Lecture 12: Making the Sun Shine

Readings:  Sections 18-1, 18-4 and Box 18-1

 

Key Ideas

Stars shine because they are hot—need an internal energy source to stay hot

Kelvin-Helmholtz Mechanism

         Energy from Gravitational Contraction       

DoesnÕt work in the Sun now, but is important during the early stages of a starÕs life

         Nuclear Fusion Energy

                  Energy from fusion of 4 hydrogen atoms into 1 helium atom

                  Proton-proton nuclear reaction chain

                  CNO nuclear reaction chain

 

Why do stars shine?

Stars shine because they are hot

         Emit light with a roughly thermal (blackbody) spectrum

         Internal heat ŌleaksĶ out of their surfaces

 

Luminosity=rate of energy loss

 

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

 

Case Study: The Sun

Question

         How long can the Sun shine?

 

Need two numbers

         How much internal heat is there in the Sun?

         How fast this heat is lost (Luminosity)

 

 

 

Sources of Energy

In the 19th century, two energy sources were known:

 

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 1

The most powerful chemical reactions could work for only a few thousand years

 

Meteorites could work for about 1 million years

 

But: Geologists estimated that the Earth was at least a few 10s to a 100s of million years old

 

Logical Inconsistency:

         How can the Earth be older than the Sun?

 

Kelvin-Helmholtz Mechanism

Energy from Gravitational Contraction of the Sun

 

As gas contracts, its temperature rises as energy stored as gravitational potential energy is released

 

This energy is radiated into space, cooling the star. Gravity keeps contracting the star, more and more energy is radiated away. When the star has completely collapsed, youÕve gotten all the energy you can from the Kelvin-Helmholtz mechanism.

 

Predicts that the SunÕs size will change with time (though really slowly).

        

The Age Crisis: Part II

Late 1800s:

         Kelvin estimated the Sun could shine for about 30 million years

Geologists estimated that the Earth is at least 2 billion years old, based on measuring the amount of uranium that had decayed to lead in rocks.

 

In an interesting twist, the phenomenon of radioactivity, which sealed the rejection of the Kelvin-Helmholtz mechanism, also started providing the clues that pointed out the real answer.

 

Nuclear Energy

1896 Ršntgen & Becquerel discover radioactivity

1905 Einstein demonstrates equivalence of Mass & Energy. Conservation says that

 the sum of matter and energy does not change.

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.

Payne-Gaposhkin showed that the SunÕs atmosphere was mostly H.

 

Fusion Energy

Fuse 1 gram of hydrogen into 0.993 grams of helium

Leftover 0.007 grams is converted into energy

 

 

Enough energy to lift 64,000 Tons of rock to height of 1 km.

 

The Age Crisis: Averted

Luminosity of the Sun is about 4x1033 erg/sec (4x1026watts)

         Must fuse about 600 million tons of H into He each second

         Converts about 4 million tons of matter into energy each second

Sun contains about 1021 million tons of H, but only 10% is hot enough for fusion

Fusion Lifetime is about 10 billion years. The Earth is 4.5 billion years old, so the Sun has enough energy to keep going for about 5 billion years. Phew!

 

Nuclear Fusion 101

Gravity unimportant, the forces that are important are the strong nuclear, the electromagnetic, and the weak nuclear force. Weak force at work when neutrons change into protons and vice versa.

 

 

Nuclear particles

Proton (positively charged)

Neutron (neutrally charged)

4He and bigger particles

Not all possible combinations of neutrons and protons exist

         5He doesnÕt

         2He doesnÕt

         and many others

 

Fusion==combining positively charged nuclei together

 

Electromagnetic Force

         Like charges repel

         Opposite charges attract

So trying to put protons together is difficult. Proton with 4He is even tougher.

 

BUT strong force, which binds protons and neutrons together, is stronger than electromagnetic repulsion.

 

BUT strong force is short range (<10-15 meters), so the protons need to get really close together before they will stick

 

BUT protons donÕt like to get close together. They need to be traveling fast enough so the repulsive force canÕt stop them. Remember that temperature measures the speed of particles in a gas. Therefore what we need is a high temperature.

 

Rate of nuclear fusion depends on temperature

 

Proton-Proton Chain

 

 

note that the atoms are all completely ionized. IÕve dropped the + for convenience.

 

The Bottom Line

Fuse 4 protons (1H) into one 4He nucleus plus the following reaction by-products

         2 photons = Energy

         2 positrons (positive electrons, will annihilate and produce more energy)

         2 neutrinos (ne) that leave the Sun carrying energy

 

Additional Details:

 

         Protons do not just collide with protons in the center of the Sun. There are other nuclei floating about and protons can collide with these. These lead to the pp-II and pp-III chains. These reactions also release neutrinos, neutrinos that have higher energy than neutrinos from the pp-I chain.

 

 

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 p-p chain

 

What are Neutrinos?

Weakly interacting neutral subatomic particles

         Very nearly massless

         Travel 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 SunÕs core would stream out of the Sun, not interacting with the protons, electrons, helium atoms, etc. in the Sun. This is good! They also only rarely interact with detectors on Earth. This is bad!

 

The Sun emits about 1033 neutrinos/sec

(FYI, humans emit about 3x108 neutrinos/day from the decay of radioactive potassium)

Every second we have many neutrinos pass through our bodies: 400,000 billion from the Sun, 50 billion from the Earth and 100 billion from nuclear power plants. This is not dangerous, because the neutrinos do not interact.

 

 

Detection of neutrinos is hard

         Need massive detectors

         Work deep underground to shield out other radiation

 

Homestake Mine experiment

         100,000 gallons of tetrachloroethylene, a common cleaning fluid.

         Very rarely, a solar neutrino will change a 37Cl into a 37Ar atom.

Set up your tank, wait a few months, then find the few dozen 37Ar atoms in your tank that has 1030 atoms in it.

Calculate the solar neutrino flux!

 

Results:

         We detect neutrinos from fusion in the Sun, with the expected energies, in all of the experiments to date.

 

 

 

The CNO cycle

In stars with central temperatures hotter than the SunÕs, H is fused into He using carbon, nitrogen and oxygen nuclei as catalysts. The hotter temperatures mean that the large repulsion between the 6-8 protons and the proton can be overcome. And there is no more annoying step where you need to proton to change into a neutron as the moment the two protons are interacting.

 

 

Note that you start with 12C, add 4 protons, and end up with a 12C and a 4He.

 

These reactions happen at higher temperatures because the repulsive force increases as the number of protons in the nuclei increases, and the nuclei have to be moving faster to overcome the repulsion.

 

We will discuss other stages of nuclear fusion (such as helium fusing into carbon) later in the course.