Another look at the Abell cluster inertial frame bulk flow

Recently, use has been made of the relationship between absolute magnitude and galaxy structure for the first-ranked galaxies in Abell clusters out to 15,000 km s(-1), in a determination of a large bulk how for this volume (see the recent work of Lauer & Postman). The technique uses the logarithmic slope of the galaxy luminosity profile, at 10 h(-1) kpc, parameterized by alpha, as an indicator of the galactic structure. In examining this M-alpha relation, it is shown to be similar to a magnitude-radius relation. Fitting a de Vaucouleurs R(1/4) law profile to the Abell brightest cluster galaxy (BCG) sample of Lauer & Postman, the M-log r(e) relationship is used to test for Local Group motion with respect to the Abell cluster inertial reference frame (ACIF), defined by the BCG. A motion of 459 +/- 371 km s(-1) toward l = 203 degrees, b = -29 degrees (+/-32 degrees) is obtained when using the entire sample of 119 BCGs. This differs from the Local Group velocity inferred by the cosmic microwave background dipole, implying that the ACIF has a bulk flow of 738 +/- 158 km s(-1) toward l = 330 degrees, b = +45 degrees (+/-26 degrees). Both vectors are consistent with those derived by Lauer & Postman. The BCGs studied are shown to be a very homogeneous set of objects, with their radial size-corrected magnitudes having a scatter of only 0.26 mag, making them a powerful tool in measuring galaxy distances and peculiar velocities. Using accurate CCD photometry, the galaxy light profiles are seen to be well fitted by an R(1/4) law. The slope of the mu(e)-log r(e) relation, for the BCG, is found to have a value of 2.87. Furthermore, there is negligible evidence for curvature in this bright portion of the fundamental plane. It is shown that use of the M-alpha relation is preferred over the M-log r(e) relation in this type of analysis of bulk flow motion, as it results in considerably smaller error bars.