Giants and Dwarves (Life of Stars, Part III)

Dylan Lee, Stellar Astronomy

So far in this series, we've looked at the chaotic births of stars as well as their harmonious main sequence lifetimes. Now, after millions or billions of years, we approach the later part of a star's life, which is arguably even more turbulent than its birth. In this post, we'll explore how stars go through various stages near the end of their lives that can make them enormous giants or tiny dwarves.

Giants

In the last article, we left the stars in their stable main sequence. Recall that during the main sequence, they are formed completely of hydrogen, and the hydrogen at the core is hot enough to fuse into helium. Since helium is more massive than the hydrogen, it experiences a stronger gravitational attraction toward the center of the star and thus accumulates in the center of the core. Additionally, since it is more massive, it would require more energy and higher temperatures in order to fuse. The star's core, which is only hot enough to fuse hydrogen, cannot fuse helium.

When the hydrogen in the core is completely used up, the entire core is made of helium. Fusion no longer occurs in the star, so no energy is released. This means that the star is no longer in the main sequence since it is no longer in hydrostatic equilibrium - gravity has won. The core of the star thus begins to collapse again, in similar fashion to the collapse of a protostar. Just as a protostar heats up as it collapses, a star's core also heats up as it collapses. This heat then increases the temperature of a spherical "shell" of hydrogen around the core, which was previously not hot enough to undergo nuclear fusion. However, the compression of the helium core provides the heat necessary to begin hydrogen fusion in the shell around the core.

A diagram of the compressed helium core providing the heat necessary to fuse a shell of hydrogen (Source: Astronomy - Fraknoi, et al.)

In fact, a surplus of heat is provided, and the hydrogen fusion that takes place in the shell occurs much faster than the fusion that took place during hydrostatic equilibrium. This huge outburst of energy from renewed hydrogen fusion has two effects. The first is an increase in the luminosity of the star. The second is that the energy from fusion actually overcomes the gravitational attraction of the star, and the radius of the star increases (some of the gas at the surface actually escapes, decreasing the mass of the star, though it has no effect on the events at the core). This expansion of the star causes the gas at the surface to cool down because they are further from the heat source at the center. Therefore, the effective temperature of the star decreases and it becomes redder. Due to the reddening as well as its increased size, these stars with helium cores are called red giants, or red supergiants. Red supergiants are larger than red giants, but there is no clear distinction between the sizes for giants or supergiants. Notice that the positions of giants and supergiants are at the top right of the H-R Diagram, indicating their high luminosity but low temperature.

Supergiants and giants are at the top right of the H-R Diagram, having high luminosity and low temperature

A diagram of a star's "onion-like" layers once helium fusion begins (Source: Astronomy - Fraknoi, et al.)

The increasing temperatures in the helium core do eventually become high enough to fuse some of the helium at the very center of the core. This process of helium fusion is called the triple-alpha process, as it combines three helium nuclei (alpha particles) to form carbon, which is much more massive than helium. Occasionally, an extra helium atom is fused to form oxygen, which is even more massive than carbon. Once again, due to higher masses, carbon and oxygen require more energy and a higher temperature to fuse. The star does not have this much energy, so the carbon and oxygen simply settle at the center of the core, similar to the helium from before. The star can now be pictured as an onion, with a carbon-oxygen core, a shell of helium fusion, a shell of non-fusing helium, a shell of hydrogen fusion, and finally a hydrogen "envelope" that surrounds all of the cores.

This cycle of compression then fusion of ever-heavier elements repeats until the compression of the core does not provide enough heat for fusion. It is at this point that a star dies.

Dwarves

For stars that begin with a low mass (less than about 2 times the mass of the Sun), death can occur as early as the completion of the carbon-oxygen core - in other words, when all the hydrogen and helium are depleted. This death, however, is not an explosive death like the one that will be discussed below. When the hydrogen and helium are depleted, gravity once again takes over, and begins to compress the star. The compression continues until the particles in the star called electrons become degenerate. To understand what this means, we must first touch on the Pauli exclusion principle. This principle states that no two fermions (which include protons, neutrons, and electrons) in the same quantum system may occupy the same quantum state. In general, this "quantum system" is just an atom, and a "quantum state" can be thought of as an energy level, which dictates how much energy the fermion possesses. However, when stars undergo compression of this extent, the electrons from everywhere in the core are actually ripped out of the atoms, and form one big "sea" of electrons, which is now a single quantum system. The natural tendency of all of these electrons would be to attempt to occupy the lowest quantum state possible (this is called the ground state). However, the Pauli exclusion principle forbids all of the electrons from occupying the same energy level, so some electrons are forced into higher energy levels (excited states), and thus possess more energy. This is what it means for an electron to be degenerate. Although its tendency is to occupy the ground state, it is forced to occupy an excited state.

The ground state has the lowest energy, while excited states have higher energy.

Recall that during hydrostatic equilibrium, nuclear fusion released energy, which created the gas pressure necessary to counteract gravity. When the electrons are forced to occupy higher energy levels, the energy that they possess will also exert a pressure. It is not gas pressure anymore, however. The kind of pressure that the degenerate electrons exert is known as electron degeneracy pressure (what a creative name!). This electron degeneracy pressure now takes the place of nuclear fusion as the resistance to gravity, and the resulting corpse of a star is called a white dwarf. These white dwarfs have very low luminosities since there is no nuclear fusion to release light. However, because of the energy that degenerate electrons possess, they have very high temperatures. Therefore, white dwarfs occupy the lower left of the H-R Diagram (see above).

Keep in mind that only low-mass stars end up as white dwarfs. In the next post, we'll cover the explosive deaths of more massive stars.

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Fraknoi, Andrew, et al. Astronomy. Houston, Texas, OpenStax, Rice University, 2017.

Redd, Nola Tyler. "Red Giant Stars: Facts, Definition & the Future of the Sun," Space, Future US, Inc., 28 March 2018, https://www.space.com/22471-red-giant-stars.html.

Nave, Rod. "White Dwarfs and Electron Degeneracy," HyperPhysics, Georgia State University, http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/whdwar.html.

Photos are linked to sources.

Cover photo is the P1 Gruis, taken by the Precision Integrated-Optics Near-infrared Imaging ExpeRiment (PIONIER) instrument on the European Southern Observatory’s Very Large Telescope Interferometer: https://www.tasnimnews.com/en/news/2018/02/01/1645010/astronomers-get-best-look-yet-at-surface-of-a-red-giant-star