The uncertainties in the synthetic indices for stellar populations

The study of line strengths in the spectra of early-type galaxies has proved to be a powerful tool for investigating the age and the metallicity of these systems. When computing models for spectrophotometric narrow-band indices, index calibrations as functions of the relevant stellar parameters (e.g. temperature, gravity and metal content) are used. Thus synthetic indices depend upon these calibrations (called fitting functions), as well as on the stellar evolution ingredients adopted. All these inputs suffer from uncertainties, which impact on the derived value for the indices. In this paper we address this problem quantitatively. We compute synthetic Mg-2, Fe 5270, Fe 5335 and H-beta indices for simple stellar populations (SSPs) of various ages and metallicities, under different prescriptions for the fitting functions. This allows us to estimate the impact of the uncertainties in the fitting functions. By comparing our models to those of other authors computed with the same fitting functions, we estimate the uncertainty associated with the use of different stellar evolution prescriptions. It is found that the modelling of the horizontal branch impacts particularly on Fe and H-beta. In the range of parameters explored, the uncertainties introduced by the use of different fitting functions can be appreciably larger than the error affecting the observational data. This typically occurs at high Z for the metallic line strengths, and at low Z for the H-beta index.