The power spectrum of galaxies in the 2dF 100k redshift survey

TL;DR

This work develops and applies a PKL-based, quadratic-estimator framework to the 2dFGRS, delivering uncorrelated, minimum-variance measurements of the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra across 27 $k$-bands while carefully controlling angular and radial selection effects. By separating angular and radial selection functions, applying finger-of-god compression, and using Fisher decorrelation to disentangle the three spectra, the authors obtain precise constraints on $P_{ m gg}(k)$ and informative bounds on redshift-space distortions through $eta$ and $r$, consistent with a flat concordance cosmology. The analysis finds no significant baryon wiggles and demonstrates robust reliability through extensive internal validation, systematics tests, and sensitivity analyses, including a public data release. The results reinforce the 2dFGRS's role in constraining large-scale structure and cosmological parameters, and outline a clear path for exploiting future, larger surveys with improved bias modeling and nonlinear treatments.

Abstract

We compute the real-space power spectrum and the redshift-space distortions of galaxies in the 2dF 100k galaxy redshift survey using pseudo-Karhunen-Loeve eigenmodes and the stochastic bias formalism. Our results agree well with those published by the 2dFGRS team, and have the added advantage of producing easy-to-interpret uncorrelated minimum-variance measurements of the galaxy-galaxy, galaxy-velocity and velocity-velocity power spectra in 27 k-bands, with narrow and well-behaved window functions in the range 0.01h/Mpc < k < 0.8h/Mpc. We find no significant detection of baryonic wiggles, although our results are consistent with a standard flat Omega_Lambda=0.7 ``concordance'' model and previous tantalizing hints of baryonic oscillations. We measure the galaxy-matter correlation coefficient r > 0.4 and the redshift-distortion parameter beta=0.49+/-0.16 for r=1 (beta=0.47+/- 0.16 without finger-of-god compression). Since this is an apparent-magnitude limited sample, luminosity-dependent bias may cause a slight red-tilt in the power spectum. A battery of systematic error tests indicate that the survey is not only impressive in size, but also unusually clean, free of systematic errors at the level to which our tests are sensitive. Our measurements and window functions are available at http://www.hep.upenn.edu/~max/2df.html together with the survey mask, radial selection function and uniform subsample of the survey that we have constructed.

Figures (28)

• Figure 1: The upper half shows the 59832 2dF galaxies in our baseline sample, in equatorial 1950 coordinates. The lower half shows the corresponding angular mask, the relative probabilities that galaxies in various directions get included.
• Figure 2: Number of galaxies surviving as a function of uniform magnitude cut.
• Figure 3: The redshift distribution of the galaxies in our sample is shown both as a histogram (top) and relative to the expected distribution (bottom), in comoving coordinates assuming a flat $\Omega_m=0.3$ cosmology. The curves correspond to the the radial selection function ${\bar{n}}(r)$ employed in our analysis (solid) and by C01 (dotted). The four vertical lines indicate the redshift limits employed in our analysis ($10\,h^{-1}{\rm Mpc}<r<650\,h^{-1}{\rm Mpc}$) and where spectral type subsamples are available ($33\,h^{-1}{\rm Mpc}<r<538\,h^{-1}{\rm Mpc}$).
• Figure 4: The effect of our Fingers-of-god (FOG) removal is shown in the southern slice $\delta=-27.7^\circ$, $-35^\circ<RA<53^\circ$. The slice has thickness $2^\circ$ and has been rotated to lie in the plane of the page. From left to right, the panels show all 15,055 galaxies in the slice, the 6,211 that are identified as belonging to FOGs (with density threshold 100) and the same galaxies after FOG compression, respectively.
• Figure 5: A sample of four angular pseudo-KL (PKL) modes are shown in Hammer-Aitoff projection in equatorial coordinates, with grey representing zero weight, and lighter/darker shades indicating positive/negative weight, respectively. From top to bottom, they are angular modes 1 (the mean mode), 3, 20 and 106, and are seen to probe successively smaller angular scales.