Cluster abundance and large scale structure

Abstract

We use the presently observed number density of large X-ray clusters and the linear mass power spectra to constrain ${\sigma }_8$ and the redshift distortion parameter $\beta$, in both OCDM and $\Lambda$CDM models. The best fit to the observed mass power spectra gives $n=0.84\pm 0.67$ and $\Gamma =0.27_{-0.16}^{+0.42}$, with the theoretically expected degeneracy ${\Gamma }^{\prime }=0.247\Gamma \exp (1.4n)=0.220_{-0.031}^{+0.036}$ (all at 95% confidence level). Based on this, we then calculate the cluster-abundance-normalized ${\sigma }_8$, using different models of mass function: Press & Schechter (1974), Sheth & Tormen (1999), and Lee & Shandarin (1999). The ${\sigma }_8$ based on the non-spherical-collapse models (ST & LS) are significantly lower, mainly due to the larger mass function within the scale range of our interest. In particular, we found ${\sigma }_{8(\mathrm{ST}+\mathrm{LS})}=0.477{\Omega }_{m0}^{\alpha }$, where $\alpha =-0.3-0.17{\Omega }_{m0}^{0.34}-0.13{\Omega }_{\Lambda 0}$. We also derive the probability distribution function of cluster formation redshift using the Lacey-Cole formalism (1993), but with modifications to incorporate non-spherical collapse. The uncertainties in our ${\sigma }_8$ are mainly contributed from the normalization in the virial mass-temperature relation. We also obtain for the IRAS galaxies ${\sigma }_{8(\mathrm{I})}=0.78\pm 0.06$ (at 95% confidence level), and found ${\beta }_{\mathrm{I}(\mathrm{ST}+\mathrm{LS})}=0.613{\Omega }_{m0}^{0.24-0.16({\Omega }_{m0}+{\Omega }_{\Lambda 0})}$. This is more consistent with the recent observations than the result based on the PS formalism.

11 pages, 8 figures MNRAS, in press (2001)

References in corpus (5)

• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• The PSCz Catalogue
• First Estimations of Cosmological Parameters From BOOMERANG
• Power spectrum normalization from the local abundance of rich clusters of galaxies
• Linear Redshift Distortions and Power in the PSCz Survey

Cited by in corpus (9)

• The Mass Function of an X-Ray Flux-Limited Sample of Galaxy Clusters
• Weak Lensing Results from the 75 Square Degree CTIO Survey
• The Cluster Mass Function from Early SDSS Data: Cosmological Implications
• Mass Function of Rich Galaxy Clusters and Its Constraint on sigma_8
• Formation times and masses of dark matter haloes
• The power spectrum amplitude from clusters revisited: σ_8 using simulations with preheating and cooling
• Extraction of cluster parameters with future Sunyaev-Zel'dovich observations
• S-Z Anisotropy & Cluster Counts: Consistent Selection of sigma_8 and the Temperature-Mass Relation
• CMB Comptonization in Clusters: Spectral and Angular Power from Evolving Polytropic Gas