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Low-mass stars can undergo two evolutionary phases called red-giant phases. What is the difference between them?

A) In the first, the primary production of energy is from hydrogen burning in the core. In the second, the primary production of energy is from helium burning in the core.
B) In the first, the primary production of energy is from helium burning in the core. In the second, the primary production of energy is from helium burning in a shell around the core.
C) In the first, the star's track on the Hertzsprung-Russell diagram lies along the red- giant branch. In the second, the track lies along the horizontal branch.
D) During the first red-giant phase, the star moves up and to the right along the red-giant branch. During the second red-giant phase the star's track is down and to the left along the same red-giant branch.

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Final answer:

The first red-giant phase of a low-mass star is marked by hydrogen shell burning around a contracting core, whereas the second red-giant phase involves helium shell burning around a carbon-oxygen core after the helium flash.

Step-by-step explanation:

Low-mass stars indeed experience two distinct red-giant phases during their evolution. The first red-giant phase occurs after a star exhausts hydrogen in its core and begins to burn hydrogen in a shell around the core. During this phase, the core contracts, the outer layers expand, and the star moves up the red-giant branch on the Hertzsprung-Russell (H-R) diagram, becoming more luminous and cooler at the surface.

The second red-giant phase, also known as the Asymptotic Giant Branch (AGB) phase, occurs after the star has ignited helium in its core, known as the helium flash, and has briefly stabilized while helium burning into carbon and oxygen. Once the helium is exhausted, the star resumes shell hydrogen and helium burning around an inert carbon-oxygen core, becoming a red giant for the second time. This phase is characterized by high luminosity and a cooler surface temperature as the star moves again on the H-R diagram but this time with different internal fusion processes.

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