Open AccessCluster abundance and large‐scale structure
Author(s) -
Proty Wu JiunHuei
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04807.x
Subject(s) - physics , cosmic microwave background , astrophysics , redshift , galaxy , spectral density , galaxy cluster , virial theorem , spectral index , cluster (spacecraft) , cosmic background radiation , amplitude , cosmic cancer database , planck , cosmology , virial mass , spectral line , statistics , astronomy , quantum mechanics , mathematics , anisotropy , computer science , programming language
We use the presently observed number density of X‐ray clusters and the linear mass power spectra to constrain the amplitude of matter density perturbations on the scale of 8 h −1 Mpc ( σ 8 ) and the redshift distortion parameter ( β ), in various background cosmologies. The best fit to the observed mass power spectra gives a spectral index and a shape parameter , with the theoretically expected degeneracy (all at the 95 per cent confidence level). These are consistent with the recent cosmic microwave background (CMB) results. We then calculate the cluster‐abundance‐normalized σ 8 , using different models of mass function: Press & Schechter (PS), Sheth & Tormen (ST) and Lee & Shandarin (LS) . The σ 8 based on non‐spherical models (ST and LS) are significantly lower, mainly because of the larger mass function on the cluster scales. In particular, we find , where In our analysis, we also derive the probability distribution function of cluster formation redshift using the Lacey–Cole formalism, but with modifications to incorporate non‐spherical collapse. The origins of the uncertainties in our σ 8 results are investigated in detail, with the main contributor being the normalization in the virial mass–temperature relation. From the Point Source Catalogue Redshift Survey (PSCz) power spectrum alone and using the above Γ′ as the prior, we also obtain (at 95 per cent confidence level) for the IRAS galaxies. By combining this with the σ 8 result, we obtain This is more consistent with the recent observations than the result based on the PS formalism, which is higher.