When compressed, ordinary gas heats up but degenerate gas does not. Why, then, does a degenerate core heat up as the star continues shell burning around it? a. It is heated by the radiation from fusion. b. It is heated by the gravitational collapse of the shell. c. It is heated by the weight of helium falling on it. d. It is insulated by the shell.

In astrophysics, degenerate gas refers to a gas composed of particles that obey the rules of quantum mechanics. Unlike ordinary gas, where the pressure is a function of temperature and volume, the pressure in a degenerate gas depends solely on the density. This is due to the Pauli exclusion principle, which prevents fermions (like electrons) from occupying the same quantum state. As a result, when a degenerate gas is compressed, it does not necessarily heat up as an ordinary gas would. The particles are already in their lowest energy states, and additional compression mostly increases the kinetic energy without raising the temperature significantly. This unique property is crucial in understanding the behavior of white dwarfs and the cores of evolved stars.

Shell burning occurs in the later stages of a star's life cycle when it has exhausted its core hydrogen fuel. At this point, the star starts burning hydrogen in a surrounding shell outside the core. This process releases a significant amount of energy, contributing to the heating and expansion of the star's outer layers. Shell burning is an essential phase in the evolution of medium and high-mass stars and often leads to the creation of heavier elements through nucleosynthesis. The added mass from shell burning can exert pressure on the surrounding areas, impacting the star's core and outer layers. As the shell continues to burn, it can cause more material to accumulate onto the core, affecting the star's overall energy dynamics.

Gravitational compression is the process by which a body, such as a stellar core, is compressed under the force of its own gravity. In the context of a star's degenerate core, the weight of material (such as helium produced in shell burning) falling onto it increases the core's density. Even though the material is composed of degenerate gas, the increased density can result in heating. This heating happens because the compression work done by gravity increases the internal energy of the particles, compensating for the otherwise low-temperature change in degenerate gas. Therefore, gravitational compression ensures that the core remains hot and dense enough to eventually trigger further stages of nuclear fusion, depending on the star's mass.

Stellar evolution is the process of change that a star undergoes over its lifespan, from its formation to its eventual death. This journey involves various stages, including hydrogen burning in the core, shell burning, and the formation of degenerate cores. As a star evolves, different nuclear processes take place, which alter its structure and composition. During the main sequence phase, stars fuse hydrogen into helium in their cores. Once the hydrogen is depleted, the star expands and enters the red giant or supergiant phase, beginning shell burning around the core. In the later stages, massive stars might develop iron cores leading to supernova explosions, while low- to medium-mass stars may shed their outer layers and leave behind white dwarfs. Understanding stellar evolution helps astronomers predict the future of our own Sun and the life cycles of other stars in the universe.