Constraints on the fluctuation amplitude and density parameter from X-ray cluster number counts

Tetsu Kitayama; Yasushi Suto

doi:10.1086/304915

paper

Constraints on the fluctuation amplitude and density parameter from X-ray cluster number counts

arXiv:astro-ph/9702017 · doi:10.1086/304915

Abstract

We find that the observed log N - log S relation of X-ray clusters can be reproduced remarkably well with a certain range of values for the fluctuation amplitude $σ_{8}$ and the cosmological density parameter $Ω_{0}$ in cold dark matter (CDM) universes. The $1 σ$ confidence limits on $σ_{8}$ in the CDM models with $n = 1$ and $h = 0.7$ are expressed as $(0.54 \pm 0.02) Ω_{0}^{- 0.35 - 0.82 Ω_{0} + 0.55 Ω_{0}^{2}}$ ( $λ_{0} = 1 - Ω_{0}$ ) and $(0.54 \pm 0.02) Ω_{0}^{- 0.28 - 0.91 Ω_{0} + 0.68 Ω_{0}^{2}}$ ( $λ_{0} = 0$ ), where $n$ is the primordial spectral index, and $h$ and $λ_{0}$ are the dimensionless Hubble and cosmological constants. The errors quoted above indicate the statistical ones from the observed log N - log S only, and the systematic uncertainty from our theoretical modelling of X-ray flux in the best-fit value of $σ_{8}$ is about 15%. In the case of $n = 1$ , we find that the CDM models with $(Ω_{0}, λ_{0}, h, σ_{8}) ≃ (0.3, 0.7, 0.7, 1)$ and $(0.45, 0, 0.7, 0.8)$ simultaneously account for the cluster log N - log $S$ , X-ray temperature functions, and the normalization from the COBE 4 year data. The derived values assume the observations are without systematic errors, and we discuss in details other theoretical uncertainties which may change the limits on $Ω_{0}$ and $σ_{8}$ from the log N - log S relation. We have shown the power of this new approach which will become a strong tool as the observations attain more precision.

15 pages. Substantial revision. Accepted for publication in Astrophysical Journal, Part 1

Constraints on the fluctuation amplitude and density parameter from X-ray cluster number counts

Abstract

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