Context. Cosmic chronometers offer a model-independent way to trace the expansion history of the Universe via the dating of passively evolving objects. This enables testing the validity of cosmological models without concrete assumptions about their energy content. Aims. The main goal of this work is to derive model-independent constraints on the Hubble parameter up to z ∼ 0.4 using stellar ages from the fitting of Lick index absorption lines in passively evolving galaxies. Contrary to recent, related studies that rely on finite differences to obtain a discrete measurement of the expansion of the Universe at an average redshift, our goal is to perform a cosmographic fit of H(z) in terms of the Hubble constant (H0) and the deceleration (q0) and jerk (j0) parameters. Methods. We carefully selected spectra of massive and passively evolving galaxies from the SDSS Legacy Survey. After applying a stacking procedure to ensure a high S/N, the strength of Lick indices was fitted using two stellar population models (TMJ and Knowles) to derive stellar population parameters. A cosmographic fit to the stellar ages was performed, which in turn enabled the sampling of the Hubble parameter within the considered redshift range. Results. The baseline result comes from using the TMJ-modelled ages, and it yields a value of H0 = 70.0+4.17.6 km s1 Mpc1 for the Hubble constant, where uncertainties refer only to the statistical treatment of the data. The sampling of the Hubble parameter at 0.05< 0.35 is competitive with discrete model-independent measurements from the literature. As a by-product of the Lick index fitting procedure, we provide scaling and dispersion relations of stellar population parameters with respect to velocity dispersion using the low-redshift end of our sample. We finally draw attention to an unexpected oscillating pattern in a number of critical indices with respect to redshift, which translates into a similar behaviour in the t-z relations. These features have never been discussed before, although they are present in previous measurements. We show that they do not originate from our methodology, suggesting a possible origin in the data reduction process.
