Helium Fusion and Degenerate Electron Pressure

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  • 0:03 Difficult Sounding Terms
  • 0:47 Your Typical…
  • 2:54 Overcoming the Coulomb Barrier
  • 4:30 The Helium Flash & Degeneracy
  • 6:47 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

Standard gas laws need not apply under the special circumstances described in this lesson with concepts like degeneracy, degenerate electron pressure, helium fusion, and the Coulomb barrier.

Difficult Sounding Terms

This lesson will explore some very foreign and scary-sounding terms, including degeneracy, quantum, Coulomb barrier, helium flash, degenerate electron pressure, and helium fusion. I hope I didn't scare you away already. Those terms sound pretty bad, and they're actually quite complex. However, I will simplify them for you in a logical manner so you can go and brag to your friends about your newfound knowledge after you nail everything down. All of these terms can be used outside the scope of this lesson, but for right now we'll focus in on how they relate to helium fusion in red giants, stars that have run out of hydrogen to produce energy.

Your Typical Properties of a Gas

Before we can explore how red giants generate energy, we have to take a small step back and explore the properties of gases, like those found on Earth. In most cases, the way gases behave on Earth correlates well with the way they behave inside of a star. How do these gases behave? Really quickly put: the pressure exerted by a gas is directly proportional to the density and the temperature of a gas. When you compress a gas, it becomes denser and its temperature increases. When the temperature increases, the pressure increases.

Inside of a main sequence star, an adult star, one that fuses hydrogen to produce helium in its core in order to generate energy, there is a sort of safety valve system that uses this principle. A normal adult star doesn't expand like crazy nor does it collapse because of an equilibrium maintained between the inward force of gravity trying to contract the star and the expansive outward force of gas pressure fighting against gravity. The stalemate between such forces maintains the star's shape and temperature. It's like a spring, where you can press downward on the spring, but the spring will push up against you to try and resist the compressive forces.

If, for example, the rate of nuclear reactions in the star's core were to decrease, the core would cool down and it would contract due to the now-overbearing inward forces. But such compression will actually increase the temperature inside the core as per the gas rules I outlined before. Increasing temperatures speed up the rate of thermonuclear reactions, and the core would expand back to a normal size. However, if the thermonuclear reactions were to increase by way too much, the core would expand as a result, cool as it expands, and, thus, eventually contract back down to normal.

Overcoming the Coulomb Barrier

But this isn't how things work in red giants that have masses that are between approximately 0.4 solar masses and about two to three solar masses. Red giants with more than about two to three solar masses undergo a gradual onset of helium fusion, as opposed to the former ones, which undergo an explosive helium flash. A main sequence star burns hydrogen and produces helium during its thermonuclear reactions in order to generate energy. Once the finite amount of hydrogen in the core is depleted, it logically becomes a helium core.

But the helium doesn't immediately fuse to produce energy thereafter. That's because the core is initially not hot enough for this. Helium requires much larger temperatures to undergo thermonuclear reactions, which produce carbon from helium. This is because helium nuclei have positive charges that are twice that of hydrogen nuclei.

It's sort of like the helium nuclei are much more powerful opposing magnets than hydrogen nuclei. This means that you'll need much higher speeds to overcome the Coulomb barrier, which refers to the electrostatic repulsion between two or more bodies of similar charge that must be overcome for nuclear fusion to begin. The only way to get these higher speeds in the core is to increase the temperature of the core.

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