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Red Giant Evolution

A star in its red giant phase remains in this phase to the end of its life of thermonuclear fusion. A red giant evolves through several cycles, each beginning when one nuclear fuel is exhausted at the star's core, causing the core of the star shrinks until its temperature is sufficiently high to cause the next heavier element to burn. Cycle by cycle, the star burns at its core first helium, then carbon, and then oxygen. Beyond oxygen, thermonuclear fusion is too rapid to create a stable, long-lived star, so burning of these heavier elements to iron is part of a star's collapse to a neutron star or black hole. From the outside, each cycle appears as an expansion of the photosphere and the reddening of the star, followed by an increase in luminosity, a contraction of the photosphere, and a shift in color to the blue.

During these cycles of core fusion, thermonuclear fusion of lighter elements continues in shells that surround the core. The outermost shell burns hydrogen. Additional shells of burning material are created at the end of each cycle, starting with the creation of a helium-burning shell, followed by creation of a carbon burning shell. Often most of the energy generated by a red giant comes from these shells, with the hydrogen shell generating the largest portion of this power. Despite this, thermonuclear burning at the core determines the structure and appearance of the star.

The size of a star's core is related directly to the core temperature. The reason is that when the pressure exactly balances gravitational force, as it does at the center of a star, the kinetic energy in the gas is equal to the magnitude of the gravitational potential energy. The temperature is therefore inversely proportional to the radius of the core. The transition from hydrogen burning to helium burning, which requires the temperature to rise from around 2 × 107° K to 108° K, requires the core to contract by a factor of 5. The transition from helium to carbon requires the temperature to rise to 6 × 108° K, which requires the core to contract by another factor of 6. The transition from carbon to oxygen only requires an increase in temperature to 109° K, which only requires the core to contract by 1.7. Transitions to helium burning and to carbon burning therefore produce dramatic changes to the structure of a star.

When burning stops with the depletion of a fuel and the core starts contracting, the temperature gradiant in the star between the core and the photosphere steepens. This causes heat to diffuse to the photosphere faster. This energy goes to expanding the outer envelope of the star, which flattens the temperature gradient. The photosphere of a red giant therefore expands to counter the effect of a shrinking, hot core on the temperature gradient through the star. At the same time, because much of the energy generated by the shrinking of the core and by the burning of light elements in shells surrounding the core goes into gravitational potential energy of the expanding outer regions of the star, the luminosity of the star declines. This means less energy is emitted from a larger photosphere, so the photosphere becomes cooler and redder.

The cooling of the photosphere ceases before the core reaches the temperature for renewed fusion. At some point, the temperature of the photosphere drops so low that the photosphere ceases to be a plasma; all of the free electrons recombine with the ions to create a neutral gas. This has a dramatic effect on how radiation propagates out of the star. The atmosphere of a star is opaque because of H, a hydrogen atom containing two electrons. It may seem odd that such an atom could exist in a hot environment, but in fact it exists in small quantities when free electrons are available for capture by neutral hydrogen. This extra electron causes the hydrogen to easily absorb light, making the atmosphere opaque. When an atmosphere becomes neutral gas, free electrons disappear, H cannot form in the atmosphere, and the atmosphere becomes transparent. We see through this neutral gas down to where the temperature is still high enough to keep the gas ionized and opaque. This effect occurs when the photosphere of a red giant is around 3,000 ° K. Once this point is reached, the temperature of a red giant photosphere remains fixed as the core shrinks. The photosphere's radius, however, continues to increase, so the red giant becomes brighter.

Eventually the core becomes hot enough to reignite thermonuclear fusion. Once started, the fusion spreads through the core, halting and reversing to some extent the contraction of the core. The evolution of the star is then governed by thermonuclear fusion, both within the core and within the shells surrounding the core. From outside, the evolution reverses to some extent the reddening during core shrinkage. As core thermonuclear fuel is consumed, the core contracts slightly, the star becomes more luminous, the photosphere radius shrinks, and the photosphere temperature rises. The star therefore appears to become brighter and bluer as core nuclear fuel is consumed.

The effect of a contracting core is most pronounced in the transition from the main-sequence to the helium-burning stage. For a 3 solar mass star, the photosphere temperature drops from 12,000° K to 4,000 in this transition, while for a 9 solar mass star, the photosphere temperature drops from 25,000° K to 4,000. The reverse of this cooling as helium fusion commences is considerably less pronounced. The photosphere of a 3 solar mass star heats back up to 6,000° K as helium fusion proceeds, while the photosphere of a 9 solar mass star heats back up to 14,000° K.

The amount of energy liberated by burning helium and other heavier elements is considerably less than that liberated by burning hydrogen. Helium fusion liberates 9% of the energy per nucleon that hydrogen liberates. Because the power generated during helium fusion is higher than during core hydrogen burning, the time a star spends burning helium at its core is less than 9% of the time spent on the main-sequence. The carbon and oxygen burning stages are considerably shorter than the helium-burning stage, as carbon burning releases no more than 90% of the energy per nucleon of helium burning, and oxygen burning releases less than this amount. As a consequence, a star is a red giant for about 10% to 25% of its fusion life.

The time for a core to shrink from one burning stage to the next is much shorter than each of the burning stages. For instance, a 9 solar mass star transitions from the main sequence to core helium burning in 1% of the time that the star is on the main sequence. A 3 solar mass star makes this same transition in 5% of the time that it is on the main sequence. This relatively rapid transition means that only a minority of the red giants we see are in this transition phase.

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