Download Lecture 12: Energy Generation in Stars

Lecture 6:
Energy Generation
and Transport in the
Sun
Nuclear Energy
1896:
Röntgen & Becquerel discover radioactivity.
1905:
Einstein demonstrates equivalence of Mass &
Energy: E=mc2
1920s:
Eddington noted that 4 protons have 0.7% more
mass than 1 Helium nucleus (2p+2n).
If 4 protons fuse into 1 Helium nucleus, the
remaining 0.7% of mass is converted to energy.
Fusion Energy
The Age Crisis: Averted
Fuse 1 gram of Hydrogen into 0.993
grams of Helium.
Leftover 0.007 grams is converted into
energy:
Luminosity of the Sun is ~4x1033 erg/sec
E = mc2 = 6.3x1018 ergs
Enough energy to lift 64,000 Tons of rock
to a height of 1 km.
• Convert ~4 Million tons of mass into energy
per second
• Must fuse ~600 Million Tons of H into He
every second..
• Sun contains ~1021 Million tons of H
• Only ~10% is hot enough for fusion to occur
Fusion Lifetime is ~10 Billion Years.
Hydrogen Fusion
High temperature fusion.
Question:
The positively charged protons repel each
other.
How do you fuse 4 1H (p) into 4He (2p+2n)?
Issues:
• Four protons colliding at once is unlikely.
• Must turn 2 of the protons into neutrons.
• Must be hot: >10 Million K to get protons
close enough to fuse together.
To overcome this repulsive force, the
temperature needs to be very hot, so that the
protons move very fast.
The core of the Sun has such high temperature.
Proton-Proton Chain
Deuterium
P-P Chain:
p  p2 H  e  e (twice)
H  p3 He   (twice)
3
He3 He4 He  p  p
2
3-step Fusion Chain
The Bottom Line
Controlled Nuclear Fusion
Fuse 4 protons (1H) into one 4He nucleus
plus the following reaction by-products:
Nuclear fusion is Temperature sensitive:
• Energy in the form of Gamma-ray photons
• 2 positrons (positive electrons)
• 2 neutrinos that leave the Sun
• Higher Core Temperature = More Fusion
BUT,
• More fusion makes the core hotter,
• Hotter core leads to even more fusion, …
Why don’t stars blow up like H-Bombs?
Hydrostatic Thermostat
Thermal Equilibrium
If fusion reactions run too fast:
Heat always flows from hotter regions into
cooler regions.
• core heats up, leading to higher pressure
• pressure increase makes the core expand.
• expansion cools core, slowing fusion.
If fusion reactions run too slow:
• core cools down, leading to lower pressure
• pressure drop makes the core contract.
• contraction heats core, increasing fusion.
In a star, heat must flow:
• from the hot core,
• out through the cooler envelope,
• to the surface where it is radiated as light.
Energy Transport
Radiation (also Radiative Diffusion)
There are 3 ways to transport energy:
Radiation:
Energy is carried by photons.
Energy is carried by photons
Convection:
Energy carried by bulk motions of fluid
Conduction:
Energy carried by particle motions
Random Walk
• Photons leave the core
• Hit an atom or electron within ~1cm and
get scattered.
• Slowly staggers to the surface (“random
walk”)
• Breaks into many low-energy photons.
Takes ~1 Million years to reach the surface.
Convection
Energy carried by bulk motions of the gas.
Analogy is water boiling:
Hot blob rises
cooler
water
sinks
Conduction
In the Sun the energy is transported by
Radiative Diffusion and Convection
Heat is passed from atom-to-atom in a
dense material from hot to cool regions.
Analogy:
Holding a spoon in a candle flame, the
handle eventually gets hot.
Test: Solar Neutrinos
Question:
How do we know that fusion is occurring in
the core of the Sun?
Answer:
Look for the neutrinos created by the nuclear
fusion reactions.
What are Neutrinos?
Solar Neutrinos: Observed!
Weakly interacting neutral subatomic
particles.
Detection of neutrinos is very difficult:
• Mass-less (or very nearly mass-less).
• Travel at (or very near) the speed of light.
• Interact with matter via the weak nuclear
force.
• Can pass through lead 1 parsec thick!
Neutrinos created by nuclear fusion in the
Sun’s core would stream out of the Sun.
• Need massive amounts of detector
materials.
• Work deep underground to shield out other
radiation.
Answer:
• We detect neutrinos from nuclear fusion in
the Sun, with the expected energies, in all
of the experiments performed to date.
The Solar Neutrino Problem
Observed neutrino flux
(number/second/cm2) is only 1/3rd of
the neutrino flux predicted from
standard models of the Sun.
Q. Hydrogen burning by fusion reactions
occurs in the center of the Sun, because
this is the only place where
A) There is sufficient hydrogen
B) The temperature is low enough and density
high enough
C) The density is low enough and temperature
high enough
D) The conditions of high temperature and high
density occur.
Q.: Which of the following will provide
the most direct information on the
process of nuclear fusion occurring in
the Solar core?
A)
B)
C)
D)
Protons in the solar wind
X-rays
Neutrinos
Visible light
Q. When the principle of hydrostatic
equilibrium is applied to the Sun, it implies:
A) The center of the Sun is extremely hot
B) The surface temperature of the Sun is ~6000K
C) The Sun should collapse in a matter of
hundreds of years
D) The lifetime of the Sun is 10 billion years
Q.: Nuclear fusion is:
A) Splitting of heavier nuclei to produce
lighter nuclei + energy
B) Combining of electrons with nuclei to
produce atoms + energy
C) Combining together H atoms to
produce H molecules + energy
D) Joining together light nuclei to produce
heavier nuclei + energy