The shapes of galaxy groups: Footballs or frisbees?

We derive probability density functions for the projected axial ratios of the real and mock 2PIGG galaxy groups, and use this data to investigate the intrinsic three-dimensional shape of the dark matter ellipsoids that they trace. As well as analyzing the raw data for groups of varying multiplicities, a convolution-corrected form of the data is also considered which weights the probability density function according to the results of multiple Monte Carlo realizations of discrete samples from the input spatial distributions. The important effect observed is that the best-fit distribution for all the raw data is a prolate ellipsoid with a Gaussian distribution of axial ratios with (beta) over bar = 0.36 and sigma = 0.14, while for the convolved data the best-fit solution is that of an oblate ellipsoid, (beta) over bar = 0.22 and sigma = 0.1. Previously, only prolate distributions were thought compatible with the data, this being interpreted as evidence of filamentary collapse at nodes. We also find that even after allowing for sampling effects, the corrected data are better fit using separate multiplicity bins that display a trend toward more spherical halos in higher multiplicity groups. Finally, we find that all results in the real data are in good agreement with the mock data from Lambda CDM simulations, with K-S tests showing that all comparative data have been drawn from the same distributions within the 1 sigma confidence limits.