arXiv subjects

Peter Coles

Publications and source records attributed to Peter Coles.

83 records · Page 5Linked to original sources

arXiv1998

From Snakes to Stars, the Statistics of Collapsed Objects - I. Lower--order Clustering Properties

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).

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arXiv1998

Generalised Cumulant Correlators and Hierarchical Clustering

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.

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arXiv1998

The Clustering of Lyman-break Galaxies

We calculate the statistical clustering of Lyman-break galaxies predicted in a selection of currently-fashionable structure formation scenarios. These models are all based on the cold dark matter model, but vary in the amount of dark matter, the initial perturbation spectrum, the background cosmology and in the presence or absence of a cosmological constant term. If Lyman-break galaxies form as a result of hierarchical merging, the amplitude of clustering depends quite sensitively on the minimum halo mass that can host such a galaxy. Interpretation of the recent observations by Giavalisco et al. (1998) would therefore be considerably clarified by a direct determination of the relevant halo properties. For a typical halo mass around $10^{11} h^{-1} M_\odot$ the observations do not discriminate strongly between cosmological models, but if the appropriate mass is larger, say $10^{12} ~h^{-1} M_\odot$ (which seems likely on theoretical grounds), then the data strongly favour models with a low matter-density.

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arXiv1998

Modelling galaxy clustering at high redshift

We discuss the theoretical interpretation of observational data concerning the clustering of galaxies at high redshifts. Building on the theoretical machinery developed by Matarrese et al. (1997), we make detailed quantitative predictions of galaxy clustering statistics for a variety of cosmological models, taking into account differences in spatial geometry and initial fluctuation spectra and exploring the role of bias as a complicating factor in these calculations. We demonstrate that the usual description of evolution (in terms of the parameters $ε$ and $r_0$) is not useful for realistic galaxy clustering models. We compare the detailed predictions of the variation of correlation functions with redshift against current observational data to constrain available models of structure formation. Theories that fit the present-day abundance of rich clusters are generally compatible with the observed redshift evolution of galaxy clustering if galaxies are no more than slightly biased at $z\sim 1$. We also discuss the interpretation of a concentration of Lyman-break galaxies found by Steidel et al. (1998), coming to the conclusion that such concentrations are not unexpected in `standard' models of structure formation.

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arXiv1998

The Bull's-Eye Effect as a Probe of $Ω$

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, $Ω_0$.

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arXiv1996

Redshift evolution of clustering

We discuss how the redshift dependence of the observed two-point correlation function of various classes of objects can be related to theoretical predictions. This relation involves first a calculation of the redshift evolution of the underlying matter correlations. The next step is to relate fluctuations in mass to those of any particular class of cosmic objects; in general terms, this means a model for the bias and how it evolves with cosmic epoch. Only after these two effects have been quantified can one perform an appropriate convolution of the non-linearly evolved two-point correlation function of the objects with their redshift distribution to obtain the `observed' correlation function for a given sample. This convolution in itself tends to mask the effect of evolution by mixing amplitudes at different redshifts. We develop a formalism which incorporates these requirements and, in particular, a set of plausible models for the evolution of the bias factor. We apply this formalism to the spatial, angular and projected correlation functions from different samples of high-redshift objects, assuming a simple phenomenological model for the initial power-spectrum and an Einstein-de Sitter cosmological model. We find that our model is roughly consistent with data on the evolution of QSO and galaxy clustering, but only if the effective degree of biasing is small. We discuss the differences between our analysis and other theoretical studies of clustering evolution and argue that the dominant barrier to making definitive predictions is uncertainty about the appropriate form of the bias and its evolution with cosmic epoch.

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arXiv1996

Large-Scale Structure in Mixed Dark Matter Models with a Non-thermal Volatile Component

We investigate the properties of large--scale structure predicted in a class of mixed dark matter models in which the volatile component (made of particles with high rms velocity) derives from the decay of a heavier particle. Such models based on cold+volatile dark matter (CVDM) differ from the standard mixture of CDM and massive neutrinos, usually known as CHDM, in that they involve a component which has a non--thermal phase space distribution function. As a consequence, and differently from CHDM models, the value of the redshift at which volatile particles become non relativistic, $z_{nr}$, can be varied almost independently of the volatile fraction, $Ω_X$. We compute transfer functions for a selection of such models, having $0.1\le Ω_X\le 0.5$ and different values of $z_{nr}$. Using linear theory and assuming a scale--free primordial spectrum, we compare such models with observational constraints on large--scale galaxy clustering and bulk flows, as well as on the abundance of galaxy clusters and high--redshift damped Ly$α$ systems. We find that these constraints enable us to discriminate between different $Ω_X$ and $z_{nr}$; within the range of the models inspected, those which can be most easily accommodated by the data correspond to the parameter choice $Ω_X\simeq 0.2$ and $z_{nr} \simeq 2\times 10^4Ω_X$.

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arXiv1996

Quantifying the Topology of Large-Scale Structure

We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological characteristics, based on concepts, on the one hand, from differential topology and, on the other, from integral geometry. The former approach leads one to concentrate on properties of the contour surfaces which, in turn, leads to the algorithms CONTOUR2D and CONTOUR3D familiar to cosmologists. The other approach, which we adopt here, actually leads to much simpler algorithms in both two and three dimensions. (The 2D algorithm has already been introduced to the astronomical literature.) We discuss the 3D case in some detail and compare results obtained with it to analogous results using the CONTOUR3D algorithm.

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arXiv1995

The Cluster Distribution as a Test of Dark Matter Models. III. the Cluster Velocity Field

We study the large-scale velocity fields traced by galaxy clusters in numerical simulations of a box of side 960 $h^{-1}$ Mpc, and compare them with available data on real clusters. In order to test the reliability of the simulations, which are based on an optimized version of the Zel'dovich approximation, we compare their cluster velocities with those of "exact" N-body simulations, and find a remarkable agreement between the two according to a variety of statistical tests. We analyse Cold Dark Matter models with density parameter in the range $0.2\le Ω_0\le 1$, both with and without the cosmological constant term to provide a flat geometry. We also simulate a Cold+Hot Dark Matter model, with 30% provided by the hot component. Comparison with real data is performed by applying tests based on the cumulative velocity frequency distribution (CVFD) and bulk flow statistics. For the CVFD, we use observational velocity data from different authors. By merging all available data in a combined sample, the CVFD test is able to exclude only open models with $Ω_0\le 0.4$ and flat models with $Ω_0=0.2$. However, the analysis of individual observational samples gives contradictory results; in particular the recent Giovanelli data, which imply much lower velocities (with significantly smaller uncertainties) than the other data, are actually only consistent with the open $Ω_0=0.4$ and the flat $Ω_0=0.2$ models, i.e. the models which are excluded by the other data. Furthermore, CVFD and bulk flow analyses of the Branchini et al. reconstructed velocity data disfavour precisely those models accepted on the grounds of Giovanelli's sample. Finally, we confirm that the Lauer & Postman bulk flow determination is an extremely rare event in the cosmological models we have analysed.

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arXiv1995

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $Ω$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.

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arXiv1995

Approximation Methods for Non-linear Gravitational Clustering

We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high--peak model and the lognormal model; (ii) {\em dynamical} approximations, including the Zel'dovich approximation and its extensions; (iii) non--linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hierarchical closure {\em ansatz} for BBGKY, fractal models and the thermodynamic model of Saslaw; (v) numerical techniques based on particles and/or hydrodynamics. We compare the results of full dynamical evolution using particle codes and the various other approximation schemes. To put the models we discuss into perspective, we give a brief review of the observed properties of galaxy clustering and the statistical methods used to quantify it, such as correlation functions, power spectra, topology and spanning trees.

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