Flux-calibrated stellar population models of Lick absorption-line indices with variable element abundance ratios

We present new stellar population models of Lick absorption-line indices with variable element abundance ratios. The models are based on our new calibrations of absorption-line indices with stellar parameters derived from the MILES stellar library. The key novelty compared to our previous models is that they are now available at the higher spectral resolution of MILES (~2.7A FWHM) and flux-calibrated, hence not tied anymore to the Lick/IDS system. This is essential for the interpretation of galaxy spectra where calibration stars are not available, such as large galaxy redshift surveys or other high-redshift observations. We note that the MILES resolution appears to be comparable to SDSS resolution, so that our models can be applied to SDSS data without any corrections for instrumental spectral resolution. For the first time we provide random errors for the model predictions based on the uncertainties in the calibration functions and the underlying stellar parameter estimates. We show that random errors are small except at the edges of the parameter space (high/low metallicities and young ages <1 Gyr) where the stellar library is under-sampled. We calibrate the base model for the parameters age, metallicity and alpha/Fe ratio with galactic globular cluster and galaxy gradient data. We discuss two model flavours with different input stellar evolutionary tracks from the Frascati and Padova groups. The new model release now includes abundance variations of the elements C, N, Mg, Na, Si, Ca, Ti, Cr, and Fe. The individual elements that are best accessible with these models and the standard set of Lick absorption features are C, N, Mg, Ca, Ti, and Fe. The model data is available at www.icg.port.ac.uk/~thomasd.