The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15

TL;DR

The paper presents a robust 4% BAO distance measurement at $z_{\rm eff} \approx 0.15$ from the SDSS DR7 main galaxy sample by applying density field reconstruction and validating a large set of $1000$ mock catalogs. It combines isotropic BAO information from $P(k)$ and $\xi(s)$ with a carefully modeled covariance, yielding $D_V(z_{\rm eff}) = (664 \pm 25) (r_d/r_d^{\rm fid})$ Mpc and $\alpha = 1.040 \pm 0.037$, while demonstrating a non-Gaussian likelihood. When integrated with Planck and other BAO data, the result tightens constraints on $H_0$ and the dark energy equation of state $w_0$ by about 15%, though it modestly increases tension with direct $H_0$ measurements. Overall, the findings support a concordance LCDM framework while highlighting the continued utility of BAO as a precision cosmological probe.

Abstract

We create a sample of spectroscopically identified galaxies with $z < 0.2$ from the Sloan Digital Sky Survey (SDSS) Data Release 7, covering 6813 deg$^2$. Galaxies are chosen to sample the highest mass haloes, with an effective bias of 1.5, allowing us to construct 1000 mock galaxy catalogs (described in Paper II), which we use to estimate statistical errors and test our methods. We use an estimate of the gravitational potential to "reconstruct" the linear density fluctuations, enhancing the Baryon Acoustic Oscillation (BAO) signal in the measured correlation function and power spectrum. Fitting to these measurements, we determine $D_{V}(z_{\rm eff}=0.15) = (664\pm25)(r_d/r_{d,{\rm fid}})$ Mpc; this is a better than 4 per cent distance measurement. This "fills the gap" in BAO distance ladder between previously measured local and higher redshift measurements, and affords significant improvement in constraining the properties of dark energy. Combining our measurement with other BAO measurements from BOSS and 6dFGS galaxy samples provides a 15 per cent improvement in the determination of the equation of state of dark energy and the value of the Hubble parameter at $z=0$ ($H_0$). Our measurement is fully consistent with the Planck results and the $Λ$CDM concordance cosmology, but increases the tension between Planck$+$BAO $H_0$ determinations and direct $H_0$ measurements.

Figures (10)

• Figure 1: The right ascension and declination positions (J2000) of the 63,163 SDSS DR7 main galaxy survey galaxies we include in our sample. Their footprint occupies 6813 deg$^2$.
• Figure 2: The number density of the sample we use plotted as function of redshift. The error-bars represent the standard deviation of $n(z)$ for the mock realizations. The curve is the best-fit model assuming two linear relationships with a transition redshift, which is a good fit to the data.
• Figure 3: The number density of our galaxy sample as a function of stellar density, Galactic extinction, and seeing. The error-bars denote the standard deviation found in the mock galaxy samples and are only due to stochastic variations in the galaxy field. The variations in number density are consistent with the expected level of fluctuation.
• Figure 4: The measured correlation function, $\xi(s)$ (points with error-bars), pre- (grey diamonds) and post- (open circles) reconstruction. The error-bars are determined from the variance of the 1000 mock galaxy samples. One can see that reconstruction reduces the clustering amplitude, due to removal of large-scale redshift space distortions, and sharpens the BAO peak.
• Figure 5: The measured power spectrum, $P(k)$ (points with error-bars), pre- (grey diamonds) and post- (black circles) reconstruction. The error-bars are determined from the variance of the 1000 mock galaxy samples. The clustering amplitude of the post-reconstruction data is decreased across all $k$ due to the removal of large-scale redshift space distortions.