arXiv subjects
Publications and source records attributed to Adrian L. Melott.
We argue that there has been substantial evolution in the ellipticity of rich galaxy clusters between 0 < z < 0.1, and suggest that this is additional evidence for a low matter-density Universe.
We have examined whether the major axes of rich galaxy clusters tend to point toward their nearest neighboring cluster. We have used the data of Ulmer, McMillan, and Kowalski, who used position angles based on X-ray morphology. We also studied a subset of this sample with updated positions and distances from the MX Northern Abell Cluster Survey (for rich clusters ($R \geq 1$) with well known redshifts). A Kolmogorov-Smirnov (KS) test showed no significant signal for nonrandom angles on any scale $\leq 100h^{-1}$Mpc. However, refining the null hypothesis with the Wilcoxon rank-sum test, we found a high confidence signal for alignment. Confidence levels increase to a high of 99.997% as only near neighbors which are very close are considered. We conclude there is a strong alignment signal in the data, consistent with gravitational instability acting on Gaussian perturbations.
The sizes and shapes of voids in a galaxy survey depend not only on the physics of structure formation, but also on the sampling density of the survey and on the algorithm used to define voids. Using an N-body simulation with a CDM power spectrum, we study the properties of voids in samples with different number densities of galaxies, both in redshift space and in real space. When voids are defined as regions totally empty of galaxies, their characteristic volume is strongly dependent on sampling density; when they are defined as regions whose density is 0.2 times the mean galaxy density, the dependence is less strong. We compare two void-finding algorithms, one in which voids are nonoverlapping spheres, and one, based on the algorithm of Aikio and Mahonen, which does not predefine the shape of a void. Regardless of the algorithm chosen, the characteristic void size is larger in redshift space than in real space, and is larger for low sampling densities than for high sampling densities. We define an elongation statistic Q which measures the tendency of voids to be stretched or squashed along the line of sight. Using this statistic, we find that at sufficiently high sampling densities (comparable to the number densities of galaxies brighter than L_*), large voids tend to be slightly elongated along the line of sight in redshift space.
We examine the relationship between the total X-ray and optical luminosities of groups and clusters of galaxies taken from various samples in the literature. The clusters and groups were drawn from four different catalogs: (1) the Abell/ACO catalog, (2) the Edinburgh-Durham Cluster Catalog, (3) the RASS Bright Cluster Sample, and (4) galaxy groups selected from the CfA redshift survey. These catalogs represent a significant cross-section of cluster selection tchniques as well as a wide range in mass scale and can be considered statistically independent. We have calculated new cluster X-ray and optical luminosities if not available in the literature. Based on 126 systems, our analysis shows that the total optical luminosity of a cluster is directly proportional to the total X-ray luminosity over a wide mass range and across all four cluster samples studied herein. We also show that total cluster optical luminosity is a good indicator of cluster virial mass, but richness is not. Our results suggest that (1) the selection method of galaxy clusters may not be crucial, providing wider latitude in assembling catalogs, (2) the luminosity per baryon does not vary systematically between systems ranging from groups to very rich clusters. We propose that future optical catalogs of clusters use the total optical luminosity of a cluster, instead of galaxy richness, as luminosity appears to be a better measure of cluster mass and can be directly related to X-ray catalogs of clusters. This will also facilitate the first direct comparison between the growing number of X-ray and optical catalogs.
We compare the statistical properties of structures normal and transverse to the line of sight which appear in observational data from redshift surveys. We present a statistic which can quantify this effect in a conceptually different way from standard analyses of distortions of the power-spectrum or correlation function. From tests with N-body experiments, we argue that this statistic represents a new, more direct and potentially powerful diagnostic of the cosmological density parameter Omega.
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.
With the availability of large-scale redshift survey data, it is now becoming possible to explore correlations between large-scale structure and the properties and morphologies of galaxy clusters. We investigate the spatial distributions of a 98% complete, volume-limited sample of nearby (z<0.1) Abell clusters with well-determined redshifts and find that cooling flow clusters with high mass-accretion rates have nearest neighbors which are much closer than those of other clusters in the sample (at the 99.8% confidence level), and reside in more crowded environments out to 30/h Mpc. Several possible explanations of this effect are discussed.
We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical descriptors such as cumulants, cumulant correlators and factorial moments. We use this approach to establish key scaling relations describing various measurable statistical quantities if clustering follows a simple general scaling ansatz, as expected in hierarchical models. We test these detailed predictions against high-resolution numerical simulations. We show that, when appropriate variables are used, the count probability distribution function (CPDF) and void probability distribution function (VPF) shows clear scaling properties in the non-linear regime. Generalising the results to the two-point count probability distribution function (2CPDF), and the bivariate void probability function (2VPF) we find good match with numerical simulations. We explore the behaviour of the bias associated with collapsed objects in limit of large separations, finding that it depends only on the intrinsic scaling parameter associated with collapsed objects and that the bias for two different objects can be expressed as a product of the individual biases of the objects. Finally we use hierarchal ansatz to develop a novel technique for correcting finite-volume effects in the estimation of multi-point statistical quantities from observational data (abridged).
The highly nonlinear regime of gravitational clustering is characterized by the presence of scale-invariant form of many-body correlation functions. Useful insights can be obtained by investigating the consequences of a generic scaling {\em ansatz}. Extending earlier studies by Bernardeau & Schaeffer (1992) we calculate the detailed consequences of such scaling. We generalise the two-point cumulant correlators to a hierarchy of multi-point cumulant correlators (MCC). We introduce the concept of reduced cumulant correlators (RCC) and their related generating functions. Using analytical and diagrammatic method we show that every new vertex of the tree representation of higher-order correlations has its own reduced cumulant correlator. In the limit of large separations, MCCs of arbitrary order can be expressed in terms of RCCs of the same and lower order. We relate the generating functions of RCCs with the statistics of {\em collapsed} objects. We develop the hierarchy for the correlation functions of overdense regions. In this vein, we compute the lower-order cumulants and cumulant correlators for overdense regions. Our study shows how they vary as a function of the initial power spectrum of primordial density fluctuations (abridged).
The cumulant correlators, $C_{pq}$, are statistical quantities that generalise the better-known $S_p$ parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the $C_{pq}$ for projected clustering data, such as the APM survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogs, finding very good agreement. We extend the idea of cumulant correlators to multi-point {\em generalised} cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly nonlinear regime to express the generalised cumulant correlators in terms of the underlying ``tree amplitudes'' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogs and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical {\em ansatz} of Bernardeau & Schaeffer (1992) with extended and hyperextended perturbation theory to infer values of the tree amplitudes in the highly nonlinear regime.
We compare the statistical properties of structures normal and transverse to the line of sight which appear in theoretical N-body simulations of structure formation, and seem also to be present in observational data from redshift surveys. We present a statistic which can quantify this effect in a conceptually different way from standard analyses of distortions of the power-spectrum or correlation function. From tests with $N$--body experiments, we argue that this statistic represents a new and potentially powerful diagnostic of the cosmological density parameter, $Ω_0$.
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions and related moments. Methods based on factorial moments of two point count probability distribution (cumulant correlators) were recently shown to be efficient in subtracting discreteness effects and extracting useful information from galaxy catalogs. We use these cumulant correlators $Q_{NM}$ to study clustering in scale free simulations both in two and three dimensions. Using this method in the highly nonlinear regime we were able to separate hierarchal amplitudes $Q_3, R_a and R_b$ associated with different tree graphs contributing to third and fourth order correlation functions. They were found to increase with power on large scales. Results based on factorial moments of one point cumulants show very good agreement with that on cumulant correlators. Comparison of simulation results with perturbation theory and extended perturbation theory were found to be in reasonable agreement. Comparisons were also made against predictions from hierarchal models for higher order correlations. We argue that finite volume corrections are very important for computation of cumulant correlators.
We report on a series of tests of agreement between three types of N-body simulations: PM, P$^3$M, and Tree codes. We find good agreement in both the individual and the statistical properties only on scales larger than the mean interparticle separation. As a result, we question most numerical results at and below below galaxy scales, either concerning primordial dark matter or baryonic matter coupled to it by gravitation. Mass resolution (specifically, sufficient to have the mean interparticle separation comparable to the smoothing scales) appears be necessary for results to converge.
We explore some of the effects that discreteness and two-body scattering may have on N-body simulations with ``realistic'' cosmological initial conditions. We use an identical subset of particles from the initial conditions for a $128^3$ Particle-Mesh (PM) calculation as the initial conditions for a variety P$^3$M and Tree code runs. We investigate the effect of mass resolution (the mean interparticle separation) since most ``high resolution'' codes only have high resolution in gravitational force. The phase-insensitive two--point statistics, such as the power spectrum (autocorrelation) are somewhat affected by these variations, but phase-sensitive statistics show greater differences. Results converge at the mean interparticle separation scale of the lowest mass-resolution code. As more particles are added, but the force resolution is held constant, the P$^3$M and the Tree runs agree more and more strongly with each other and with the PM run which had the same initial conditions. This shows high particle density is necessary for correct time evolution, since many different results cannot all be correct. However, they do not so converge to a PM run which continued the fluctuations to small scales. Our results show that ignoring them is a major source of error on comoving scales of the missing wavelengths. This can be resolved by putting in a high particle density. Since the codes never agree well on scales below the mean comoving interparticle separation, we find little justification for quantitative predictions on this scale. Some measures vary by 50%, but others can be off by a factor of three or more. Our results suggest possible problems with the density of galaxy halos, formation of early generation objects such as QSO absorber clouds, etc.
We investigate a distortion in redshift-space which causes galaxies to appear to lie in walls concentric about the observer, forming a rough bull's-eye pattern. We simulate what an observer would see in a thin slice of redshift-space, including a magnitude limit and constant slice angle. The result is an enhanced ring of galaxies encircling the observer at a distance roughly corresponding to the peak of the selection function. This ring is an artificial enhancement of weak features in real-space. This may explain visually prominent features such as the ``Great Wall'' and periodicity found in deep narrow fields.
We test tree-level perturbation theory for Gaussian initial conditions with power spectra $P(k)\propto k^n$ by comparing the probability distribution function (PDF) for the density predicted by the Local Lagrangian Approximation (LLA) with the results of numerical gravitational clustering simulations. Our results indicate that our approximation correctly reproduces the evolved density PDF for $-3 \leq n \leq-1$ power spectra up to the weakly nonlinear regime, while it shows marginal agreement for power indices n=0 and +1 in the linear regime and poor agreement beyond this point. This suggests that tree-level perturbation theory (as realized in the Local Lagrangian Approximation) can accurately predict the density distribution function for $-3 \leq n \leq -1$ but fails for $n \ge 0$.
In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density parameters ($Ω_0 = 0.2$ to 1.0). Furthermore, unlike most theoretical studies we mimic most observers by removing all particles which lie at distances greater than 2 1/h Mpc from the cluster center of mass. We computed the axial ratio and the principal axes using the inertia tensor of each cluster. The mean ellipticity of clusters increases strongly with increasing $n$. We also find that clusters tend to become more spherical at smaller radii. We compared the orientation of a cluster to the orientation of neighboring clusters as a function of distance (correlation). In addition, we considered whether a cluster's major axis tends to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations were computed in three dimensions and in projection to mimic observational surveys. Our results show that significant alignments exist for all spectra at small separations ($D < 15 h^{-1}$ Mpc) but drops off at larger distance in a strongly $n-$dependent way.
The potential is a constant to linear order in cosmological gravitational clustering. In this Letter we present results of testing the conjecture, proposed by Pauls and Melott (1995), that the effect of nonlinear evolution on the potential can be better described by smoothing it on the scale of nonlinearity. We show two-dimensional simulations consisting of an N-body code in which particles are accelerated not by their mutual attraction, but by the gradient of the initial potential smoothed on the current scale of nonlinearity. This approximation produces results considerably improved over using a constant potential to move particles, and it is generally better than any approximation we have tested, lending further support to the smoothing description of the evolved potential.