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AGB - AGB - Asymptotic Giant BranchAsymptotic Giant Branch

wykład IIwykład II

Ryszard Szczerba

Centrum Astronomiczne im. M. Kopernika, Toruń

szczerba@ncac.torun.pl

(56) 62 19 249 ext. 27

http://www.ncac.torun.pl/~szczerba/

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„„Asymptotic Giant Branch”Asymptotic Giant Branch”

Harm Habing, Hans Olofsson (Eds.)

A&A Library, 2004 Springer-Verlag

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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=mc2 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: 2),(),( cNZmNmZmNZQ np

A

NZQ ),(

• A more significant quantity is the total binding energy per nucleon:

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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 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

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Nucleosynthesis: solar abundance distribution

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nucleosynthesis: stability of nuclei

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Rate of capture of a by X per unit volume:

Here: f(E) is Maxwell-Boltzmann distribution, and

With theaveragedcross-section

Basic Nuclear Physics

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where X(a,b)Y represents the reaction X+a → Y+band Z(c,d)Y represents the reaction Z+c → X+d

Statistical equilibrium if

The general problem:

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Elemental abundance curveNucleosynthesis

Primordial:1H 4He 2D 3He 7Li

Stellar:H burningHe burningα processe processs processr processp process

Cosmic Ray:x process

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PPI:p p → 2D e+ ν2D (p,γ) → 3He3He 3He →4He p p

→H burningHe burningα processe processs processr processp processx process

Proton-Proton Chain

Core burning in Main Sequence starsShell burning in red giants

T ~ 1.5 x107 Kq ~ 8 x1018 erg/g

Rpp ~ ρ T 3.95 near 1.5 x107 K

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PP-I (T<1.3 107 K)

Qeff= 26.20 MeV

proton-proton chain

p + p 2H + e+ + p + 2H 3He +

3He + 3He 4He + 2p

86% 14%

3He + 4He 7Be +

2 4He

7Be + e- 7Li + 7Li + p 2 4He

7Be + p 8B + 8B 8Be + e+ +

99.7% 0.3%

PP-II(T>1.3 107 K)

Qeff= 25.66 MeV PP-III(T<3 107 K)

Qeff= 19.17 MeV

net result: 4p 4He + 2e+ + 2 + Qeff

proton-proton chain at T~1.5 107 K

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→H burningHe burningα processe processs processr processp processx process

CNO cycle

Shell burning in red giantsCore burning in massive MS stars

T ~ 1.8 x107 Kq ~ 8 x1018 erg/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

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12C(p,)13N(e+)13C(p,)14N(p,)15O(e+)15N(p,)12C

C

N

O

13

15

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13 14 15

6 7 8

CNO isotopes act as catalysts

net result: 4p 4He + 2e+ + 2 + Qeff Qeff = 26.73 MeV

cycle limited by decay of 13N (t ~ 10 min) and 15O (t ~ 2 min)

CNO cycle

cold CNO

12C(p,)13N(p,)14O(e+,)14N(p,)15O(e+)15N(p,)12C

C

N

O

13

15

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13 14 15

6 7 8

hot CNO

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cycle limited by decay of 14O (t ~ 70.6 s) and 15O (t ~ 2 min)

T8 ~ 0.8 – 1

T8 < 0.8

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H burning→ He burningα processe processs processr processp processx process

Triple Alpha Process

He flash in degenerate cores, M < 2 Msolar

Core burning in HB red giantsShell burning on the AGB

T ~ 1 – 2 x108 Kq ~ 8 x1017 erg/g

R3α ~ ρ2 T 41.0 near 108 K

4He (2α, γ) 12C

12C (α,γ) 16O

further helium burning in red giants:

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Successive Nuclear Fuel

in massive red giants, M > 9 Msolar

T ~ 0.6 – 5 x109 K

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 burningHe burning→ α process→ e process→ s process→ r process→ p processx process

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Successive Nuclear Fuel

core burning timescales:

H ~ 107 – 1010 yrsHe ~ 106 – 108 yrsC ~ 300 yrsNe ~ 1 yrO ~ 8 mo.Si ~ 4 days

H burningHe burning→ α process→ e process→ s process→ r process→ p processx process

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16O20Ne24Mg28Si32S24Ar40Ca

Alpha Nuclei (16 < A < 40, even-Z even-N)

α source: 20Ne (γ,α) 16O

AX (α,γ) A+4Y

H burningHe burning→ α processe processs processr processp processx process

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Iron Peak (50 < A < 60)

T ~ 3 x109 Kthermal photodissociation of heavy nuclei → statistical equilibrium

H burningHe burningα process→ e processs processr processp processx process

i.e.

responsible for supernovae light curves:

28Si → → → 56Ni (e-,ν γ) 56Co (e-,ν γ) 56Fe

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Slow Neutron Capture (60 < A < 209)

beta decay rate >> neutron capture rateT ~ 1 – 2 x108 K

n sources: 13C (α,n) 16O 14N (α,γ) →→ 22Ne (α,n) 25Mg

H burningHe burningα processe process→ s processr processp processx process

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Rapid Neutron Capture (70 < A < 209)

neutron capture rate >> beta decay rateT ~ 0.8 – 5 x109 K

explosive shell burning in supernovae

also produces trans-bismuth elements: Th, U

H burningHe burningα processe processs process→ r processp processx process

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Proton Capture (p,γ) or (γ,n)

proton-rich isotopes of heavy elementsT ~ 2 – 3 x109 K

supernovae envelopes?explosive 16O shell burning?

H burningHe burningα processe processs processr process→ p processx process

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Spallation

6Li 9Be 10B 11B

fragmentation of CNO cosmic raysby collision with ISM

H burningHe burningα processe processs processr processp process→ x process

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Elemental abundance curveNucleosynthesis Round-up

PrimordialH 4He 2D 3He 7Li

StellarH burningHe burningα processe processs processr processp process

Cosmic Rayx process

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Open Questions

ejection of nuclear material (mass loss problem)

binary evolution and nuclear burning by accretion

convective mixing-induced burning processes

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AGB Stars: evolution•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~RM; ~1.5-2.5, ~0.5-1.0

The fundamental mode period grows rapidly during „superwind” phase.

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AGB stars: structure

•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.

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AGB Stars: structure

•Comparison between structure of 1 and 5 Mo stars.

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AGB Stars: nucleosynthesis - T

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AGB Stars: nucleosynthesis

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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()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!

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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% - 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: =Mdredge/Mc

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AGB Stars: nucleosynthesis

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AGB Stars: production of the s-process elements• 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:1. 22Ne(,n)25Mg = 22Ne +25Mg+n2. 13C(,n)16O ....

• Ad 1. The intershell region is rich in 14N and during shell flash the reactions: 14N(,n)18F()18O()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?

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AGB Stars: the 13C pocket.• The number of protons should be „moderate” to

avoid reaction in the CNO cycle: 13C(p,)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).

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AGB stars: nucleosynthesis

11 AAnAAnA NnNn

dt

dN

• The simple extremes can be defined depending on the number of free neutrons available:1. neutron capturs dominate the decays (nn >

1020 cm-3; rapid: r-process)2. -decays dominate the neutron capture (nn <

108 cm-3; slow: s-process)•NA – abundance of the isobar of mass A;• <v>A - the thermally averaged neutron-capture cross section for the isobar, <v>A = <Av>T: v>T- is the thermal velocity of neutrons. – the neutron exposure: a time-integrated neutron flux [mbarn] (1 barn = 10-24 cm2)

dtn Tn

11 AAAAA NN

d

dN

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AGB Stars: nucleosynthesis

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AGB Stars: nucleosynthesis

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AGB Stars: F production14N() 18F() 18O(p,) 15N() 19F (Jorrisen et al.

1992)

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AGB Stars: F production

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AGB Stars: nucleosynthesis

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Massive AGB Stars: Hot Bottom BurningIf 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".

Destruction of 12C!!!

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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.

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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:

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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.

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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) (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.

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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 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).

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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

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Synthetic AGB evolution:

• L during TP

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Synthetic AGB evolution:

• The Core Mass – L relation (CMLR).

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Synthetic AGB evolution:

• L for massive AGB stars (HBB).

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Synthetic AGB evolution:

• The time evolution on TP-AGB:

HC L

X

q

dt

dM .1

q - the mass burnt per unit of energy releasedX – the H abundance (in mass fraction)LH – function (t, Mc, Menv, Z)

),,,(.2 int ZMMt envc

),,,(.3 ZMMtT envceff

),,,(.4 ZMMtM envcloss

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Synthetic AGB evolution:

• Nucleosynthesis:The minimum core mass Mc,min for dredge-up

to occur

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Synthetic AGB evolution:

• Nucleosynthesis:The efficiency of dredge-up

c

updredge

M

M

The chemical composition of material being dredge-up

updredgeenv

updredgeISCZ

ienvold

inewi MM

MYMYY

• 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)

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Synthetic AGB evolution

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AGB Stars: nucleosynthesis

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AGB Stars: nucleosynthesis

dttMXtXkM

mpmkM

loss

m

o

okky

ky

)(])([)(

)()(

)(

)(mpk -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).

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Stellar yields

•Groenwegen(up) Marigo (bottom):

Similar trends are seenH & He – mirror-like behaviourPeaks around 2-3 Mo are related to the largest number of TP’s 12C yield is larger for lower Z

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Synthetic AGB evolution:

• Form one star to population synthesisN(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

dxxZMTMdMMNZMt

o G

AGB

]),([)()(),(

)(

)(

])[(

])[(1

1

Mt

M

T

t

yrMM

MM

AGB

G

AGB

o

o

),()),(()()( ZMtZMTMdMMN AGBG

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Observational constraints

•Initial-Final Mass Relation (IMFR).

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Observational constraints

•Carbon Star Luminosity Function (CSLF).

•Dredge-up is active in stars with Mi>1.2-1.4Mo

•Dredge-up efficiency ~0.5-0.6

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Observational constraints

• C-stars are cooler (redder) than M type stars

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Observational constraints

• abundances in PNe