Stellar population models of Lick indices with variable element abundance ratios

We provide the whole set of Lick indices from CN1 to TiO2 in the wavelength range 4000 less than or similar toless than or similar tolambdaless than or similar to 6500 Angstrom of simple stellar population models with, for the first time, variable element abundance ratios, [alpha/Fe ]= 0.0, 0.3, 0.5, [alpha/Ca ]=-0.1, 0.0, 0.2, 0.5 and [alpha/N]=-0.5, 0.0. The models cover ages between 1 and 15 Gyr, metallicities between 1/200 and 3.5 solar. The impact from the element abundance changes on the absorption-line indices is taken from Tripicco & Bell, using an extension of the method introduced by Trager et al. Our models are free from the intrinsic alpha/Fe bias that was imposed by the Milky Way template stars up to now, hence they reflect well-defined alpha/Fe ratios at all metallicities. The models are calibrated with Milky Way globular clusters for which metallicities and alpha/Fe ratios are known from independent spectroscopy of individual stars. The metallicities that we derive from the Lick indices Mg b and Fe5270 are in excellent agreement with the metallicity scale by Zinn & West, and we show that the latter provides total metallicity rather than iron abundance. We can reproduce the relatively strong CN- absorption features CN1 and CN2 of galactic globular clusters with models in which nitrogen is enhanced by a factor of 3. An enhancement of carbon, instead, would lead to serious inconsistencies with the indices Mg-1 and C-2 4668. The calcium sensitive index Ca4227 of globular clusters is well matched by our models with [Ca/Fe]= 0.3, including the metal-rich bulge clusters NGC 6528 and 6553. From our alpha/Feenhanced models we infer that the index [MgFe] defined by Gonzalez is quite independent ofalpha/Fe but still slightly decreases with increasing