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Astron. Astrophys. 364, 349-368 (2000)

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1. Introduction

For the past decade, the study of the spatial Large-Scale Structure (LSS) of the universe has become a major tool for constraining the cosmological models. In particular, provided many assumptions on how morphological type correlates with colour, how mass is correlated with optical luminosity, and how local density correlates with morphology, recent CDM hierarchical N-body simulations and semi-analytic models of galaxy formation are able to make tentative predictions on the clustering evolution of the galaxies as a function of their redshifts, spectral types and star formation rates (Kauffmann et al. 1999a,b). By measuring redshifts for [FORMULA] or more galaxies, the next generation redshift surveys such as the VIRMOS survey (Le Fevre et al., 1998), the DEEP survey (Davis & Faber, 1998), and the LZT survey (Hickson et al., 1998; see also http://www.astro.ubc.ca/LMT/lzt/index.html ) will allow detailed studies of the large-scale clustering and its evolution to [FORMULA].

Until these surveys are completed, the measurement of the 2-point angular correlation functions [FORMULA] of large photometric galaxy samples remains the best alternative to constrain galaxy clustering at [FORMULA]. The major caveat of [FORMULA], as opposed to the 2-point spatial correlation function [FORMULA], is that it probes the projection of a 3D distribution of the galaxies onto the 2D celestial sphere. i.e. one cannot tell whether a given galaxy is a faint nearby object or a bright remote one. As a consequence, [FORMULA] is sensitive to the effects of both the intrinsic 3D clustering and the luminosity evolution (LE) of galaxies for a given set of cosmological parameters. To avoid this degeneracy, one must choose between two approaches to extract sensible information from [FORMULA]. First, one may use past observations to assume a scenario of galaxy evolution with given LEs and redshift distributions for each galaxy population, and then deduce the clustering evolution. A second approach would be to assume a clustering scenario, cosmological parameters, and to measure the evolution of the correlation function in order to validate the theoretical LE used to model the galaxy counts, e.g. Roche et al. (1993). In this paper, we favour the first approach. We use the Canada-France Redshift Survey (CFRS; Lilly et al. 1996) luminosity function and redshift distribution to invert the angular correlation function with Limber's formula (cf Sect. 5 on modeling of [FORMULA], [FORMULA] and [FORMULA]) to compute the spatial correlation length from the amplitude of [FORMULA]. This approach has several limits which are discussed in Sect. 7.

An extensive literature covers the evolution of clustering using [FORMULA]. The first attempts to describe clustering using counts in cells is due to Limber (1954). The two-point correlation function as a statistical diagnosis of clustering has been popularized in astrophysics by Hauser & Peebles (1973) and applied to the Zwicky Catalog (Peebles & Hauser, 1974). Since these pioneering studies, the method, fully described by Peebles (1980), has been applied to many photographic catalogues in diverse photometric bands e.g. see Groth & Peebles (1977), Koo & Szalay (1984), Maddox et al. (1990b) where the clustering of local galaxies is studied on large angular scales. Using Limber's (1953) formula relating [FORMULA] to the spatial correlation function [FORMULA], these studies establish that the spatial clustering of local galaxies can be parameterized as a power law, [FORMULA], where the correlation length [FORMULA] Mpc ([FORMULA]) and the slope [FORMULA].

A second generation of studies based on small-scale CCDs, probes smaller areas to deeper magnitudes (Efstathiou et al., 1991; Campos et al., 1995; Neuschaefer et al., 1992; Neuschaefer et al., 1995; Roukema & Peterson, 1994; Brainerd et al., 1995; Brainerd & Smail, 1998; Brainerd et al., 1999; Hudon & Lilly, 1996; Lidman & Peterson, 1996; Roche et al., 1993; Roche et al., 1996; Woods & Fahlman, 1997), therefore allowing to measure the evolution of the correlation length to redshifts [FORMULA]. The most recent studies take advantage of large area CCD detectors (Roche & Eales, 1999; Postman et al., 1998) to measure the angular correlation function, and of the use of photometric redshifts (Koo, 1999) to estimate the spatial correlation function from deep photometric surveys (Villumsen et al., 1997; Arnouts et al., 1999). Despite these numerous studies, our knowledge of the clustering of galaxies is still rudimentary. The main trends are that while a mild luminosity evolution seems to be required to explain faint number counts in the I-band, weak or no evolution in the galaxy clustering with redshift is detected out to [FORMULA].

The existing surveys measuring the galaxy angular correlation function, and covering a broad range of magnitude bands and limits, constrain the value of [FORMULA] to the range [FORMULA]Mpc for [FORMULA]. The dispersion is mainly due to the uncertainty in our knowledge of the luminosity functions and redshifts distributions for the different galaxy types at [FORMULA] (Sect. 7), and possibly to the varying selection biases from survey to survey. To be consistent with the values of [FORMULA] measured from the nearby redshift surveys and ranging from 4[FORMULA]Mpc to 8[FORMULA]Mpc (de Lapparent et al., 1988; Loveday et al., 1995; Cole et al., 1994; Tucker et al., 1997; Ratcliffe et al., 1998; Guzzo et al., 1998), most observations of the galaxy clustering favour either constant or increasing clustering with time in proper coordinates, which is consistent with N-body simulations of CDM hierarchical universes (Davis et al., 1985; Baugh et al., 1999; Hudon & Lilly, 1996).

Note that only a few redshift surveys allow a direct study of the evolution of the spatial clustering (Lilly et al., 1995; Connolly et al., 1998; Arnouts et al., 1999; Carlberg et al., 2000): these surveys measure [FORMULA]Mpc for [FORMULA]. We underline that except for the results of Carlberg et al. (2000), corresponding to the high value of [FORMULA], the limited area of the mentioned surveys makes them very sensitive to cosmic variance, and the corresponding results on the correlation function must be taken with caution.

Moreover, the existing analyses have not yet answered convincingly to the following two questions: Is there an evolution of the angular correlation function slope [FORMULA] at faint limiting magnitudes? And do red-selected objects and blue-selected objects show a true difference in 3-D clustering? In addition to providing another measure of the galaxy clustering at [FORMULA], the new sample presented here allows us to address these questions. The paper is organized as follows, the observations are described in Sect. 2, Sect. 3 presents the data reduction, Sect. 4 addresses the star/galaxy separations and counts. Sect. 5 details the analysis of the correlation function, Sect. 6 gives the results, and Sect. 7 provides a discussion of our results and a comparison with previous work.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001