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 (10 3 -10 4 our SUN) Very cold (2000-3000 K)

CO Core He-shell H-shell Earth radius (~10 -2 R SUN )

Practically, a nut in a 300 mts hot air balloon

AGB structure Earth-Sun (~200 R SUN )

The s-process in AGB stars 13 C(α,n) 16 O reaction 22 Ne(α,n) 25 Mg reaction TDU TDU HOT BOTTOM BURNING (Boothroyd & Sackmann 1991)

Busso et al. 1999

The FRANEC Code

( F rascati RA ppson N ewton E volutionary C ode) (Chieffi & Straniero 1989; Straniero et al. 1997; Chieffi et al. 2001; Straniero et al. 2006; Cristallo et al. 2007; Cristallo et al. 2009) Four first-order non-linear constant coefficients differential

equations

Three characteristic

relations

HYDROSTATIC, NO ROTATION, NO MAGNETIC FIELDS

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

T

Atomic opacities Molecular opacities 4000-5000 K 2000 K Grains

C/O<1 C/O>1

TiO – H 2 O - CO CO – C 2 – CN - C 2 H 2 – C 3 Marigo 2002; Cristallo et al. 2007

C and N enhancements

Metallicity 2 x 10 -2 Solar ≡ 1.4

x 10 -2 1 x 10 -2 & 8x10 -3 3 x 10 -3 & 6 x 10 -3 1 x 10 -3 1 x 10 -4 12 C & 14 N enh. factors 1, 1.5, 1.8, 2.2, 5 1, 1.5, 1.8, 2.2, 4 1, 1.8, 2.2, 5, 10 1, 2, 5, 10, 50 1, 5, 10, 50, 200 1, 10, 100, 500, 2000 See also: Lederer & Aringer 2009; Weiss & Ferguson 2009 Ventura & 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

Mass loss law

AGB PHASE 1. BC K - temperature (Fluks et al. 1994) 2. Luminosity - M BOL 3. M K =M BOL -BC K 4. Period-M K (Whitelock et al. 2003) 5. Period – Mass-loss GRAINS DRIVE THE MASS-LOSS

Vassiliadis&Wood 1993 Straniero et al. 2006

Grains: opacities and mass-loss

Winds 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.

2.

3.

4.

grains opacity (how they interact with radiation); grains growth process; grains nucleation phase (in particular for C/O>>1); 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 1.

2.

3.

4.

Amount of silicates scales with Z Silicates are produced in IMS (strongly dependence on HBB) Mass-loss rate dtermines the dust condensation degree For C-stars, the main source of uncertainty is the amount of dredged up carbon 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) Mass of silicates Mass of carbon dust

EOS for IMS

For 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 envelope, we assume that the velocity profile drops following an exponentially decaying law REF: Freytag (1996), Herwig (1997), Chieffi (2001), Straniero (2006), Cristallo (2001,2004,2006,2009) v = v bce · exp (-d/

β

H p )

• • • •

V bce is the convective velocity at the inner border of the convective envelope (CE) d is the distance from the CE

H p

is the scale pressure height β = 0.1

WARNING: v bce =0 except during Dredge Up episodes

Gradients profiles exponentially decaying velocity profile RADIATIVE He-INTERSHELL CONVECTIVE ENVELOPE

During a TDU episode

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

C-pocket

14

N-pocket

23

Na-pocket

Variation of the

13

C-pocket pulse by pulse

X( 13 C eff )=X( 13 C)-X( 14 N)*13/14 14 N strong neutron poison via 14 N(n,p) 14 C reaction 1 st 11 th Cristallo et al. 2009

13 C pocket and dredge up as a function of b

Third TP of 2 M

ʘ

at Z=Z

ʘ

and Z=10

-4

Convective

13

C burning

He-intershell elements enrichments

J=Iω=mr 2 ω

Cristallo et al. 2009

F.R.U.I.T.Y.

( F ranec R epository of U pdated I sotopic T ables & Y ields) August the 9 th 2012: added 1.3 M SUN models at all metallicities Z=10 -4 models (within the end of November) Dedicated mailing list with upgrades On line at www.oa-teramo.inaf.it/fruity (1.5,2.0,2.5,3.0) M SUN with Z=(1 x 10 -3 ,3 x 10 -3 ,6 x 10 -3 ,8 x 10 -3 ,1 x 10e -2 ,sun,2 x 10e -2 )

M=2M

ʘ

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

Final AGB

n(

13

C

eff

) /n(

56

Fe)

composition for 0.0001

13

C is primary like

56

Fe is secondary like

s-process indexes (I)

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

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

Ba & CH stars Post-AGB Intrinsic C-rich Intrinsic O-rich

[ls/Fe]=([Sr/Fe]+[Y/Fe]+[Zr/Fe])/3 Cristallo et al. 2011 [hs/Fe]=([Ba/Fe]+[La/Fe]+[Nd/Fe] +[Sm/Fe])/4

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 agree with theoretical models.

Ernst Zinner (this morning)

A new set of FRANEC rotating AGB models

1.

2.

3.

4.

5.

6.

Centrifugal forces lead to deviations from spherical symmetry; 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); 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 f μ and f c ; 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); 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; No magnetic braking is considered.

THANKS!