On the Use of the Main-sequence Knee (Saddle) to Measure Globular Cluster Ages

In this paper, we review the operational definition of the so-called main-sequence knee (MS-knee), a feature in the color-magnitude diagram (CMD) occurring at the low-mass end of the MS. The magnitude of this feature is predicted to be independent of age at fixed chemical composition. For this reason, its difference in magnitude with respect to the MS turn-off (MS-TO) point has been suggested as a possible diagnostic to estimate absolute globular cluster (GC) ages. We first demonstrate that the operational definition of the MS-knee currently adopted in the literature refers to the inflection point of the MS (which we here more appropriately named MS-saddle), a feature that is well distinct from the knee and which cannot be used as its proxy. The MS-knee is only visible in near-infrared CMDs, while the MS-saddle can be also detected in optical-NIR CMDs. By using different sets of isochrones, we then demonstrate that the absolute magnitude of the MS-knee varies by a few tenths of a dex from one model to another, thus showing that at the moment stellar models may not capture the full systematic error in the method. We also demonstrate that while the absolute magnitude of the MS-saddle is almost coincident in different models, it has a systematic dependence on the adopted color combinations which is not predicted by stellar models. Hence, it cannot be used as a reliable reference for absolute age determination. Moreover, when statistical and systematic uncertainties are properly taken into account, the difference in magnitude between the MS-TO and the MS-saddle does not provide absolute ages with better accuracy than other methods like the MS-fitting.