Mounib El Eid

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 M_y(?)

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_y (slightly dependent on initial metallicity)

♦do not suffer core helium flash since helium burning

proceeds under weakly degenerate conditions

♦Progenitors of high-mass white dwarfs

Low mass stars:

♦ M ≤ 2 M_y (slightly dependent on initial metallicity)

♦ Suffer core helium flash owing to their central evolution at relatively strong degenerate conditions

(example of 2 M_y follows)

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):

3 ) 4

1 4

*

(

∇ −

−

= α

δ

ad

c

c

Where: _{ad ad}

p T ) ln ( ln

∂

≡ ∂

∇ (adiabatic temperature gradient)

P

T T

P )

ln ( ln ,

ln ) ( ln

∂

− ∂

∂ ≡

≡ ∂ ρ δ ρ

α obtained from

the equation of state: ^d α ^dP_P δ ^dT_T ρ

ρ _{= −}

Discussion

] 40 . 0 5 / 2 1

[α =δ = ∇_ad = =

) 0

5 1 8

*

=

( − <

a) Ideal gas: c

Using :

=

and > 0 → =

< 0

dT dq dq

dT c dq

Since cooling, overproduction of nuclear energy will be reduced

→ stabilization of stellar layers c^* < 0 acts as stabilizer

b) Degenerate non-relativistic gas:

] 5 / 3 ,

0

[ δ → α =

3 /

)

(

e

A

P µ

= ρ

c

> 0

With adding heat (dq >0), then → dT >0 : heating leads eventually to thermal runaway. Indeed this is the case of helium flash

One can show that

: and 0 0

) 3 4

(

3 → =

= − ρ δ

α δ δ

ρ

ρ

T dT d

c c

c c

c

constant y

essentiall remains

while ,

up

T

Therefore, in thermal runaway:

ρ

Core helium flash is an example: let’s see in case of a 2 M_y

C) Thermal Pulsations (AGB stage)

D

Thin shell

r

r

r r

=

+

D r

r r

r

m ≈ ρ

( −

) = ρ

) ] / 4

( 1 4

*

[

D c r

c

∇ −

−

= α

δ

:

*

> 0

c

:

dt c dT

d ε =

d ε > 0 ⇒ dT > 0

] 40 . 0 5 / 2 1

[α =δ = ∇_ad = =

Ideal Gas:

4 / 1 /

0 / )

4 4 5

1 2

*

( > ⇔ <

− −

=

D c r

c _P

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.

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 M_y star through the core helium flash and thermal pulsations

2 M_yStar initial Z=0.02

Core Helium flash

T K

η = µ (Degeneracy parameter)

Devoted to the Andalusian Astronomer

Azarquiel 905 years after his death From an Arab/ German

Astrophysicist

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

2 M

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.

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

(see previous HR diagram)

Log (T/ 10⁸)

Log ρ

Pulsation in progress what a hard work

Thermally pulsating 2 M

on the AGB

3 M_y star with Z=0.02

With neutrino losses

Without

neutrino losses

Central Evolution

2 M_y

Neutrino losses switched off

3 M

4x10⁴

5x10⁴

5.5x10⁴ 5x104

6.5x10⁴

3 M

8x10⁴

6.5x10⁴

5.5x10⁴

M

M

With neutrino losses

M

M

Without neutrino losses

The world of pre-solar grains:

Properties:

♦ ¹²C/¹³ C<10

♦ ¹⁴N/¹⁵N =30 – 30000 significant fraction

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

Did AGB stars contribute to presolar A+B grains?

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

C N

p

C ^{13 13}

12 ( ,γ ) (β ⁺,ν )

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