Cosmography via stellar archaeology of low-redshift early-type galaxies from SDSS

TL;DR

This work employs a model‑independent cosmographic expansion of $H(z)$, using stellar ages derived from Lick indices in a carefully selected SDSS Legacy ETG sample, to constrain $H_0$, $q_0$, and $j_0$ up to $z\sim0.4$. Ages are obtained by stacking high‑S/N spectra and fitting two SPS models (TMJ and Knowles) to a fixed set of Lick indices, with a six‑bin velocity‑dispersion stratification allowing six independent zero‑age anchors $t_{0,v}$. The TMJ‑based analysis yields a credible $H_0 = 70.0^{+4.1}_{-7.6}$ km s$^{-1}$ Mpc$^{-1}$ and a $q_0$ distribution near the physical bound $q(z) > -1$, while $j_0$ remains weakly constrained; the sampling is competitive with other model‑independent measurements at low redshift, and Planck2018 LCDM is consistent within 1σ. However, the Knowles model produces excessively tight but conflicting ages, requiring ad hoc dispersion factors to recover reasonable fits, highlighting model‑dependence and systematic uncertainties in stellar population modeling. Beyond cosmography, the study provides scaling relations of stellar population parameters with velocity dispersion and documents oscillations in several index–redshift relations around $0.16 \lesssim z \lesssim 0.19$, which appear tied to SDSS data reduction rather than the cosmic signal. The results underscore the potential of cosmic chronometers for low‑ redshift cosmography while signaling the need for higher‑redshift data and deeper scrutiny of SPS systematics and index calibrations.

Abstract

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 of their energy content. The main goal of this work is to derive model-independent constraints on the Hubble parameter up to $z \sim 0.4$ using stellar ages from the fitting of Lick index absorption lines in passively evolving galaxies. Contrary to recent related works 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 ($H_0$) and the deceleration ($q_0$) and jerk ($j_0$) parameters. We carefully select spectra of massive and passively evolving galaxies from the SDSS Legacy Survey. After applying a stacking procedure to ensure a high signal-to-noise ratio, the strength of Lick indices is fit using two stellar population models (TMJ and Knowles) to derive stellar population parameters. A cosmographic fit to the stellar ages is performed, which in turn enables the sampling of the Hubble parameter within the considered redshift range. The baseline result comes from using the TMJ-modelled ages, and it yields a value of $H_0 = 70.0^{+4.1}_{-7.6} \text{ km s}^{-1} \text{ Mpc}^{-1}$ for the Hubble constant, where uncertainties refer only to the statistical treatment of the data. The sampling of the Hubble parameter at $0.05 < z < 0.35$ is competitive with discreet model-independent measurements from the literature. 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.

Figures (23)

• Figure 1: Distribution of D$4000_\text{n}$ and three Balmer-line indices over the parent (grey), query (blue) and final (maroon) galaxy samples.
• Figure 2: Distribution of sources in the $(\text{u} - \text{r})_0 \text{ vs } (\text{r}-\text{z})_0$ colour-colour plane. The parent sample is shown in grey, while the increasingly restrictive subsamples (adding velocity dispersion, query and spectroscopic information) are shown in light blue, dark blue and maroon, respectively. The dashed black line defines the passive galaxy region holden12
• Figure 3: Properties of the ancillary stacks. Left panel: distribution of the number of galaxies included in the ancillary stacks defined by a linear constant spacing in both $\sigma$ and $z$. Right panel: relation between the S/N and the number of galaxies in each ancillary stack as a function of redshift.
• Figure 4: RMS wavelength resolution ($\sigma_\text{R}$) of SDSS stacked spectra as a function of rest-frame wavelength for different redshifts.
• Figure 5: Age, metallicity and $\alpha$-enhancement distributions for the TMJ (left panels) and Knowles (right panels) models, interpolated to a grid of 50 points in each parameter within the original ranges. Results are shown for the Lick index fit to both single galaxies (in blue) and stacks (in yellow) of the final cosmic chronometer sample.