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Sterren – College 7
Nuclear Fusion
Basic physics
Hydrogen burning
Advanced nuclear burning
LB 206-210
LB 216-218
LB 218-226
LB 230-236
Introduction
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As a star contracts half of the energy is radiated away (Chapter 2).
The amount of energy radiated away for a given star with constant
density is (Sect. 2.3):
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The Kelvin-Helmholtz contraction timescale is defined as:
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which for the sun is 107 yrs, while the age of the earth is 4.5 109 yrs
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Hence gravitational energy is not the main heat source. Also
chemical reactions will not work.
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Fusion up to the ''iron peak elements'' creates energy
Energy gain through fusion:
Example: For 4He average binding energy per nucleon is
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Forces
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Electromagnetic force
Weak nuclear force, responsible for both the radioactive decay and nuclear fusion
Strong nuclear force, ensures the stability of ordinary matter, confining the quarks into
protons and neutrons
Properties of particles
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Mass
Charge
Spin
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Particle physics
Fermions: particle with spin k x 1/2, with k=1,3,....
Bosons: particles with integer spin
Matter/antimatter: for every particle created there is an antiparticle, when a particle and
a antiparticle meet, they annihilate and a high energy photon is created
Families of particles
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Fermions
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Leptons: interact with weak and not with strong force, have spin ½, example: electron, positron
(=anti-election), muons
Quarks
Baryons: interact with weak and strong force, made up of quarks, examples: proton,
neutron
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Leptons
A lepton is an elementary, spin-1⁄2 particle that does not undergo strong interaction. Leptons are not believed to be
composed of any simpler particles. The best known of all leptons is the electron. Two main classes of leptons exist:
charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos.)
Charged leptons can combine with other particles to form various composite particles such as atoms, while neutrinos
rarely interact with anything, and are consequently rarely observed.
There are six types of leptons, known as flavours, forming three generations.
Electrons have the least mass of all the charged leptons. The heavier muons (~207 time mass electron) and tauons
(3482 times mass electron) will rapidly change into electrons through a process of particle decay: the transformation
from a higher mass state to a lower mass state. Lifetimes are respectively 2 10-6 and 3 10-13 sec. Thus electrons are
stable and the most common charged lepton in the universe, whereas muons and tauons can only be produced in high
energy collisions (such as those involving cosmic rays and those carried out in particle accelerators).
For every lepton flavour there is a corresponding type of antiparticle, known as anti-lepton, that differs from the
lepton only in that some of its properties have equal magnitude but opposite sign. However, according to certain
theories, neutrinos may be their own antiparticle, but it is not currently known whether this is the case or not.
http://en.wikipedia.org/wiki/Lepton
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Muons
The muon is an elementary particle similar to the electron, with unitary negative
electric charge of −1 and a spin of 1⁄2, but with a 207 times greater mass (105.7 MeV/c2). It is classified as a lepton, together with the electron (mass 0.511 MeV/c2), the tauon (mass 1777.8 MeV/c2), and the three neutrinos.
The muon is an unstable subatomic particle with a mean lifetime of 2.2 µs. The
decay of the muon is mediated by the weak interaction exclusively. Muon decay
always produces at least three particles, which must include an electron of the
same charge as the muon and two neutrinos of different types.
Like all elementary particles, the muon has a corresponding antiparticle of
opposite charge (+1) but equal mass and spin: the antimuon (also called a
positive muon). Muons are denoted by μ− and antimuons by μ+.
http://en.wikipedia.org/wiki/Muon
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Tauons
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The tau (τ), also called the tau lepton, tau particle or tauon, is an
elementary particle similar to the electron, with negative electric
charge and a spin of 1⁄2. Together with the electron, the muon, and the
three neutrinos, it is classified as a lepton. Like all elementary
particles, the tau has a corresponding antiparticle of opposite charge
but equal mass and spin, which in the tau's case is the antitau (also
called the positive tau). Tau particles are denoted by τ− and the antitau
by τ+.
Tau leptons have a lifetime of 2.9×10−13 s and a mass of 1776.82
MeV/c2 (compared to 105.7 MeV/c2 for muons and 0.511 MeV/c2 for
electrons). Since their interactions are very similar to those of the
electron, a tau can be thought of as a much heavier version of the
electron.
As with the case of the other charged leptons, the tau has an
associated tau neutrino, denoted by ντ.
http://en.wikipedia.org/wiki/Tau_(particle)
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Quarks
A quark is an elementary particle. Quarks combine to form composite particles called hadrons, the
most stable of which are protons and neutrons. Quarks are never directly observed or found in
isolation
There are six types of quarks, known as flavors: up, down, strange, charm, bottom, and top. Up
and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up
and down quarks through a process of particle decay: the transformation from a higher mass state
to a lower mass state. Because of this, up and down quarks are generally stable and the most
common in the universe, whereas strange, charm, top, and bottom quarks can only be produced
in high energy collisions
Quarks have various intrinsic properties, including mass, color charge, spin and electric charge:
the have spin ½ and hence are
fermionen
http://en.wikipedia.org/wiki/Quark
A proton consists of 2 up and one down quark(uud), a neutron two down and one up (udd).
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Nuclear reactions respect
conservation principles:
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Conservation of electric charge
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Conservation of baryon numbers
= 1 for proton and neutron
= -1 for anti-proton and anti-neutrino
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Conservation of lepton numbers
= 1 for electron and neutrino
= -1 for positron and anti-neutrino
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Important examples
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Fusion hydrogen to deuterium:
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which involves
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due to quark transformation:
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energy gain:
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positron annihilates and yield energy of
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baron number = 2, lepton number =0 and electric charges
conserved
as a neutrino leaves the star, there is an energy sink of 0.263
MeV (related to the solar neutrino problem – now solved)
Hence the total energy gained:
Neutron decay:
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which involves:
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important for the formation of heavy elements
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Nuclear fusion
Quantum tunnelling: a quantum mechanical effect that enables an incoming
nucleus to overcome the Coulomb potential making fusing possible. This effect is
and
x
Coulomb forces are higher for higher charged nuclei, hence fusion of highly charged
nuclei happens only at relatively high temperatures;
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First H burns, and as the star gets hotter/evolves, other species start burning
Main sequence burning
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On the main sequence hydrogen is burned
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For masses between 0.08 and 1.5 solar masses:
proton-proton chain
Larger masses/higher temperatures: CNO cycle
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Proton-Proton chains
Fractions are for the current Sun
Summarizing PPI chain:
Note
- Neutrinos are an energy sink
- positrons annihilate, yielding
energy (1.02 MeV)
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CNO cycle
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Simplified:
Note this was not possible in the first stars
as C, O were not present
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Detailed
calculations
Cross over for MS stars with 1.5 solar
masses
where T9 is the temperature in units of
109 K, X is the mass fraction of
hydrogen and Z is the mass fraction of
the metals.
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Two slides from Lecture 2
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Lifetime on the main sequence
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Fractional energy released by fusion of 4 H:
Detailed calculations show that only the central ~10 %
of the star can be fused
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We can then estimate the total energy available:
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The main-sequence lifetime therefore is:
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Helium burning
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Hydrogen into Helium burning leads to an increase in molecular
weight and hence lowers the pressure
Due to the weight of the outer layers the core contracts, increasing
the density and temperature (and pressure)
If the star is > 0.5 solar masses, it will heat up to 108 K so that Helium
fusion can start, with an accompanying outer layer of H burning (this
is call shell burning)
Triple alpha (i.e. 3 times 4He nuclei) reaction chain provides 7.2 MeV:
or:
- The first nuclear reaction above is an endothermic reaction and requires an input of
at least approximately 92 keV of energy, hence the high temperatures required
- The 8Be nucleus is unstable to decay (into two 4He nuclei) but has a lifespan that
is large enough to allow for a second capture of a 4He nucleus.
- The symbol 12C* represents a carbon nucleus found in an excited nuclear energy
state.
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Helium burning is a relatively short phase
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Energy production per nucleon by the triple
alpha is relatively small (see slide 3).
Helium burning occurs at the red giant phase
when the star has a large luminosity and hence
the nuclear production rate needs to be large
Hence life time of this phase is relatively short
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Advanced burning
Only in massive stars
Leads to the higher elements
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