Japan-Germany Joint Workshop on Chemical Evolution in the Early Universe
May 25th, 2020

s-process in AGB and superAGB stars
Takuma Suda（Open U. / RESCEU, U-Tokyo）

Contents• Stellar Evolution and AGB stars• s-process in AGB stars: radiative 13C-pocket, convective
22Ne burning• s-process in metal-poor stars: convective 13C burning in
RGB and AGB stars• Super-AGB stars• s-process by 22Ne burning• s-process by dredge-out• AGB / Super-AGB stars at low-metallicity (Appendix)

Stellar Evolution and AGB stars

Current situations of stellar evolution• Standard stellar evolution theory is almost establishedin one-dimensional framework.

• Main concern is the application of the mixing length
theory (MLT), which is thought to be a crude
approximation.

• Simulations with large nuclear reaction network arepossible with developing computational capacity.
• 3D hydrodynamical models have been developed in thelast decade, mainly focus on convective mixing.

• Simulations in very short time scale, which cannot bestellar evolution.

• Numerical results are available by MESA code.
• Updated periodically (Paxton+11,13,15,18).

• Seismology is expected to constrain stellar structure.
• Kepler to TESS.

Mass - Lifetime relation
10.5

Age of the univrerse (13.7, billion years)Ᏹᐂᖺ㱋䠄㻝㻟㻣൨ᖺ䠅

109.5
98.5
87.5

Solar chemical composition（weak sensitivity totemperature）

Low-mass survivors㼘㼛㼓㻝㻜㻔㻌୺⣔ิ䛾ᑑ࿨㼇ᖺ㼉㻌㻕

log10 (Main sequence lifetime [yr] )11AGB mass loss

76.5
0.5

Type II SNe
0.8 1

23 4 5 6
ึᮇ㉁㔞㻌㼇ኴ㝧㉁㔞㼉

10

Initial mass [solar masses]15 20

系外惑星の事典

Final fate of AGB / SAGB stars• The key parameters to determine the ﬁnal fate ofintermediate-mass stars are as follows, although they
are aﬀected by the uncertainties associated with theinput physics.
Mup: the minimum initial mass required to ignite carbon.
~7 M⦿ with small metallicity dependenceMn:the minimum initial mass that forms a neutron star
resulting from an electron-capture supernovae.
~9 M⦿ with small metallicity dependence

Mmas: the minimum initial mass that forms an iron corecollapse supernovae.
~9.5 M⦿ with small metallicity dependence
Gil-Pons+18

Structure of AGB stars

Karakas+Lattanzio14

r

Mr =

4 r2 ⇥drStandard picture of AGB evolution- 3rd dredge-up and 13C pocket

0M=2M⦿, Z=0.01

H-burning

He-burning

Herwig05

Thermally Pulsating AGB (TPAGB) stars
M=2M⦿, Z=0.02

Weiss+Ferguson09

Keywords for the evolution of (S)AGB stars
Dredge-up
Mixing of nuclear burning products by the convective envelope.
“1st”, “2nd”, and “3rd dredge-up” are deﬁned.

Hot Bottom Burning
Nuclear burning (CNO cycles) at the bottom of the convective
envelope. Carbon rich stars turn to carbon-normal stars.

Mass Loss
Ejection of the convective envelope. It prevents from theexplosion of intermediate-mass stars.

Core Mass
Mass of the hydrogen-exhausted core, also called “He-core”. It
determines the characteristics of stellar evolution.

Third Dredge-Up: Carbon Enhancement• Deepening of convective envelope during
the AGB phase (Iben75)• Observational counterparts: C stars• Criteria for TDU• Luminosity• Helium core mass

TDU at 7M⦿, Z=0.02
Iben+Renzini83• Inconsistent with the observations oftheoretical limit

Scalo76

Magellanic Clouds.
• Mc needs to be >~0.6M⦿ for TDU tooccur (Iben+Renzini83).
• Carbon star mystery (Iben81)
Latest models ﬁnd TDU with Mc < 0.6M⦿.
• Weiss+Ferguson09: Mc = 0.508M⦿ for1.0M⦿

2. s-process• 中性子捕獲によって合成される元素のうち、中性子捕獲よりもβ崩壊の方が素早く起こるような環境で作られる元素。
• 観測的証拠はAGB星での99Tcの検出。

• 半減期2.13x105 yrでAGB thermal pulseの周期と同程度• 表面で観測されれば、s-processによる合成と表面への輸送の証拠となる。

• AGB星での検出はMerrill52が最初。
• 定量的な観測は、Smith+Wallerstein83, Dominy+Wallerstein86など。

• AGB星で作られると考えられており、中性子源は以下の２つの反応によって放出される(Cameron55)。

• 13C(α,n)16O• 13C pocket: TDUの後に表面対流層の底に水素が混入

炭素の水素捕獲• 22Ne(α,n)25Mg• Massive AGB stars (Mc >~ 1 M⦿)のHe対流層で14Nから22Neが作られる。

• 22Neソースの方が13Cソースよりも高温の環境で機能する。

• 13C pocketの効率はfree parameter• opacity? shear mixing? overshooting?

s-process by 13C Pocket
13C pocket内での組成分布

s-processの金属量依存性

13C(α,n)16Oが起こる前

light smain sheavy s1.5M⦿ model@15th pulse

Goriely+Mowlavi00

2M⦿ modelBusso+99

Parameter Search of 13C Pocket Eﬃciency

Bisterzo+10

Hot Bottom Burning: CNO Cycle at theBase of Convective Envelope• Temperature at the bottom of convective envelope becomes high
(TBCE > 50 MK) at large core mass, where CN cycles operate(Iben75,76).

• 12C/13C approaches a equillibrium value (~3.4) at TBCE ~ 80MK
(Truran72).

• HBB ﬁrst discovered in a 7M⦿ model(Iben75).
• Application to chemical evolution models(Iben+Truran78)• Determination of the mass range of HBB (Renzini+Voli81)。
• Occurrence of HBB strongly depends on mixing length parameter(α = lmix/HP)(Iben76).
• (α, MHBB) = (2, 3.3M⦿), (1.5, 4M⦿), (1, 6.8M⦿)(Renzini+Voli81)• HBB is prohibited in thin envelope mass(Frost+98, Karakas+Lattanzio07)• Mcrit = 1.5 M⦿ (Karakas+Lattanzio07)• No direct evidence of HBB in the observations of AGB stars?
• N > C conﬁrmed by observation (Smith+Lambert83,85)• Metal-poor AGB star: CS30322-023 (Masseron+06)

Mass Loss
• Mechanisms are poorly understood.
• Reimers formula for RGB stars (Reimers75)

Population synthesis of ωCen

• free parameter ηR = 0.3-1.0• eﬀective only for low-mass(~0.8M⦿) giants.
• consistent with the horizontal branch of GCs.

• Dust-driven mass loss (Bowen+Willson91,Wachter+08)• Carbon-dust (SiC) is promising for mass loss.

• Observed mass loss rate for AGB stars (Vassiliadis+Wood93)• Period-Luminosity relation in Mira variables• Mass loss rate increases at certain luminosity (superwind)。

• Planetary nebulae are caused by superwind (dM/dt~10-5 M⦿/yr)?

• Mass loss from O-rich AGB stars (van Loon+05)

Lee+05

Summary of the events in AGB stars

Karakas+Lattanzio14

Extremely Metal-Poor Stars: Hydrogen Ingestion
Into the Helium Flash Convective Zone
0.640

2M⦿, [Fe/H]=-440.635

30.625

M10.620

Mbhs

0.615

1[N/Fe]0.610

0[C/Fe]

0.605
0.600

2[X/Fe]Mr(Msun)

0.630

MCO

20 40 60 80 100 110

112

114116Time (year)

Suda+Fujimoto10

He対流層への水素の混入。水素層とのentropybarrierが少ないために起こる。水素ﬂashを伴い、その後の表面対流層の侵入によってCNが増大。

118

120 500

1000-1Campbell+Lattanzio08

1.5M⦿, [Fe/H]=-3.3
Lau+09Final Fate of Stellar Evolution[Fe/H]• SF10, CL08, L09のどの計算でも水素混合が起こる境界は似ている。
• 水素混合が起こる[Fe/H]は-2.5--3• Carbon Injection:
He層の炭素が水素層に混入。
• Hot third dredgeup: TDUよりも深いdredge-up。
Herwig03でも報告されている。

-1

Off-centre [central]
He-burning
Case IV-2

boundaries ofThird dredge-up

Campbell+Lattanzio08-3
He-FDDM-A

He-FDDM-R

10-2

0.1

10-510-8-510Lau+09
1010-510-70-3

Case II-410-6

Mup
(SNe)

He-FDDM-A

0.1-2

Hot Third Dredge-up
He-FDDM-A
Case IV’

C burning

0He-FDDM-A
Case II’
Third Dredge-up
Hot Bottom Burning

Third Dredge-up

Carbon Injection
Case III

Case IHe-FDDM-R

Z=00.81.0

computedmodels

1.2

1.5

2.0

2.5 3.0
Mini

4.05.06.0 7.0 8.0 9.0

Suda+Fujimoto10

Convective s-process in Extremely Metal-PoorStars• He対流層への水素混合によって13C(α,n)16Oが起こり中性子捕獲反応が進行する(Fujimoto+00, Suda+04)• He core ﬂashの場合のpost-processing (Campbell+10)
1M⦿, [Fe/H]=-6.5

Campbell+10[X/Fe]conv[X/Fe]surfSuper-AGB Stars

Super-Asymptotic Giant Branch Stars• ONeMg core: Miyaji+80, Nomoto84, Nomoto87• Super-AGB: Garcia-Berro+Iben94, Ritossa+96
Kippenhahn Diagram
Mass of H-exhausted core (No envelopes in the code)[M⦿]

convective zones

Nomoto84

t=0: end of calculation

Recovery of H-burning and thermal pulses
M=10M⦿, Z=0.02

Ritossa+96

Summary of SAGB evolution

shorter than AGB (>10000yr)

thinner than AGB (> 10-3 M⦿)Doherty+17

22Ne neutron source

Key parameters for the evolution of SAGB stars
Mup
the minimum initial mass required to ignite carbon.

Mn
the minimum initial mass that forms a neutron star resulting froman electron-capture supernovae.

Mmas
the minimum initial mass that forms an iron core-collapse
supernovae.

λ: Dredge-up parameterdeﬁned by “dredge-up mass by the 3rd dredge-up” / “mass ofthe growth of core mass during the interpulse phase”. If λ > 1,core will decrease with time.

Metallicity dependence of Mup, Mn, and Mmas

Doherty+17

Evolution to C-burning phase
M=8M⦿, Z=0.02 & 10-4

smaller radius at low Z

higher Tc at low Z

Doherty+17

AGB models of low-metallicity stars
M=4-9M⦿, Z=10-5

Gil-Pons+13

Hot bottom burning and the eﬀect of opacity
M=2M⦿, Z=10-7M=3M⦿, Z=10-7

Tashibu+17

Total mass as time

M=4M⦿, Z=10-7

Dredge-up parameters

Poelarends+08

s-process in SAGB stars
Stellar models from
Doherty+14a,b
Nuclear network from
Lugaro+14 (324 species)
neutron source by 22Ne
Nn~1014 cm-3
τ~0.04 mbarn-1
production of Kr (Z=36),
Rb (37), and light sprocess elements (Sr:38, Y: 39, Zr:40)
weak Fe dependence dueto small τ
small amount due tosmall convective shells(5x10-4 M⦿)RbKrSrYZrBaPb

Doherty+17
Mc (He-core mass) ~ 1.15 M⦿, tint (duration ofthermal pulses) ~ 6x104 yr, Npulse (number ofthermal pulses) ~ 100M=7.5M⦿, Z=0.001

Dredge-out in SAGB stars• Envelope is enriched in CNO elements.
(Ritossa+99)• Proton ingestion into He- and C-richregion produces a substantial numberof free neutrons by 13C(a,n)16O.

M=9.5M⦿, Z=0.001

Doherty+17

Jones+16

Dredge-out

Takahashi+13

s-process by dredge-out events• neutron density, Nn = 1015 cm-3
• intermediate n-capture regime (known as ʻi-processʼ)• no calculated yields: 3D simulations, cross sections, etc.

• possible origin of CEMP-s/r (Jones+16)• concern is the small intershell mass (~10-4 M⦿), evenrepeated exposure and dredge-up events may not leadto overabundances.

• rejected based on an IMF argument, the relatively few
SAGB stars seem unlikely to be a major source ofpollution of the CEMP-s/r stars (Abate+16).

Summary - 4 s-process channels
1. radiative 13C burning• “standard” s-process contributed by low-mass AGB stars.

2. convective 22Ne burning• small contribution to s-process elements by high-mass
AGB and SAGB stars.

3. convective 13C burning by H-ingestion• large contribution to s-process elements by low-mass lowmetallicity AGB stars.

4. convective 13C burning by C dredge-out• potentially large contribution to s-process elements bySAGB stars.

AGB / Super-AGB Stars at LowMetallicity

Occurrence of SN I1/2
• At low metallicity, He burns ina steady state.
• No pulse-driven stellar
winds are expected.
• Core mass will grow tohave Chandrasekhar mass
limit, which leads tosupernova explosions.
• SN I1/2 is a thermonuclear
explosion (Type I) with a Hemission lines in its spectra
Fujimoto+84(Type II).

Helium shell ﬂashes
are prohibited.

core mass

Stability of helium shell ﬂashes
F > 0: unstableF < 0: stable
Stability of helium shell ﬂashes
are mainly controlled by

1 ✏⌫ =✓@ ln ✏n@ ln T◆ν⇢

temperature dependence ofnuclear burning rate

2 f: ﬂatness parameter
geometry of He-burning shell,
f ~ 0, spherical symmetry,
weak ﬂash
f ~ 1, strong ﬂash

3 electron degeneracy
P /⇢

5/3

Fujimoto+82Sugimoto+Fujimoto78

complete degeneracy, non-relativistic.
See also Schwarzschild+Harm65, Sackmann77, Yoon+04

End of thermal pulses
M=7M⦿, Z=0• No third dredge-ups• Eﬃcient hot bottom burning

No mass loss

590 thermal pulses in 1.1x105 yrs
Reimers mass loss

Hot H-burning at low Z-> Hot He-burning-> smaller temperaturedependence of 3-α reactions

Lau+08

Suppression of Mass Loss during the AGB Phase
1.5M⦿, [Fe/H]=-4.2

6M⦿, [Fe/H]=-4.2

RvL

1.5M⦿, [Fe/H]=-0.6

Wood11Growth of pulsations during thethermal pulses on the AGB phase

Luminosity is increased
from 11,000 L⦿ to 13,000 L⦿.

Luminosity is taken for
maximum possible value for an
AGB star that is not undergoing HBB.