Final answer:
Stars may enter the horizontal branch in post-sequence evolution to become RR Lyrae or Cepheid Variable stars. This occurs after the star has become a red giant, characterized by a core contraction and outer layer expansion. In studying a star cluster's H-R diagram, the cluster's age and the main sequence turnoff point help identify whether stars are evolving towards or away from the main sequence.
Step-by-step explanation:
Stars may enter the horizontal branch in post-sequence evolution and become an RR Lyrae or Cepheid Variable star. When a star has consumed the hydrogen in its core and evolves off the main sequence, it may enter a phase known as the horizontal branch on the Hertzsprung-Russell diagram (H-R diagram). This stage of stellar evolution typically happens after the star has passed through the red giant branch, where it has expanded and cooled after exhausting its core hydrogen fuel.
In the context of an H-R diagram for a star cluster, deciphering whether the stars above and to the right of the main sequence are red giants or young stars approaching the main sequence would depend on the overall context of the cluster's age and evolution. Typically, for a cluster whose most massive stars have already turned off the main sequence to become red giants or supergiants, positioning above and to the right indicates stars that have left the main sequence. Conversely, in young clusters, stars in that location could be contracting toward the main sequence.
The turnoff point where stars begin to evolve away from the main sequence serves as a measure to determine the age of a star cluster because more massive stars evolve faster and leave the main sequence sooner. By studying the turnoff point, we can ascertain whether the stars above the main sequence are aging red giants or younger stars still in the process of reaching the main sequence.