Lauro Moscardini

Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North

ABSTRA C T The evolution of galaxy clustering from za 0t oz . 4:5 is analysed using the angular correlation function and the photometric redshift distribution of galaxies brighter than IAB < 28:5 in the Hubble Deep Field North. The reliability of the photometric redshift estimates is discussed on the basis of the available spectroscopic redshifts, comparing different codes and investigating the effects of photometric errors. The redshift bins in which the clustering properties are measured are then optimized to take into account the uncertainties of the photometric redshifts. The results show that the comoving correlation length r0 has a small decrease in the range 0 & z & 1 followed by an increase at higher z. We compare these results with the theoretical predictions of a variety of cosmological models belonging to the general class of Cold Dark Matter scenarios, including Einstein‐de Sitter models, an open model and a flat model with non-zero cosmological constant. Comparison with the expected mass clustering evolution indicates that the observed high-redshift galaxies are biased tracers of the dark matter with an effective bias b strongly increasing with redshift. Assuming an Einstein‐de Sitter universe, we obtain b . 2: 5a tz . 2 and b . 5a tz . 4. These results support theoretical scenarios of biased galaxy formation in which the galaxies observed at high redshift are preferentially located in more massive haloes. Moreover, they suggest that the usual parameterization of the clustering evolution as jOr; zUajOr; 0UO1 1 zU 2O31eU is not a good description for any value of e . Comparison of the clustering amplitudes that we measured at z . 3 with those reported by Adelberger et al. and Giavalisco et al., based on a different selection, suggests that the clustering depends on the abundance of the objects: more abundant objects are less clustered, as expected in the paradigm of hierarchical galaxy formation. The strong clustering and high bias measured at z . 3 are consistent with the expected density of massive haloes predicted in the frame of the various cosmologies considered here. At z . 4, the strong clustering observed in the Hubble Deep Field requires a significant fraction of massive haloes to be already formed by that epoch. This feature could be a discriminant test for the cosmological parameters if confirmed by future observations.

Redshift evolution of clustering

We discuss how the redshift dependence of the observed two-point correlation function of various classes of objects can be related to theoretical predictions. This relation involves first a calculation of the redshift evolution of the underlying matter correlations. The next step is to relate fluctuations in mass to those of any particular class of cosmic objects; in general terms, this means a model for the bias and how it evolves with cosmic epoch. Only after these two effects have been quantified can one perform an appropriate convolution of the non-linearly evolved two-point correlation function of the objects with their redshift distribution to obtain the `observed correlation function for a given sample. This convolution in itself tends to mask the effect of evolution by mixing amplitudes at different redshifts. We develop a formalism which incorporates these requirements and, in particular, a set of plausible models for the evolution of the bias factor. We apply this formalism to the spatial, angular and projected correlation functions from different samples of high-redshift objects, assuming a simple phenomenological model for the initial power-spectrum and an Einstein-de Sitter cosmological model. We find that our model is roughly consistent with data on the evolution of QSO and galaxy clustering, but only if the effective degree of biasing is small. We discuss the differences between our analysis and other theoretical studies of clustering evolution and argue that the dominant barrier to making definitive predictions is uncertainty about the appropriate form of the bias and its evolution with cosmic epoch.

Modelling galaxy clustering at high redshift

We discuss the theoretical interpretation of observational data concerning the clustering of galaxies at high redshifts. Building on the theoretical machinery developed by Matarrese et al. (1997), we make detailed quantitative predictions of galaxy clustering statistics for a variety of cosmological models, taking into account differences in spatial geometry and initial fluctuation spectra and exploring the role of bias as a complicating factor in these calculations. We demonstrate that the usual description of evolution (in terms of the parameters ǫ and r0) is not useful for realistic galaxy clustering models. We compare the detailed predictions of the variation of correlation functions with redshift against current observational data to constrain available models of structure formation. Theories that fit the present-day abundance of rich clusters are generally compatible with the observed redshift evolution of galaxy clustering if galaxies are no more than slightly biased at z � 1. We also discuss the interpretation of a concentration of Lyman-break galaxies found by Steidel et al. (1998), coming to the conclusion that such concentrations are not unexpected in ‘standard’ models of structure formation.

Cluster cross-sections for strong lensing: analytic and numerical lens models

The statistics of gravitationally lensed arcs was recognized earlier as a potentially powerful cosmological probe. However, while fully numerical models find orders of magnitude difference between the arc probabilities in different cosmological models, analytic models tend to find markedly different results. In this paper we introduce an analytic cluster lens model that improves upon existing analytic models in four ways. (i) We use the more realistic Navarro‐Frenk‐White profile instead of singular isothermal spheres, (ii) we include the effect of cosmology on the compactness of the lenses, (iii) we use elliptical instead of axially symmetric lenses and (iv) we take the intrinsic ellipticity of sources into account. While these improvements to the analytic model lead to a pronounced increase of the arc probability, comparisons with numerical models of the same virial mass demonstrate that the analytic models still fall short by a substantial margin of reproducing the results obtained with numerical models. Using multipole expansions of cluster mass distributions, we show that the remaining discrepancy can be attributed to substructure inside clusters and tidal fields contributed by the cluster surroundings, effects that cannot reasonably and reliably be mimicked in analytic models.

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics. We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N-body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White (1997) density profile. We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 ′′ , while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 ′′ .

cD galaxy contribution to the strong lensing cross‐sections of galaxy clusters

We perform ray-tracing simulations evaluating the effect of a cD galaxy on the strong lensing properties of five galaxy cluster haloes obtained from N-body simulations. The cD galaxy is modelled using both axially symmetric and elliptical models and assuming several masses for its dark matter halo. The effect of the cD orientation with respect to the mass distribution of the host galaxy cluster is also investigated. The simulations are carried out in an open and a flat model universe with cosmological constant. We find that the enhancement of the cluster lensing cross-sections for long and thin arcs owing to the presence of a massive cD at the cluster centre is typically less than 100 per cent, depending on the model used for the cD galaxy and its orientation. The impact of the cD on the cluster efficiency for producing radially magnified images is larger only for those clusters with a lensing cross-section for radial arcs that is very small in absence of the central galaxy. We conclude that the presence of a cD galaxy at the cluster centre can only moderately influence the cluster efficiency for strong lensing and, in particular, fails to explain the discrepancy between the observed number of giant arcs in galaxy clusters and their abundance predicted from lensing simulations in the currently most favoured ACDM model.

A study of the core of the Shapley Concentration — IV. Distribution of intercluster galaxies and supercluster properties

(abridged) We present the results of a redshift survey of intercluster galaxies in the central region of the Shapley Concentration supercluster, aimed at determining the distribution of galaxies in between obvious overdensities. Our sample is formed by 442 new redshifts, mainly in the b_J magnitude range 17-18.8. Adding the data from our redshift surveys on the A3558 and A3528 complexes, which are close to the geometrical centre of this supercluster, we obtain a total sample of ~2000 radial velocities. Using the 1440 galaxies of our total sample in the magnitude range 17 - 18.8, we reconstructed the density profile in the central part of the Shapley Concentration; moreover we detected another significant overdensity at ~30000 km/s (dubbed S300). We estimate the total overdensity in galaxies, the mass and the dynamical state of these structures, and discuss the effect of considering a bias between the galaxy distribution and the underlying matter. We find an indication that the value of the bias between clusters and galaxies in the Shapley Concentration is higher that that reported in literature, confirming the impression that this supercluster is very rich in clusters. Finally, from the comparison with some theoretical scenarios, we find that the existence of the Shapley Concentration is more consistent with the predictions of the models with a matter density parameter<1, such as open CDM and Lambda CDM.

Giant cluster arcs as a constraint on the scattering cross- section of dark matter

We carry out ray tracing through five high resolution simulat ions of a galaxy cluster to study how its ability to produce giant gravitationally lens ed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dar k matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long (“collisionless”) and short (“fluid”) mean free path limits. We stud y the size and shape distributions of arcs and compute the cross-section for producing “extreme” arcs of various sizes. Even a few collisions per particle modify the core structure enou gh to destroy the cluster’s ability to produce long, thin arcs. For larger collision frequencie s the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the “fluid ” limit) is able to produce radial arcs; even the case with the smallest scattering cross-sect ion must be scaled to the upper limit of observed cluster masses before it produces radial a rcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm 2 g −1 , to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.

Eulerian Perturbation Theory in Non-Flat Universes: Second Order Approximation

The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter

Predicting the clustering of X-ray selected galaxy clusters in flux-limited surveys

Omega