Constraints on Primordial Nongaussiantiy from the High-Redshift Cluster MS1054--03

Abstract

The implications of the massive, X-ray selected cluster of galaxies MS1054--03 at $z=0.83$ are discussed in light of the hypothesis that the primordial density fluctuations may be nongaussian. We generalize the Press-Schechter (PS) formalism to the nongaussian case, and calculate the likelihood that a cluster as massive as MS1054 would appear in the EMSS. The probability of finding an MS1054-like cluster depends only on $\omegam$ and the extent of primordial nongaussianity. We quantify the latter by adopting a specific functional form for the PDF, denoted $\psi_\lambda,$ which tends to Gaussianity for $\lambda\gg 1,$ and show how $\lambda$ is related to the more familiar statistic $T,$ the probability of $\ge 3\sigma$ fluctuations for a given PDF relative to a Gaussian. We find that Gaussian initial density fluctuations are consistent with the data on MS1054 only if $\omegam\simlt 0.2.$ For $\omegam\ge 0.25$ a significant degree of nongaussianity is required, unless the mass of MS1054 has been substantially overestimated by X-ray and weak lensing data. The required amount of nongaussianity is a rapidly increasing function of $\omegam$ for $0.25 \le \omegam \le 0.45,$ with $\lambda \le 1$ ($T \simgt 7$) at the upper end of this range. For a fiducial $\omegam=0.3,$ $\omegal=0.7$ universe, favored by several lines of evidence we obtain an upper limit $\lambda \le 10,$ corresponding to a $T\ge 3.$ This finding is consistent with the conclusions of Koyama, Soda, & Taruya (1999), who applied the generalized PS formalism to low ($z\simlt 0.1$) and intermediate ($z\simlt 0.6$) redshift cluster data sets.