The Abell Cluster Inertial Frame

In this paper we present a reanalysis of Fauer & Postman's (1994) finding that the Abell cluster inertial frame (ACIF), defined by the 119 Abell clusters within 15,000 km s^-1^, is moving at almost 700 km s^-1^ with respect to the cosmic microwave background. Such a motion is inconsistent with most cosmological models at a confidence level of 95% or higher. We examine the use of the relation between the metric luminosity of brightest cluster galaxies and the slope of their luminosity profiles as an estimator of distances and peculiar velocities. We obtain an exact expression for a cluster's peculiar velocity in terms of the residual magnitude about this relation and compare this to the approximation used by Lauer and Postman. We critically examine the method used by Lauer and Postman to recover the local Group motion from the scatter in this relation, and develop improved procedures including a maximum likelihood method that provides a direct estimate of the uncertainty in the derived motion. Simulations show this method yields an unbiased estimate for the local Group motion with significantly smaller uncertainties than Lauer and Postman's original method. We reanalyze Lauer and Postman's data to obtain an improved estimate for the motion of the local Group. We find that the local Group is moving relative to the ACIF at 626+/-242 km s^-1^ toward l = 216^deg^, b= -28^deg^ (+/-20^deg^). This implies that the ACIF is itself moving relative to the cosmic microwave background at 764+/-160 km s^-1^ toward l = 341^deg^, b= 49^deg^ (+/-20^deg^). This motion is consistent with that derived by Lauer and Postman but has a 10% larger amplitude and 20% smaller uncertainties, making it even harder to reconcile with cosmological models