Evolution of the Number Density of Clusters of Galaxies

Objective

We calculate the abundance of clusters of galaxies in several cosmological models and compare that to appropriate observations.

Approach

There is a standard semianalytic technique for calculating the abundance of "virialized" (i.e., near-equilibrium) objects as a function of their mass. However, observations almost never measure the total bound mass of the largest objects, because the edges are typically fuzzy, and "confusion errors" can dominate the observations near the edges. So, we develop a "mapping" from a measured quantity such as the velocity dispersion of galaxies along the line of sight, or the emission-weighted X-ray temperature, and use that along with the semianalytic technique to calculate expected abundances for each cosmological model.

Accomplishments

We have written a serial model normalizer based upon CMBFAST that adjusts the logarithmic slope and normalization of the primordial fluctuation spectrum in order to match two present-day observations: the COBE/DIRBE measurement of fluctuations in the microwave background and the ENACS measurement of the low-redshift number density of clusters of galaxies with line-of-sight velocity dispersions greater than 800 km/s.

We have run the model normalizer on four commonly discussed models: standard cold dark matter, a low-density model with a cosmological constant, a low-density model without a cosmological constant, and a critical-density model with 20 percent of its mass density in two species of massive neutrinos. The evolution of clusters of galaxies for models normalized in this manner indicates critical (or high) density if cluster masses are estimated from the virial theorem, and low density if they are estimated from X-ray temperatures.

We have also surveyed 96 more exotic models containing both massive neutrinos and a cosmological constant, using theHIVE to implement an embarrassingly parallel parameter search. These models are then compared to the measured fluctuation spectrum at low redshift, and microwave background fluctuations on scales of around one degree, to pick the most promising set of parameters. We find two moderately promising models, one with relatively high density (60 percent of critical) and one with relatively low density (40 percent), but nothing compelling. We believe the results from this study are the first scientific results to come from Goddard's Beowulf computers.

Significance

The evolution in number density of clusters of galaxies has been investigated several times in the past few years. However, the subtlety of mapping observables to total masses has been overlooked. The number density is an approximately exponential function of mass at masses appropriate to clusters, so factor of ~2 errors in the mass estimations, which are often considered "close enough," get greatly magnified by the exponential dependence. We have chosen to ignore observers' mass measurements entirely and compare direct observables.

The data at high redshift is very sparse, and the analysis contains very many simplifying assumptions (such as cluster sphericity). While our technique is an improvement over previous techniques, it is still not possible to conclusively distinguish between models based upon these semianalytic studies.

Status/Plans

We are currently adding line emission to the X-ray temperature analysis. Until now, we have assumed the X-rays are generated by a thermal plasma consisting of fully ionized hydrogen and helium. In particular, iron line emission is likely to be significant for few-keV emission.

A program of full N-body simulations of the best models is beginning now.