The topology of the IRAS Point Source Catalogue Redshift Survey

Abstract

We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15 000 galaxies over 84.1 per cent of the sky, and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N‐body simulations of four variants of the cold dark matter (CDM) cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random‐phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 to 32 h−1 Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. When scaled to a common normalization, the amplitude drop depends primarily on the shape of the power spectrum. We find that the constant‐bias standard CDM model can be ruled out at high significance, because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large‐scale power all fit the PSCz data almost equally well, with a slight preference for a high‐density τCDM model.

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second‐Order Perturbation Theory

“…Thus, the perturbation theory predicts that the values of genus at positive and negative troughs differ by 14% for the À ¼ 0:3, 8 ¼ 1 CDM model, and so on. This difference increases with the shape parameter C. The degree of deviation is qualitatively consistent with the numerical result in Figure 9 of Canavezes et al (1998), although quantitative comparison is still difficult because of the noise in the simulation.…”

“…Unfortunately, previous earlier simulations do not have enough resolution to be quantitatively compared in the weakly nonlinear regime. Canavezes et al (1998) use much larger simulations than those in earlier works and give the genus curve in the weakly nonlinear regime in their Figure 9. Relative depths of left and right troughs in the genus curve show a slight meatball shift, which is consistent with our prediction.…”

“…These statistics provide assuring characterizations of the clustering pattern that cannot be perceived only by the hierarchy of cumulants or by the PDF. The genus statistic is a powerful measure of the morphology in the three-dimensional Moore et al 1992;Park, Gott, & da Costa 1992;Beaky, Scherrer, & Villumsen 1992;Rhoads, Gott, & Postman 1994;Vogeley et al 1994;Protogeros & Weinberg 1997;Sahni, Sathyaprakash, & Shandarin 1997;Canavezes et al 1998;Springel et al 1998;Colley et al 2000) and two-dimensional Gott et al 1992;Coles & Plionis 1991;Plionis, Valdarnini, & Coles 1992;Davies & Coles 1993;Coles et al 1993;Colley 1997) clustering of galaxies and clusters and also of the pattern of temperature fluctuations of CMB radiation (Bond & Efstathiou 1987;Torres 1994;Smoot et al 1994;Torres et al 1995;Park et al 1998). The peak statistics of the threedimensional density field are frequently used in connection with the statistics of the collapsing object (Kaiser 1984;Mann, Heavens, & Peacock 1993;Croft & Efstathiou 1994;Watanabe, Matsubara, & Suto 1994;Cen 1998;Gabrielli, Labini, & Durrer 2000), while the peak statistics of the CMB fluctuations (Sazhin 1985;Bond & Efstathiou 1987;Coles & Barrow 1987;Vittorio & Juszkiewicz 1987;Kogut et al 1995;Cayon & Smoot 1995;Fabbri & Torres 1996;Heavens & Sheth 1999) and of the weak lensing field...…”

Breaking the Degeneracy of Cosmological Parameters in Galaxy Redshift Surveys

“…IRAS 1.2 Jy is not the largest existing near all-sky galaxy redshift catalog, and it has now been superseded by PSCz (Canavezes et al 1998), which contains D15,000 galaxies, so this application is simply an illustration of how the LAP method can be used to break the degeneracy in the estimates of b and…”

“…This distortion, quantiÐed by the parameter permits us to solve the equations for d and b \ ) m 0.6/b, at least perturbatively (see, e.g., Dekel 1994 ;Coles & ¿, Sahni 1995), and measurements of b have been investigated in much detail in the literature (Strauss & Willick 1995 ;Dekel 1994Dekel , 1999aDekel, Burstein, & White 1997). In addition, in view of the fact that the bias parameter is almost certainly dependent on the selected sample, estimates have been computed for given for IRAS galaxies (Dekel b IRAS , b I et al 1993 ;Fisher et al 1995a ;Willick et al 1997aWillick et al , 1997bSigad et al 1998) and more recently from the Point Source Catalog Redshift survey (PSCz) sample (Canavezes et al 1998 ;Tadros et al 1999 ;Saunders et al 2000) and from the Optical Redshift Survey (ORS ; Hudson et al 1995 ;Santiago et al 1995 ;Baker et al 1998). The Mark III peculiarvelocity survey similarly yields estimates of b from redshift distortions (Willick et al , 1996(Willick et al , 1997a(Willick et al , 1997bDekel et al 1997 ;Sigad et al 1998).…”