Comments on

Mounib El Eid American University of Beirut Department of Physics

Granada Feb 6, 2006 Content:

1. General comments a) basic mechanism of thermal runaway b) Convection and mass loss on AGB 2. Some results a) Evolution without core helium flash: 3 My b) Evolution with core helium flash: 2 My When we deal with the evolution to the Asymptotic Giant Branch (AGB) stage

In stellar evolution, we are directly concerned to the evolution of low and

intermediate-mass stars, that is with a mass range up to about 8 My (?) where this upper limit depends on initial metallicity (Z) and ????. Any way, the white dwarfs are formed in such mass range. We distinguish low mass stars from intermediate-mass stars:

Intermediate-mass stars: ♦M > 2 M (slightly dependent Low mass stars: y on initial metallicity) ♦ M ≤ 2 M (slightly dependent on y ♦do not suffer core helium flash initial metallicity) since helium burning ♦ Suffer core helium flash owing to proceeds under weakly their central evolution at relatively degenerate conditions strong degenerate conditions ♦Progenitors of high-mass (example of 2 M follows) y white dwarfs 1 a) Basic mechanism of thermal runaway Thermal runaway is a secular instability which may occur when nuclear burning becomes unstable and is governed by thermal relaxation. Secular instability in degenerate regions leads to core helium flash. Secular instability in thin non-degenerate regions leads to quasiperiodic thermal pulsation. Analyzing this instability is nicely accomplished by considering the gravothermal specific heat . Stars are surprising since they have negative gravothermal specific heat reflecting the fact that they heats up while losing energy by radiation.

The gravothermal specific heat (c*) is introduced by the following equation (see Kippenhahn & Weigert 1990 for details): 4δ c* = c (1− ∇ ) P ad 4α − 3 ∂ ln T Where: ∇ ≡ ( ) (adiabatic temperature gradient) ad ∂ ln p ad ∂lnρ ∂lnρ obtained from α ≡ ( )T , δ ≡ −( )P d ρ dP dT ∂lnP ∂lnT = α − δ the equation of state: ρ P T Discussion: 8 a) Ideal gas: [α = δ =1 ∇ = 2 / 5 = 0.40] c* = c (1− ) < 0 ad P 5 dq Using : dq=c* dT and dq>0 → dT = <0 c* Since cooling, overproduction of nuclear energy will be reduced → stabilization of stellar layers

c* < 0 acts as stabilizer b) Degenerate non-relativistic gas:

ρ 5 / 3 P = A( ) → [δ →0, α =3/5] c* > 0 µ e With adding heat (dq >0), then → dT >0 : heating leads eventually to thermal runaway. Indeed this is the case of helium flash dρ 3δ dT One can show that : c c δ = and dρc → 0 for δ = 0 ρc (4α −3) Tc Therefore, in thermal runaway: Tc up , while ρc remains essentially constant

Core helium flash is an example: let’s see in case of a 2 My C) Thermal Pulsations (AGB stage) Thin shell

r = r 0 + D D 2 2 m ≈ ρ r0 (r − r0 ) = ρ r0 D

* 4δ r r c = c [1− ∇ ] 0 P ad (4α − r / D)

c* > 0: Shell source unstable, since: dT dε = c * and for: dε >0 ⇒ dT>0 dt

Ideal Gas: [α = δ =1 ∇ad = 2 / 5 = 0.40] 2 4 c* = c (1− ) > 0 ⇔ R/ r <1/ 4 P 5 4−r / D

It depends on D whether the shell source is stable or not. The point is that the temperature sensitivity of nuclear burning has to exceed a certain limit to have instability and this is the case for helium burning.

Why Convection is so important? Schematic structure of an AGB star

♦Mixing of Nucleosynthesis product to the surface: in particular the s-process products

♦Semiconvection (diffusion?) or a kind of overshooting is required to mix a sufficient amount of protons into the layers processed during the pulse by the helium flash Z=0.02 Evolution of a 2 My star through the core helium flash and thermal pulsations

µ η = (Degeneracy parameter) K T

2 My Star initial Z=0.02

Core Helium flash

The center cannot remain in the high degeneracy Region, it “moves away

Devoted to the Andalusian Astronomer Azarquiel 905 years after his death From an Arab/ German Astrophysicist 2 My star : begin of core helium flash

The characteristic of the core helium flash: Triple-alpha reaction leads to am enormous increase of the helium luminosity. Log ρ However, this released power is used to exapnd the overlying mass. The hydrogen shell power is reduced and the star’s luminosity decreases to the location of the horizontal branch Log (T/ 108)

(see previous HR diagram) Thermally pulsating 2 My on the AGB

Pulsation in progress what a hard work Central Evolution 3 My star with Z=0.02

With neutrino losses Without neutrino losses 2 My Neutrino losses switched off 3 My With Neutrino losses

5x104 5x104 4 4x104 5.5x10 8x104

7.5x104 6.5x104 3 My 5.5x104 6.5x104 With neutrino losses

MHe

MCO Without neutrino losses

M He

M CO Did AGB stars contribute The world of pre-solar grains: to presolar A+B grains?

Properties: ♦ 12C/13 C<10 ♦ 14N/15N =30 – 30000 significant fraction solar of the A+B grains have subsolar values ♦ It seems that these grains have condensed from atmospheres having solar s-process nuclei, 96Zr enhanced, but Mo-isotopes solar. solar

The challenging issue here is: The sources of A+B grains have Experienced H-burning of low 12C/13C ratio while marinating carbon-rich environment in which The s-process was inefficient Nucleosynthesis considerations:

Low value of 12C/13C implies production of 13C by the branching of the CNO cycle 12 C ( p,γ )13 N (β + ,ν )13 C But this cannot happen when the CNO cycle operates in equilibrium, since the ratio 12C/13 C=3 nearly independent of temperature. While 14 N/ 15N is very sensitive to temperature through the resonant reaction 15N(p,α)12C.

H-burning occurs in various stellar environments:

Core H-burning on the main sequence Hot Bottom Burning on AGB Late Helium flash on post AGB

Core helium flash Novae and SNe

Except the first in first case, 13C is mixed into the H-rich zone and the reaction chain above is initiated . The more challenging issue is that the A+B grains seem to be produced in a carbon-rich environment