iii. stellar evolution, thermonuclear reactions, and stellar ...02.12.2019 1 1 iii. stellar...
TRANSCRIPT
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III. Stellar Evolution, Thermonuclear Reactions,
and Stellar Nucleosynthesis
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1. Stellar Evolution The Hertzsprung- Russell diagram
M, R, L and Te do not vary
independently.
Two major relationships
L with T
L with M
The first is known as the
Hertzsprung-Russell (HR)
diagram or the colour-
magnitude diagram.
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Basic parameters to compare theory and observations:
• Mass (M)
• Luminosity (L)
– The total energy radiated per second i.e. power (in W)
• Radius (R)
• Effective temperature (Te)
– The temperature of a black body of the same radius as the star that would radiate the same amount of energy. Thus
L= 4R2 Te4
where is the Stefan-Boltzmann constant (5.67 10-8 W m-2 K-4)
Observable properties of stars
3 independent quantities
L Ld0
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Sun
1,2. Why are Stars as they are?
Trying to understand the physical
concept of stellar structure!
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)r(L)r(Tr
)r()r(
dr
)r(dT R
3264
3
2r
)r()r(GM
dr
)r(dP
)r(rdr
)r(dM 24
T(r))ρ(r) ε(r,πrdr
dL(r)
Material functions of stellar matter:
Equation of state P = P (, T, chemical composition)
Opacity R = R(, T, chemical composition)
Energy production = (, T, chemical composition) WS 2019/20 CCE.III
The equations of stellar structure We have four differential equations, which govern the
structure of stars (note – in the absence of convection).
r = radius
P = pressure at r
M = mass of material within r
= density at r
L = luminosity at r (rate of energy flow across sphere of radius r)
T = temperature at r
R = Rosseland mean opacity at r
= energy release per unit mass per unit time
Figure 12.1 Hydrostatic Equilibrium
Internal structure of the Sun
Internal models
shown for ZAMS
Sun (subscript z)
and for present
day Sun (radius
reaching out to
1.0, subscript )
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2. Nuclear Reactions
How much nuclear energy can
be gained from mass deficit
by means of fusion reactions?
Hence the only known way of producing sufficiently large amounts of
energy is through nuclear reactions. There are two types of nuclear
reactions, fission and fusion. Fission reactions, such as those that
occur in nuclear reactors, or atomic weapons can release ~ 510-4 of
rest mass energy through fission of heavy nuclei (uranium or
plutonium).
But also fusion reactions are known!
Task: How many fusion reactions of e.g. H He4 are necessary to release enough
energy to power the Sun (atomic weight of H=1.008172 and He4=4.003875)?
Given the limits on P(r) and T(r) that we have just obtained - are the central
conditions suitable for fusion ?
Mm
cmE
lost
426
2
1010 kg
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The kinetic energy of particles at central stellar temperature Tc = few 106 – 107 K is 3/2 kTc ≈ 1 keV
At large T, the Maxwellian v2
distribution decreases as
At Tc gas is fully ionized and positively charged nuclei with number of protons in each nucleus = z1, z2 act with repulsive energy of ~ 1 MeV (e= electron charge = 1.6 · 10-19 C, 0 = permittivity of free space
= 8.85 · 10-12 C2 N-1 m-2 )
To fuse nuclei, must surmount the Coulomb barrier. There is a finite probability for a particle to penetrate This barrier: “tunnel” effect
kT
mv
e 2
2
2.1. Fusion Reactions
r
ezz
0
2
21
4
kT
mv
evkT
m)v(f 22
23 2
24
:distr. Maxwell
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The Gamow peak
Quantum effect discovered by George Gamow (1928). Penetration probability (calculated by Gamow) is given as: Schematically this is plotted, and the fusion most likely occurs in the energy window defined as the Gamow Peak. The Gamow peak is the product of the Maxwellian distribution and tunnelling probability. The area under the Gamow peak determines the reaction rate:
.
vh
eZZ
e 0
221
kT
vm
vh
eZZ
ee)fusion.(probab 2
2
0
221
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2.2.The binding energy of atomic nuclei
The higher the electric charges of the interacting nuclei, the greater
the repulsive force, hence the higher Ekin and T before reactions
occur.
Highly charged nuclei are obviously the more massive, so reactions
between light elements occur at lower T than reactions between
heavy elements
In any nuclear reaction the following must be conserved:
1. The baryon number – protons, neutrons and their anti-particles
2. The lepton number – light particles, electrons, positrons,
neutrinos, and anti-neutrinos.
3. Charge
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The total mass of a nucleus is known to be less than the mass of the
constituent nucleons. Hence there is a decrease in mass if a
companion nucleus is formed from nucleons, and from the Einstein
mass-energy relation E = m c2
the mass deficit is released as energy. This difference is known as the
binding energy of the compound nucleus. Thus if a nucleus is
composed of Z protons and N neutrons, it’s binding energy is
For our purposes, a more significant quantity
is the total binding energy per nucleon:
And we can then consider this number
relative to the hydrogen nucleus
2c)N,Z(mNmZm)N,Z(Q np
A
)N,Z(Q
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Binding energy per nucleon
Peak binding energy: 56Fe
Nuclei with A > 56 form via p, s, r processes.
More stable if A is a multiple of 4:
4He 8Be 12C 16O 20Ne 24Mg 28Si …. 56Fe
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The variation of binding energy per nucleon with baryon number A
• General trend is an increase of Q with atomic mass up to A= 56 (Fe).
Then slow monotonic decline.
• Steep rise from H through 2H, 3He, to 4He fusion of H to He should
release larger amount of energy per unit mass than say fusion of He
to C.
• Energy may be
gained by fusion
of light elements
to heavier, up to
iron Fe.
• Or from fission of
heavy nuclei into
lighter ones down
to Fe.
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2.3. p-p chain The most important series of fusion
reactions are those converting H to He
(H-burning). This dominates ~90% of
lifetime of nearly all stars.
• Fusion of 4 protons to give one 4He is
completely negligible.
• Reaction proceeds through steps –
involving close encounter of 2 part.s.
• We will consider the main ones:
the pp-chain and the CNO cycle
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Solar Composition Change
Figure 12.2
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Relative importance
of PPI and PPII chains
(branching ratios)
depend on conditions
of H-burning (T, ,
abundances). The
transition from PPI to
PPII occurs at
temperatures in
excess of 1.3107 K.
Above 3107 K the
PPIII chain dominates
over the other two,
but another process
takes over in this
case.
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Further p-He paths
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PPI Chain
1 p + p d + e+ + e
2 d + p 3He +
3 3He + 3He 4He + 2p
PPII Chain
3' 3He + 4He 7Be +
4' 7Be + e 7Li + e
5' 7Li + p 4He + 4He
PPIII Chain
4'' 7Be + p 8B +
5'' 8B 8Be + e+ + e
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or
Bethe-Weizäcker cycle
2.4. CNO Cycle
At birth present stars
contain a small (2%)
mix of heavy elements,
some of the most
abundant of which are
carbon, oxygen, and
nitrogen (CNO).
These nuclei may
induce a chain of H-
burning reactions in
which they act as
catalysts.
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Timescale of the CNO Cycle
1 12C + p 13N +
2 13N 13C + e+ + e
3 13C + p 14N +
4 14N + p 15O +
5 15O 15N + e+ + e
6 15N + p 12C + 4He
In the steady state case, the abundances of isotopes must take values such that the isotopes which react more slowly have higher abundance. The slowest reaction is p capture by 14N. Hence most of 12C is converted to 14N.
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pp chain and CNO Cycle: T dependence
The two processes have very different temperature dependences.
The rate of energy production in each:
64
0
2
0
.
HppT
TX
716
601025
.
NCNOHCNO
TfXX
K 112
1
7
501071
.
CN
H
X
X.T
Below this temperature the pp
chain dominates, and above it
the CNO Cycle, that is in stars
slightly more massive than the
Sun e.g. 1.2-1.5M
.
Equating these two gives the T
at which they produce the
same rate of energy:
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Red Giant state Figure 12.4
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• Stage 8 - Subgiant branch
• Stage 9 - Red Giant branch
• H depleted at center, He core grows
• Core pressure decreases,
gravity not
• He core contracts, H shell
burning increases
• Star’s radius increases,
surface cools, lumin. increases
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2.5. He Burning: Triple- Process
Simplest reaction in a helium gas should be the fusion of two
helium nuclei. There is no stable configuration with A=8. For
example the beryllium isotope 8Be has a lifetime of only 2.610-16 s.
4He + 4He 8Be But a third He nucleus
can be added to 8Be
before decay,
forming 12C by the
“triple-” reaction 4He + 4He 8Be 8Be + 4He 12C +
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• Red Giant core contracts (no
nuclear burning there)
• Central temperature reaches 108 K
• Fusion of He starts abruptly -
Helium flash for a few hours
• Star re-adjusts over 105 years
from stage 9 to 10
• H and He burning with C core -
horizontal branch
Figure 12.5
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Horizontal Branch stage 10: He Fusion
Reascending the Giant Branch
• C core contracts (no
nuclear burning there)
• Gravitational heating
• H and He burning
increases
• Radius and luminosity
increases
Figure 12.7
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Evolution of a Sun-like Star
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Maeder & Meynet (1989)
When they die their nucleosynthe-sis products are fixed. Depending on their mass loss, at least part of fresh elements are released to the interstellar medium.
2.6. Stellar lifetimes
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from binary stars
tMS (yrs) ≈ 1010 (M/M )-2.8 o .
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3. Stars as Manufactories of Elements
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3.1 Nucleosynthesis by intermediate-mass Stars
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) are characteristic
for their He, C and N production and enrichment. CCE.III WS 2019/20
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Thermal pulses during the AGB phase lead
to convection and by this to a mixing of
different burning layers.
Lattanzio (2002)
Lattanzio & Karakas (2001)
Typical s-process elements: 14N, 22Na, 25Mg, 26Al, Ba, Xe
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H shines in red
[OIII] 4959 Å, 5007 Å in the green
blue color from [NeIII] 3869 Å u.a.
Rosetta Nebula Ring Nebula
Intermediate-mass Stars
end-up by PNe and
release Elements
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3.2. Nucleosynthesis by Massive Stars
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Massive stars release their
nucleosynthesis products
by peeling of the outer-
most layers by stellar
winds and final typeII
supernova explosions.
The most abundant
elements produced and
released by massive stars
are: 16O, 20Ne, 24Mg, 28Si, 32S
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3.3. Wolf-Rayet Bubbles are hot
NGC 6888
HII regions are used to determine ISM abundances: unaffected by released elements?
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Maeder & Meynet (1987)
WR winds peel off burning shells – Release of C, N, O - Influence on abundance determination?
Massive stars produce heavy elements up to 56Fe. The most abundant elem.s are produced by subsequent α-burning shells and released winds and as supernovae II: 16O, 20Ne, 24Mg, 28Si, 32S
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Pre-Supernova “Onion Skin” Structure
(g cm-3) T (108 ºK) 102 0.2
104 2
105 5
106 10
106 20
107 40
Core collapses at M ~ 1.4M
Fe-Ni
core
Prominent
constituents
H, He, 2% CNO, 0.1% Fe
He, 2% 14N
12C, 16O, 2% 22Ne
16O, 20Ne, 23Na, 24Mg
16O, 24Mg, 23Na
28Si
Heavy elements
settle into layers.
Shell burning at
interfaces.
Composition of
layers dominated by
more stable nuclei
(a multiple of 4)
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3.4. Major nuclear burning processes
Common feature is release of energy by consumption of nuclear fuel.
Rates of energy release vary enormously. Nuclear processes can also
absorb energy from radiation field, we shall see consequences.
Nuclear
Fuel
Process Tthreshold
106K
Products Energy per nucleon
(Mev)
H PP ~4 He 6.55
H CNO 15 He 6.25
He 3 100 C,O 0.61
C C+C 600 O,Ne,Ma,Mg 0.54
O O+O 1000 Mg,S,P,Si ~0.3
Si Nuc eq. 3000 Co,Fe,Ni <0.18
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Carbon burning: 12C + 12C 24Mg + γ
23Na + p
20Ne + α
16O + 2α
Neon burning: 20Ne + α 24Mg + γ
20Ne + γ 16O + α
Photodesintegration above 1.5 109 K
Oxygen burning: 16O + 16O 32S + γ
31S + n
31P + p
28Si + α
24Mg + 2α
16O + α 20Ne + γ at T~109 K
Silicon burning: 28Si + 28Si 56Ni + γ
56Ni 56Co + e+ + νe
56Co 56Fe + e+ + νe
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Periodic Table
16O + 16O 32S + energy 4He + 16O 20Ne + energy
Light Elements Heavy Elements
4 (1H) 4He + energy 3(4He) 12C + energy 12C + 12C 24Mg + energy 4He + 12C 16O + energy 28Si + 7(4He) 56Ni + energy 56Fe C-N-O Cycle
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Stellar Nucleosynthesis
p
n
Add protons or
neutrons,
then beta decay back
to valley of stability.
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Many low-mass stars. Long lives (> Hubble time).
A few high-mass stars: Quickly go Supernova (SN),
enrich the ISM with metals. M* > 8 M
SN => enrichment of ISM
M* < 8 M
retain most of their metals, => little enrichment of ISM
Intermediate mass stars: ( 1 < M*/M < 8 )
Make He, … C, N, O, …, Fe, but no SN.
Some ISM enrichment ( stellar wind, planetary nebulae )
but most metals stay locked up in collapsed remnant
( ~ 0.5-0.8 M
WD ).
3.5. Role of Supernovae
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Exploding Supernova Ejecta
Remnant
NS or BH
explosive O-burning (s-process?, p-
process?)
explosive C-burning (s-process?)
explosive He-burning (r-process?)
explosive H-burning (p-process?)
explosive Si-burning
Stellar surface
Core collapse (few ms),
bounces at nuclear density,
outward shock wave (few
hours), ignites shells and
expels the stellar envelope
(V>104 km/s).
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3.6. Neutron Capture In stars and in explosions free neutrons are captured by heavy
elements: AX + n A+1X + γ
Rapid neutron capture leads to r-process elements with large N, i.e.
n-capture faster than β-decay n p + e- + νe.
Slow (s-)process isotopes decay to larger p numbers. CCE.III WS 2019/20
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Origin of Heavy Elements
Problem: Coulomb repulsion too high for fusion beyond Fe Solution: Neutrons
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Neutron Capture Processes
r-process
s-process • Capture several n’s
• beta decay
• Repeat • Capture one n
• beta decay
• Wait for next n
• Repeat
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Neutron capture processes: classical picture
neutrons
pro
tons
N=50
N=82
dn~1023cm-3
T~109K
r (rapid) (n, ) (,n) b
dn~106cm-3
T~107K
s (slow)
s process, close to stability, slow
neutron captures
r process, far from stability, rapid
neutron captures
- Sn : location of (n,g)- (g,n) equil.
- T1/2 : accumulation time, increase Z
- Pn smoothing of abundance curve
- sn going further from stability
- fission when reaching highest Z.
s r r s
Solar abundance
Mass Number
Log
(Ab
un
dan
ce)
Sneden & Cowan 2003
135 131 134 132 133
133 135 134
137 138 136 134 135
136
Xe
Cs
Ba
136
r only
r process
s only
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r-process
s-process
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Neutron Capture Processes
• Main site: Late stages of stars
of 1-3 M☉ during AGB phase.
• Require > 1 Gyr from birth.
• Should not contribute in the
early Galaxy
• Nuclear physics inputs are well
constrained by experiments.
s-process r-process
• NS-NS and NS-BH mergers
(GW170817!)
• CCSN: neutrino-wind Z≲50,
Jets/MR CSSN?
• Associated with massive stars
• Problem: Considerable
theoretical uncertainties
Early Galaxy: Only r-process should
operate in the early Galaxy
All heavy element pattern should
look like Solar-r 87
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Neutron Capture: Speed Matters
r-process
departs from
valley of stability
s-process
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Elemental breakdown in r and s components
143 144
s r r s
Mass Number
Log
(So
lar
abu
nd
ance
)
Sneden & Cowan 2003
In the solar system:
Eu is a pure r element
Ba is mainly an s
element
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r-process: Rapid neutron capture:
High n0 flux: absorb many n0s before b emission.
n
Fe56
26 Fe60
26
27
61Co
b
n
n
Fe59
26….
n
These processes require energy. Occur only at high r & T :
Core & shell burning: p & s process
Supernovae: p & r process
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Nucleosynthesis Sites and Production Timescales
Massive stars (M > 10 M
) and SNe II: synthesis of most of the
nuclear species from oxygen through zinc, and of the r-process heavy
elements ( < 108 years)
Red Giant Stars (1 < M < 10 M
): synthesis of carbon and of the
heavy s-process elements ( > 109 years)
SNe Ia: synthesis of the 1/2-2/3 of the iron peak nuclei not produced
by SNe II ( > 1.5-2 x109 years)
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Slow Neutron Capture: s-Process
Main neutron source: 13C(α,n)16O
22Ne(α,n)25Mg
Typical s-process elements: 14N, 22Na, 25Mg, 26Al, Ba, Xe
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Intermediate mass AGB > 3 M Higher temperature 3 108 K 14N(,)18F(b)18O(,)22Ne(,n) Flux 1013 n cm-3
Duration 10 y, A ≈ 60-80 Weak component
Low mass AGB stars < 3 M Low temperature 108 K 12C(p,)13N(b)13C(,n) Flux 108 n cm-3
Duration 105 y, A > 80 Main component
o . . o
Time
Mas
s
Neutron sources in the s process
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s process examples
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p-process: Proton capture:
s-process: Slow neutron capture:
Absorb n0, then … later … emit e- (b-particle).
Repeat. Progress up the valley of stability.
n
Ouf!
Fe56
26 Fe57
26
27
57Co
b
p 56Fe
Ouf!
57Co
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Solar s and r patterns
Sneden et al 2008
[Ba/Eu]r = -0.8
[Ba/Eu]s = 1.6
Very different
abundance patterns
B
a E
u
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Sneden et al. 2003
Robust r-process pattern
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