What happens when a sun-like star runs out of hydrogen?

When a star similar to the Sun exhausts its hydrogen fuel in the core, it undergoes significant changes leading to its expansion and transformation into a red giant. In the core of the star, hydrogen fusion ceases, causing the core to contract under gravity. As the core contracts, the temperature rises, which eventually allows hydrogen in a shell around the core to start fusing into helium. The energy produced by this fusion increases the pressure in the outer layers of the star, causing them to expand significantly.

As a result of this expansion, the outer envelope of the star cools and takes on a reddish appearance, hence the term "red giant." This phase of the star's lifecycle is important because it leads to the eventual ejection of the outer layers, forming a planetary nebula, while the core itself can eventually become a white dwarf after helium fusion concludes.

The other choices depict different processes that are not applicable to a sun-like star running out of hydrogen. For instance, black dwarfs are theoretical remnants of white dwarfs after they have cooled down significantly, which is a much later stage. Neutron stars and supernovae are associated with much more massive stars and their end-of-life scenarios, not those similar to the Sun.