LMS & IMS: their evolution, nucleosynthesis and dusty end

S. Cristallo

in collaboration with Oscar Straniero and Luciano Piersanti

Osservatorio Astronomico di Teramo - INAF

AGBs: a theoretician perspective

Very luminous(103-104 our SUN)

Very cold(2000-3000 K)

AGB structure

CO CoreHe-shellH-shell

Earth radius(~10-2 RSUN)

Earth-Sun(~200 RSUN)

Practically, a nut

in a 300 mts hot air balloon

The s-process in AGB stars

Busso et al. 1999

13C(α,n)16O reaction 22Ne(α,n)25Mg reaction

HOT BOTTOM BURNING (Boothroyd & Sackmann 1991)

TDU

TDU

HYDROSTATIC, NO ROTATION, NO MAGNETIC FIELDS

Four

first-order non-linear

constant coefficients

differential equations

Three

characteristic relations

The FRANEC Code(Frascati RAppson-Newton Evolutionary Code)

(Chieffi & Straniero 1989; Straniero et al. 1997; Chieffi et al. 2001;Straniero et al. 2006; Cristallo et al. 2007; Cristallo et al. 2009)

Major uncertainty sources in stellar evolutionary codes and their link with grains

1. Opacities;2. Mass-loss law;3. Equation of State (IMS); 4. Convection treatment;5. Non convective mixing mechanisms (LMS).

Opacities

T2000 K4000-5000 K

Atomic opacities

Molecular opacities

Grains

C/O>1 CO – C2 – CN - C2H2 – C3 Marigo 2002; Cristallo et al. 2007

C/O<1 TiO – H2O - CO

Metallicity 12C & 14N enh. factors

2x10-2 1, 1.5, 1.8, 2.2, 5

Solar ≡ 1.4x10-2 1, 1.5, 1.8, 2.2, 4

1x10-2 & 8x10-3 1, 1.8, 2.2, 5, 10

3x10-3 & 6x10-3 1, 2, 5, 10, 50

1x10-3 1, 5, 10, 50, 200

1x10-4 1, 10, 100, 500, 2000

C and N enhancements

See also:Lederer & Aringer 2009; Weiss & Ferguson 2009Ventura & Marigo 2009; Marigo & Aringer 2009

Karakas et al. 2010

Results

The C-enhanced low temperature opacities

make the stars redder in the AGB phase

Effects on surface temperatures and, therefore, on mass-loss and nucleosynthetic yields

AGB PHASE

Vassiliadis&Wood 1993

Straniero et al. 2006

1. BCK - temperature (Fluks et al. 1994)2. Luminosity - MBOL

3. MK=MBOL-BCK

4. Period-MK (Whitelock et al. 2003)5. Period – Mass-loss

Mass loss law

GRAINSDRIVE THEMASS-LOSS

Grains: opacities and mass-lossWinds of carbon stars are considered to be dust-driven winds. Photons lead to a radiative acceleration of grains away from the star.Subsequently, momentum is transferred to the surrounding gas by gas-grains collisions.

UNKNOWNS

1.grains opacity (how they interact with radiation);2.grains growth process;3.grains nucleation phase (in particular for C/O>>1);4.stellar pulsation physics.

It is commonly assumed that grain sizes are small compared to the relative wavelenght: that’s not always true (see e.g. Mattsson et al. 2011)

The Luminosity function of Galactic C-stars

Guandalini et al. 2006 (A&A, 445, 1069)Cristallo et al. 2011 (ApJS, 197, 2)

The Luminosity function of Galactic C-stars

Guandalini & Cristallo, in preparation

Distances from van Leeuwen 2007 P-L from Whitelock et al. 2006

First attempt (to my knowledge) to evaluate the amount and type of dust production in AGB stars with a stellar evolutionary model

Total mass of dust as a function of the stellar mass

Ventura et al. 2012 (MNRAS 424, 2345)

Ventura et al. 2012 (MNRAS 420, 1442)

1. Amount of silicates scales with Z2. Silicates are produced in IMS (strongly

dependence on HBB)3. Mass-loss rate dtermines the dust condensation

degree4. For C-stars, the main source of uncertainty is

the amount of dredged up carbon

Mass of silicates Mass of carbon dust

EOS for IMSFor Intermediate Mass Stars, the temperature at the bottom of the convective

envelope is high enough (T>4e7 K) to allow proton captures: HOT BOTTOM BURNING (Boothroyd & Sackmann 1991)

Convection treatment• Schwarzschild criterion: to determine convective borders

• Mixing length theory: to calculate velocities inside the convective zones

• Mixing efficiency: proportional to the ratio between the convective time scale and the time step of the calculation (Spark & Endal 1980);

• ΔX depends linearly on Δr (NOT diffusive approach).

At the inner border of the convective At the inner border of the convective envelopeenvelope, we assume that the velocity , we assume that the velocity profile drops following an profile drops following an exponentially decaying lawexponentially decaying law

v = vbce · exp (-d/β Hp) • Vbce is the convective velocity at the

inner border of the convective envelope (CE)

• d is the distance from the CE

• Hp is the scale pressure height

• β = 0.1

REF: Freytag (1996), Herwig (1997),REF: Freytag (1996), Herwig (1997),Chieffi (2001), Straniero (2006), Chieffi (2001), Straniero (2006), Cristallo (2001,2004,2006,2009)Cristallo (2001,2004,2006,2009)

WARNING: vbce=0 except during Dredge Up episodes

Gradients profiles WITHOUT exponentially decaying velocity profileGradients profiles WITH exponentially decaying velocity profile

CONVECTIVEENVELOPE

RADIATIVE He-INTERSHELL

Duringa TDUepisode

An interesting by-product: the formation of the 13C pocket

13C-pocket

23Na-pocket

14N-pocket

Variation of the 13C-pocket pulse by pulse

X(13Ceff)=X(13C)-X(14N)*13/14

1st 11th

14N strong neutron poison via

14N(n,p)14C reaction

Cristallo et al. 2009

13C pocket and dredge up as a function of

Third TP of 2 MThird TP of 2 Mʘʘ at Z=Z at Z=Zʘʘ and Z=10 and Z=10-4-4

Convective 13C burning

Cristallo et al. 2009

He-intershell elements enrichments

J=Iω=mr2ω

F.R.U.I.T.Y.(Franec Repository of Updated Isotopic Tables & Yields)

August the 9th 2012: added 1.3 MSUN models at all metallicities

Z=10-4 models (within the end of November)

On line at www.oa-teramo.inaf.it/fruity

(1.5,2.0,2.5,3.0) MSUN with Z=(1x10-3,3x10-3,6x10-3,8x10-3,1x10e-2,sun,2x10e-2)

Dedicated mailing list with upgrades

Final AGB composition for 0.0001<Z<Z

A key quantity:the neutron/seed ratio, that is

n(13Ceff) /n(56Fe)

13C is primary like56Fe is secondary like

M=2Mʘ

[ls/Fe]

[Pb/Fe]

[hs/Fe]

s-process indexes (I)[ls/Fe]=([Sr/Fe]+[Y/Fe]+[Zr/Fe])/3

[hs/Fe]=([Ba/Fe]+[La/Fe]+[Nd/Fe] +[Sm/Fe])/4

Cristallo et al. 2011

[ls/Fe]=([Sr/Fe]+[Y/Fe]+[Zr/Fe])/3 [hs/Fe]=([Ba/Fe]+[La/Fe]+[Nd/Fe] +[Sm/Fe])/4

Ba & CH stars

Post-AGB

Intrinsic C-rich

Intrinsic O-rich

Observations vs theory (II): [hs/ls] distributions

FRUITY Models vs Grains (measurements from Barzyk et al. 2007)

FRUITY Models vs Grains (measurements from Barzyk et al. 2007)

FRUITY and MONASH models vs Grains (measurements from Avila et al. 2012)

The most interesting data are those that do not agreewith theoretical models.

Ernst Zinner (this morning)

A new set of FRANEC rotating AGB models

1. Centrifugal forces lead to deviations from spherical symmetry;2. Differential rotation is considered and, following Endal & Sofia (1976,1978), the evolution of

angular momentum (J) through the star is followed via a nonlinear diffusion equation (except at the inner border of the convective envelope, where we apply the same formalism of the chemical transport), by enforcing rigid rotation in convective regions (constant angular velocity);

3. Efficiency of both dynamical (Solberg-Hoiland, dynamical shear) and secular (Eddington-Sweet circulation, Goldreich-Shubert-Fricke, secular shear) instabilities are evaluated by computing the corresponding diffusion coefficients as described in Heger et al. (2000), but without their proposed fμ and fc;

4. Angular momentum transport equation is solved contemporary to the chemical evolution equations to take into account the feedback of chemical mixing on molecular weight profile, which could inhibit secular instabilities (μ-current);

5. In solving the angular momentum transport and chemical mixing equations, we computed the effective diffusion coefficient as the sum of the convective one and those related to secular and dynamical rotationally instabilities;

6. No magnetic braking is considered.

PRELIMIN

ARY

THANKS!