Chapter 11: Problem 8

Explain how it is possible for the core of a red giant to contract at the same time that its outer layers expand.

Short Answer

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Answer: The core of a red giant contracts while its outer layers expand due to the balance between gravitational and thermal forces. When hydrogen fuel in the core is almost exhausted, the core contracts under the force of gravity, leading to an increase in temperature. This triggers hydrogen shell burning, releasing a large amount of energy and causing the outer layers to expand. Later, helium burning in the core will also contribute to the contraction and expansion process.

Step by step solution

Understanding the Forces Acting on a Star

Inside a star, there are two main forces that balance each other: gravity and thermal pressure. Gravity pulls everything inwards, while the thermal pressure, created by nuclear reactions in the core, pushes everything outwards. This equilibrium state is known as hydrostatic equilibrium.

Formation of a Red Giant

A star becomes a red giant when the hydrogen fuel in its core is almost exhausted. The core contracts due to the force of gravity. The core's temperature increases as a result of the contraction, which leads to the ignition of hydrogen in a shell around the core. This hydrogen shell burning releases a large amount of energy, causing the star's outer layers to expand significantly. The star's surface temperature decreases, giving it a reddish color, hence the name "red giant."

Hydrogen Shell Burning

As the hydrogen shell burning continues, helium accumulates in the core, causing the core's mass to increase. The core continues to contract under the force of gravity, further increasing its temperature.

Helium Burning in the Core

When the temperature in the core becomes high enough, helium fusion reactions begin, converting helium into carbon and oxygen. These fusion reactions release even more energy, increasing the thermal pressure in the core. The core's contraction temporarily slows down, and it may even expand slightly. However, this equilibrium will not last long as the available helium in the core is eventually depleted.

Results of Core Contractions and Expanding Outer Layers

The contracting core and expanding outer layers can occur simultaneously in a red giant due to the balance between gravitational and thermal forces. Gravity pulls the core inward, causing it to contract and increase the core temperature, which triggers further fusion reactions. The released energy from these reactions exerts thermal pressure on the outer layers, causing them to expand. This explains how it is possible for the core of a red giant to contract while its outer layers expand.

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Explain how it is possible for the core of a red giant to contract at the same time that its outer layers expand.

Short Answer

Step by step solution

Understanding the Forces Acting on a Star

Formation of a Red Giant

Hydrogen Shell Burning

Helium Burning in the Core

Results of Core Contractions and Expanding Outer Layers

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