arXiv subjects

S. Borgani

Publications and source records attributed to S. Borgani.

198 records · Page 11Linked to original sources

arXiv1997

Peculiar Velocities of Clusters in CDM Models

Recently, peculiar velocity measurements became available for a new sample of galaxy clusters. From an accurately calibrated Tully-Fisher relation for spiral galaxies, we compute the rms cluster peculiar velocity and compare it to the linear theory predictions of COBE-normalized low-density and open CDM models (LambdaCDM and OCDM, respectively). Confidence levels for model rejection are estimated using a Monte Carlo procedure to generate for each model a large ensemble of artificial data sets. Following Zaroubi et al. (1997), we express our results in terms of constraints on the (Omega_0,n_pr,h) parameter space. Such constraints turn into sigma_8 Omega_0^{0.6}=0.50^{+0.25}_{-0.14} at the 90% c.l., thus in agreement with results from cluster abundance. We show that our constraints are also consistent with those implied by the shape of the galaxy power spectrum within a rather wide range for the values of the model parameters. Finally, we point out that our findings disagree at about the 3sigma level with respect to those by Zaroubi et al. (1997), based on the Mark III catalogue, which tend to prefer larger Omega_0 values within the CDM class of models.

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arXiv1997

Cosmology Using Cluster Internal Velocity Dispersions

We compare the distribution of internal velocity dispersions of galaxy clusters for an observational sample to those obtained from a set of N-body simulations of seven COBE-normalised cosmological scenarios: the standard CDM (SCDM) and a tilted (n=0.85) CDM (TCDM) model, a CHDM model with 25% of massive neutrinos, two low-density LCDM models with Omega_0=0.3 and 0.5, two open OCDM models with Omega_0=0.4 and 0.6. Simulated clusters are observed in projection so as to reproduce the main observational biases and are analysed by applying the same algorithm for interlopers removal and velocity dispersion estimate as for the reference observational sample. Velocity dispersions for individual clusters can be largely affected by observational biases in a model-dependent way: models in which clusters had less time to virialize show larger discrepancies between 3D and projected velocity dispersions. From the comparison with real clusters we find that both SCDM and TCDM largely overproduce clusters. The CHDM model marginally overproduces clusters and requires a somewhat larger sigma_8 than a purely CDM model in order to produce the same cluster abundance. The LCDM model with Omega_0=0.3 agrees with data, while the open model with Omega_0=0.4 and 0.6 underproduces and marginally overproduces clusters, respectively.

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arXiv1996

Constraining the Power Spectrum using Clusters

(Shortened Abstract). We analyze a redshift sample of Abell/ACO clusters and compare them with numerical simulations based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, on which we estimate cosmic variance effects. We analyse correlation statistics, the probability density function, and supercluster properties from percolation analysis. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 < Γ< 0.25 and an effective spectral index at 20Mpc/h in the range [-1.1,-0.9] are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press--Schechter approach, whose reliability is explicitly tested against N--body simulations. We conclude that, of the cosmological models considered here, the only viable models are either Cold+Hot DM ones with Ω_ν= [0.2-0.3], better if shared between two massive neutrinos, and flat low-density CDM models with Ω_0 = [0.3-0.5].

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arXiv1996

Statistical Tests for CHDM and \LambdaCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulations of two currently viable cosmological models: a mixed dark matter model, having $Ω_ν=0.2$ contributed by two massive neutrinos (C+2\nuDM), and a Cold Dark Matter model with Cosmological Constant (\LambdaCDM) with $Ω_0=0.3$ and h=0.7. Our aim is to compare simulated galaxy samples with the Perseus-Pisces redshift survey (PPS). We consider the n-point correlation functions (n=2-4), the N-count probability functions P_N, including the void probability function P_0, and the underdensity probability function U_ε(where εfixes the underdensity threshold in percentage of the average). We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish efficiently between the models, while U_εis only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent of the scale, in agreement with hierarchical scaling predictions and estimates based on redshift surveys. Among our results, we emphasize the remarkable agreement between PPS data and C+2\nuDM in all the tests performed. In contrast, the above \LambdaCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.

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arXiv1996

Minkowski Functionals of Abell/ACO Clusters

We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function and the mean genus) deliver a global description of the spatial distribution of clusters on scales from $10$ to $60\hMpc$ with a clear geometric interpretation. Comparisons with mock catalogues of N--body simulations using different variants of the CDM model demonstrate the discriminative power of the description. The standard CDM model and the model with tilted perturbation spectrum cannot generate the Minkowski functionals of the cluster data, while a model with a cosmological constant and a model with breaking of the scale invariance of perturbations (BSI) yield compatible results.

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arXiv1995

Sampling Effects on Cosmological Dipoles

We use numerical simulations to investigate the behaviour of the dipole moment of the spatial distribution of different kinds of mass tracers. We select density peaks of the simulated matter distribution with mean separations of 38 and 30 $h^{-1}$ Mpc to represent two samples of rich clusters of galaxies. We extract, from the same simulations, samples selected to mimic the full 3D galaxy distribution of IR galaxies, and the flux--limited IRAS and QDOT galaxy samples. We compare the dipole moments of these ``galaxy'' and ``cluster'' samples in order to assess the effects of sampling uncertainties and shot--noise on the relationship between the ``true'' underlying galaxy dipole and the dipoles obtained for clusters and for the flux--limited galaxy samples. The results of this analysis demonstrate that the dipoles of both the IRAS and QDOT--like catalogues should trace the full 3D dipole shape fairly accurately, with the loss however of about 15--20$\%$ of the total 3D dipole amplitude. Furthermore, using a simple argument based on linear perturbation theory, on the linear biasing assumption and on the amplitude of the cluster dipole relative to that of galaxies, we can estimate their relative biasing factors quite accurately and in agreement with results obtained by other methods.

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arXiv1995

The Cluster Distribution as a Test for Dark Matter Models. II: The Dipole Structure

We study the dipole for a redshift sample of Abell/ACO clusters. To elucidate the constraints it places on dark matter models, we use numerical simulations based on the Zel'dovich approximation. We run 20 realizations of each of six different dark matter models: four of these have a density parameter $Ω_0=1$, while the other two have $Ω_0=0.2$, one with and one without a cosmological constant term. For the Abell/ACO sample, we evaluate the parameter $β=Ω_0^{0.6}/b_{ cl}$, which reaches its asymptotic value at $R=160 Mpc/h$. We find $β=0.15\pm 0.04$ and $0.25\pm 0.06$ in LG and CMB frames respectively. After identifying in the simulations LG-like observers, we construct mock cluster samples. We find that an alignment between the cluster dipole and observer velocity, such as that observed (about 20 degrees) should not be expected necessarily in the simulations. This, together with the large observer-to-observer variance estimates of $β$, makes it difficult to place any firm constraints on cosmological models. Our results demonstrate that the large amplitude and convergence depth of the cluster dipole cannot be taken as strong evidence either for or against a low--density Universe.

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arXiv1995

The Cluster Distribution as a Test for Dark Matter Models. I: Clustering Properties

We present simulations of the cluster distribution in several dark matter models, using an optimized version of the truncated Zel'dovich approximation (TZA). We compare them with N-body cluster simulations and find that the TZA provides a very accurate description of the cluster distribution as long as fluctuations on the cluster mass scale are in the mildly non-linear regime. The simulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) with n=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant (h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with Ω_0=0.2. We compare the simulations with a redshift sample of Abell/ACO clusters, using the integral of the 2-point correlation function and the probability density function. We find that the best models at reproducing the data are CHDM and LCDM. All the other models are ruled out. The reduced skewness S_3 is fairly constant with S_3=1.9, independent of the DM model and consistent with observational data. The abundances of clusters predicted using the Press--Schechter theory provide strong constraints: only the CHDM, LOWH and LCDM models appear to produce the correct number-density of clusters.

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arXiv1995

MASS SEGREGATION IN DARK MATTER MODELS.

We use the moments of counts of neighbors as given by the Generalized Correlation Integrals, to study the clustering properties of Dark Matter Halos (DH) in Cold Dark Matter (CDM) and Cold+Hot Dark Matter (CHDM) models. We compare the results with those found in the CfA and SSRS galaxy catalogs. We show that if we apply the analysis in redshift space, both models reproduce equally well the observed clustering of galaxies. Mass segregation is also found in the models: more massive DHs are more clustered compared with less massive ones. In redshift space, this mass segregation is reduced by a factor 2-3 due to the peculiar velocities. Observational catalogs give an indication of luminosity and size segregation, which is consistent with the predictions of the models. Because the mass segregation is smaller in redshift space, it is suggestive that the real luminosity or size segregation of galaxies could be significantly larger than what it is found in redshift catalogs.

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arXiv1994

Moments of the Cluster Distribution as a Test of Dark Matter Models

We estimate the variance and the skewness of the cluster distribution in several dark matter (DM) models. The cluster simulations are based on the Zel'dovich approximation, the low computational cost of which allows us to run 50 random realizations of each model. We compare our results with those coming from a similar analysis of a redshift sample of Abell/ACO clusters. Within the list of the considered models, we find that only the model based on Cold+Hot DM (with $Ω_{\rm hot}=0.3$) provides a good fit to the data. The standard CDM model and the low-density ($Ω_{\circ}=0.2$) CDM models, both with and without a cosmological constant term ($Ω_Λ=0.8$) are ruled out. The tilted CDM model with primordial spectral index $n=0.7$ and a low Hubble constant ($h=0.3$) CDM model are only marginally consistent with the data.

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arXiv1994

The Cluster Distribution as a Test for Dark Matter Models. I: Clustering Properties

We present extended simulations of the distribution of galaxy clusters in different dark matter models, using an optimized version of the Zel'dovich approximation. Six different dark matter models are studied: Standard CDM, Open CDM, Tilted CDM, Cold + Hot DM, low-density CDM with cosmological constant, and low Hubble constant ($h=0.3$) CDM. We compare simulations with an Abell/ACO redshift sample. We find that the models that best reproduce the clustering of the real data sets are the Cold + Hot DM model and the CDM model with a cosmological constant. The probability density function of all models and data is always well approximated by a lognormal distribution. We also find that the linear biasing parameter for the simulated clusters is nearly constant over a large range of scales, but its value depends on the model. We also note that the abundances of clusters predicted by the Press-Schechter theory provide strong constraints on these models: only the Cold + Hot DM model and the low-H CDM model appear to produce the correct number-density of clusters. Taking this constraint together with the cluster clustering statistics leads one to conclude that the best of our models is the Cold + Hot DM scenario.

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arXiv1994

Sizes of Voids as a test for Dark Matter Models

We use the void probability statistics to study the redshift-space galaxy distribution as described by a volume-limited subsample of the Perseus-Pisces survey. We compare the results with the same analysis realized on artificial samples, extracted from high-resolution N-body simulations by reproducing the observational biases of the real data set. Simulations are run for the Cold+HotDM model (CHDM) and for unbiased and biased (b=1.5) CDM models in a 50 Mpc/h box. We identify galaxies as residing in peaks of the evolved density field. We fragment overmerged structures into individual galaxies so as to reproduce both the correct luminosity function (after assuming M/ L values for the resulting galaxy groups) and the two-point correlation function. Our main result is that a void-probability function (VPF) from the standard CHDM model with fractions 60% cold, 30% hot, 10% barions, exceeds the observational VPF with a high confidence level. CDM models produce smaller VPF independent of the biasing parameter. We verify the robustness of this result against changing the observer position in the simulations and the galaxy identification in the evolved density field.

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arXiv1994

Is there any Scaling in the Cluster Distribution ?

We apply fractal analysis methods to investigate the scaling properties in the Abell and ACO catalogs of rich galaxy clusters. We also discuss different technical aspects of the method when applied to data sets with small number of points as the cluster catalogs. Results are compared with simulations based on the Zel'dovich approximation. We limit our analysis to scales less than 100 $\hm$. The cluster distribution show a scale invariant multifractal behavior in a limited scale range. For the Abell catalog this range is 15--60$\hm$, while for the ACO sample it extends to smaller scales. Despite this difference in the extension of the scale--range where scale--invariant clustering takes place, both samples are characterized by remarkably similar multifractal spectra in the corresponding scaling regime. In particular, the correlation dimension turns out to be $D_2\simeq 2.2$ for both Abell and ACO clusters. Although it is difficult to point out the scale at which homogeneity is reached with the present size of these redshift surveys, our results indicate that the cluster distribution shows a tendency to homogeneity at large scales, disproving the picture of a pure scale invariant fractal structure extending to arbitrarily large distances.

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arXiv1994

Lick Galaxy Correlation Function Revised

We re-estimate the angular 2-point galaxy correlation function from the Lick galaxy catalogue. We argue that the large-scale gradients observed in the Lick catalogue are dominated by real clustering and therefore they should not be subtracted prior to the estimation of the 2-p correlation function. We find that if no such correction is introduced the galaxy correlations are perfectly consistent with the those found in the APM survey. Thus, the long standing discrepancy between the Lick and APM angular correlations is lifted.

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arXiv1993

Cluster Correlations in the Zel'dovich Approximation

We show how to simulate the clustering of rich clusters of galaxies using a technique based on the Zel'dovich approximation. This method well reproduces the spatial distribution of clusters obtainable from full N-body simulations at a fraction of the computational cost. We use an ensemble of large--scale simulations to assess the level and statistical significance of cluster clustering in open, tilted and flat versions of the Cold Dark Matter (CDM) model, as well as a model comprising a mixture of Cold and Hot Dark Matter (CHDM). We find the open and flat CDM models are excluded by the data. The tilted CDM model with a slight tilt is in marginal agreement, while larger tilt produces the right amount of clustering; CHDM is the best of all our models at reproducing the observations of cluster clustering. We find that {\em all} our models display a systematically weaker relationship between clustering length and mean cluster separation than seems to be implied by observations. We also note that the cluster bias factor, is not constant in any of the models, showing that one needs to be very careful when relating cluster clustering statistics to primordial density fluctuations.

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arXiv1993

Non-Linear Clustering in the Cold+Hot Dark Matter Model

We use high resolution PM N-body simulations to follow the development of non-linear clustering in a flat Universe, dominated by Cold + Hot Dark Matter (CHDM) with 60% of CDM, 30% of HDM and 10% of baryons; a simulation box of 100 Mpc a side ($h=0.5$) is used. We analyze two CHDM simulations with $b =1.5$ (COBE normalization). We also compare them with CDM simulations with $b=1.5$ and $b=1$. We evaluate high-order correlation functions and the void-probability-function (VPF). Correlation functions are obtained both from counts in cells and counts of neighbors. The analysis is made for DM particles and for galaxies, identified as massive halos in the evolved density field. We also check the effects of dynamical evolution and redshift space distortions. We find that clustering of DM particles exhibits deviations from the hierarchical scaling, which decrease somewhat in redshift space. Galaxies follow hierarchical scaling far more closely, with coefficients S_3=2.5 and S_4=7.5, in general agreement with observational results, just marginally affected by redshift distortions and on the choices for the initial spectra. The hierarchical scaling of galaxy clustering is confirmed by the VPF analysis and in all the cases considered a good agreement with observational results is obtained.

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arXiv1993

Angular Distribution of Clustersin Skewed CDM Models

We perform a detailed investigation of the statistical properties of the projected distribution of galaxy clusters obtained in Cold Dark Matter (CDM) models with both Gaussian and skewed primordial density fluctuations. We use N-body simulations to construct a set artificial Lick maps. An objective cluster--finding algorithm is used to identify clusters of different richness. For Gaussian models, the overall number of clusters is too small in the standard CDM case, but a model with higher normalisation fares much better; non--Gaussian models with negative skewness also fit faily well. We apply several statistical tests to compare real and simulated cluster samples, such as the 2-point correlation function, the minimal spanning tree construction, the multifractal analysis and the skewness of cell counts. The emerging picture is that Gaussian models, even with a higher normalization, are in trouble. Skew-positive models are also ruled out, while skew-negative models can reproduce the observed clustering of galaxy clusters in the CDM framework.

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arXiv1993

Large--Scale Angular Correlations in CDM Models

We generate artificial Lick maps using $N$--body simulations and compare the angular correlation function, $w(\vartheta)$, measured from the simulations with the APM correlation. For the Gaussian CDM model, neither the standard biassed model nor a more evolved model (as suggested by the COBE data), reproduce the correlations on large angular scales. We come to a similar conclusion about CDM models with positively skewed initial fluctuation distributions. In contrast, models with initially negatively skewed fluctuations produce a $w(\vartheta)$ that declines much more gently on large scales. Such models are therefore in principle capable of reconciling the lack of large--scale power of the CDM spectrum with the observed clustering of APM galaxies.

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