Four New Observational $H(z)$ Data From Luminous Red Galaxies of Sloan Digital Sky Survey Data Release Seven

TL;DR

This work adds four new measurements of the Hubble parameter $H(z)$ derived from the differential ages of luminous red galaxies in SDSS DR7, expanding the OHD catalog to 25 points. Ages are inferred via ULySS full-spectrum fitting of SSP BC03 models to obtain an age–redshift relation $t(z)$, which yields $H(z_{eff})=-(1/(1+z_{eff}))(dt/dz)$ at four effective redshifts. Incorporating these data with existing OHD modestly tightens flat and non-flat ΛCDM constraints, though uncertainties remain large due to spectral SNR and sample limitations. The study demonstrates OHD’s potential and highlights the need for higher-SNR spectra and deeper chronometer samples to fully exploit this cosmological probe.

Abstract

By adopting the differential age method, we utilize selected 17832 luminous red galaxies (LRGs) from Sloan Digital Sky Survey Data Release Seven (SDSS DR7) covering redshift $0<z<0.4$ to measure Hubble parameters. Using a full spectrum fitting package UlySS, these spectra are reduced with single stellar population (SSP) models and optimal age information of our selected sample are derived. With the decreasing age-redshift relation, four new observational $H(z)$ data (OHD) points are obtained, which are $H(z)=69.0\pm19.6$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.07$, $H(z)=68.6\pm26.2$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.12$, $H(z)$=$72.9\pm29.6$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.2$ and $H(z)$=$88.8\pm36.6$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.28$, respectively. Combined with other 21 available OHD data points, a performance of constraint on both flat and non-flat $Λ$CDM model is presented.

Figures (7)

• Figure 1: Redshift distribution of 17832 LRGs.
• Figure 2: Best fit with BC03 model and the residual spectrum for a galaxy. The top panel shows the spectrum in black and the best fit in blue. The red regions are rejected from the fit, the indigo line is the multiplicative polynomial. The bottom panel shows the residuals from the best fit. The continuous green lines represent the 1$\sigma$ deviation.
• Figure 3: Fitting results of the 17832 LRGs. For clarity, the ages less than 7Gyr have not been plotted. The red line shows the theoretical age of the universe $t(z)$ for a $\Lambda$CDM model with $\Omega_m=0.29$ and $H_0=69$ km s$^{-1}$ Mpc$^{-1}$ . The blue line indicates $t(z)+3$Gyr, whose derivation of the 3Gyr comes from the systematic errors. A clear trend is present: the oldest ages of the galaxies decrease with redshift.
• Figure 4: The oldest ages in each bin when we divide the subsamples into their corresponding $n_{best}$ bins and their optimal fitted results. The solid line represents the best fitting for each subsample. In the first subsample $z_{min}=0.033$, $z_{max}=0.109$, and $z_{eff}=0.07$. In the second subsample, $z_{min}=0.090$, $z_{max}=0.156$, $z_{eff}=0.12$. In the third subsample, $z_{min}=0.170$, $z_{max}=0.236$, $z_{eff}=0.20$, and in the forth subsample, $z_{min}=0.243$, $z_{max}=0.315$, $z_{eff}=0.28$.
• Figure 5: All available OHD points. The solid line plots the theoretical Hubble parameter $H_{fid}$ as a function of $z$ from the spatially flat $\Lambda$CDM model with $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0$ = 72 km s$^{-1}$Mpc$^{-1}$. The OHD points are listed in Tab. \ref{['tab:AOHD']}