# Chapter 15: The Sun: A Nuclear Powerhouse

When the Sun shines, it puts out a tremendous amount of energy. Where does this energy come from? With energy, there is no free lunch. Energy cannot be created from nothing, but must have a source. What is the source for the Sun?

## 15.1 Thermal and Gravitational Energy

This question was asked by many famous scientists, but it was not until the 20th century that it could be answered.

Early scientists knew of only two possible sources for the Sun's energy:

• chemical energy [called thermal energy in the text] (as comes from burning oil), and
• gravitational energy.
Neither of these is the actual source, although gravitational energy will come up later as the main source of energy to get a star going.

## 15.2 Mass, Energy, and the Special Theory of Relativity

Our understanding of the energy source in the Sun had to await the development of nuclear physics and the special theory of relativity.

The special theory of relativity is the first of Einstein's two theories of relativity. It deals with the behavior of objects at very high speed, near the speed of light. Out of this work comes the most famous equation in science: E=mc2. This equation tells us that mass is just another form of energy, and this is the equivalent amount of energy for a certain mass. It is like saying that cents = dollars×100. This tells us the equivalence between dollars and cents, but doesn't tell us how or where to convert dollars to cents or vice versa.

Likewise, E=mc2 tells us the equivalent amount of energy for a given amount of mass, but it doesn't tell us how to convert that mass into energy.

In the formula, c is the speed of light, 3.0×108m/s. This is a rather large number, and squaring it makes it even bigger. This means that a relatively small amount of mass yields a lot of energy. Just 1 gram of mass is equivalent to the energy from 15,000 barrels of oil.

We can account for all the energy produced by the Sun in a year by the conversion of 4 million tons of mass into energy. That sounds like a lot of mass, but it is just a tiny fraction of the Sun's mass, and at that rate, the Sun can continue shining for billions of years.

To understand how mass is converted into energy, we need to understand something about the process of fusion that occurs in the Sun. We begin by learning about the objects involved in fusion.

### Elementary Particles

There are 5 objects that play a fundamental role in the fusion process that takes place in the Sun.

ParticleMass (kg)Charge
proton1.67265×10-27+1
neutron1.67495×10-270
electron9.11×10-31-1
neutrino<10-370
photon00

The proton and neutron are building blocks for atomic nuclei. The electron orbits nuclei to form atoms. The photon we've discussed before; it is a particle of light. The neutrino is probably new to you. It is a by-product of the fusion process and detecting neutrinos from the Sun is an important confirmation that fusion is the source of the Sun's energy.

Additionally we will encounter the anti-particle of the electron, called the positron. Positrons have the same mass as electrons but the opposite charge -- positrons are positive. When an electron and a positron meet, they annihilate, a fancy term meaning that the mass of the electron and positron is converted into energy (actually into two gamma rays).

### The Atomic Nucleus

The Sun produces energy by changing atomic nuclei. This sounds like alchemy (changing lead into gold), but this is also the source of energy for nuclear reactors. Nuclear reactors capture the energy released when Uranium nuclei with 92 protons and 143 neutrons fission into lighter nuclei and neutrons, and convert some of that energy into electricity. Fission means that a heavy nucleus breaks up into a lighter nucleus (or nuclei).

A slightly different process is at work inside the Sun. Inside the Sun, light nuclei combine (are fused) to create heavier nuclei, releasing energy in the process. Combining lighter nuclei into heaver nuclei is called fusion.

How can it be that if a heavy nucleus is split into lighter nuclei we get energy, and if two light nuclei are fused into a heavy nucleus we again get energy? For the same set of nuclei, it is not possible to get energy out in both cases. If energy is released in one process, then energy must be absorbed when that process runs in reverse.

However, we are not speaking about the same set of nuclei. Fission involves, for example, the nuclei of Plutonium, Uranium, Barium, and Krypton (as shown in Figure 15.3). The process of fusion in the Sun involves Hydrogen and Helium. As a general rule, for nuclei lighter than Iron, energy is released in a fusion process that results in a heavier nucleus, closer to Iron. For nuclei heavier than Iron, energy is released in a fission process that results in lighter nuclei. The Iron nucleus (specifically 56Fe) is energetically the most stable nucleus.

Is there a simple way to understand why energy is released when light nuclei are fused into heavier nuclei? Yes. The mass of a nucleus equals the sum of the masses of its constituents minus the binding energy of the nucleus. The binding energy is the energy required to break the nucleus into its components. Naturally occurring nuclei have positive binding energies, otherwise they would disintegrate immediately.

Thus it is possible that the mass of a nucleus is less than the mass of its components. For instance, in atomic mass units, the helium nucleus has a mass of 4.0026. It is composed of 2 protons (mass of 1.0078 each) and 2 neutrons (mass of 1.0087 each). The constituents sum to a mass of 4.0330 while the helium nucleus mass is only 4.0026. The difference is the binding energy of helium, 0.0304 amu.

### Nuclear Attraction Versus Electrical Repulsion

How do light nuclei manage to fuse into heavier nuclei? Why is this occurring in the Sun but not on Earth?

To fuse two nuclei together they must be pushed next to each other (isn't this obvious). However, nuclei are positively charged, and like charges repel each other -- this is the electromagnetic force. To push two nuclei next to each other we must push harder than the electromagnetic repulsion. Once the two nuclei are close, then they will bind together by a nuclear force that is much greater than the electromagnetic repulsion, but only has an effect within a short distance from the nucleus.

Since the Sun can't actually "push" nuclei around, fusion occurs when the nuclei are moving fast enough (have a good running start) to get close to each other. When the nuclei (atoms) in a region are all moving fast (not all in the same direction), then the temperature in that region is very high. In the core of the Sun where fusion occurs, the temperature is about 15 million K.

### The p-p Chain

The primary reactions occurring in the Sun are called the proton-proton cycle or p-p chain. The p-p chain is 3 steps that result in Hydrogen nuclei fusing into Helium nuclei.
 1H + 1H --> 2H + e+ + ν 2H + 1H --> 3He + γ 3He + 3He --> 4He + 21H

## 15.3 The Interior of the Sun: Theory

Astronomers use computer calculations to understand what is going on inside the Sun. The computer is given information we have measured about the Sun and about the processes which occur inside. All this information is combined to give a consistent picture of what is happening inside the Sun, and to determine how things will change with time.

### The Sun Is a Gas (plasma)

The Sun is so hot that everything inside is a gas. In a gas, each atom or molecule moves independently of other atoms and molecules. In liquids and solids, the atoms or molecules are linked, and don't move independently.

### The Sun Is Stable

A gas is described by its pressure, temperature, and density. The pressure in the Sun is what balances the force of gravity and keeps the Sun from collapsing in on itself. The pressure is related to the temperature of the gas: the higher the temperature, the greater the pressure. If the pressure is not enough to keep the Sun from contracting, then it will contract, releasing gravitational energy, thereby heating the Sun and increasing the pressure until it is sufficient to keep the Sun from further contracting. If the pressure is too high, then the Sun will expand, cool, and the pressure will be reduced until gravity stops the Sun from expanding. We say that the Sun is in stable equilibrium, meaning that the Sun tends to adjust itself automatically to keep pressure and gravity balanced.

### The Sun Is Not Cooling Down

The Sun radiates energy from its surface. From this we can infer that the interior is hotter than the exterior -- otherwise energy would flow into the Sun, not out of it. If there were not a source of energy inside the Sun, then it would cool down, and stop radiating energy. The same logic holds for other stars. In our Sun, the energy is produced via fusion of hydrogen into helium.

### Heat Transfer in a Star

The energy produced by fusion comes out in two forms: gamma rays from electron-positron annihilation, and neutrinos. The Sun is very opaque to gamma rays, and in fact to any electromagnetic radiation. (This is a characteristic of blackbodies, and the Sun is a good blackbody.) The gamma ray travels only a short distance, about a centimeter, before it is absorbed. It will be re-emitted very quickly, but the direction and the wavelength will change. It will tend to be absorbed and re-emitted numerous times on its million year trek to the surface of the Sun. Technically, it's not possible to claim to follow a singly photon through the Sun, but cheating a bit, we can say that by the time the photon leaves the Sun, it's bounced around inside for about a million years, and it has gone from being a gamma ray to being visible light.

The Sun is nearly transparent to neutrinos. The neutrinos zip right out from the core and reach the surface of the Sun in about 2 seconds.

## 15.4 The Solar Interior: The Observations

Astronomers have two ways to learn about the Sun's interior:

• by studying small changes in the motion of the surface of the Sun, and
• by observing the neutrinos emitted by the Sun.
I will talk a little about the observation of neutrinos.

### Solar Pulsations

The study of solar pulsations is done by measuring the doppler shift of light from the surface. As regions of the surface move up and down, the frequency of the light is shifted slightly, but enough to be measured. Then, using computer models, scientists study how waves propagate through the solar interior. This is similar to how seismologists study the propagation of waves generated by earthquakes to learn about the Earth's interior. For this reason, studies of solar pulsations are referred to as solar seismology.

### Solar Neutrinos

In the first step of the p-p cycle, two hydrogen nuclei fuse to form a deuterium nucleus, a positron, and a neutrino. These neutrinos are able to pass unhindered through the Sun, and emerge from the core about 2 seconds after they are produced. (A small number are stopped in the Sun and don't make it out, but we can neglect them.)

Eventually, some of these neutrinos reach the Earth. At the Earth, about 35 million billion (3.5\times1016) neutrinos pass through a square meter every second! Imagine! Not to worry, the neutrinos do not present a hazard. Mostly they pass through the Earth as if it weren't there.

In the 1960's, a group of physicists led by Raymond Davis, Jr., set out to detect some of the neutrinos from the Sun. Very rarely a solar neutrino will interact with an atom producing a measurable signal. Davis used 400,000 liters of cleaning fluid placed about a mile underground to try to detect some of the neutrinos. The cleaning fluid contains chlorine atoms (Cl) which can sometimes be transformed by a striking neutrino into argon atoms (Ar). He would then process the cleaning fluid, to try to detect the one argon atom produced per day.

Davis detected solar neutrinos, but only at about a third the expected rate. The low rate was found by other experiments that followed. The fact that only one third of the expected number of neutrinos was seen became known as the solar neutrino puzzle. Did this mean that our understanding of the fusion process in the Sun was wrong?

The puzzle was recently resolved. Neutrinos come in three types, only one of which is produced in the Sun, and only that same type was detected by Davis's experiment. On their way from the Sun to the Earth, the neutrinos are able to transform from their original type to any of the three types. Since most of the experiments can only detect neutrinos of the original type, they only see one third of the total!

Interestingly, the solar neutrino measurements have verified our model of the Sun and led us to discover something fundamental about neutrinos. We have learned that neutrinos have mass. Their mass is very small when compared to protons or electrons, but it is not zero. And we have learned that neutrinos can transform from one type to another.

Raymond Davis, Jr. was awarded the 2002 Nobel Prize in physics for his work to detect solar neutrinos, definitively showing that fusion is the source of the Sun's energy.