The power spectrum of galaxy clustering in the APM Survey

Abstract

We measure the power spectrum of galaxy clustering in real space from the APM Galaxy Survey. We present an improved technique for the numerical inversion of Limber's equation that relates the angular clustering of galaxies to an integral over the power spectrum in three dimensions. Our approach is underpinned by a large ensemble of mock galaxy catalogues constructed from the Hubble volume N‐body simulations. Mock catalogues are used to test for systematic effects in the inversion algorithm and to estimate the errors on our measurement. We find that we can recover the power spectrum to an accuracy of better than 15 per cent over three decades in wavenumber. A key advantage of the use of mock catalogues to infer errors is that we can apply our technique on scales for which the density fluctuations are not Gaussian, thus probing the regime that offers the best constraints on models of galaxy formation. On large scales, our measurement of the power spectrum is consistent with the shape of the mass power spectrum in the popular ‘concordance’ cold dark matter model. The galaxy power spectrum on small scales is strongly affected by non‐linear evolution of density fluctuations, and, to a lesser degree, by galaxy bias. The rms variance in the galaxy distribution, when smoothed in spheres of radius 8 h−1 Mpc, is σg8= 0.96+0.17−0.20 and the shape of the power spectrum on large scales is described by a simple fitting formula with parameter Γ= 0.19+0.13−0.04 (these errors are the 1σ ranges for a two‐parameter fit). We use our measurement of the power spectrum to estimate the galaxy two‐point correlation function; the results are well described by a power law with correlation length r0= 5.9 ± 0.7 h−1 Mpc and slope γ= 1.61 ± 0.06 for pair separations in the range 0.1 < r/(h−1 Mpc) < 20.

Evidence of turbulence-like universality in the formation of galaxy-sized dark matter haloes

“…These values are smaller than the classical 1.8 slope, but consistent with recent observational results, especially for galaxies (e.g. Padilla & Baugh 2003;Hawkins et al 2003).…”

A strong clustering of FIR-selected galaxies in the AKARI All-Sky Survey

“…It is well approximated by a single power-law and is consistent with the previous study using IRAS PSCz catalog [3]. In Fig.1, we compare our result with three galaxy samples from APM survey [4], SDSS [5], and GALEX [6]. It is found that FIRselected galaxies have lower clustering strength than optical-selected galaxies, but on the other hand, their clustering strength is higher than UV-selected galaxies.…”

A coarse-grained field theory for density fluctuations and correlation functions of galaxies and clusters

“…Taking the observed value λ 0 120 ∼ 200 h −1 Mpc yields the peak location k 0 0.031 ∼ 0.052 h Mpc −1 . The peak has been, to some degree, indicated by several cluster surveys (Ratcliffe et al 1996;Tadros et al 1998;Hoyle et al 1999;Collins 2000;Schuecker et al 2001;Carretti et al 2002;Einasto 2002;Einasto et al 2002;Tago et al 2002;Padilla & Baugh 2003; Percival 2005). Thirdly, as shown in Fig.…”

“…A real spectrum cannot have an infinitely sharp peak, which should be smoothed by some damping effects. Recent observations have indicated that the measured P(k) has a rather flat peak with large systematic errors on large scales (Outram et al 2003;Padilla & Baugh 2003;Tegmark et al 2004;Maller et al 2005;Percival 2005). …”