The strength of the HÎ² index is computed for the integrated spectra of model globular clusters from the evolutionary population synthesis. For the first time, these models take into account the detailed systematic variation of horizontal-branch (HB) morphology with age and metallicity. Our models show that the HÎ² index is significantly affected by the presence of blue HB stars. Because of the contribution from blue HB stars, the HÎ² does not monotonically decrease as metallicity increases at a given age. Instead, it reaches a maximum strength when the distribution of HB stars is centered around 9500 K, the temperature at which the HÎ² index becomes strongest. Our models indicate that the strength of the HÎ² index increases as much as 0.75 Ã… because of the presence of blue HB stars. The comparison of the recent Keck observations of the globular cluster system in the Milky Way with those in the giant elliptical galaxies NGC 1399 and M87 shows a systematic shift in the HÎ²-metallicity plane. Our models suggest that this systematic difference is explained if the mean age of globular cluster systems in giant elliptical galaxies is several billion years older than the Galactic counterpart. Further observations of globular cluster systems in the external galaxies from the large ground-based telescopes and space UV facilities will enable us to clarify whether this difference is indeed due to the age difference or whether other explanations are also possible.
Hyun Chul Lee, et. al., (2000) The HÎ² index as an age indicator of old stellar systems: The effects of horizontal-branch stars.Astronomical Journal120:2998. DOI: http://doi.org/10.1086/301471