Astronomy 162:
Introduction to Stellar, Galactic, & Extragalactic Astronomy
Lecture 12: The Age of the Sun
Key Ideas:
- Stars shine because they are hot.
- need an energy source to stay hot.
- Kelvin-Helmholtz Mechanism
- generate energy via gravitational contraction
- cannot work to power the Sun
- Nuclear Fusion Energy
- Energy from fusion of 4 1H into 1 4He
- proton-proton chain
Why do stars shine?
Stars shine because they are hot.
- emit thermal (blackbody) radiation
- heat "leaks" out of their photospheres.
Luminosity = rate of energy loss.
To stay hot, stars must make up for the lost energy,
otherwise they would go out.
Case Study: The Sun
Question:
- How long can the Sun shine?
Answer:
- Consider the internal heat content of the Sun.
- Luminosity = rate of heat loss.
Lifetime = Internal Heat / Luminosity
What if no source of energy?
The Sun's Luminosity losses would not be balanced by input of
new internal heat.
The Sun would steadily cool off & fade out.
18th Century:
- Assumed a solid Sun (iron & rock)
- Found Lifetime ~ 10 Million Years
No Problem:
Earth was thought to be a few tens of thousands of years old.
The Age Crisis: Part I
Late 1800s:
Geologists found that the Earth was 10's of millions of years
old.
This meant the the Earth was a little older than the Sun. This is a
logical inconsistency, hence an "Age Crisis".
Astronomers also found that the Sun is a big ball of gas in
Hydrostatic Equilibrium.
Kelvin & Helmholtz proposed Gravitational Contraction as a
source of energy.
Kelvin-Helmholtz Mechanism
Luminosity radiates away heat
- Outer layers of the Sun cool at little, lowering the gas pressure,
- Lower Pressure means Gravity gets the upper hand and the star
contracts a little,
- Contraction compresses the core, heating it up a little and
adding heat to the Sun.
Sun could shine for ~100 Million years by this mechanism.
The Age Crisis: Part II
Early 1900s:
- Geologists show that the Earth is >2 Billion
years old.
Kelvin Says: The Geologists are wrong.
Nature Says: Kelvin is wrong.
There is new physics Kelvin doesn't know about...
Nuclear Fusion
1905: Einstein demonstrates that Mass and Energy are equivalent:
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
Fuse 1 gram of Hydrogen into 0.993 grams of Helium.
Leftover 0.007 grams converted into Energy:
E = mc2 = 6.3x1018 ergs
Enough energy to lift ~64000 Tons of rock to a height of 1 km.
Hydrogen Fusion
Question:
- How do you fuse 4 1H (p) into a 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.
Proton-Proton Chain
3-Step Fusion Chain
Proton-Proton Chain Schematic:
The Bottom Line:
Convert 4 protons (1H) into 1 4He nucleus.
Release energy in the form of:
- 2 Gamma-ray photons
- 2 neutrinos that leave the Sun
- 2 positrons that hit nearby electrons, creating two more Gamma-ray
photons
- Extra motions (heat) of the final 4He nucleus and the
2 protons leftover from the 6 that went into the p-p chain.
The Age Crisis Averted
Luminosity of the Sun is ~4x1033 erg/sec
- Must fuse ~600 Million Tons of H into He every second.
- ~4 Million tons converted to energy per second.
- Sun contains ~1021 Million Tons of Hydrogen
- Only ~10% is hot enough for fusion to occur.
Fusion Lifetime is ~10 Billion Years.
Test: Solar Neutrinos
Question: How do we know that fusion is occurring in
the core of the Sun?
Answer: Look for the neutrinos liberated in Step 1 of the
Proton-Proton chain.
Properties of Neutrinos:
- Massless, weakly interacting neutral particles.
- Travel at the speed of light.
- Can pass through a block of lead 1 parsec thick!
Therefore: Any neutrinos created by nuclear fusion in the Sun's core
would stream out of the Sun at the speed of light.
Solar Neutrinos: Observed
Detection of neutrinos is very hard:
- Need massive amounts of detector materials
- Work underground to shield out other radiation
Answer: We detect neutrinos from the P-P chain in all experiments
performed to date!
Success! But...
The Solar Neutrino Problem
We detect only ~1/3 the number expected...
Why?
- Is the solar structure model wrong in some minor or important
detail?
- Is there something wrong with subatomic particle theory as
applied to neutrinos?
The last seems most plausible; recent evidence suggests that
neutrinos may have mass, for example. But the real answer may
come from the physics of the next century.