n in the de effect y #20%. analysis with oth-process ult 22 from shoot and no rotation. Top: First postprocessing model after the end of the 13 13 16 shows the same interpulse phase as the middle panel in Fig. 6 with respect 13 Evolution of low- & intermed. mass stars Rotation and magnetic fields next generation ?!? odynamical Processes in Rotating Main Sequence Stars reach the ravity, and ind which Meynet et magnetism. netic field lities, that entum and ud 2002a; ynet 2004; Mathis & Zahn et al. ito-inertial zones may um. They deposit anmped, thus cal distrialon et al. harbonnel t al. 2007; n of rotatmical abunnitude diaalso modll soon be r range of pted to the m to comhe present magnetic he angular usively by These di- 23 Time scales (log tchar) Secular scales (evolution; ! : 109 yrs) Dynamical scales (convection, instabilities, turbulence; !: month) Rotational transport equations coupled with stellar evolution codes “A Model of Magnetic Braking of Solar Rotation That Satisfies Observational Constraints” Denissenkov (2010) • improving on Charbonneau & MacGregor Global numerical simulations prescriptions and constraints on theoretical hypothesis lth(<10) lnum Angular resolution lnat (!: 4000) (log l) Fig. 1. Modelling strategy to study dynamical stellar evolution. The diagram presents timescales of the typical physical processes as a function of the angular resolution necessary to properly describe these processes. The angular resolution is expressed in terms of the l index of the spherical harmonics Yl,m (θ, φ). lnum ! 600 indicates the maximum angular resolution (in term of spherical harmonics nodes) presently achieved in global numerical simulations. bulent motions in the vertical direction. This leads to a strongly anisotropic turbulent transport that is more efficient in the horizontal direction (along isobars) than in the vertical one. As a result, the horizontal gradients of all scalar fields (temperature, angular velocity. . . ) are much smaller than their vertical gradients, which allows their expansion in a few spherical harmonics. This scale separation, both in space and in time, is illustrated in Fig. 1. Considering the axisymmetric case, each scalar field is thus written as the sum of its horizontal average on an isobar, and its “Secular hydrodynamic processes in rotating stars” Decressin et al (2009) (1993) • strongly anisotropic rotation-driven turbulent diffusion with dominating horizontal components • numerical solution of the azimuthal components of the coupled momentum and magnetic induction equations in 2D “Numerical Simulations of a Rotating Red Giant Star. I. Three-dimensional Models of Turbulent Convection and Associated Mean Flows” Brun & Palacios, 2009 Rayleigh Taylor instability (Weiss et al. 2004). With ∆ρ/ρ ∼ M. Mocák, S. W. Campbell, E. Müller and K. Kifonidis: The core helium flash revisited −4 5 × 10 , inferred from our simulation (Fig. 6 a), we find v2 ∼ gΛ ∆ρ ∼ 7 × 105 cm s−1 ρ (1) Evolution of low- & intermed. mass stars where g ∼ 108 cm s−2 is the gravitational acceleration at the base of the convection zone, and Λ ∼ 107 cm the approximate length of the fingers (Fig. 7). The above estimate agrees well with the results of an analysis of our simulation, where the gas inside the fingers sinks at a bit smaller velocities ranging from ∼ 1 × 105 cm s−1 up to 3.5 × 105 cm s−1 (Fig. 6 and 7). It confirms that the “buoyancy work” (∼ v2 ) is consistent with the acceleration of gas seen in the simulation, and suggests that the mixing is the result of the Rayleigh-Taylor instability. Hence, we propose to call it Rayleigh-Taylor finger instability mixing (RTFI). The velocities observed inside the finger-like structures (Fig. 6 e) are smaller than those predicted by Eq. (1), likely because of the friction caused by our numerical scheme between the ambient medium and the sinking overdense blob. Note that the initial density fluctuations can result from wrinkling of the contact discontinuity at the boundary of the convection zone due to the convective flow, turbulence, g-modes or p-modes. Eggleton et al. (2006) also found Rayleigh-Taylor instabilities driven by a molecular weight inversion caused by the 3 He (3 He,2p) 4 He reaction in hydrodynamic simulations of the hydrogen-rich layers residing above the hydrogen burning shell in low-mass red giants. The corresponding mixing is qualitatively similar to RTFI mixing. The mixing velocities observed by Eggleton et al. (2006) agree very well with those theoretically estimated for a RT instability according to the formula v2 ∼ gH p ∆µ/µ, where equal relative density and composition fluctuations, i.e., ∆ρ/ρ = ∆µ/µ, were assumed. However, Fig. 12. Temporal evolution of the radial distribution of the 2 any density fluctuation necessarily lead toaveraged composition (color coded)will logarithm of the angular radial (vand r /2; 2 temperature fluctuations ∆T angular as well. Moreover, the component formula of upper panel) and vθ /2; lower panel) of −1 the(2006) specificholds kinetic energy (in ideal erg ggas, ) of theonly 2D if model Eggleton et al. only for an and the heflpopIII.2d.2. blobs are in pressure equilibrium with the ambient medium and have the same temperature as the surrounding matter. The finger-like structures RTFI mixing in our is roughly eight timesresulting higher thanfrom that due to triple-α burning in 9 −1 −1 the inner zone #̇etal ∼ 1.72010a,b × 10 erg g the s ),surrounding convective motions max simulations are in pressure equilibrium with gas, Mocak first appear within the inner convection zone after about 200 s. as they moveThe with subsonic velocities (the speed of sound is 8 −1 onset of convection in the outer zone is delayed until about c s ∼ 10 cm s500 sin(Fig. the12, corresponding layers). However, theyinto area Fig. 16). After some time the model relaxes where the r.m.s values always thansteady-state, the ambient medium, i.e., Tof>theTangular + ∆T , 24 coolerquasi 1 ≡ T velocity 11 He-core flash simulations (here 2D) at low Z show Hingestion main results • hydrodynamic results do not agree with 1D stellar evolution • entrainment at bottom of He-core flash convection zone (cf. ‘overshooting’ at bottom of He-shell flash convection zone) Fig. 13. Adiabatic temperature gradient ∇ad (solid-black), temperature gradient of the 2D model heflpopIII.2d.2 averaged from 1000 s to 3200 s (dashed-red), and temperature gradient of the initial model SC (solid-blue), respectively, as a function of radius. • mixing due to Nevertheless, the convective flow decays fast in both convection zones – at a rate of 4 × 1040 erg s−1 (Fig. 16), probably because the initial conditions represented by the stabilized initial model are too different from those of the original stellar model. They disfavor convection since the stabilized model has a slightly lower temperature gradient than the original one (Fig. 2, Fig. 13). However, we note that stabilization of the initial model was essential to prevent it from strongly deviating from hydrostatic equilibrium. Shortly after convection is triggered in both the outer and the inner zone this double convection structure vanishes, and after about 2000 s there is no evidence left for two separate convection zones (Fig. 12). Due to the relatively short temporal coverage of the evolution and due to the decaying convective flow, we did not analyze the energy fluxes and turbulent entrainment of this model. Penetrating plumes do not exist in the convection zone (initially determined by the Schwarzschild criterion), as it is dominated rather by g-modes. Hence, firm conclusions are difficult to deFig.but 8. we Relative angular mean molecular rive, plan to address this fluctuations issue elsewhere.ofWethe are now going to introduce basic internal gravity weight ∆µ/µ =some (µ−%µ& / %µ&θ at theofbase of the convection zone θ ) characteristic waves or g-modes that are required to draw further conclusions. in the 2D model hefl.2d.3 at t = 30 000 s (a), t = 60 000 s (b), 1 2 and t3 = 120 000 s (c), respectively. In each panel the black solid G-modes In the a convectively stable region, any displaced mass of the mean line gives angular averaged radial distribution RT finger instabilities at the bottom of convective shells Evolution of low- & intermed. mass stars Multi-dimensional stars 25 abundance of H-rich material entrained from above into convection zone at ~20ks Next generation He-shell flash convection i. 3D 4π star-in-a-box simulations (e.g. Herwig etal 2010, arXiv:1002.2241) 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 26 20 log D [cgs] horizontal and vertical vrms <uθ,φ> <ur> 18 16 14 0 12 -1 10 -2 8 -3 6 -4 D(t0) D(t1) 2 XH(t0) XH(t1) 0 0.597 0.598 0.599 -5 4 14 12 10 8 6 -6 -7 0.6 0.601 0.602 0.603 0.604 mr/Msun 4 2 0 10 15 20 25 30 radius / Mm comparison 1D and 3D averaged profiles See poster for details on nucleosynthesis implications: NIC_XI_224, see also arXiv: 1002.2241 log XH [mass fraction] 1D mixing profiles 3D 4π star-in-a-box simulations velocity / km/s Evolution of low- & intermed. mass stars Multi-dimensional stars Busso, M., Gallino, R., Lambert, D. L., Travaglio, C., & Smith, V Evolution of low- & intermed. mass stars Calder, A. C., Fryxell, B., Plewa, T., Rosner, R., Dursi, L. J., We Convective-reactive proton-12C combustion J. in O., Sakurai’s object (V4334 Remington, B. A., Drake, Sagittarii) R. P., Dimonte, G., Zing and implications for the evolution and yields P., from the first stars MacNeice, P., generations & Tufo, H. M.of 2002, ApJS, 143, 201 27 –3– Campbell, S. W. & Lattanzio, J. C. 2008, A&A, 490, 769 (arXiv:1002.2241 for details) Cassisi, S., Iben, I. J., & Tornambe, A. 1998, ApJ, 496, 376 of highly exothermic nuclear reaction and the convective fluid flow time scales are of the same order. Colella, P. & Woodward, P. R. 1984, Journal of Computational Ph The ratio of the mixing time scale and the reaction time scale is called the Damköhler number: Dillmann, τmix I., Heil, M., Käppeler, F., Plag, R., Rauscher, T., & Thie Dα = (1) of. Physics Conference Series, Vol. 819, Capture Gammaτreact A. Woehr & A. Aprahamian, 123–127 MLT is concerned with averaged properties both in time over many convective turn-overs and in space over Dimotakis, P. E. 2005, Annu. Rev. Fluid Mech., 37, 329 the order of a pressure scale height. In the categories of Dimotakis (2005) diffusion coeffiecients derived from MLT may describe level-1 mixing (while mixing induced rotation involves dynamics that Duerbeck, H. W.,by Liller, W., Sterken, C., flow Benetti, S., van Gendere fully mixed burning, MLT appropriate Voskes, • Dα <<1: T., Brogt, E., Arentoft, T., vantime-dependent der Meer, A., & D are altered by mixing processes and labeled in this scheme as level-2 mixing). Therefore, • Dα ~1 : combustion regime, MLT and 1D spherical symmetry assumption mixing through a diffusion algorithm with diffision coefficients derived from MLT is appropriate for regimes inappropriate because: with Dα ! ★ 1. The difficulty of simulating convective-reactive phases in present one-dimensional stellar MLT describes convection only in a time and spatially averaged sense evolution codes appears asfuels the inability MLT (or any similar convection theory) to properly account ★ inthen combustion are not of completely mixed for the additional dynamic effectsfeedback introduced through rapidburn and dynamically relevant nuclear energy release ★ localized energy from nuclear feeds back into hydro in level-3 mixing associated numbers Dαcommon, ≈ 1. in low- with and Damköhler zero-metallicity stars including both low-mass and • combustion massive, rotating and non-rotating stars, X-ray bursts, SD SN Ia projenitors, etc Convective-reactive episodes can be encountered in numerous phases of stellar evolution, including the He-shell flash of AGB stars of extremely low metal content (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; Evolution of low- & intermed. mass stars How nucleosynthesis? Different strategies: 28 • synthetic stellar structures (i.e. fit- formula to full stellar evolution) and more or less complete processing • Stellar evolution first, then nucleosynthesis post-processing of a few key locations, e.g. the 13Cpocket etc (the Gallino etal approach) • Stellar evolution with an inlined network ✴ smaller network of charged particles, plus co-processing of heavier elements in separate larger network (e.g. Lattanzio, Karakas etal) ✴inlining of complete network into stellar evolution code (e.g. Cristallo etal) • NuGrid approach: stellar evolution first with energy suficient network, write out all strucutre information, complete post-processing of all zones and timesteps for dynamic and complete network of entire evolution (made possible vie parallel computing) Evolution of low- & intermed. mass stars How nucleosynthesis? 29 Why http://nugrid.phys.uvic.ca ? • create a framework that allows to process large, internally consistent and comprehensive yield sets • facilitate easy and routine production of large sets of observables that allow simultaneous validation of stellar physics in a wide range of situations • detach (as far as possible) stellar evolution and explosion (SEE library) business from nucleosynthesis business (PPN - post-processing network code suite) NIC_XI_255 Pignatari M. etal. Neutron capture processes in stars between the s process and the r process NIC_XI_285 Pignatari M. etal. Nucleosynthesis in the He-burning shell in massive stars NIC_XI_244 Bennett M. etal. The effect of 12C + 12C rate uncertainties on the weak s-process component Evolution of low- & intermed. mass stars Results: Set 1 •2 metallicities: Z=0.02, 0.01 •masses: 1.65, 2, 3, 5, 15, 20, 25 (32 and 60 for Z=0.02 only), massive star tracks with Geneva code, low-mass tracks with MESA code •all tracks to the end of the AGB or end of Si burning •synthetic explosions for massive stars •complete post-processing of all tracks with the NuGrid ppn codes: all reactions and isotopes that could have taken place are considered Evolution of low- & intermed. mass stars Results Set 1: 2Msun star Z=0.01 Nucleosynthesis including s-process in the He-shell flash thermal pulses of AGB stars from the NuGrid collaboration Evolution of low- & intermed. mass stars Results Set 1: 2Msun star Z=0.01 Nucleosynthesis in the 13C-pocket Evolution of low- & intermed. mass stars Results Set 1: 20Msun star Z=0.01 Nucleosynthesis in a massive star Evolution of low- & intermed. mass stars Availability of results 34 all data will be made available along with convenient tools to explore the data, e.g. SEexplorer: interactive data exploration and visualization as well as Python tools Evolution of low- & intermed. mass stars Next steps: Set2 35 • 21 masses between 0.8 and 60Msun for 5 metallicities between Z=0.04 and 1.e-4 • again non-rotating, no B-fields • improved convective boundary mixing, mass loss • 1D and 3D explosions • SN Ia contributions • again complete post-processing data sets of all tracks with the NuGrid ppn codes with all reactions and isotopes that could have taken place HRD of a subset of preliminary Set 2 calculations to the end of He-core burning Evolution of low- & intermed. mass stars Concluding remarks 36 •progress is being made in many areas now by investigating multi-dimensional effects in the stellar interior. •many approaches needed - don’t expect the golden bullet •great opportunities for nuclear astrophysics: as we push to simulate shorter timescales we need new diagnostics sensitive on shorter time scales -> branchings, radiaoctive beams, nuclear physics of radioactive targets