What is the second-parameter problem in globular cluster colour-magnitude diagrams?

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The "second-parameter" problem refers to an enigma in the study of globular cluster colour-magnitude diagrams.

While the shape and extent of stellar sequences in these diagrams are primarily governed by the cluster's age and its chemical composition—specifically the abundance of metals, which is considered the "first parameter"—these factors do not fully explain observed variations. Astronomers have identified cases where two clusters appear nearly identical in both age and metal abundance, yet possess significantly different horizontal branches; one may be short and stubby, while the other extends far toward the blue.

This discrepancy indicates that an additional, as-yet-unidentified "second parameter" influences the structure of these stellar populations. Although stellar rotation was once proposed as a potential candidate for this second parameter, that theory is now considered unlikely.1