# NUCLEAR FUSION IN THE SUN

### WHAT ARE THE REQUIREMENTS FOR A FUSION-POWERED SUN?

• Lots of protons - no problem, the Sun is made mostly of hydrogen.

Element   Abundance (by #)
Hydrogen
Helium
Oxygen
Carbon
Nitrogen
The rest
90%
9.2%
0.08%
0.04%
0.01%
--

• High temperature - for the P-P Chain, T     107 K

Q. Is there any place in the sun where the temperature is high enough for nuclear fusion to take place?
This is an excellent question. We know the temperature at the surface of the Sun is far too cool for fusion. What about as we go deeper towards the center? This is the subject of a topic called Stellar Structure.

### How do we infer the temperature in the center of the Sun?

It's all based on the concept of HYDROSTATIC EQUILIBRIUM - the downward force due to gravity (i.e the weight) of the gas must be balanced by the upward thermal pressure of the gas. If these forces were not equal, the star would be collapsing inward or expanding outward.

The pressure exerted by a gas increases as the temperature of the gas increases. If you think about a container filled with gas atoms or molecules, the thermal pressure exerted on the walls of the container is due to all the atoms and molecules bouncing off the walls. Remember, temperature is a measure of the mean kinetic energy of the gas particles.

At each level moving down towards the center of the Sun, the total column of mass above every point increases, so the Gravitational Pressure increases as you move in from the surface of the Sun. To maintain Hydrostatic Equilibrium, the Thermal Pressure must also increase with depth which requires that the temperature increase toward the center of the Sun.

With computers it is possible to build (we think) very accurate models of the Sun and other stars based on the the requirement of hydrostatic equilibrium and the laws of chemistry and physics. We can predict the temperature and density of the Sun at each radius from the center to the surface.

You can see that the temperature at the center of the sun (T = 1.5 x 107 K) is much greater than the temperature at the surface of the sun (T = 5800K). The central temperature of the sun is definitely high enough for nuclear fusion to take place there. Actually the temperature is high enough that fusion can take place in the inner 10% of the sun.

### BACK TO A FUSION-POWERED SUN

• It looks like Hydrogen fusion will work as the power source of the Sun. We have lots of the right fuel, the conditions in the inner 10% of the Sun are right for the P-P cycle to run, and it is a very efficient source of energy.

• Q.   How does the energy get from proton mass into visible light photons flying from the surface of the Sun into space?

A.   gamma-rays are released during the P-P fusion chain and almost immediately (after traveling on average 1 cm) absorbed and re-emitted. The energy contained in that original -ray bounces its way outward, and after ~100,000 years and 1022 absorptions and re-emissions, it leaves the surface of the Sun "downgraded" into visible light photons (because of the temperature gradient in the Sun).

• An interesting Aside: The Sun must be losing mass as it is converted into energy.

How Much?

 4 x 1033 ergs/sec   x 1 =   6.25 x 10 14 grams/sec 6.4 x 1018 ergs/gram

This comes to:
685 million tons of hydrogen is mass converted to helium each second.