Final answer:
A star cooling and swelling while maintaining brightness is likely a Red Giant. During its life, a star like the Sun will evolve off the main sequence, become a red giant as it cools and expands, until finally shedding its outer layers, leaving a white dwarf.
Step-by-step explanation:
A star that is cooling and swelling while maintaining the same total brightness is likely in the stage of becoming a Red Giant. The evolution of a star like our Sun from the main-sequence phase to becoming a white dwarf is a complex process that involves significant changes in a star's structure and energy production. Initially, during the main-sequence phase, a star like the Sun fuses hydrogen into helium in its core. Over time, as hydrogen is depleted, the core contracts and heats up, leading to the expansion of the outer layers. This causes the star to swell and cool, becoming a red giant. Eventually, the core collapses further, and the outer layers are shed, leaving behind a hot core that cools over time to become a white dwarf.
As stars evolve off the main sequence, their luminosity and surface temperature change. Massive stars may become red supergiants, whereas stars like the Sun swell into red giants, becoming more luminous but cooler. Their cores contract, fueling the expansion and cooling of the outer layers, and they move upward and to the right on the H-R diagram. The description of red giants having 'split personalities,' with contracting cores and expanding outer layers, captures this transitional phase in a star's lifecycle. A red giant appears orange or orange-red rather than deep red. Stars eventually leave the main-sequence phase and evolve into different stages of their lifecycle represented as other regions on the H-R diagram such as giants, supergiants, and white dwarfs.