The Abell Cluster Inertial Frame

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Abstract
A re-analysis of Lauer & Postman's (1994; LP) finding that the Abell cluster inertial frame (ACIF), defined by the 119 Abell clusters within 15,000 km/s, is moving at almost 700 km/s 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 obtain an exact expression for a cluster's peculiar velocity in terms of the residual magnitude about the mean relation between the metric luminosity of brightest cluster galaxies and the slope of their luminosity profiles. We compare this to the approximation used by LP. We develop a maximum likelihood procedure for recovering the Local Group motion from the scatter in this relation which yields an unbiased estimate for the motion with significantly smaller uncertainties than LP's method. We re-analyse LP's data and find that the Local Group is moving relative to the ACIF at 626 (+/-242) km/s towards l=216, b=-28 (+/-20). This implies that the ACIF is itself moving relative to the cosmic microwave background at 764 (+/-160) km/s towards l=341, b=49 (+/-20). This motion is consistent with that derived by LP but has a 10% larger amplitude and 20% smaller errors, making it even harder to reconcile with cosmological models
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