Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4853-4858, June 1993 Colloquium Paper This paper was presented at a coUoquium entitled "Physical Cosmology," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA. Redshift survey with multiple pencil beams at the galactic poles A. S. SZALAY*t, T. J. BROADHURSTt, N. ELLMAN§, D. C. Koo§, AND R. S. ELLIS¶ *Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218; tDepartment of Physics, E6tv6s University, Budapest, H-1088 Hungary; tRoyal Observatory, Edinburgh, EH9 3HJ, United Kingdom; §University of California Observatories, Lick Observatory, University of California, Santa Cruz, CA 95064; and 1Department of Physics, University of Durham, DH1 3LE, United Kingdom ABSTRACT Observations of the large-scale structure of Pisces supercluster extends to large distances in the trans- the universe suggest inhomogeneities on scales between 100h-1 verse directions. Also, the angular two-point correlation and 150h-1 Mpc (where h 0.5-1 is the Hubble constant in function of the automated plate measuring (APM) survey units of 100 kmns-l-Mpc'1; 1 pc = 3.09 x 1016 m). A deep indicates a statistically significant deviation from CDM (9). redshift survey with a "pencil-beam" geometry of galaxies at The advent ofefficient multi-object spectrographs on large the galactic poles indicated strong clustering, with a provoca- optical telescopes has considerably accelerated the progress tive regularity at 128h1- Mpc [Broadhurst, T. J., Ellis, R. S., toward completing redshift surveys of faint galaxies. The Koo, D. C. & Szalay, A. S. (1990) Nature (London) 343, instrumentation used in such surveys typically sample 10-50 726-7281. Using newly acquired data, we demonstrate how galaxies within fields of 10- to 40-arcmin diameter, and thus multiple deep probes overcome most of the statistical problems "pencil-beam" geometries are produced which are charac- associated with single pencil beams. Our results from cross teristically different from strategies used to map the galaxy correlations of multiple pencil beams, containing over 1200 distribution locally. With 40 fields on 4-m telescopes, the galaxies, indicate that the strong peak in the power spectrum diameter of the survey at the median redshift of about z 0.3 results from structures of large transverse size, in agreement is 6h-1 Mpc; such geometries are close to optimal for with our original conjecture. We also discuss the sensitivity of detecting wall-like topologies on scales comparable to those pencil-beam surveys to the topology of large-scale structures revealed in the CfA surveys. and compare them with sparsely sampled wide-angle local Broadhurst et al. (10), hereafter BEKS, provided evidence surveys. from a combined sample of galaxies in the north and south galactic poles for structures on scales > lOOh-1 Mpc with a provocative regularity. The BEKS survey consisted of two 1. Introduction deep surveys spanning 2000h-1 Mpc-the deepest so far- and two previous brighter surveys by others (5, 11), which To model the large-scale structure of the universe, cosmol- together cover a volume well approximated by a cylinder of ogists consider a variety of initial conditions and follow the a constant comoving radius. The two northern fields lie subsequent evolution with combined analytic and numerical within the CfA slice, and the Great Wall is readily detected. techniques, making certain additional assumptions. The pre- Surprisingly, however, at large radial distances most galaxies dictions are compared with the distribution of galaxies and lie in a few discrete "spikes" separated typically by 130h-1 fluctuation limits for the cosmic background radiation (CBR). Mpc. This is revealed by using the one-dimensional pair The most popular galaxy formation theory is the cold dark counts and the one-dimensional power spectrum, which has matter (CDM) model (1), in which most of the mass density a very sharp peak at the wavenumber corresponding to is in the form of noninteracting dark particles. Together with 130h-1 Mpc. a scale-invariant Zeldovich-Harrison spectrum for the initial In this paper we present additional data collected in the density fluctuations, the theory satisfies many observational same direction, but using a slightly different strategy, con- constraints on small (< lOOh-1 Mpc) scales (2). However, to firming our original results. In Section 2 we begin by con- explain the absence of CBR fluctuations, its proponents trasting two rather different observing strategies, the sparse- invoked the concept of "biasing," whereby galaxies form sampled local survey and the deep pencil-beam surveys, only at high peaks of the mass fluctuations. Much stronger demonstrating the unique features of each. In Section 3 we correlations are predicted in the distribution of visible gal- discuss the statistical consequences of the one-dimensional axies than for the underlying mass (3, 4). nature of the pencil beams and discuss the effect of using The standard biased CDM scenario predicts a universe multiple pencil beams. In Section 4 we present a more relatively homogeneous on scales above 30-40h-1 Mpc. detailed statistical analysis of data acquired recently, and in Observationally, it becomes more and more apparent that Section 5 we summarize our results. there is stronger large-scale clustering than the CDM predic- tion. Almost a decade ago, Kirshner et al. (5) found a 2. Strategies for Mapping Large-Scale Structure 60h-1-Mpc sphere with a large underdensity in the galaxy distribution. deLapparent et al. (6) delineated the "Great First we discuss the question of the best strategy for delin- Wall" in their Center for Astrophysics (CfA) surveys-a eating the large-scale distribution of galaxies, given that its structure connecting several known Abell clusters over a precise topology remains unclear. With the exception of spatial extent of lOOh-1 by 50h-1 Mpc. Chincarini et al. (7) dedicated telescopes, a typical redshift survey can measure and Giovanelli et al. (8) had earlier shown that the Perseus- only a few thousand redshifts in a few years of observation. Indeed, there is probably no single strategy optimal in all The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" Abbreviations: APM, automated plate measuring; BEKS, Broad- in accordance with 18 U.S.C. §1734 solely to indicate this fact. hurst et al.; CDM, cold dark matter. 4853 Downloaded by guest on September 26, 2021 4854 Colloquium Paper: Szalay et al. Proc. Natl. Acad Sci. USA 90 (1993) situations, since the choice is strongly influenced by what Voronoi foam, R= 1.6, smoothed original presumptions hold about the statistical properties and the topology of the large-scale galaxy distribution. There is a fundamental difference between the strategies and goals of the sparse-sampled wide-angle surveys and those ofthe deep pencil-beam surveys. Their correlation functions measure different statistical aspects of the same distribution. In gen- eral, answers depend on what questions were asked. When discussing large-scale structure, one should first specify what these words mean. For some, large-scale structure is equal to the large-scale behavior of the galaxy two-point correlation function. Others like to draw maps ofthe galaxy distribution and associate that with the large-scale structure. These data sets contain different information, and this represents the fundamental difficulty in obtaining a single coherent view of the universe. We will elaborate on these differences below and focus on finding large coherent structures, our working definition of large-scale structure. If fluctuations in the universe are strictly Gaussian, their full statistical description is contained in the two-point cor- relation function or in its Fourier transform, the power spectrum. The phases of the individual Fourier components, the "plane waves" are random for such a process. In this case the sparse-sampled survey is indeed the best way to Voronoi foam, R= 1.6, random phases obtain this information. If the universe, however, contains some very sharp large-scale features, such as the Great Wall, a sparsely sampled survey may fail to identify those. The presence of such structures also means that higher-order correlations are present, or equivalently, that the phases of the fluctuations are correlated. The result can be very dif- ferent from a homogeneous isotropic Gaussian random field with the same second-order statistical properties. We demonstrate this with a simple graphic example. Fig. 1 Upper is a two-dimensional Voronoi foam, generated by the median surfaces between Poisson "seeds" at the mean separation of lOOh-1 Mpc. In this simple toy model, galaxies reside only on the walls of the foam, smoothed, so the walls have a finite thickness. The structure has a well-defined second-order statistic but also has well-correlated phases. By using an image-processing program developed by George Djorgovski, this picture has been Fourier-transformed, all the phases randomized, and then transformed back again. The result (Fig. 1 Lower) is another two-dimensional density plot, with the same second-order properties, but with a Gaussian distribution. It is obvious how different the two distributions are. If we use a two-point correlation function estimator with sparse sampling, neither the statistic nor the distribution of FIG. 1. Simulation of a Gaussian (Lower) and a non-Gaussian the sparsely sampled points will tell us the difference. How- (Upper) process containing strong phase correlations, with identical ever, if we observe both pictures with well-sampled pencil- second-order statistical properties in two dimensions (done with the beam surveys, in the Voronoi image every beam would go help of George Djorgovski). through a sequence of walls, yielding very strong features in each one-dimensional correlation function. An average over determined by the number of redshifts obtained, and the an infinite number of pencil beams would provide a signal "clustering noise" is from the observed small-scale correla- similar for both images.