Final answer:
The oldest galaxy cluster can be determined from the H-R diagram by the main-sequence turnoff point. The older the cluster, the lower the main-sequence stars before they turn off towards the red giant region. Globular clusters such as 47 Tucanae demonstrate this by having only the very bottom of the main sequence remaining.Option 4 is the correct answer.
Step-by-step explanation:
From the H-R diagram, to determine which galaxy cluster is the oldest, we need to consider the main-sequence turnoff point. This point indicates where stars are beginning to leave the main sequence and therefore indicates the cluster's age. The older the cluster, the lower the point on the main sequence where this occurs.
Globular clusters, known to be at least 11 billion years old, show an H-R diagram where highly luminous blue stars have all evolved off the main sequence. Instead, there are only low-mass stars left near the bottom of the main sequence, and no new luminous blue stars.
Therefore, the oldest cluster will likely be the one where the main-sequence turnoff occurs at the lower masses, which also means a lower luminosity since the upper more massive and luminous stars have already turned off the main sequence. This will tie in with the cluster whose H-R diagram (from the locations provided in the question - Top Left, Second top Left, Second top Right, Top Right) shows the lower point on the main sequence or where only the very bottom of the main-sequence remains.
This type of H-R diagram would be consistent with a globular cluster such as 47 Tucanae, which is an old cluster with a significantly reduced luminosity scale on the H-R diagram when compared to younger clusters.