The Horizontal-Branch Second Parameter Problem Recast as a Quantitative Age Test

Metallicity is the first parameter of horizontal-branch morphology, but clusters of nearly identical composition can show strikingly different branches — one red and stubby, the other extended and blue. This study asks, in numbers, how much of that difference age alone could supply. For three classic matched pairs it divides the age difference that horizontal-branch models require by the observed morphology difference, obtaining a mean sensitivity of 2.42 billion years per unit of morphology index. The largest age difference required, 1.8 billion years, exceeds the independently measured turnoff age differences of the same pairs, so age alone fails as the second parameter in at least the extreme cases. Helium differences between sub-populations, which shift morphology at fixed age, must carry part of the effect. The calculation uses published catalogue and modelling values; it is not a new observation.