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Clustering is a fundamental property of galaxies in that it establishes the link with the background cosmology and with the properties and distribution of the dark matter. The extent to which the perturbations detected in the cosmic microwave background radiation have grown after the first ~ 15% of the age of the universe (i.e., at the epoch of the U-band dropouts) depends sensitively on the cosmological parameters. In general, interpreting clustering observations of galaxies is complicated by the lack of knowledge on how these trace the mass-density field. However, if one understands the evolution of some well-defined category of galaxies (of which the Lyman-break galaxies are an example), one can hope to constrain the background cosmology by following the clustering evolution of these systems over a substantial range of cosmic time.

The high efficiency of the Lyman-break technique and its well-controlled selection criteria are key features to study galaxy clustering at redshifts as high as z ~ 4. The large samples that can be put together with small effort probe the cosmic density-perturbation field much more densely and to smaller scales than other high-redshift galactic systems, such as quasars and radio-galaxies. With the LBGs one can study high-redshift clustering and morphology of large-scale structure on spatial scales that are directly relevant to the physics of galaxy formation. Furthermore, this allows for direct comparisons with studies of galaxy clustering in the local and intermediate redshift universe.

6.1. Large structures at high redshifts

The spectroscopic survey of Lyman-break galaxies has revealed the presence of large spatial concentrations of these systems already at redshifts z ~ 3 (Steidel et al. 1998). Along the line of sight (i.e., along the redshift axis) these concentrations overall resemble the redshift spikes observed at more modest redshifts (e.g., Broadhurst et al. 1990; Cohen et al. 1996). However, the comoving volumes that are probed in each pointing in the case of the Lyman-break galaxies are much larger. As a result, the observed spikes are directly associated to physical grouping of galaxies in narrow volumes and are not the result of the intersection of narrow pencil-beams with the complex topology of the large-scale structure (e.g., Kaiser & Peacock 1991). We have shown that the redshift spikes of Lyman-break galaxies are associated to structures with mass similar to that of rich clusters, or M ~ 1015 Msun. At redshifts z ~ 3 this has interesting cosmological consequences.

Figure 9a shows an example of spikes in the SSA22 field, one of the best studied regions of our survey. The shaded regions represent the overall redshift distribution of the whole survey, which is, in practice, the redshift selection function. A large overdensity of galaxies at z ~ 3.1 is clearly visible, together with another smaller concentration at redshift z ~ 3.4. We find that similar structures are actually ubiquitous and we detect similar overdensities in essentially every field that we have surveyed. As discussed in Steidel et al. (1998), the statistics of these spikes and their size allow us to place constraints on the mass-to-light biasing parameter of the Lyman-break galaxies.

Figure 9

Figure 9. Distribution of LBG redshifts towards the SSA22 field plotted together with the redshift selection function of the whole survey (dashed line). The prominent spike at z ~ 3.1 is clearly visible. b) Volume density of redshift concentrations with density delta geq deltaL as a function of deltaL for three different CDM cosmologies and for a choice of the light-to-mass biasing parameter together with the values derived from the redshift distribution in the SSA22 field. The size of the boxes represent the error bars. As the figure shows, such redshift concentrations do not exist in the CDM cosmogonies, unless the LBGs are rather biased tracers of the mass.

In Figure 9b we plot the function n(deltal), namely the volume density of spikes with linear density contrast deltal or larger, from the CDM power spectrum for three different choices of the cosmological parameters Omega and Lambda along with the data from the SSA22 field. As the diagram shows, the concentrations that give origin to the observed redshift spikes would not exist in standard CDM cosmogonies unless the Lyman-break galaxies were very biased tracers of the mass-density field. The amount of bias required depends on the choice of the cosmological parameters and it is rather large - b ~ 8 - in the case of the standard CDM model, while it is more moderate in an open universe, with b ~ 2 if Omega = 0.2 and Lambda = 0.

Thus, if a CDM power spectrum is a good approximation to the true one, the implications are that the Lyman-break galaxies are rather biased tracers of the mass and an immediate conclusion would be that they are more strongly clustered than the mass. As we will show in the next section, the correlation function of the LBGs provides direct empirical support for this. In turn, since the most massive dark halos are the most strongly clustered and heavily biased (Mo & Fukugita 1997), the derived bias implies that the characteristic mass associated with the Lyman-break galaxies is large. For the choices of cosmological parameter shown in Figure 9b, the derived values of the bias point to halos with mass M ~ 1012 Msun. This is a strong evidence in support of the interpretation that the Lyman-break galaxies are associated with massive structures, comparable to present-day bright (L*) galaxies.

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