The Luminosity Function of M30: Evidence for Rapidly Rotating Cores in the Cluster Giants?

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Abstract
The observed luminosity function (LF) of M30 shows an excess in the number of red giants relative to the number of turnoff stars as compared with the predictions of canonical models. This well‐known problem is reexamined in the light of new stellar evolutionary models that have been constructed using an improved equation of state formulation as well as recent opacities and nuclear reaction rates. Neither the improvements to the basic physics of stars nor the adoption of different choices, within reason, for the cluster distance (and hence age), chemical composition, or initial mass function have any appreciable effect on the LF discrepancy. However, it seems to be possible to reconcile theory with observation if the cluster stars retain significant amounts of angular momentum throughout their evolution. Stellar models, which treat rotation in the simple spherically symmetric approximation and which conserve angular momentum—leading to structures on the giant branch with rapidly rotating cores and slowly rotating envelopes—predict LFs in good agreement with that observed for M30. The amount of angular momentum that is required to achieve this consistency appears to be insufficient to have detectable consequences for the tightness of the observed color‐magnitude diagram (though this needs to be checked using a two‐dimensional code) or to affect predicted age versus turnoff‐luminosity relations at more than the few percent level.