The Correlation Function of Rich Clusters of Galaxies in CDM-like Models

We use ensembles of high-resolution CDM simulations to investigate the shape and amplitude of the two point correlation function of rich clusters. The standard scale-invariant CDM model with $\Omega=1$ provides a poor description of the clustering measured from the APM rich cluster redshift survey, which is better fitted by models with more power at large scales. The amplitudes of the rich cluster correlation functions measured from our models depend weakly on cluster richness. Analytic calculations of the clustering of peaks in a Gaussian density field overestimate the amplitude of the N-body cluster correlation functions, but reproduce qualitatively the weak trend with cluster richness. Our results suggest that the high amplitude measured for the correlation function of richness class $R \geq 2$ Abell clusters is either an artefact arising from incompleteness in the Abell catalogue, or an indication that the density perturbations in the early universe were very non-Gaussian.Comment: uuencoded compressed postscript ,MNRAS, in press, OUAST-93-1

Anthropic versus cosmological solutions to the coincidence problem

In this paper we investigate possible solutions to the coincidence problem in flat phantom dark energy models with a constant dark energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the $\Lambda {\rm CDM}$ model. This relates a cosmological solution to the coincidence problem with a dynamical dark energy component having an equation of state parameter not too close to -1 at the present time. We further show, that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.Comment: 7 pages, 7 figure

Evolution of the Pairwise Peculiar Velocity Distribution Function in Lagrangian Perturbation Theory

The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observations and explicitly shown in N-body simulations. Here we calculate its statistical distribution function using the Zel'dovich approximation assuming that the primordial density fluctuations are Gaussian distributed. We show that the exponential distribution is realized as a transient phenomena on megaparsec scales in the standard cold-dark-matter model.Comment: 19 pages, 8 Postscript figures, AAS LaTe

The mass function

We present the mass functions for different mass estimators for a range of cosmological models. We pay particular attention to how universal the mass function is, and how it depends on the cosmology, halo identification and mass estimator chosen. We investigate quantitatively how well we can relate observed masses to theoretical mass functions.Comment: 14 pages, 12 figures, to appear in ApJ

Luminosity density estimation from redshift surveys and the mass density of the Universe

In most direct estimates of the mass density (visible or dark) of the Universe, a central input parameter is the luminosity density of the Universe. Here we consider the measurement of this luminosity density from red-shift surveys, as a function of the yet undetermined characteristic scale R_H at which the spatial distribution of visible matter tends to a well defined homogeneity. Making the canonical assumption that the cluster mass to luminosity ratio M/L is the universal one, we can estimate the total mass density as a function \Omega_m(R_H,M/L). Taking the highest estimated cluster value M/L ~300h and a conservative lower limit R_H > 20 Mpc/h, we obtain the upper bound \Omega_m < 0.1 . We note that for values of the homogeneity scale R_H in the range R_H ~ (90 +/- 45) hMpc, the value of \Omega_m may be compatible with the nucleosynthesis inferred density in baryons.Comment: 16 pages, latex, no figures. To be published in Astrophysical Journal Letter

Properties and use of CMB power spectrum likelihoods

Fast robust methods for calculating likelihoods from CMB observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximation, how accurate the covariance needs to be, and how to estimate the covariance from simulations. For a simple case with azimuthal symmetry we compare optimality of hybrid pseudo-C_l CMB power spectrum estimators with the exact result, indicating that the loss of information is not negligible, but neither is it enough to have a large effect on standard parameter constraints. We then discuss the number of samples required to estimate the covariance from simulations, with and without a good analytic approximation, and assess the use of shrinkage estimators. Finally we discuss how to combine an approximate high-ell likelihood with a more exact low-ell harmonic-space likelihood as a practical method for accurate likelihood calculation on all scales.Comment: 15 pages, 11 figures; updated to match version accepted by PR

An Isocurvature CDM Cosmogony. I. A Worked Example of Evolution Through Inflation

I present a specific worked example of evolution through inflation to the initial conditions for an isocurvature CDM model for structure formation. The model invokes three scalar fields, one that drives power law inflation, one that survives to become the present-day CDM, and one that gives the CDM field a mass that slowly decreases during inflation and so ``tilts'' the primeval mass fluctuation spectrum of the CDM. The functional forms for the potentials and the parameter values that lead to an observationally acceptable model for structure formation do not seem to be out of line with current ideas about the physics of the very early universe. I argue in an accompanying paper that the model offers an acceptable fit to main observational constraints.Comment: 11 pages, 3 postscript figures, uses aas2pp4.st

Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations

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.Comment: Revised version to be published in Astrophysical Journal. One figure changed; expanded discussion, more information on code parameters. Latex, 44 pages, including 19 figures. Higher resolution versions of Figures 10-15 available at: ftp://kusmos.phsx.ukans.edu/preprints/nbod

Formation of early-type galaxies from cosmological initial conditions

We describe high resolution Smoothed Particle Hydrodynamics (SPH) simulations of three approximately $M_*$ field galaxies starting from \LCDM initial conditions. The simulations are made intentionally simple, and include photoionization, cooling of the intergalactic medium, and star formation but not feedback from AGN or supernovae. All of the galaxies undergo an initial burst of star formation at $z \approx 5$, accompanied by the formation of a bubble of heated gas. Two out of three galaxies show early-type properties at present whereas only one of them experienced a major merger. Heating from shocks and -PdV work dominates over cooling so that for most of the gas the temperature is an increasing function of time. By $z \approx 1$ a significant fraction of the final stellar mass is in place and the spectral energy distribution resembles those of observed massive red galaxies. The galaxies have grown from $z=1 \to 0$ on average by 25% in mass and in size by gas poor (dry) stellar mergers. By the present day, the simulated galaxies are old ($\approx 10 {\rm Gyrs}$), kinematically hot stellar systems surrounded by hot gaseous haloes. Stars dominate the mass of the galaxies up to $\approx 4$ effective radii ($\approx 10$ kpc). Kinematic and most photometric properties are in good agreement with those of observed elliptical galaxies. The galaxy with a major merger develops a counter-rotating core. Our simulations show that realistic intermediate mass giant elliptical galaxies with plausible formation histories can be formed from \LCDM initial conditions even without requiring recent major mergers or feedback from supernovae or AGN.Comment: accepted for publication in Ap