The shape of the SDSS DR5 galaxy power spectrum

TL;DR

This work analyzes the SDSS DR5 combined Main and LRG galaxy sample with a Fourier-based method to measure the redshift-space power spectrum and to constrain the matter density from spectral shape. It shows that fits to CDM shapes depend on the k-range used, with $\Omega_M=0.22\pm0.04$ for $0.01<k<0.06$ and $\Omega_M=0.32\pm0.01$ for $0.01<k<0.15$, indicating a significant scale-dependent discrepancy that cannot be explained by simple, scale-independent bias. The authors argue that scale-dependent bias—especially for LRGs—and luminosity-dependent bias are viable explanations, supported by subcatalogue analyses showing increasing clustering strength with luminosity. Through extensive robustness tests across angular/radial selections and bias models, the study reveals that the observed tension likely reflects real galaxy–mass relations rather than simple systematic errors, emphasizing the need for sophisticated bias modelling in cosmological inferences from galaxy clustering. Overall, the paper highlights the complex interplay between galaxy bias, redshift-space distortions, and non-linear growth in shaping the observed power spectrum and its cosmological implications.

Abstract

We present a Fourier analysis of the clustering of galaxies in the combined Main galaxy and Luminous Red Galaxy (LRG) Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) sample. The aim of our analysis is to consider how well we can measure the cosmological matter density using the signature of the horizon at matter-radiation equality embedded in the large-scale power spectrum. The new data constrains the power spectrum on scales 100--600h^-1Mpc with significantly higher precision than previous analyses of just the SDSS Main galaxies, due to our larger sample and the inclusion of the LRGs. This improvement means that we can now reveal a discrepancy between the shape of the measured power and linear CDM models on scales 0.01<k<0.15hMpc^-1, with linear model fits favouring a lower matter density (Omega_m=0.22+/-0.04) on scales 0.01<k<0.06hMpc^-1 and a higher matter density (Omega_m=0.32+/-0.01) when smaller scales are included, assuming a flat LCDM model with h=0.73 and n_s=0.96. This discrepancy could be explained by scale-dependent bias and, by analysing subsamples of galaxies, we find that the ratio of small-scale to large-scale power increases with galaxy luminosity, so all of the SDSS galaxies cannot trace the same power spectrum shape over 0.01<k<0.2hMpc^-1. However, the data are insufficient to clearly show a luminosity-dependent change in the largest scale at which a significant increase in clustering is observed, although they do not rule out such an effect. Significant scale-dependent galaxy bias on large-scales, which changes with the r-band luminosity of the galaxies, could potentially explain differences in our Omega_m estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.

Figures (19)

• Figure 1: Part of the SDSS DR5 sample region plotted as a function of celestial coordinates. Note that this is not an equal area projection, so the plate outlines (solid lines) do not form perfect circles. Different colours delineate groups of pixels where the completeness of the survey is expected to be the same (see text for details). Black points show the positions of the galaxies. White regions are bad areas excluded from the survey mask. Where these areas are due to bad photometric fields, the regions often follow the drift scanning strategy of the photometric survey -- hence the white stripes at $\alpha\simeq132^{\circ}$, $\delta\simeq48^{\circ}$.
• Figure 2: Radial distributions of the SDSS DR5 main galaxies (solid circles) to an apparent r magnitude limit of 17.5 (lower panel), and 17.77 (middle panel). The sharp increase in the number of galaxies at $z=0.08$ is predominantly the effect of the "Sloan Great Wall" gott05. These data are fitted using equation (\ref{['eq:zfit']}), shown by the solid lines baugh93. In the upper panel we show the distribution of the number density of the LRGs (excluding those in the main galaxy sample). These data are fitted with a smooth cubic spline (solid lines) with nodes selected to allow the curve to fit the sharp distortions caused by spectroscopic features moving through the SDSS filters used to select the LRGs, and the mixture of cut-I and cut-II LRGs (see text for details).
• Figure 3: The colour of 5% of the main galaxies in the SDSS DR5 sample, selected at random. The well-known bimodal split between red and blue galaxies is clear, approximately split by ${\rm M}_{^{0.1}g}-{\rm M}_{^{0.1}r}=0.8$ (dashed line). This plot highlights the fact that as we change the magnitude of the samples, we also change the average colour, with the more luminous main galaxies being predominantly redder.
• Figure 4: The redshift distributions of two of our pseudo-volume limited catalogues (solid lines). The selection of these catalogues was based on absolute magnitudes without K-corrections or corrections for evolution, and so are not strictly volume limited. These effects were instead included in estimating the redshift distribution of the samples to create matched random catalogues (dotted lines; see text for details). For comparison, the dashed curves show the redshift distribution that the catalogues would have if they were strictly volume limited -- as can be seen these are a poor fit to the data.
• Figure 5: The distribution of the SDSS galaxies in the redshift -- luminosity plane. Absolute magnitudes were calculated assuming a flat $\Lambda$ cosmology with $\Omega_M=0.3$ and have not been K-corrected or corrected for evolution. The upper and lower apparent magnitude limits of the main galaxy sample are shown by the dashed lines. The redshift and magnitude limits of the pseudo-volume limited catalogues analysed to calculate the relative bias as a function of absolute magnitude are shown by the overlaid rectangles.