Constraints on primordial non-Gaussianity from the high-redshift cluster MS 1054-03

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 (Ohm(M) + Ohm(A) = 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 Ohm(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 Psi(lambda), which tends to Gaussianity for lambda > 1 but is significantly non-Gaussian for lambda less than or similar to 10, and show how lambda is related to the more familiar statistic T, the probability of greater than or equal to 3 a 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 Q(M) less than or similar to 0.2. For Ohm(M) greater than or equal to 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 Ohm(M) for 0.25 less than or equal to Ohm(M) less than or equal to 0.45, with lambda less than or equal to 1 (T less than or equal to 7) at the upper end of this range. For a fiducial Ohm(M) = 0.3, Ohm(A) = 0.7 universe, favored by several lines of evidence we obtain an upper limit lambda less than or equal to 10, corresponding to a T greater than or equal to 3. This finding is consistent with the conclusions of Koyama, Soda, & Taruya, who applied the generalized PS formalism to low (z less than or similar to 0.1) and intermediate (z less than or similar to 0.6) redshift cluster data sets.