Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix

The evolution of differential ages of passive galaxies at different redshifts (cosmic chronometers) has been proved to be a method potentially able to constrain the Hubble parameter in a cosmology-independent way, but the systematic uncertainties must be carefully evaluated. In this paper, we compute the contribution to the full covariance matrix of systematic uncertainties due to the choice of initial mass function, stellar library, and metallicity, exploring a variety of stellar population synthesis models. Through simulations in the redshift range 0 < z < 1.5, we find that the choice of the stellar population synthesis model dominates the total error budget on H(z), with contributions at a level of ∼4.5%, discarding the most discordant model. The contribution due to the choice of initial mass function is <0.5%, while that due to the stellar library is ∼6.6%, on average. We also assess the impact of an uncertainty in the stellar metallicity determination, finding that an error of ∼10% (5%) on the stellar metallicity propagates to a 9% (4%) error on H(z). These results are used to provide the combined contribution of these systematic effects on the error budget. For current H(z) measurements, where the uncertainties due to metallicity and star formation history were already included, we show that, using the more modern stellar libraries, the additional systematic uncertainty is between 5.4% (at z = 0.2) and 2.3% (at z = 1.5). To reach the goal of keeping the systematic error budget below the 1% level, we discuss the efforts needed to obtain higher resolution and signal-to-noise spectra and improvements in the modeling of stellar population synthesis.