arXiv subjects

G. Boerner

Publications and source records attributed to G. Boerner.

24 records · Page 2Linked to original sources

arXiv1995

The Zel'dovich-type approximation for an inhomogeneous universe in general relativity: second-order solutions

The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those given in the Lagrangian perturbation theory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinear dynamics of cosmological perturbations. We present the complete second-order solutions, which extend and improve earlier works.

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arXiv1995

The velocity dispersion profiles of clusters of galaxies: a cosmological test and the sampling effect

In this paper we investigate the velocity dispersion profiles of clusters of galaxies for seven cosmological models. One model is the SCDM model, and the others are six low-density models with the density parameter $Ω=0.1$, 0.2 or 0.3 and with or without a cosmological constant $Λ=1-Ω$. We find that the velocity dispersion profiles depend both on $Ω$ and on $Λ$. For $Λ=0$, the profiles are steeper in a lower-$Ω$ model than in a higher-$Ω$ one. The cosmological constant significantly weakens the dependence on $Ω$: the difference in the profile distributions between two flat models is much smaller than that between the two corresponding open models with the same $Ω$. These results in principle can be used to constrain the cosmological parameters when a large sample of the velocity dispersion profiles is available. Motivated by the practical situation that a sample of $\sim 100$ clusters with $\sim 100$ measured redshifts per cluster is still the best sample available in the foreseen future, we examine carefully to what degree the cosmological parameters can be constrained with the velocity dispersion profiles of such a sample of clusters. The limited sampling around clusters and the limited number of clusters seriously degrade the discriminative power of the velocity dispersion profiles among cosmological models. We find that the five models of $Ω\ge 0.2$ cannot be distinguished by this type of observation. Due to the limited sampling, one should be very cautious in extracting information about the density profile and/or the dynamics around single clusters from the diluted velocity dispersion profiles

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arXiv1995

Three-point correlation function of galaxy clusters in cosmological models: a strong dependence on triangle shape

In this paper, we use large $\pppm$ N-body simulations to study the three-point correlation function $ζ$ of clusters in two theoretical models. The first model (LCDM) is a low-density flat model of $Ω_0=0.3$, $Λ_0=0.7$ and $h=0.75$, and the second model (PIM) is an Einstein-de-Sitter model with its linear power spectrum obtained from observations. We found that the scaled function $Q(r,u,v)$, which is defined as the ratio of $ζ(r, ru, ru+rv)$ to the hierarchical sum $ξ(r)ξ(ru)+ ξ(ru) ξ(ru+rv) +ξ(ru+rv)ξ(r)$ (where $ξ$ is the two-point correlation function of clusters), depends weakly on $r$ and $u$, but very strongly on $v$. $Q(r,u,v)$ is about 0.2 at $v=0.1$ and 1.8 at $v=0.9$. A model of $Q(r,u,v)=Θ10^{1.3v^2}$ can fit the data of $ζ$ very nicely with $Θ\approx 0.14$. This model is found to be universal for the LCDM clusters and for the PIM clusters. Furthermore, $Q(r,u,v)$ is found to be insensitive to the cluster richness. We have compared our N-body results with simple analytical theories of cluster formation, like the peak theories or the local maxima theories. We found that these theories do not provide an adequate description for the three-point function of clusters. We have also examined the observational data of $ζ$ presently available, and have not found any contradiction between the observations and our model predictions. The $v$-dependence of $q$ in a projected catalogue of clusters is shown to be much weaker than the $v$-dependence of $Q$ found in the three-dimensional case. It would be important to search for the $v$-dependence of $Q$ in redshift samples of rich clusters.

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arXiv1994

Substructures and Density Profiles of Clusters in Models of Galaxy Formation

In this paper we investigate, using high resolution N-body simulations, the density profiles and the morphologies of galaxy clusters in seven models of structure formation. We show that these properties of clusters are closely related to the occurrence of a significant merging event in the recent past. The seven models are: (1) the standard CDM model (SCDM) with $Ω_0 = 1$, $Λ_0=0$ and $h=0.5$; (2) a low-density flat model (FL03) with $Ω_0=0.3$, $Λ_0=0.7$ and $h=0.75$; (3) an open model (OP03) with $Ω_0=0.3$, $Λ_0=0$ and $h=0.75$; (4) a low-density flat model (FL02) with $Ω_0=0.2$, $Λ_0=0.8$ and $h=1$; (5) an open model (OP02) with $Ω_0=0.2$, $Λ_0=0$ and $h=1$; (6) a low-density flat model (FL01) with $Ω_0=0.1$ and $Λ_0=0.9$; (7) an open model (OP01) with $Ω_0=0.1$ and $Λ_0=0$. We find that the density profiles and morphologies of clusters depend both on $Ω_0$ and on $Λ_0$. For $Λ_0=0$, these properties are a monotonic function of $Ω_0$. Clusters in OP01 have the steepest density profiles, their density contours are the roundest and show the smallest center shifts. The other extreme case is SCDM, where clusters show the least steep density profiles and the most elongated contours. For a given $Ω_0$ ($<1$), clusters in the flat model (i.e. with $Λ_0=1-Ω_0$) have flatter density profiles and less substructures than in the corresponding open model. In particular, our results show that low-density flat models with $Ω_0\sim 0.3$, which are currently considered as a successful alternative to SCDM, can produce a substantial fraction of clusters with substructures. This is in contrast to the conception that this kind of models may have serious problem in this aspect.

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arXiv1994

Substructures of Clusters and Cosmological Models

We investigate, using high resolution N-body simulations, the density profiles and the morphologies of galaxy clusters in three models of structure formation. We show that these properties are closely related to the occurrence of a significant merging event to a cluster in the recent past. The three models are: (1) the standard CDM model (SCDM) with $Ω_0 = 1$, $Λ_0=0$ and $h=0.5$; (2) a low-density flat model (LCDM) with $Ω_0=0.3$, $Λ_0=0.7$ and $h=0.75$; (3) a CDM dominated open model (OCDM) with $Ω_0=0.1$, $Λ_0=0$. We find that the clusters in the OCDM model have the steepest density profiles, their density contours are the roundest and show the smallest center shifts, among the three models. The clusters in the SCDM model have contours that are most elongated and show the largest center shifts, indicating the existence of frequent mergers in the recent past. The clusters in the LCDM model have density profiles and center shifts (in their density contours) similar to those in the SCDM model, although the density contours tend to be rounder. Our results show that, although the density profiles and morphologies of clusters depend on models of structure formation, the LCDM model, which is currently considered as a successful alternative to the SCDM model, can do as well in producing a substantial fraction of clusters with substructures. This is in contrast to the conception that this model may have serious problem in this aspect.

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arXiv1993

The large-scale structure in a universe dominated by cold plus hot dark matter

Using numerical simulations, we investigate the large-scale gravitational clustering in a flat universe dominated by cold plus hot dark matter (i.e., $Ω_0=\ocdm+\ohdm+\obaryon=1$). Primordial density fluctuation spectrum is taken to have the Zel'dovich-Harrison form. Three models are studied, with Model I having $\ocdm=0.69$, $\obaryon=0.01$, and $\ohdm=0.30$ in one flavor of neutrinos; Model II having $\ocdm=0.60$, $\obaryon=0.10$, and $\ohdm=0.30$ in one flavor of neutrinos; Model III having $\ocdm=0.69$, $\obaryon=0.01$, and $\ohdm=0.30$ in three flavors of neutrinos. The initial density spectra are normalized by the COBE quadrupole measurement, and galaxies are identified from the peaks of initial density fields above a certain threshold chosen, to match the observed two-point correlation on scales $\ls 10\mpc$. Thus the clustering properties of both the mass and the galaxies are completely specified. The biasing parameter (for the `galaxies') determined in this way is $b_g\approx 1.2$ for Model I, 1.5 for Model II and 1.6 for Model III. The clustering and motions of the simulated `galaxies' are compared with recent observations. The spatial distributions of galaxies in the hybrid models are very frothy; filaments, sheets, voids etc. of sizes 10 -- 50$\mpc$ are frequently seen in the simulations.

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