The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications

TL;DR

This study delivers a refined 2dFGRS power-spectrum analysis using an enhanced survey mask and a robust PVP estimator that accounts for luminosity- and colour-dependent bias. The authors validate their approach with Hubble Volume and log-normal mocks, demonstrate the presence of baryon oscillations, and derive precise cosmological constraints: $Ω_m h = 0.168±0.016$ and $Ω_b/Ω_m = 0.185±0.046$, with $σ_8^{gal}=0.924±0.032$. When combined with WMAP CMB data, they infer $Ω_m = 0.231±0.021$, reinforcing a ΛCDM universe with a non-negligible baryon fraction. The work also shows robustness to multiple systematic tests and clarifies the impact of non-linearities and redshift-space distortions on the recovered spectrum, underscoring the value of large-scale structure surveys in precision cosmology.

Abstract

We present a power spectrum analysis of the final 2dF Galaxy Redshift Survey, employing a direct Fourier method. The sample used comprises 221,414 galaxies with measured redshifts. We investigate in detail the modelling of the sample selection. A new angular mask is derived, based on revisions to the photometric calibration. The redshift selection function is determined by dividing the survey according to rest-frame colour, and deducing a self-consistent treatment of k-corrections and evolution for each population. The covariance matrix for the power-spectrum estimates is determined using two different approaches to the construction of mock surveys which are used to demonstrate that the input cosmological model can be correctly recovered. We are confident that the 2dFGRS power spectrum can be used to infer the matter content of the universe. On large scales, our estimated power spectrum shows evidence for the `baryon oscillations' that are predicted in CDM models. Fitting to a CDM model, assuming a primordial $n_{s}=1$ spectrum, $h=0.72$ and negligible neutrino mass, the preferred parameters are $Ω_{M} h = 0.168 \pm 0.016$ and a baryon fraction $Ω_{b} /Ω_{M} = 0.185\pm0.046$ (1$σ$ errors). The value of $Ω_{M} h$ is $1σ$ lower than the $0.20 \pm 0.03$ in our 2001 analysis of the partially complete 2dFGRS. This shift is largely due to the signal from the newly-sampled regions of space, rather than the refinements in the treatment of observational selection. This analysis therefore implies a density significantly below the standard $Ω_{M} =0.3$: in combination with CMB data from WMAP, we infer $Ω_{M} =0.231\pm 0.021$. (Abridged.)

Figures (26)

• Figure 1: Maps of the extinction-corrected ${\rm b_J}$ survey magnitude limit in the NGP (upper) and SGP (lower) strips. The original target was a constant limit at ${\rm b_J}=19.45$; the variations from this reflect revisions to the photometric calibration and alterations in corrections for galactic extinction.
• Figure 2: Photographic ${\rm b_J}-r_{\rm F}$ colour versus redshift for the 2dFGRS, as observed (top) and in the rest frame (middle). The separation between 'early-type' (red) and 'late-type' (blue) galaxies is very clear. The third panel shows the histogram of $k$-corrected restframe colours, which is very clearly bimodal. This is strongly reminiscent of the distribution of spectral type, $\eta$, and dividing the sample at a rest frame colour of $({\rm b_J}-r_{\rm F})_{z=0}=1.07$ (dotted line) achieves a very similar separation of early-type 'class 1' galaxies from classes 2--4, as was done using spectra by madgwick02.
• Figure 3: Maps of the overall redshift completeness, $R(\theta)$, averaged over apparent magnitude, in the NGP and SGP strips.
• Figure 4: Maps illustrating the redshift completeness at ${\rm b_J}=19.5$ relative to that at bright magnitudes. The magnitude dependence of this redshift completeness is assumed to be proportional to $1-\exp({\rm b_J}-\mu)$ and the parameter $\mu$ is estimated for each sector in the survey mask. Here, we plot the factor $1-\exp({\rm b_J}-\mu)$ for a fiducial magnitude of ${\rm b_J}=19.5$.
• Figure 5: The solid curves in the upper panel show stepwise estimates of the overall 2dFGRS luminosity function and estimates for red and blue subsets, split at a restframe colour of ${\rm b_J}-r_{\rm F}=1.07$. They are plotted as a function of absolute magnitude at $z=0.1$, which we define in terms of $z=0$ absolute magnitude as $M^{* z=0.1}_{{\rm b_J}} \equiv M^{* z=0}_{{\rm b_J}} +k(z=0.1)+ e(z=0.1)$. The smooth dashed curves are Schechter functions convolved with the model of the magnitude measurement errors. It is these luminosity functions that are used to construct random unclustered galaxy catalogues. The corresponding maximum likelihood estimates of the $k+e$ corrections (relative to their values at $z=0.1$) are shown by the solid curves in the lower panel. The long-dashed line in the upper panel is an STY estimate of the overall luminosity function when the $k+e$ correction shown as the long-dashed line in the lower panel is adopted.