Final answer:
Following hydrogen depletion in its core, a star's core shrinks and heats up, leading to the ignition of helium fusion. This additional energy causes hydrogen fusion in outer shells, which makes the star expand and heat up, increasing its size and luminosity.
Step-by-step explanation:
After the hydrogen in a star's core is depleted, the core shrinks and heats up. This occurs because the nuclear energy generation that was sustaining the core's pressure ceases, causing the core to collapse under its own gravity. As the core becomes more compressed, it releases heat, which in turn causes the helium above the core to reach temperatures high enough for helium fusion to begin. This process creates a new flow of energy.
The added heat from the core causes hydrogen in a shell around the helium to also heat up and begin hydrogen fusion. This new fusion process generates even more energy, causing the outer layers of the star to expand and heat up. This expansion and heating is a complex process that involves the star becoming much larger and increasing in luminosity. The star's outer layers grow and the star reaches enourmous proportions, becoming a red giant for a brief period.