The H Beta Index as an Age Indicator of Old Stellar Systems: The Effects of Horizontal-Branch Stars

The strength of the H$\beta$ index has been computed for the integrated spectra of model globular clusters from the evolutionary population synthesis. These models take into account, for the first time, the detailed systematic variation of horizontal-branch (HB) morphology with age and metallicity. Our models show that the H$\beta$ index is significantly affected by the presence of blue HB stars. Because of the contribution from blue HB stars, the H$\beta$ 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 where the H$\beta$ index becomes strongest. Our models indicate that the strength of the H$\beta$ index increases as much as 0.75 {\AA} due to the presence of blue HB stars. The comparison of the recent Keck observations of the globular cluster system in the Milky Way Galaxy with those in giant elliptical galaxies, NGC 1399 and M87, shows a systematic shift in the H$\beta$ against metallicity plane. Our models suggest that this systematic difference is understood if the globular cluster systems in giant elliptical galaxies are several billion years older, in the mean, 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 to clarify whether this difference is indeed due to the age difference or other explanations are also possible.