Final answer:
The cluster whose brightest main-sequence stars are yellow is the oldest as these stars indicate a longer lifespan when compared to white main-sequence stars. Neutron stars and a low turnoff point from the main sequence in the H-R diagram also signify an older age, as seen in globular clusters.
Step-by-step explanation:
The oldest star cluster is the one whose brightest main-sequence stars are yellow. This is because the color of the brightest main-sequence stars in a cluster tells us about the cluster's age. Main-sequence stars shine in different colors depending on their temperature and mass.
Hotter, more massive stars are blue and have shorter lifespans, while cooler, less massive stars are red and live longer. A yellow main-sequence star is cooler than a white one, indicating it has been shining for a longer time. Therefore, a cluster with yellow brightest main-sequence stars is older than one whose brightest main-sequence stars are white.
The ages of star clusters can also be assessed by the presence of certain types of post-main-sequence stars. For instance, neutron stars are remnants of massive stars that have exploded in supernovae, events that occur later in a star cluster's life. Additionally, the turnoff point from the main sequence on an H-R diagram is used by astronomers to determine the cluster's age. Older clusters, such as globular clusters, have a low turnoff point and no high-mass blue main-sequence stars because they have already evolved off the main sequence.