The Hβ 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 integratedspectra of model globular clusters from the evolutionary population synthesis.These models take into account, for the first time, the detailed systematicvariation of horizontal-branch (HB) morphology with age and metallicity. Ourmodels show that the H$\beta$ index is significantly affected by the presenceof 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 iscentered around 9500 K, the temperature where the H$\beta$ index becomesstrongest. Our models indicate that the strength of the H$\beta$ indexincreases 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 systemin the Milky Way Galaxy with those in giant elliptical galaxies, NGC 1399 andM87, shows a systematic shift in the H$\beta$ against metallicity plane. Ourmodels suggest that this systematic difference is understood if the globularcluster systems in giant elliptical galaxies are several billion years older,in the mean, than the Galactic counterpart. Further observations of globularcluster systems in the external galaxies from the large ground-based telescopesand space UV facilities will enable to clarify whether this difference isindeed due to the age difference or other explanations are also possible.