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22 févr. 2014 (il y a 3 années et 6 mois)

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Stellar Evolution in general and in
Special Effects:

Core Collapse, C
-
Deflagration,
Dredge
-
up Episodes


Cesare Chiosi



Department of Astronomy


University of Padova, Italy

Part C:

Low and intermediate mass stars

The kingdom of Type IA SN

The formation of CO White
Dwarfs

Low and intermediate mass


stars (to about 6 Mo) at

the end of their evolution

generate “White Dwarfs”

made of a mixture of C & O

Burnings in the T
c

vs
r
c

plane

Generalities


Low mass stars are those igniting core He
-
burning in
degenerate conditions (M < 2.2 Mo)



Intermediate mass stars are those igniting He
-
burning in non degenerate conditions, but develop


strongly degenerate CO core (2.2 Mo < M < 8 Mo).



In these stars C
-
ignition fails unless the CO core
mass can grow to Mch = 1.4 Mo



All present the AGB phase.

The beginning of the AGB phase





Mr/M






Typical structure of an AGB star


Following central He
-
exhaustion,
the star is structured as follows:


A contracting, degenerate CO
core;


Two burning shells;


An expanding convective envelope;


The star climbs the Hayashi line
and loses mass by stellar wind.

Two important facts


Because of the expansion the H
-
burning shell temporary extinguishes. The


external convection penetrates very deeply almost reaching the He
-
burning


shell. Variations in the surface chemical abundances (II dredge
-
up).


Extiction of the H
-
shell causes contraction of the envelope followed by


reignition of the H
-
shell very close to the He
-
shell. A very thin layer of


matter separates the two shells.


Because of this, two important facts occur:


(1) the two shells get thermally coupled;


(2) the He
-
shell becomes thermally unstable
.

Thermal coupling


Two burning shells close each other do thermally interact as both require a


certain temperature to exixt. For instance if a He
-
shell gets


very close to a H
-
shell we expect an enormous increase of


H
-
burning.


Each shell has its own speed in processing matter unless the corresponding


luminosities are in a suitable ratio.


Let X
i
be the abundance of a fuel and qi the energy liberated per gram




Thermal coupling requires





K)

10
2
(T
8


K)

10
3
(T
7


i
i
i
i
X
q
L
dt
dM

H
H
H
He
He
He
He
H
X
q
L
X
q
L
dM
dt
dt
dM

Stationarity conditions

Given that



q
H
/q
He

= 10, X
H
=0.7 and X
He

=1



the situation is stationary only if



L
H

= 7 L
He



THIS REQUIRES THAT TIME TO TIME

THE He
-
SHELL UNDERGOES STRONG

ACTIVITY

He
-
shell thermal instability


In general the He
-
shell is quiet and scarcely efficient, whereas


the H
-
shell dominates the energy production.


However, with regular periodicity, the He
-
shell dramatically


increases the energy production, burns out the available fuel,


induces a tiny convective region just above it, and triggers the


expansion of the overlaying envelope causing the temporary


extinction of the H
-
shell.


The He
-
shell gets quiet again thus allowing the envelope to


recontract and the H
-
shell to reignite.


The cycle repeats itself from several to many times (depending on


the star mass and efficiency of mass loss).



WHY?


Positive gravothermal specific heat

D

r
o

Suppose we have a shell of thickness D confined

between ro and ro + dr (D<< ro)

The mass in the shell is


Suppose that following a perturbation in
e
sh
it

expands dr=D and suppose that the mass variation

is negligile







P A
d
ρ dD r dr dP dr
=- =- and =-4
ρ D D r P r
the gravotermal specific heat is
4
δ
c*=c (1- )
r
4 -
D
for D very small c* can be > 0 even for
a normal gas.
Thermal Runaway of the He-shell.
D
r
M
o
sh
2
r


The third dredge
-
up


Complicate interplay between
the extinction of the H
-
burning shell, the penetration
of the external convection
and possible overlap with the
intermediate thin convective
shell


Mr/M

Some general considerations


While the thermal cycles work, and the nuclear shell increases the mass of
the CO core (which becomes more and more electron degenerate), mass loss
by stellar wind continuously decreases the mass of the external envelope until
it is completely expelled.


a CO White Dwarf is left or the CO core can
grow to the Chandrasekhar limit and C
-
deflgration may occur (depends on the
total mass of the star).



The number of cycles depends on the envelope mass with respect to the core


and total mass: low mass AGBs have a small envelope and hence a few cycles,


stars of intermediate mass have bigger envelopes and hence a large number
of cycles.


Every cycle may bring some C to the surface. When the abundance of C
exceeds that of O, a M
-
star is turned into C
-
star.


Finally, as a result of the game between the H
-

and He
-
shells and internal +


external convection, the intershell region can become a good site for s
-
process nucleosynthesis.

Number of pulses and Mc vs L




Interplay between internal and

external convection from pulse

to pulse

Number of pulses

Mc(luminosity)

S
-
process nucleosynthesis in AGB


S
-
process nucleosythesis is the capture of neutrons by heavy elements on


time scale slow with respect to beta
-
decay.



There are at least two sources of neutrons




During the thermal pulses, external convection extends to layers in which


H
-
burning was active in the previous pulse. H
-
rich material is brought to


regions in which He
-
burning occurs and protons are used in the reactions






Mg
n
Ne
O
n
C
25
22
16
12
)
,
(

and

)
,
(


.
and

ith
interact w
can then

neutrons

The

)
,
(





)
,
(
)
,
(
)
,
(
)
,
(





)
,
(
)
,
(
)
,
(
20
13
20
14
17
17
16
16
14
13
13
12
Ne
C
N
n
N
p
O
F
p
O
O
n
N
p
C
N
p
C














In addition……


Alternatively the H
-
shell converts C and O (via the CNO cycle)


into N which is mixed into the He
-
shell thus activating the series


of reactions

Mg
n
Ne
O
F
N
25
22
18
18
14
)
,
(
)
,
(
)
,
(
)
,
(









Another source of neutrons.


The efficiency of the various reactions, processes depends on


many parameters. They are responsible of the synthesis of


elements heavier than Fe via a complex story of n
-
captures,


followed by

and

-
decays

The path to WD
-
deflagration
& detonation

Gravity in close binaries: 1

Gravity in close binaries: 2

Gravity in close binaries: 3

Gravity in close binaries: 4

Mass transfer & accretion disk

Different types of close binaries

Useful definitions for
abundances

Origin of SN IA

SN IA in a snapshot

Type Ia SN: Nuclear Deflagration

How does explosion

proceed?


The case of a WD + MS companion

Most popular model for Type Ia SN consists of a WD
growing to M
Ch
,

presumably


by

accretion

from

a
companion,

and
being

disrupted

by


thermonuclear


explosion.

No remnant is left.

C
-
ignition: in brief………….


C
-
burning first ignites quietly in the WD core but
convectively unstable

DT cause local run
-
away.



Explosive burning
starts
near center or off
-
center
;
flame
front propagates subsonically (deflagration) until it may or

may


not

change into

a
detonation (supersonic)


at

lower
densities
, and eventually
disrupt
s

the star.



Turbulence may develop


turbulent flame


Rayleigh
-
Taylor instabilities by buoyancy of hot ashes with respect to
dense unburned material.



The consequences of all this are……………

Turbulent Combustion

Merging Flame Fronts


EASY TO CHECK THAT ON A SHORT

TIME SCALE

E
n >> |
W
g|

Chemical structure

Before….

After….

Chemical Structure

Chemical abundances

Elements production & energetics

Wide and Close Binary Systems:
CO+CO

S
ecret everybody favoured scheme !!

Wide

Close

But others are possible:

CO+He & He+He

CO+He

He+He

Formation Frequency of SNI
Precursors



Connection between SN Types
and Progenitors

Single

Binaries

To conclude: Two
Nasty
Questions



Why do Type II SN not explode ?



Where are the progenitors of Type
Ia ?


What are Type II SN……..

……….and Modelers doing?



Virginia Trimble 2004


Is CO+CO in troubles ?

Virginia Trimble 2004