The effect of formation redshifts on the cluster mass–temperature relation

I employ an ensemble of hydrodynamical simulations and the xspec mekal emission model to reproduce observable spectral and flux-weighted temperatures for 24 clusters. Each cluster is imaged at 16 points in its history, which allows the investigation of evolutionary effects on the mass–temperature relation. In the zero-redshift scaling relations, I find no evidence for a relationship between cluster temperature and formation epoch for those clusters that acquired 75 per cent of their final mass since a redshift of 0.6. This result holds for both observable and intrinsic intracluster medium temperatures, and implies that halo formation epochs are not an important variable in analysis of observable cluster temperature functions.     

The cluster substructure–alignment connection

Using a sample of 903 APM clusters we investigate whether their dynamical status, as evidenced by the presence of significant substructures, is related to the large-scale structure of the Universe. We find that the cluster dynamical activity is strongly correlated with the tendency of clusters to be aligned with their nearest neighbour and in general with the nearby clusters that belong to the same supercluster. Furthermore, dynamically active clusters are more clustered than the overall cluster population. These are strong indications that clusters develop in a hierarchical fashion by anisotropic merging along the large-scale filaments within which they are embedded.     

Influence of cluster environments on X-ray cluster morphology

We investigated the influence of environment on cluster morphology by examining the alignment of the cluster position angle with respect to the nearest neighbour cluster. The cluster position angle and ellipticity were measured using high spatial resolution X-ray data taken from the Chandra archive, while the nearest neighbour sample was extracted from the Abell cluster catalogue. We found high confidence for an alignment when neighbour distance (Dn) was less than  70  h ⁻¹  Mpc, while we found no significant variations of the confidence level at various values of Dn less than  70  h ⁻¹  Mpc.     

The effect of weak lensing on the angular correlation function of faint galaxies

The angular correlation function ο(θ) of faint galaxies is affected both by non-linear gravitational evolution and by magnification bias resulting from gravitational lensing. We compute the resulting ο(θ) for different cosmological models and show how its shape and redshift evolution depend on Ω and Λ. For galaxies at redshift greater than 1 ( R magnitude fainter than about 24), magnification bias can significantly enhance or suppress ο(θ), depending on the slope of the number–magnitude relation. We show, for example, how it changes the ratio of ο(θ) for two galaxy samples with different number count slopes.     

The power spectrum of flux-limited X-ray galaxy cluster surveys

We compute the redshift space power spectrum of two X-ray cluster samples: the X-ray Brightest Abell Cluster Sample (XBACS) and the Brightest Cluster Sample (BCS) using the method developed by Feldman, Kaiser & Peacock. The power spectra derived for these samples are in agreement with determinations of other optical and X-ray cluster samples. For XBACS we find the largest power spectrum amplitude expected, given the high richness of this sample ( R ≥2) . In the range 0.05< k <0.4  h  Mpc⁻¹ the power spectrum shows a power-law behaviour P ( k )∝ k ⁿ with an index n ≃−1.2 . In a similar range, 0.04< k <0.3  h  Mpc⁻¹ , the BCS power spectrum has a smaller amplitude with index n ≃−1.0 . We do not find significant evidence for a peak at k ≃0.05  h  Mpc⁻¹ , suggesting that claims such of feature detections in some cluster samples could rely on artificial inhomogeneities of the data. We compare our results with power spectrum predictions derived by Moscardini et al. within current cosmological models (LCDM and OCDM). For XBACS we find that both models underestimate the amplitude of the power spectrum but for BCS there is reasonably good agreement at k ≳0.03  h  Mpc⁻¹ for both models.     

The real- and redshift-space density distribution functions for large-scale structure in the spherical collapse approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the p -order hierarchical amplitudes S _p , in both real and redshift space. We compare our results with numerical simulations, focusing on the     standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for     , where σ _L is the linearly evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for     . Numerical simulations also yield a simple empirical relation between the real-space PDF and the redshift-space PDF: we find that for     , the redshift-space PDF, [ P δ _{( z )}], is, to a good approximation, a simple rescaling of the real-space PDF, P [ δ ], i.e.,     where σ and σ _{( z )} are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the ΛCDM model. It breaks down for SCDM at     , but provides a good fit to the ΛCDM models for σ _L as large as 0.8.     

Self-consistent gravitational lens reconstruction

We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellization of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellization can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.     

The cluster abundance in cosmic string models for structure formation

We use the present observed number density of large X-ray clusters to constrain the amplitude of matter density perturbations induced by cosmic strings on the scale of 8  h ⁻¹ Mpc ( σ ₈), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of σ ₈ than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of σ ₈ results from the mild non-Gaussianity on cluster scales, where the one-point probability distribution function is well approximated by a χ ² distribution and thus has a longer tail than a Gaussian distribution. We also show that σ ₈ normalized using cluster abundance is consistent with the COBE normalization.     

Angular cross-correlation of galaxies: a probe of gravitational lensing by large-scale structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.     

The statistics of weak lensing at small angular scales: probability distribution function

Weak gravitational lensing surveys have the potential to probe mass density fluctuation in the Universe directly. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modelling the statistics of the underlying density field in the highly non-linear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behaviour of higher order correlations of the density field. We compare our results with ray-tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.     

The cluster distribution as a test of dark matter models — IV. Topology and geometry

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 h ⁻¹ Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel'dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard cold dark matter model (SCDM); (ii) a CDM model with Ω₀ = 0.2 (OCDM); (iii) a CDM model with a 'tilted' power spectrum having n  = 0.7 (TCDM); (iv) a CDM model with a very low Hubble constant, h  = 0.3 (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low-density CDM model with Ω₀ = 0.2 and a non-zero cosmological Λ term (ΛCDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler–Poincaré characteristic; (ii) percolation properties; (iii) the minimal spanning tree construction. Taking all these tests together we find that the best-fitting model is ΛCDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models, which go far beyond the low-order correlation functions usually applied to study superclustering.     

The galaxy environment of a quasar at z= 1.226: a possible cluster merger

We have conducted ultra-deep optical and deep near-infrared observations of a field around the z =1.226 radio-quiet quasar 104420.8+055739 from the Clowes–Campusano LQG of 18 quasars at z ∼1.3, in search of associated galaxy clustering. Galaxies at these redshifts are distinguished by their extremely red colours, with I − K >3.75, and we find a factor ∼11 overdensity of such galaxies in a 2.25×2.25 arcmin² field centred on the quasar. In particular, we find 15–18 galaxies that have colours consistent with being a population of passively evolving massive ellipticals at the quasar redshift. They form 'fingers' in the V − K K , I − K K colour–magnitude plots at V − K ≃6.9, I − K ≃4.3 comparable to the red sequences observed in other z ≃1.2 clusters. We find suggestive evidence for substructure among the red sequence galaxies in the K image, in the form of two compact groups, 40 arcsec to the north, and 60 arcsec to the south-east of the quasar. An examination of the wider optical images indicates that this substructure is significant, and that the clustering extends to form a large-scale structure 2–3  h ⁻¹ Mpc across. We find evidence for a high (≳50 per cent) fraction of blue galaxies in this system, in the form of 15–20 'red outlier' galaxies with I − K >3.75 and V − I <2.00, which we suggest are dusty, star-forming galaxies at the quasar redshift. Within 30 arcsec of the quasar we find a concentration of blue ( V − I <1) galaxies in a band that bisects the two groups of red sequence galaxies. This band of blue galaxies is presumed to correspond to a region of enhanced star formation. We explain this distribution of galaxies as the early stages of a cluster merger which has triggered both the star formation and the quasar.