Determining the amplitude of mass fluctuations in the universe

Xiaohui Fan, Neta A. Bahcall, Renyue Cen

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We present a method for determining the amplitude of mass fluctuations on 8 h-1 Mpc scale, σ8. The method utilizes the rate of evolution of the abundance of rich clusters of galaxies. Using the Press-Schechter approximation, we show that the cluster abundance evolution is a strong function of σ8: d log nldz ∝ -1/σ82; low-σ8 models evolve exponentially faster than high-σ8 models, for a given mass cluster. For example, the number density of Coma-like clusters decreases by a factor of ∼103 from z = 0 to z ≃ 0.5 for σ8 = 0.5 models, while the decrease is only a factor of ∼5 for σ8 ≃ 1. The strong exponential dependence on σ8 arises because clusters represent rarer density peaks in low-σ8 models. We show that the evolution rate at z ∝ 1 is insensitive to the density parameter Ω or to the exact shape of the power spectrum. Cluster evolution therefore provides a powerful constraint on σ8. Using available cluster data to z ∼ 0.8, we find σ8 = 0.83 ± 0.15. This amplitude implies a bias parameter b ∼ σ8-1 = 1.2 ± 0.2, i.e., a nearly unbiased universe with mass approximately tracing light on large scales. When combined with the present-day cluster abundance normalization, σ8Ω0.5 ≃ 0.5, the cosmological density parameter can be determined: Ω ≃ 0.3 ± 0.1.

Original languageEnglish (US)
Pages (from-to)L123-L126
JournalAstrophysical Journal
Issue number2 PART II
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmology: theory
  • Galaxies: clusters: general
  • Galaxies: evolution
  • Galaxies: formation
  • Large-scale structure of universe


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