We examine the pattern of infall velocities induced by a rich cluster of galaxies. An infall model based on the Friedmann solution yields the exact implicit dependence of the peculiar velocity on the density enhancement {DELTA} and the mean cosmological mass density {OMEGA}_0_. The exact solution and an explicit expansion show that the infall velocity is an approximately separable function of {DELTA} and {OMEGA}_0_. We construct an analytic model for the distribution of galaxies around a cluster core in redshift space. The high-density caustics in redshift space-although smeared-appear as envelopes around rich clusters. Given the galaxy number density enhancement, the caustics yield limits on {OMEGA}_0_, independent of the value of the Hubble constant. Assuming that the galaxies trace the matter distribution, we compare model predictions with the data for four clusters. Low {OMEGA}_0_ (<~0.5) models provide a consistent explanation of the data. The caustics have a different, separable dependence on {OMEGA}_0_ and the density enhancement. In principle, with a few hundred redshift measurements in the infall region, the caustics provide a method of testing whether light traces mass. The data are consistent with the hypothesis that light traces mass in the infall region.
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Regős et al. (1989) studied this question.