AGB - Asymptotic Giant Branch wykład II

AGB - Asymptotic Giant Branchwykład II RyszardSzczerba Centrum Astronomiczne im. M. Kopernika, Toruń szczerba@ncac.torun.pl (56) 62 19 249 ext. 27 http://www.ncac.torun.pl/~szczerba/

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

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=mc2the mass deficitis 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: Nucleosynthesis • A more significant quantity is the total 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 2H, 3He, to 4He  fusion of H to He should release larger amount of energy per unit mass than say fusion of He to C Nucleosynthesis: the binding energy per nucleon

Nucleosynthesis: solar abundance distribution

nucleosynthesis: stability of nuclei

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

The general problem: where X(a,b)Y represents the reaction X+a → Y+b andZ(c,d)Yrepresents the reactionZ+c → X+d Statistical equilibriumif

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

→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 x107 K q ~ 8 x1018erg/g Rpp ~ ρ T 3.95 near 1.5 x107 K PPI: p p → 2D e+ν 2D (p,γ) →3He 3He3He→4Hep p

proton-proton chain proton-proton chain at T~1.5 107 K p + p  2H + e+ + n p + 2H 3He + g 86% 14% 3He + 3He 4He + 2p 3He + 4He 7Be + g 99.7% 0.3% PP-I(T<1.3 107 K) Qeff= 26.20 MeV 7Be + e- 7Li +n 7Be + p  8B + g 7Li + p  24He 8B 8Be + e+ +n PP-II(T>1.3 107 K) Qeff= 25.66 MeV 24He PP-III(T<3 107 K) Qeff= 19.17 MeV net result: 4p  4He + 2e+ + 2n + Qeff

→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 x107 K q ~ 8 x1018erg/g RCNO ~ ρ T 19.9 near 1.5 x107 K 12C (p,γ) 13N (e+ν)13C(p,γ)14N(p,γ) 15O (e+ν)15N (p,α) 12C

CNO cycle cold CNO T8< 0.8 15 O 12C(p,g)13N(e+)13C(p,g)14N(p,g)15O(e+)15N(p,a)12C 13 14 15 N cycle limited by  decay of 13N (t ~ 10 min) and 15O (t ~ 2 min) C 12 13 6 7 8 T8~ 0.8 – 1 hot CNO O 14 12C(p,g)13N(p,g)14O(e+,n)14N(p,g)15O(e+)15N(p,a)12C 15 cycle limited by  decay of 14O (t ~ 70.6 s) and 15O (t ~ 2 min) 13 14 15 N C 12 13 6 7 8 CNO isotopes act as catalysts net result: 4p  4He + 2e+ + 2n + Qeff Qeff= 26.73 MeV

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 Msolar Core burning in HB red giants Shell burning on the AGB T ~ 1 – 2 x108 K q ~ 8 x1017erg/g R3α ~ ρ2 T 41.0 near 108 K 4He (2α,γ)12C further helium burning in red giants: 12C (α,γ)16O

H burning He burning →α process → e process → s process → r process → p process x process Successive Nuclear Fuel in massive red giants, M > 9 Msolar T ~ 0.6 – 5 x109K 12C burning: 12C (12C,α)20Ne 20Ne burning: 20Ne (γ,α) 16O 16O burning: 16O (16O,α)28Si 28Si burning: 28Si(α,γ) → → →56Fe

H burning He burning →α process → e process → s process → r process → p process x process Successive Nuclear Fuel core burning timescales: H ~ 107 – 1010yrs He ~ 106 – 108yrs 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 Alpha Nuclei (16 < A < 40, even-Z even-N) α source: 20Ne (γ,α) 16O AX (α,γ) A+4Y 16O 20Ne 24Mg 28Si 32S 24Ar 40Ca

H burning He burning α process →e process s process r process p process x process Iron Peak(50 < A < 60) T ~ 3 x109K thermal photodissociation of heavy nuclei →statistical equilibrium i.e. responsible for supernovae light curves: 28Si→→→56Ni(e-,νγ) 56Co(e-,νγ) 56Fe

H burning He burning α process e process →s process r process p process x process Slow Neutron Capture (60 < A < 209) beta decay rate >> neutron capture rate T ~ 1 – 2 x108K n sources: 13C (α,n) 16O 14N (α,γ) →→ 22Ne (α,n) 25Mg

H burning He burning α process e process s process →r process p process x process Rapid Neutron Capture (70 < A < 209) neutron capture rate >> beta decay rate T ~ 0.8 – 5 x109K 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 Proton Capture (p,γ) or (γ,n) proton-rich isotopes of heavy elements T ~ 2 – 3 x109K supernovae envelopes? explosive 16O shell burning?

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

Elemental abundance curve Nucleosynthesis Round-up Primordial H 4He2D3He7Li Stellar H burning He burning α process e process s process r process p process Cosmic Ray x process

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

Mass loss is crucial to study of AGB evolution => leads to the termination of evolution on the AGB. • Mloss is still unknon from the first principles! • Semi-empirical formulae adopt very strong dependence of Mloss on L. • P~RaM-b; a~1.5-2.5, b~0.5-1.0 • The fundamental mode period grows rapidly during „superwind” phase. AGB Stars: evolution

A schematic view of a 1Mo 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. AGB stars: structure

Comparison between structure of 1 and 5 Mo stars. AGB Stars: structure

AGB Stars: nucleosynthesis - T

AGB Stars: nucleosynthesis

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

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% - 4He, 22% - 12C) • 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: l=DMdredge/DMc AGB: the 3rd dredge-up and making C-stars

The slow neutron capture is the most important nucleosynthesis after 12C production (see Meyer 1994 and Busso et al. 1999 for review). • Two reaction could be the neutron source: • 22Ne(a,n)25Mg = 22Ne +a=>25Mg+n • 13C(a,n)16O .... • Ad 1.The intershell region is rich in14Nand during shell flash the reactions:14N(a,n)18F(b+,n)18O(a,g)22Ne 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 13C in the intershell region? AGB Stars: production of the s-process elements

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

AGB stars: nucleosynthesis • The simple extremes can be defined depending on the number of free neutrons available: • neutron capturs dominate the b-decays (nn > 1020 cm-3; rapid: r-process) • b--decays dominate the neutron capture (nn < 108 cm-3; slow: s-process) • NA – abundance of the isobar of mass A; • <sv>A - the thermally averaged neutron-capture cross section for the isobar, • <sv>A = <s>A<v>T: <v>T- is the thermal velocity of neutrons. • t – the neutron exposure: a time-integrated neutron flux [mbarn] (1 barn = 10-24 cm2)

14N(a,g) 18F(b+,g) 18O(p,a)15N(a,g) 19F (Jorrisen et al. 1992) AGB Stars: F production

AGB Stars: F production

If the mass of the star is sufficiently high (about 4 or 5 Mo 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". Massive AGB Stars: Hot Bottom Burning Destruction of 12C!!!

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. Synthetic AGB evolution:

overview of published synthetic models; • necessary ingredients for developing a synthetic model for evolution of single AGB star; • basic information needed to construct population synthesis of AGB stars; • comparison with observations: 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<3Mo; • Neglecting the metallicity dependence in the adopted analytical formulae; • Neglecting dependence of the parameteres on the TP phase. Synthetic AGB evolution:

Neglecting the breakdown of Mc-L relation due to HBB in the most massive AGB stars (Bloecker & Schoenberner 1991). Synthetic AGB evolution: • 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) (1993-1998) 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 Mloss prescriptions; • Calculate stellar yields that are necessary in galactic chemical evolution models.

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 Mc-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 3rd dredge-up (a criterion was introduced to determine whether and when the 3rd dredge up occurs in star of given M and Z). Synthetic AGB evolution:

At the 1st TP the model should reproduce: • Mc; Menv; L; Teff; chemical composition. • For Mi~1.7-2.5 Mo (depending on Z) there is a significant mass loss on RGB. • 1st (and 2nd 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) Mc; Dominiquez et al. (1999), Girardi et al. (2000). • There is also Mloss during E-AGB (see Wagenhuber & Groenewegen 1998). • Mc,1(Mi,Z) – interpolation from the models, • L1- from the Paczyński’s like relation, • T1 - theoretically or observationally constrained Synthetic AGB evolution:

L during TP Synthetic AGB evolution:

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

AGB - Asymptotic Giant Branch wykład II