Astronomy 162: Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30

Lecture 12: As Long as the Sun Shines

Readings: Ch 18, section 18-1, 18-1, & 18-4

Key Ideas:

Stars shine because they are hot.

Need an energy source to stay hot.

Kelvin-Helmholtz Mechanism

Energy from gravitational contraction

Doesn't work in the Sun now.

Nuclear Fusion Energy

Energy from fusion of 4 Hydrogen nuclei into 1 Helium nucleus

Proton-Proton nuclear reaction chain

Why do stars shine?

• emit thermal (~blackbody) radiation
• heat "leaks" out of their photospheres.

Luminosity = rate of energy loss.

To stay hot, stars must make up for this lost energy, otherwise they would cool and eventually fade out.

Case Study: The Sun

To answer this, we need to measure two numbers:

• How much internal heat is there in the Sun?
• How fast is this heat lost as sunlight (Luminosity = Energy/second)?

Sources of Energy

Chemical Energy:

• Burning of oil or wood by oxidation
• Chemical explosives

Gravitational Energy:

• Water running downhill to power a mill.
• Heat from meteorite impacts

The Age Crisis: Part I

1. The most powerful chemical reactions known could only keep the Sun shining for a few thousand years.

2. Meteor impacts could work for at most ~1 Million Years.

The problem was that during the 1800s, Geologists had found that the Earth had to be at least 10s to 100s of Millions of years old.

This leads to a logical inconsistency:

How could the Earth be older than the Sun?

The Kelvin-Helmholtz Mechanism

Start with the Sun in Hydrostatic Equilibrium

• Internal Pressure balances Gravity

Luminosity radiates away some of the Sun's internal heat:

• Causes the Sun to cool at little bit

The cooler Sun has a lower internal pressure:

• Lower pressure means Gravity gets the upper hand
• Causes the Sun to contract a little bit

Gravitational Contraction compresses the Sun:

• Increases its internal heat
• The pressure increases, restoring hydrostatic equilibrium

The Age Crisis: Part II

• Helmholtz estimated that the Sun could shine for a little over 20 Million years via the Kelvin-Helmholtz Mechanism. ^{This corroborated estimates made by Kelvin of the age of the Earth[12.3]}
• Geologists around this same time had shown that the Earth was at least 2 Billion years old.

Nature Says: Helmholtz and Kelvin are wrong. There is new physics Kelvin doesn't know about...

Nuclear Energy

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 the mass leftover would have to be converted into energy.

Fusion Energy

Leftover 0.007 grams converted into energy:

E = mc² = 6.3x10¹⁸ ergs

Enough energy to lift about 64,000 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:

(1) Four protons colliding at once is unlikely.

(2) Must turn 2 of the protons into neutrons.

(3) Must be hot: >10 Million K to get protons close enough to fuse together.

Proton-Proton Chain

Proton-Proton Chain Schematic:

[Click on image to view full-size version (18Kb)]

The Bottom Line:

This reaction produces the following important by-products:

1. 2 photons (energy in the form of Gamma-rays)
2. 2 positrons (positive electrons)
3. 2 neutrinos that leave the Sun carrying off more energy

Is this enough energy to do the job?

The Age Crisis: Averted

• 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 the inner 10% of the Sun is hot enough for fusion to occur.

Whenn all these factors are taken into account, we find:

Fusion Lifetime is ~10 Billion Years.

Modern estimates from radioactive dating give an age of the Earth of 4.6 Billion years. The Sun can potentially shine for about twice that, averting the age crisis.

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?

• Massless (or very nearly so)
• Travel at (or very near) the speed of light.
• Interact with matter via the weak nuclear force.
• Can pass through a block of lead 1 parsec thick!

The neutrinos created by nuclear fusion in the Sun's core should simply stream out of the Sun at or near the speed of light.

Solar Neutrinos: Observed!

• Need massive amounts of detector materials (Gallium, Heavy Water, etc.)
• Must work underground to shield out other cosmic radiation

Results:

We have experimentally detected neutrinos from nuclear fusion in the Sun with the expected energies.

The solar neutrino experiments confirm that the source of power in the Sun (and by extension, other stars) in nuclear fusion.

The Solar Neutrino Problem

In the mid-1960s when the first solar neutrino experiments were getting going, the goal of those experiments was to confirm that nuclear fusion was the power source of the Sun by detecting the neutrinos.

So far so good, but a surprise of those experiments was that while they detected neutrinos of the energies expected, they did not detect enough of them.

This observation was quickly dubbed the "Solar Neutrino Problem".

It has become clear from the latest round of solar neutrino experiments that we have essentially solved the Solar Neutrino Problem. However, not by any particularly new understanding about the Sun, but by the discovery of a fundamental new property of subatomic particles!

The details are subtle, but it is a great story about how sometimes when scientists set out to answer a well-defined question they are lead instead to a surprising new result that nobody ever even dreamed of.