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

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

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

Constraining the Matter Power Spectrum Normalization using the SDSS/RASS and REFLEX Cluster surveys

We describe a new approach to constrain the amplitude of the power spectrum of matter perturbations in the Universe, parametrized by sigma_8 as a function of the matter density Omega_0. We compare the galaxy cluster X-ray luminosity function of the REFLEX survey with the theoretical mass function of Jenkins et al. (2001), using the mass-luminosity relationship obtained from weak lensing data for a sample of galaxy clusters identified in Sloan Digital Sky Survey commissioning data and confirmed through cross-correlation with the ROSAT all-sky survey. We find sigma_8 = 0.38 Omega_0^(-0.48+0.27 Omega_ 0), which is significantly different from most previous results derived from comparable calculations that used the X-ray temperature function. We discuss possible sources of systematic error that may cause such a discrepancy, and in the process uncover a possible inconsistency between the REFLEX luminosity function and the relation between cluster X-ray luminosity and mass obtained by Reiprich & Bohringer (2001).Comment: Accepted to ApJ Letters. 4 pages using emulateapj.st

Open Cold Dark Matter Models

Motivated by recent developments in inflationary cosmology indicating the possibility of obtaining genuinely open universes in some models, we compare the predictions of cold dark matter (CDM) models in open universes with a variety of observational information. The spectrum of the primordial curvature perturbation is taken to be scale invariant (spectral index $n=1$), corresponding to a flat inflationary potential. We allow arbitrary variation of the density parameter $\Omega_0$ and the Hubble parameter $h$, and take full account of the baryon content assuming standard nucleosynthesis. We normalize the power spectrum using the recent analysis of the two year {\it COBE} DMR data by G\'{o}rski et al. We then consider a variety of observations, namely the galaxy correlation function, bulk flows, the abundance of galaxy clusters and the abundance of damped Lyman alpha systems. For the last two of these, we provide a new treatment appropriate to open universes. We find that, if one allows an arbitrary $h$, then a good fit is available for any $\Omega_0$ greater than 0.35, though for $\Omega_0$ close to 1 the required $h$ is alarmingly low. Models with $\Omega_0 < 0.35$ seem unable to fit observations while keeping the universe over $10$ Gyr old; this limit is somewhat higher than that appearing in the literature thus far. If one assumes a value of $h > 0.6$, as favoured by recent measurements, concordance with the data is only possible for the narrow range $0.35 < \Omega_0 < 0.55$. We have also investigated $n \neq 1$; the extra freedom naturally widens the allowed parameter region. Assuming a range $0.9<n<1.1$, the allowed range of $\Omega_0$ assuming $h > 0.6$ is at most $0.30 < \Omega_0 < 0.60$.Comment: 12 pages, uuencoded package containing LaTeX file (using mn.sty) plus 4 postscript figures incorporated using epsf. Main change is an improved cluster abundance calculation. Overall conclusions almost unchanged though. Also two equations corrected, references updated etc. Final version, to appear MNRA

The power spectrum amplitude from clusters revisited: σ8 using simulations with preheating and cooling

The amplitude of density perturbations, for the currently-favoured CDM cosmology, is constrained using the observed properties of galaxy clusters. The catalogue used is that of Ikebe et al. The relation of cluster temperature to mass is obtained via N-body/hydrodynamical simulations including radiative cooling and pre-heating of cluster gas, which we have previously shown to reproduce well the observed temperature–mass relation in the innermost parts of clusters. We generate and compare mock catalogues via a Monte Carlo method, which allows us to constrain the relation between X-ray temperature and luminosity, including its scatter, simultaneously with cosmological parameters. We find a luminosity–temperature relation in good agreement with the results of Ikebe et al., while for the matter power spectrum normalization, we find σ8 = 0.78+0.30 −0.06 at 95 per cent confidence for 0 = 0.35. Scaling to the Wilkinson Microwave Anisotropy Probe central value of 0 = 0.27 would give a best-fitting value of σ8 ≃ 0.9