2000ApJ...530...80W

The implications of the massive, X-ray selected cluster of galaxies MS 1054-03 at z=0.83 are discussed in light of the hypothesis that the primordial density fluctuations may be non-Gaussian. We generalize the Press-Schechter (PS) formalism to the non-Gaussian case and calculate the likelihood that a cluster as massive as MS 1054 would have been found in the Einstein Medium Sensitvity Survey (EMSS). A flat universe (Ω_M+Ω_Λ=1) is assumed, and the mass fluctuation amplitude is normalized to the present-day cluster abundance. The probability of finding an MS 1054-like cluster then depends only on Ω_M and the extent of primordial non-Gaussianity. We quantify the latter by adopting a specific functional form for the probability distribution function (PDF), denoted ψ_λ, which tends to Gaussianity for λ{Gt}1 but is significantly non-Gaussian for λ≲10, and show how λ is related to the more familiar statistic T, the probability of ≥3 σ fluctuations for a given PDF relative to a Gaussian. Special attention is given to a careful calculation of the virial mass of MS 1054 from the available X-ray temperature, galaxy velocity, and weak-lensing data.

We find that Gaussian initial density fluctuations are consistent with the data on MS 1054 only if Ω_M≲0.2. For Ω_M≥0.25 a significant degree of non-Gaussianity is required, unless the mass of MS 1054 has been substantially overestimated by X-ray and weak-lensing data. The required amount of non-Gaussianity is a rapidly increasing function of Ω_M for 0.25≤Ω_M≤0.45, with λ≤1 (T≳7) at the upper end of this range. For a fiducial Ω_M=0.3,Ω_Λ=0.7 universe, favored by several lines of evidence we obtain an upper limit λ≤10, corresponding to a T≥3. This finding is consistent with the conclusions of Koyama, Soda, & Taruya, who applied the generalized PS formalism to low (z≲0.1) and intermediate (z≲0.6) redshift cluster data sets.