The Cluster Abundance in Flat and Open Cosmologies

We use the galaxy cluster X-ray temperature distribution function to constrain the amplitude of the power spectrum of density inhomogeneities on the scale corresponding to clusters. We carry out the analysis for critical density universes, for low density universes with a cosmological constant included to restore spatial flatness and for genuinely open universes. That clusters with the same present temperature but different formation times have different virial masses is included. We model cluster mergers using two completely different approaches, and show that the final results from each are extremely similar. We give careful consideration to the uncertainties involved, carrying out a Monte Carlo analysis to determine the cumulative errors. For critical density our result agrees with previous papers, but we believe the result carries a larger uncertainty. For low density universes, either flat or open, the required amplitude of the power spectrum increases as the density is decreased. If all the dark matter is taken to be cold, then the cluster abundance constraint remains compatible with both galaxy correlation data and the {\it COBE} measurement of microwave background anisotropies for any reasonable density.Comment: Uuencoded package containing LaTeX file (uses mn.sty) plus 7 postscript figures incorporated using epsf. Total length 10 pages. Final version, to appear MNRAS. COBE comparison changed to 4yr data. No change to results or conclusion

Cold dark matter models with high baryon content

Recent results have suggested that the density of baryons in the Universe, OmegaB, is much more uncertain than previously thought, and may be significantly higher. We demonstrate that a higher OmegaB increases the viability of critical-density cold dark matter (CDM) models. High baryon fraction offers the twin benefits of boosting the first peak in the microwave anisotropy power spectrum and of suppressing short-scale power in the matter power spectrum. These enable viable CDM models to have a larger Hubble constant than otherwise possible. We carry out a general exploration of high OmegaB CDM models, varying the Hubble constant h and the spectral index n. We confront a variety of observational constraints and discuss specific predictions. Although some observational evidence may favour baryon fractions as high as 20 per cent, we find that values around 10 to 15 per cent provide a reasonable fit to a wide range of data. We suggest that models with OmegaB in this range, with h about 0.5 and n about 0.8, are currently the best critical-density CDM models.Comment: 14 pages, LaTeX, with 9 included figures, to appear in MNRAS. Revised version includes updated references, some changes to section 4. Conclusions unchange

Pursuing Parameters for Critical Density Dark Matter Models

We present an extensive comparison of models of structure formation with observations, based on linear and quasi-linear theory. We assume a critical matter density, and study both cold dark matter models and cold plus hot dark matter models. We explore a wide range of parameters, by varying the fraction of hot dark matter $\Omega_{\nu}$, the Hubble parameter $h$ and the spectral index of density perturbations $n$, and allowing for the possibility of gravitational waves from inflation influencing large-angle microwave background anisotropies. New calculations are made of the transfer functions describing the linear power spectrum, with special emphasis on improving the accuracy on short scales where there are strong constraints. For assessing early object formation, the transfer functions are explicitly evaluated at the appropriate redshift. The observations considered are the four-year {\it COBE} observations of microwave background anisotropies, peculiar velocity flows, the galaxy correlation function, and the abundances of galaxy clusters, quasars and damped Lyman alpha systems. Each observation is interpreted in terms of the power spectrum filtered by a top-hat window function. We find that there remains a viable region of parameter space for critical-density models when all the dark matter is cold, though $h$ must be less than 0.5 before any fit is found and $n$ significantly below unity is preferred. Once a hot dark matter component is invoked, a wide parameter space is acceptable, including $n\simeq 1$. The allowed region is characterized by \Omega_\nu \la 0.35 and 0.60 \la n \la 1.25, at 95 per cent confidence on at least one piece of data. There is no useful lower bound on $h$, and for curious combinations of the other parameters it is possible to fit the data with $h$ as high as 0.65.Comment: 19 pages LaTeX file (uses mn.sty). Figures *not* included due to length. We strongly recommend obtaining the full paper, either by WWW at http://star-www.maps.susx.ac.uk/papers/lsstru_papers.html (UK) or http://www.bartol.udel.edu/~bob/papers (US), or by e-mailing ARL. Final version, to appear MNRAS. Main revision is update to four-year COBE data. Miscellaneous other changes and reference updates. No significant changes to principal conclusion

Apparent and actual galaxy cluster temperatures

The redshift evolution of the galaxy cluster temperature function is a powerful probe of cosmology. However, its determination requires the measurement of redshifts for all clusters in a catalogue, which is likely to prove challenging for large catalogues expected from XMM--Newton, which may contain of order 2000 clusters with measurable temperatures distributed around the sky. In this paper we study the apparent cluster temperature, which can be obtained without cluster redshifts. We show that the apparent temperature function itself is of limited use in constraining cosmology, and so concentrate our focus on studying how apparent temperatures can be combined with other X-ray information to constrain the redshift. We also briefly study the circumstances in which non-thermal spectral features can give redshift information.Comment: 7 pages LaTeX file with 13 figures incorporated (uses mn.sty and epsf). Minor changes to match MNRAS accepted versio

Cosmological Implications of the Fundamental Relations of X-ray Clusters

Based on the two-parameter family nature of X-ray clusters of galaxies obtained in a separate paper, we discuss the formation history of clusters and cosmological parameters of the universe. Utilizing the spherical collapse model of cluster formation, and assuming that the cluster X-ray core radius is proportional to the virial radius at the time of the cluster collapse, the observed relations among the density, radius, and temperature of clusters imply that cluster formation occurs in a wide range of redshift. The observed relations favor the low-density universe. Moreover, we find that the model of $n\sim -1$ is preferable.Comment: 7 pages, 4 figures. To be published in ApJ Letter