As an AGB star evolves into a white dwarf, it runs out of nuclear fuel, and one might guess that the star should cool off and move to the right on the H-R diagram. Why does the star move instead to the left? a. It becomes larger. b. More of the star is involved in fusion. c. As outer layers are lost, deeper layers are exposed. d. The star gets hotter.

The Hertzsprung-Russell (H-R) diagram is a fundamental tool in understanding stellar astrophysics. It visually represents stars based on two primary characteristics: luminosity and temperature. The x-axis of the diagram shows the surface temperature, which decreases from left to right. Hotter stars are located on the left, and cooler stars are positioned on the right. The y-axis shows the stellar luminosity, increasing upwards. This diagram helps astronomers classify stars and understand their life cycles. Stars often follow distinct paths on the H-R diagram as they evolve, indicating changes in their temperature and luminosity over time.

Stellar evolution describes the life cycle of stars, which undergo significant changes from their formation to their eventual death. Stars like our Sun start their lives as protostars, gradually entering the main sequence phase. During this phase, they fuse hydrogen into helium in their cores, maintaining a delicate balance between gravitational collapse and internal pressure. When a star exhausts its hydrogen fuel, it evolves into a giant phase. For low to intermediate-mass stars, this includes the Red Giant and Asymptotic Giant Branch (AGB) stages. These stars burn helium and other elements until they reach the end of their fuel supply. Loss of outer layers and exposure of hotter cores characterize the final evolutionary stages of such stars, leading to their transition into white dwarfs.

White dwarfs are the remnants left after low to intermediate-mass stars have completed their evolutionary processes. As an AGB star exhausts its nuclear fuel, it sheds its outer layers through intense stellar winds. The outer layers drift away, leaving behind the hot core. This core, composed mainly of carbon and oxygen, contracts and cools, eventually forming a white dwarf. White dwarfs are extremely dense, as they contain a mass comparable to that of the Sun but packed into a volume similar to that of Earth. They no longer undergo fusion reactions and slowly radiate away their remaining heat over billions of years.

Stellar temperature is a crucial property affecting a star's appearance and evolution. It is typically measured in Kelvin (K) and determines the star's color and spectral type. Hotter stars appear blue or white, while cooler stars appear red or orange. The surface temperature of a star is influenced by its internal processes, such as nuclear fusion. During different evolutionary stages, a star's temperature can change significantly. For instance, as an AGB star loses its outer layers, the hotter interior becomes exposed, leading to an increase in surface temperature. This results in the star moving left on the H-R diagram, indicating a hotter but less luminous state.

Stellar luminosity is the total amount of energy a star emits per unit of time. It is an indicator of a star's brightness and is often compared to the Sun’s luminosity, denoted as \(L_{\odot}\). Luminosity depends primarily on a star's temperature and size. The Stefan-Boltzmann law states that luminosity (L) is proportional to the fourth power of the star's temperature (T) and its surface area (A). So, large and hot stars tend to be more luminous. During the final stages of stellar evolution, such as the transition from AGB star to white dwarf, the star's luminosity decreases significantly as it loses mass and its core cools. This change reflects in the H-R diagram as a movement to a lower luminosity and higher temperature region.