The abundance and clustering of dark haloes in the standard Lambda CDM cosmogony

Much evidence suggests that we live in a flat Cold Dark Matter universe with a cosmological constant. Accurate analytic formulae are now available for many properties of the dark halo population in such a Universe. Assuming current ``concordance'' values for the cosmological parameters, we plot halo abundance against redshift as a function of halo mass, of halo temperature, of the fraction of cosmic matter in haloes, of halo clustering strength, and of the clustering strength of the z=0 descendants of high redshift haloes. These plots are useful for understanding how nonlinear structure grows in the model. They demonstrate a number of properties which may seem surprising, for example: 10^9 solar mass haloes are as abundant at z=20 as L_* galaxies are today; 10^6K haloes are equally abundant at z=8 and at z=0; 10% of all matter is currently in haloes hotter than 1 keV, while more than half is in haloes too cool to trap photo-ionized gas; 1% of all matter at z=15 is in haloes hot enough to ionise hydrogen; haloes of given mass or temperature are more clustered at higher redshift; haloes with the abundance of present-day L_* galaxies are equally clustered at all z10 are more clustered at z=0 than are L_* galaxies.Comment: 10 pages, 2 ps figures, version to be published in MNRA

Virialization of Galaxy Clusters and Beyond

Using samples of structures identified by a multi-scale decomposition from numerical simulation, we analyze the scale-dependence of the virialization of clusters. We find that beyond the scale of full virialization there exists a radius range over which clusters are quasi-virialized, i.e. while the internal structure of an {\it individual} cluster is at substantial departure from dynamical relaxation, some {\it statistical} properties of the multi-scale identified clusters are approximately the same as those for the virialized systems. The dynamical reason of the existence of quasi-virialization is that some of the scaling properties of dynamically relaxed systems of cosmic gravitational clustering approximately hold beyond the full virialization regime. The "individual-statistical" duality of the quasi-virialization provides an explanation of the observed puzzle that the total masses of clusters derived from virial theorem are statistically the same as the gravitational lensing determined masses, in spite of the presence of irregular configuration and substructures in individual clusters. It also explains the tight correlation between the velocity dispersion of optical galaxies and the temperature of X-ray emitting gas. Consequently, the virial mass estimators based on the assumptions of isothermal and hydrostatic model are statistically applicable to scales on which the clusters are quasi-virialized. In the quasi-virialization regime, the temperature functions of clusters also show scaling. This feature is a useful discriminator among cosmological models.Comment: AAS Latex file, 22 pages+ 14 figures, accepted for publication in Ap

Constraining Cosmological Models by the Cluster Mass Function

We present a comparison between two observational and three theoretical mass functions for eight cosmological models suggested by the data from the recently completed BOOMERANG-98 and MAXIMA-1 cosmic microwave background (CMB) anisotropy experiments as well as peculiar velocities (PVs) and type Ia supernovae (SN) observations. The cosmological models have been proposed as the best fit models by several groups. We show that no model is in agreement with the abundances of X-ray clusters at $\sim 10^{14.7} h^{-1}M_{\odot}$.On the other hand, we find that the BOOM+MAX+{\sl COBE}:I, Refined Concordance and $\Lambda$MDM are in a good agreement with the abundances of optical clusters. The P11 and especially Concordance models predict a slightly lower abundances than observed at $\sim 10^{14.6} h^{-1}M_{\odot}$. The BOOM+MAX+{\sl COBE}:II and PV+CMB+SN models predict a slightly higher abundances than observed at $\sim 10^{14.9} h^{-1}M_{\odot}$. The nonflat MAXIMA-1 is in a fatal conflict with the observational cluster abundances and can be safely ruled out.Comment: 17 pages, 2 figures, reference added, figures changes, substantial revision mad

Predicting the Clustering of X-Ray Selected Galaxy Clusters in Flux-Limited Surveys

(abridged) We present a model to predict the clustering properties of X-ray clusters in flux-limited surveys. Our technique correctly accounts for past light-cone effects on the observed clustering and follows the non-linear evolution in redshift of the underlying DM correlation function and cluster bias factor. The conversion of the limiting flux of a survey into the corresponding minimum mass of the hosting DM haloes is obtained by using theoretical and empirical relations between mass, temperature and X-ray luminosity of clusters. Finally, our model is calibrated to reproduce the observed cluster counts adopting a temperature-luminosity relation moderately evolving with redshift. We apply our technique to three existing catalogues: BCS, XBACs and REFLEX samples. Moreover, we consider an example of possible future space missions with fainter limiting flux. In general, we find that the amplitude of the spatial correlation function is a decreasing function of the limiting flux and that the EdS models always give smaller correlation amplitudes than open or flat models with low matter density parameter. In the case of XBACs, the comparison with previous estimates of the observational spatial correlation shows that only the predictions of models with Omega_0m=0.3 are in good agreement with the data, while the EdS models have too low a correlation strength. Finally, we use our technique to discuss the best strategy for future surveys. Our results show that the choice of a wide area catalogue, even with a brighter limiting flux, is preferable to a deeper, but with smaller area, survey.Comment: 20 pages, Latex using MN style, 11 figures enclosed. Version accepted for publication in MNRA

The ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey III: The Power Spectrum

We present a measure of the power spectrum on scales from 15 to 800 Mpc/h using the ROSAT-ESO Flux-Limited X-Ray(REFLEX) galaxy cluster catalogue. The REFLEX survey provides a sample of the 452 X-ray brightest southern clusters of galaxies with the nominal flux limit S=3.0 10^{-12}erg/s/cm2 for the ROSAT energy band (0.1-2.4)keV. Several tests are performed showing no significant incompletenesses of the REFLEX clusters with X-ray luminosities brighter than 10^{43}erg/s up to scales of about 800 Mpc/h. They also indicate that cosmic variance might be more important than previous studies suggest. We regard this as a warning not to draw general cosmological conclusions from cluster samples with a size smaller than REFLEX. Power spectra, P(k), of comoving cluster number densities are estimated for flux- and volume-limited subsamples. The most important result is the detection of a broad maximum within the comoving wavenumber range 0.022<k<0.030 h/Mpc. The data suggest an increase of the power spectral amplitude with X-ray luminosity. Compared to optically selected cluster samples the REFLEX P(k)is flatter for wavenumbers k<0.05 h/Mpc thus shifting the maximum of P(k) to larger scales. The smooth maximum is not consistent with the narrow peak detected at k=0.05 h/Mpc using the Abell/ACO richness $\ge 0$ data. In the range 0.02<k<0.4 h/Mpc general agreement is found between the slope of the REFLEX P(k) and those obtained with optically selected galaxies. A semi-analytic description of the biased nonlinear power spectrum in redshift space gives the best agreement for low-density Cold Dark Matter models with or without a cosmological constant.Comment: 22 pages, 20 figures, (A&A accepted), also available at http://www.xray.mpe.mpg.de/theorie/REFLEX

The Galaxy Pairwise Velocity Dispersion as a Function of Local Density

The standard method of measuring the galaxy pairwise velocity dispersion on small scales is heavily weighted by the densest regions in a way that is difficult to calibrate. We propose a new statistic which measures the small-scale velocity dispersion as an explicit function of density. Computing this statistic for a volume-limited subsample of the Optical Redshift Survey, we find that the small-scale velocity dispersion rises from 220 to 760 km/s as density increases. We calculate this statistic for a series of mock catalogs drawn from a hydrodynamic simulation of an \Omega h = 0.5 Cold Dark Matter universe (standard CDM), and find that the observed velocity distribution lies ~1 \sigma below the simulations in each of eight density bins, formally ruling out this model at the 7.4 \sigma level, quantifying the well-known problem that this model produces too high a velocity dispersion. This comparison is insensitive to the normalization of the power spectrum, although it is quite sensitive to the density and velocity bias of galaxies relative to dark matter on small scales. (abridged)Comment: 21 pages Latex with 6 embedded figures, submitted to Ap

Evolution of the Cluster Mass and Correlation Functions in LCDM Cosmology

The evolution of the cluster mass function and the cluster correlation function from z = 0 to z = 3 are determined using 10^6 clusters obtained from high-resolution simulations of the current best-fit LCDM cosmology (\Omega_m = 0.27, \sigma_8 = 0.84, h = 0.7). The results provide predictions for comparisons with future observations of high redshift clusters. A comparison of the predicted mass function of low redshift clusters with observations from early Sloan Digital Sky Survey data, and the predicted abundance of massive distant clusters with observational results, favor a slightly larger amplitude of mass fluctuations (\sigma_8 = 0.9) and lower density parameter (\Omega_m = 0.2); these values are consistent within 1-\sigma with the current observational and model uncertainties. The cluster correlation function strength increases with redshift for a given mass limit; the clusters were more strongly correlated in the past, due to their increasing bias with redshift - the bias reaches b = 100 at z = 2 for M > 5 x 10^13 h^-1 M_sun. The richness-dependent cluster correlation function, represented by the correlation scale versus cluster mean separation relation, R0-d, is generally consistent with observations. This relation can be approximated as R_0 = 1.7 d^0.6 h^-1 Mpc for d = 20 - 60 h^-1 Mpc. The R0-d relation exhibits surprisingly little evolution with redshift for z < 2; this can provide a new test of the current LCDM model when compared with future observations of high redshift clusters.Comment: 20 pages, 9 figures, accepted for publication in Ap

Constraints on a non-gaussian (χm2\chi_m^2) CDM model

We consider constraints on the structure formation model based on non-Gaussian fluctuations generated during inflation, which have $\chi_m^2$ distributions. Using three data sets, the abundance of the clusters at $z=0$, moderate $z$ and the correlation length, we show that constraints on the non-Gaussianity and the amplitude of fluctuations and the density parameter can be obtained. We obtain an upper bound for $\Omega_m$ and a lower bound for the non-Gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at $z \sim 0.6$, for the spectrum parameterized by cold dark matter (CDM) shape parameter $\Gamma=0.23$, we obtain an upper bound for the density parameter $\Omega_m \sim 0.5$ and lower bounds for the amplitude $\sigma_8 \sim 0.7$ and for the non-Gaussianity of fluctuations $G \sim 2$ $(m \sim 200)$, where G=1 for Gaussian.Comment: 7 pages, 3 figures, MNRAS in pres

Cosmological constraints from clustering properties of galaxy clusters

In this paper, we discuss improvements of the Suto et al. (2000) model, in the light of recent theoretical developments (new theoretical mass functions, a more accurate mass-temperature relation and an improved bias model) to predict the clustering properties of galaxy clusters and to obtain constraints on cosmological parameters. We re-derive the two-point correlation function of clusters of galaxies for OCDM and LambdaCDM cosmological models, and we compare these results with the observed spatial correlation function for clusters in RASS1 (ROSAT All-Sky Survey 1), and in XBACs (X-RAY Brighest Abell-Type) samples. The comparison shows that the best agreement is obtained for the LambdaCDM model with Omega=0.3. The values of the correlation length obtained, (r_\simeq 28.2 \pm 5.2 \rm h^{-1}} Mpc for LambdaCDM), are larger than those found in the literature and comparable with the results found in Borgani, Plionis & Kolokotronis (1999). (REST IN THE PAPER ABSTRACT)Comment: printed in A&

The mass and temperature functions in a moving barrier model

In this paper, I use the extension of the excursion set model of Sheth & Tormen (2002) and the barrier shape obtained in Del Popolo & Gambera (1998) to calculate the unconditional halo mass function, and the conditional mass function in several cosmological models. I show that the barrier obtained in Del Popolo & Gambera (1998), which takes account of tidal interaction between proto-haloes, is a better description of the mass functions than the spherical collapse and is in good agreement with numerical simulations (Tozzi & Governato 1998, and Governato et al. 1999). The results are also in good agreement with those obtained by Sheth & Tormen (2002), only slight differences are observed expecially at the low mass end. I moreover calculate, and compare with simulations, the temperature function obtained by means of the mass functions previously calculated and also using an improved version of the M-T relation, which accounts for the fact that massive clusters accrete matter quasi-continuously, and finally taking account of the tidal interaction with neighboring clusters. Even in this case the discrepancy between the Press-Schecter predictions and simulations is considerably reduced.Comment: 23 pages; 11 encapsulated figures. Accepted for publication in MNRA