Quantifying the Bull’s‐Eye Effect

We have used N-body simulations to develop two independent methods toquantify redshift distortions known as the Bull's Eye effect (large scaleinfall plus small scale virial motion). This effect depends upon the massdensity, $\Omega_0$, so measuring it can in principle give an estimate of thisimportant cosmological parameter. We are able to measure the effect anddistinguish between its strength for high and low values of $\Omega_0$. Unlikeother techniques which utilize redshift distortions, one of our methods isrelatively insensitive to bias. In one approach, we use path lengths betweencontour crossings of the density field. The other is based upon percolation. Wehave found both methods to be successful in quantifying the effect anddistinguishing between values of $\Omega_0$. However, only the path lengthsmethod exhibits low sensitivity to bias.Comment: 21 pages, 5 figures, 3 tables; Replaced version - minor corrections, replaced figure 2; To appear in ApJ, Jan. 20, 200