Improved constraints on the expansion rate of the Universe up to z~1.1 from the spectroscopic evolution of cosmic chronometers

Abstract

We present new improved constraints on the Hubble parameter H(z) in the redshift range 0.15 < z < 1.1, obtained from the differential spectroscopic evolution of early-type galaxies as a function of redshift. We extract a large sample of early-type galaxies (\sim11000) from several spectroscopic surveys, spanning almost 8 billion years of cosmic lookback time (0.15 < z < 1.42). We select the most massive, red elliptical galaxies, passively evolving and without signature of ongoing star formation. Those galaxies can be used as standard cosmic chronometers, as firstly proposed by Jimenez & Loeb (2002), whose differential age evolution as a function of cosmic time directly probes H(z). We analyze the 4000 Å break (D4000) as a function of redshift, use stellar population synthesis models to theoretically calibrate the dependence of the differential age evolution on the differential D4000, and estimate the Hubble parameter taking into account both statistical and systematical errors. We provide 8 new measurements of H(z) (see Tab. 4), and determine its change in H(z) to a precision of 5-12% mapping homogeneously the redshift range up to z \sim 1.1; for the first time, we place a constraint on H(z) at z \neq 0 with a precision comparable with the one achieved for the Hubble constant (about 5-6% at z \sim 0.2), and covered a redshift range (0.5 < z < 0.8) which is crucial to distinguish many different quintessence cosmologies. These measurements have been tested to best match a ΛCDM model, clearly providing a statistically robust indication that the Universe is undergoing an accelerated expansion. This method shows the potentiality to open a new avenue in constrain a variety of alternative cosmologies, especially when future surveys (e.g. Euclid) will open the possibility to extend it up to z \sim 2.

Figures (10)

• Figure 1: The ETG spectral evolution. In order to increase the signal-to-noise ratio and the visibility of spectral features, mean stacked spectra were obtained by co-adding individual spectra of ETGs in each redshift bin. For each stacked spectrum, the bin central redshift is indicated on the top-right. The spectra are typical of passively evolving stellar populations and do not show significant [O II]$\lambda$3727 emission. The spectra are normalized in the blue region of $D4000_{n}$ (3850-3950 Å), where the average flux is indicated by a segment in the hatched region on the left. The hatched region on the right indicates the red $D4000_{n}$ range (4000-4100 Å), where the solid segments represent the average fluxes and the dashed one indicates the average flux of the lowest redshift spectrum. A trend of decreasing red flux (i.e. $D4000_{n}$, which is defined as the ratio between the average fluxes in the red and blue ranges defined above) with increasing redshift is clearly visible. As a reference, a BC03 spectrum with delayed $\tau$ SFH ($\tau=0.1$ Gyr), solar metallicity and age of 2.5 Gyr is overplotted in red to a high-z stacked spectrum. The model spectrum has been convolved at a velocity dispersion of 250 ${\rm km s^{-1}}$, typical of the ETGs considered.
• Figure 2: Stellar mass histograms (left panel) and redshift distributions (right panel) of the ETG samples.
• Figure 3: $D4000_{n}-z$ plots for all the ETG samples separately.
• Figure 4: $D4000_{n}$-age relation for BC03 models (left panel) and for MaStro models (right panel). In the upper panel the colored lines represent models with different metallicities, with super-solar metallicity in orange ($Z/Z_{\odot}=2.5$), solar in green, and sub-solar in blue ($Z/Z_{\odot}=0.4$); for each metallicity, the models are plotted with a continuous line for $\tau=0.05$ Gyr, a dotted line for $\tau=0.1$ Gyr, a dashed line for $\tau=0.2$ Gyr and a long-dashed line for $\tau=0.3$ Gyr. Different grey shaded areas represent the ranges of the high $D4000_{n}$ and the low $D4000_{n}$ regime. The lower panel shows a zoom of the area of interest, where the models are shown in gray and the colored lines are fits to the models. The dotted line divides the high $D4000_{n}$ and the low $D4000_{n}$ regimes.
• Figure 5: $A=f(Z)$ relation (in units of [Gyr$^{-1}$], see eq. \ref{['eq:linD4000age']}) for BC03 models (left panel) and for MaStro models (right panel). The black points represent the mean slope obtained for the different metallicities in each $D4000_{n}$ regime, and the orange shaded area shows the interpolation and the associated $1\sigma$ error. In the left panel, the red shaded area represents the contribution to the range of allowed $A(Z)$ due to SFHs assumption, while the black shaded area show the total range of $A(Z)$ when is considered both SFH and metallicity uncertainty (see Sect. \ref{['sec:Hzerror']}).