1 AGB - Asymptotic Giant Branch wykład II Ryszard Szczerba Centrum Astronomiczne im. M. Kopernika, Toruń (56) ext. 27

2 „Asymptotic Giant Branch” Harm Habing, Hans Olofsson (Eds.) A&A Library, 2004 Springer-Verlag

3 Nucleosynthesis The total mass of a nucleus is known to be less than the mass of the constituent nucleons. Hence there is a decrease in mass if a companion nucleus is formed from nucleons, and from the Einstein mass-energy relation E=mc 2 the mass deficit is released as energy. This difference is known as the binding energy of the compound nucleus. Thus if a nucleus is composed of Z protons and N neutrons, it’s binding energy is: A more significant quantity is the total binding energy per nucleon:

4 Nucleosynthesis: the binding energy per nucleon General trend is an increase of Q with atomic mass up to A= 56 (Fe). Then slow monotonic decline There is steep rise from H through 2 H, 3 He, to 4 He  fusion of H to He should release larger amount of energy per unit mass than say fusion of He to C

5 Nucleosynthesis: solar abundance distribution

6

7 nucleosynthesis: stability of nuclei

8 Rate of capture of a by X per unit volume: Here: f(E) is Maxwell-Boltzmann distribution, and With the averaged cross-section Basic Nuclear Physics

9 where X(a,b)Y represents the reaction X+a → Y+b and Z(c,d)Y represents the reaction Z+c → X+d Statistical equilibrium if The general problem:

10 Elemental abundance curve Nucleosynthesis Primordial: 1 H 4 He 2 D 3 He 7 Li Stellar: H burning He burning α process e process s process r process p process Cosmic Ray: x process

11 PPI: p p → 2 D e + ν 2 D (p,γ) → 3 He 3 He 3 He → 4 He p p →H burning He burning α process e process s process r process p process x process Proton-Proton Chain Core burning in Main Sequence stars Shell burning in red giants T ~ 1.5 x10 7 K q ~ 8 x10 18 erg/g R pp ~ ρ T 3.95 near 1.5 x10 7 K

12 PP-I (T< K) Q eff = MeV proton-proton chain p + p  2 H + e + + p + 2 H  3 He +  3 He + 3 He  4 He + 2p 86%14% 3 He + 4 He  7 Be +  2 4 He 7 Be + e -  7 Li + 7 Li + p  2 4 He 7 Be + p  8 B +  8 B  8 Be + e %0.3% PP-II(T> K) Q eff = MeV PP-III(T< K) Q eff = MeV net result: 4p  4 He + 2e Q eff proton-proton chain at T~ K

13 →H burning He burning α process e process s process r process p process x process CNO cycle Shell burning in red giants Core burning in massive MS stars T ~ 1.8 x10 7 K q ~ 8 x10 18 erg/g R CNO ~ ρ T 19.9 near 1.5 x10 7 K 12 C (p,γ) 13 N (e + ν) 13 C (p,γ) 14 N (p,γ) 15 O (e + ν) 15 N (p,α) 12 C

14 12 C(p,  ) 13 N(e + ) 13 C(p,  ) 14 N(p,  ) 15 O(e + ) 15 N(p,  ) 12 C C N O CNO isotopes act as catalysts net result: 4p  4 He + 2e Q eff Q eff = MeV cycle limited by  decay of 13 N (t ~ 10 min) and 15 O (t ~ 2 min) CNO cycle cold CNO 12 C(p,  ) 13 N(p,  ) 14 O(e+, ) 14 N(p,  ) 15 O(e + ) 15 N(p,  ) 12 C C N O hot CNO 14 cycle limited by  decay of 14 O (t ~ 70.6 s) and 15 O (t ~ 2 min) T 8 ~ 0.8 – 1 T 8 < 0.8

15 H burning → He burning α process e process s process r process p process x process Triple Alpha Process He flash in degenerate cores, M < 2 M solar Core burning in HB red giants Shell burning on the AGB T ~ 1 – 2 x10 8 K q ~ 8 x10 17 erg/g R 3α ~ ρ 2 T 41.0 near 10 8 K 4 He (2α, γ) 12 C 12 C (α,γ) 16 O further helium burning in red giants:

16 Successive Nuclear Fuel in massive red giants, M > 9 M solar T ~ 0.6 – 5 x10 9 K 12 C burning: 12 C ( 12 C,α) 20 Ne 20 Ne burning: 20 Ne (γ,α) 16 O 16 O burning: 16 O ( 16 O,α) 28 Si 28 Si burning: 28 Si (α,γ) → → → 56 Fe H burning He burning → α process → e process → s process → r process → p process x process

17 Successive Nuclear Fuel core burning timescales: H ~ 10 7 – yrs He ~ 10 6 – 10 8 yrs C ~ 300 yrs Ne ~ 1 yr O ~ 8 mo. Si ~ 4 days H burning He burning → α process → e process → s process → r process → p process x process

18 16 O 20 Ne 24 Mg 28 Si 32 S 24 Ar 40 Ca Alpha Nuclei (16 < A < 40, even-Z even-N) α source: 20 Ne (γ,α) 16 O A X (α,γ) A+4 Y H burning He burning → α process e process s process r process p process x process

19 Iron Peak(50 < A < 60) T ~ 3 x10 9 K thermal photodissociation of heavy nuclei → statistical equilibrium H burning He burning α process → e process s process r process p process x process i.e. responsible for supernovae light curves: 28 Si → → → 56 Ni (e -,ν γ) 56 Co (e -,ν γ) 56 Fe

20 Slow Neutron Capture (60 < A < 209) beta decay rate >> neutron capture rate T ~ 1 – 2 x10 8 K n sources: 13 C (α,n) 16 O 14 N (α,γ) →→ 22 Ne (α,n) 25 Mg H burning He burning α process e process → s process r process p process x process

21 Rapid Neutron Capture (70 < A < 209) neutron capture rate >> beta decay rate T ~ 0.8 – 5 x10 9 K explosive shell burning in supernovae also produces trans-bismuth elements: Th, U H burning He burning α process e process s process → r process p process x process

22 Proton Capture(p,γ) or (γ,n) proton-rich isotopes of heavy elements T ~ 2 – 3 x10 9 K supernovae envelopes? explosive 16 O shell burning? H burning He burning α process e process s process r process → p process x process

23 Spallation 6 Li 9 Be 10 B 11 B fragmentation of CNO cosmic rays by collision with ISM H burning He burning α process e process s process r process p process → x process

24 Elemental abundance curve Nucleosynthesis Round-up Primordial H 4 He 2 D 3 He 7 Li Stellar H burning He burning α process e process s process r process p process Cosmic Ray x process

25 Open Questions ejection of nuclear material (mass loss problem) binary evolution and nuclear burning by accretion convective mixing-induced burning processes

26 AGB Stars: evolution Mass loss is crucial to study of AGB evolution => leads to the termination of evolution on the AGB. M loss is still unknon from the first principles! Semi-empirical formulae adopt very strong dependence of M loss on L. P~R  M  ;  ~ ,  ~ The fundamental mode period grows rapidly during „superwind” phase.

27 AGB stars: structure A schematic view of a 1M o star. The structure is similar regardless of the stellar mass: CO degenerate core + He- and H- burning shells. Pulsations take place in the convective env.

28 AGB Stars: structure Comparison between structure of 1 and 5 M o stars.

29 AGB Stars: nucleosynthesis - T

30 AGB Stars: nucleosynthesis

31 AGB Stars: nucleosynthesis The nucleosynthesis in AGB stars is mostly associated with H- and He-burnig (and proton and neutron captures). The repeated 3 rd dredge-up mixes the products to the stellar surface. 4 He, 12 C, 14 N, 16 O, 19 F, 22 Ne, 23 Na, 25,26 Mg, 26,27 Al and s-process elements are produced by AGB stars. The main reaction during shell flash is production of 12 C form 4 He via triple-alpha reaction (and 12 C(  ) 16 O). By development of intershel convective zone (ISCZ) 12 C is mixed up but at the same time 4 He is mixed down. In most calculations the composition between H- and He- shells (after dissipation of ISCZ) is mostly: 20-25% 12 C; 70-75% 4 He and a few percent of 16 O (overshooting downwards CO core) + some minor fraction of other elements 14 N, 22 Ne,... ISCZ homogenizes region from the bottom of the He-shell almost to the H-shell!

32 AGB: the 3rd dredge-up and making C-stars Iben (1975) and Sugimoto & Nomoto (1975) discovered how C- stars are produced during AGB evolution. Iben identified four phases of a TP cycle:  The „off” phase  The „on” phase (inside intershell convective zone: 75% - 4 He, 22% - 12 C)  The „power down” phase  The „dredge-up” phase (energy released during shell flash escapes from the core => the convection extentds inward in mass). Dredge-up par: =  M dredge /  M c

33 AGB Stars: nucleosynthesis

34 AGB Stars: production of the s-process elements The slow neutron capture is the most important nucleosynthesis after 12 C production (see Meyer 1994 and Busso et al for review). Two reaction could be the neutron source: Ne( ,n) 25 Mg = 22 Ne +  25 Mg+n C( ,n) 16 O.... Ad 1. The intershell region is rich in 14 N and during shell flash the reactions: 14 N( ,n) 18 F(    ) 18 O(  ) 22 Ne occur. However, reaction 1. needs T~300 milion K and such temperature is too high for lower mass stars. Ad 2. This reaction requires T~100 milion K. But, how to get sufficient amount of 13 C in the intershell region?

35 AGB Stars: the 13 C pocket. The number of protons should be „moderate” to avoid reaction in the CNO cycle: 13 C(p,  ) 14 N (Kaeppeler et al. 1990, Straniero 1995). M p ~10 -4 M o, M ISCZ ~10 -2 M o At the peak of the pulse, T is high enough (for a brief burst of neutrons from 22 Ne source).

36 AGB stars: nucleosynthesis The simple extremes can be defined depending on the number of free neutrons available: 1.neutron capturs dominate the   decays (n n > cm -3 ; rapid: r-process)   -decays dominate the neutron capture (n n < 10 8 cm -3 ; slow: s-process) N A – abundance of the isobar of mass A; A - the thermally averaged neutron-capture cross section for the isobar, A = T :  v> T - is the thermal velocity of neutrons.   – the neutron exposure: a time-integrated neutron flux [mbarn] (1 barn = cm 2 )

37 AGB Stars: nucleosynthesis

38 AGB Stars: nucleosynthesis

39 AGB Stars: F production 14 N(  ) 18 F(    ) 18 O(p,  ) 15 N(  ) 19 F (Jorrisen et al. 1992)

40 AGB Stars: F production

41 AGB Stars: nucleosynthesis

42 Massive AGB Stars: Hot Bottom Burning If the mass of the star is sufficiently high (about 4 or 5 M o at solar composition, but decreasing as the metallicity decreases) the bottom of the deep convective envelope actually penetrates the top of the H-shell. Hence nucleosynthesis occurs at the bottom of the convective envelope itself. This is known as "Hot Bottom Burning". Destruction of 12C!!!

43 Synthetic AGB evolution: Full stellar calculations are time-consuming (especially during the AGB phase). Stellar models depend critically on the free parameters:  mass loss;  mixing length;  dredge-up efficiency. Therefore, the synthetic evolutionary models, which use the „recipies” and description based on the result of full evolutionary models, can be used to „approximate” a wide grid of evolutionary models. In addition, the influence of free parameters can be tested (callibrated) by comparison with observations.

44 Synthetic AGB evolution: 1) overview of published synthetic models; 2) necessary ingredients for developing a synthetic model for evolution of single AGB star; 3) basic information needed to construct population synthesis of AGB stars; 4) comparison with observations:

45 Synthetic AGB evolution: The first attempt to develop AGB synthetic model wit aim to investigate s-process nucleosynthesis: Iben & Truran (1978). The main ideas of fully developed synthetic models were presented by Renzini & Violi (1981):  comparison between theoretical LF of C-stars with the observed one in the LMC;  comparison between predicted abundances in ejecta from AGB stars and those observed in PNe;  computation of amount and chemical composition of matter returned to the ISM (galactic chemical evolution). Weaknes of the older models:  Extrapolation of the full calculations for M<3M o ;  Neglecting the metallicity dependence in the adopted analytical formulae;  Neglecting dependence of the parameteres on the TP phase.

46 Synthetic AGB evolution:  Neglecting the breakdown of Mc-L relation due to HBB in the most massive AGB stars (Bloecker & Schoenberner 1991). The first synthetic model which took into account all the missing aspects was that by Groenewegen & de Jong (1993).  Using the LF of C stars in the LMC they determined dredge-up parameters and estimated mass loss during AGB in the LMC. In a series of papers Groenewegen (with others) ( ) extended the model to:  Compare abundances of AGB and PNe in the LMC;  Compare Period of Miras in the LMC;  Chek the influence of different M loss prescriptions;  Calculate stellar yields that are necessary in galactic chemical evolution models.

47 Synthetic AGB evolution: Marigo et al. (1996) included a more detailed description of the nucleosynthesis (she solved nuclear network to estimate the HBB effects). Marigo et al. (1998) developed a method based on envelope integration useful in case of HBB when M c -L luminosity is broken. Wagenhuber & Groenewegen (1998) derived detailed recipies as a function of M and Z, based on the full stellar evolutionary models. Marigo et al. (1999) improved the treatment of 3 rd dredge-up (a criterion was introduced to determine whether and when the 3 rd dredge up occurs in star of given M and Z).

48 Synthetic AGB evolution: At the 1 st TP the model should reproduce:  M c ; M env ; L; T eff ; chemical composition. For M i ~ M o (depending on Z) there is a significant mass loss on RGB. 1 st (and 2 nd for massive AGB stars) dredge-up change chemical composition – details can be interpolated from the full stellar evolutionary models:  Schuler et al. (1992); Pols et al. 1998) M c ; Dominiquez et al. (1999), Girardi et al. (2000). There is also M loss during E-AGB (see Wagenhuber & Groenewegen 1998). M c,1 (M i,Z) – interpolation from the models, L 1 - from the Paczyński’s like relation, T 1 - theoretically or observationally constrained

49 Synthetic AGB evolution: L during TP

50 Synthetic AGB evolution: The Core Mass – L relation (CMLR).

51 Synthetic AGB evolution: L for massive AGB stars (HBB).

52 Synthetic AGB evolution: The time evolution on TP-AGB: q - the mass burnt per unit of energy released X – the H abundance (in mass fraction) L H – function (t, M c, M env, Z)

53 Synthetic AGB evolution: Nucleosynthesis:  The minimum core mass Mc,min for dredge-up to occur

54 Synthetic AGB evolution: Nucleosynthesis:  The efficiency of dredge-up  The chemical composition of material being dredge-up Taking the efficiency of dredge-up as assumed in stellar evolutionary calculations results in carbon star mystery (Iben, 1981): Too few faint C-stars were predicted HBB nucleosynthesis (H-burning via CNO cycle)

55 Synthetic AGB evolution

56 AGB Stars: nucleosynthesis

57 AGB Stars: nucleosynthesis -the stellar yield of an element k: the mass fraction of a star with initial mass m that is converted into the element k and returned to the ISM during its entire lifetime  (m).

58 Stellar yields Groenwegen(up) Marigo (bottom):  Similar trends are seen  H & He – mirror-like behaviour  Peaks around 2-3 M o are related to the largest number of TP’s  12 C yield is larger for lower Z

59 Synthetic AGB evolution: Form one star to population synthesis  N(M) – mass distribution function (in number of stars per unit mass interval) IMF SFR the liftime of a star on the AGB the age of the system the pre-AGB lifetime of a star with mass M

60 Observational constraints Initial-Final Mass Relation (IMFR).

61 Observational constraints Carbon Star Luminosity Function (CSLF). Dredge-up is active in stars with M i > M o Dredge-up efficiency ~

62 Observational constraints C-stars are cooler (redder) than M type stars

63 Observational constraints abundances in PNe