skip navigation
Galaxy NGC4414 from HST 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?

Stars shine because they are hot.
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

Question: How long can the Sun shine?

To answer this, we need to measure two numbers:

The "shining" lifetime of the Sun is just the ratio of these two numbers:
Lifetime = Internal Heat / Luminosity

Sources of Energy

In the early 19th Century, two energy sources were known:

Chemical Energy:

Gravitational Energy:

The Age Crisis: Part I

Both chemical and meteorite energy sources have serious problems:
  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

Energy source proposed by physicists Kelvin[12.1] and von Helmholtz[12.2] in the mid-1800s:

Start with the Sun in Hydrostatic Equilibrium

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

The cooler Sun has a lower internal pressure:

Gravitational Contraction compresses the Sun:

The Sun, slightly smaller, starts the cycle again.

The Age Crisis: Part II

Late 1800s: Kelvin and Helmholtz would say: The Geologists are wrong.

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

Nuclear Energy

1896: Röntgen and Becquerel discover radioactivity.

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

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 about 64,000 Tons of rock to a height of 1 km.

Hydrogen Fusion

How do you fuse 4 1H (p) into a 4He (2p+2n)?

(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

The primary way that you can fuse 4 H into 1 He in the Sun is via a 3-step fusion reaction called the Proton-Proton Chain. [12.4]
Proton-Proton Chain

Proton-Proton Chain Schematic:

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

The Bottom Line:

Fuse four (4) protons (1H) into one Helium (4He) nucleus.

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

Luminosity of the Sun is ~4x1033 erg/sec

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

How do we know that fusion is occurring in the core of the Sun?

Look for the neutrinos created by the nuclear fusion reactions.

What are Neutrinos?

Neutrinos are weakly interacting neutral subatomic particles:

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!

Detection of neutrinos is very difficult:
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

Of course, this not quite the whole story.

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.

Return to [ Unit 2 Index | Astronomy 162 Main Page ]
Updated: 2006 January 15
Copyright Richard W. Pogge, All Rights Reserved.