Another Look at the Abell Cluster Inertial Frame Bulk Flow
Author: Alister Graham
Abstract:
Recently, use has been made of the relationship between absolute magnitude, M,
and galaxy structure, for the first ranked galaxies in Abell clusters
out to 15,000 km/s, in a determination of a large bulk flow for this
volume (Lauer & Postman 1994). The technique uses
the logarithmic slope of the galaxies luminosity profile, at 10/h Kpc,
parameterized by 
, as an indicator of the galactic structure.
In examining this M- relation, it is shown to be related to
a magnitude-radius relation. Fitting a deVaucouleurs R{1/4} law profile to
the Abell Brightest Cluster Galaxy (BCG) sample of Lauer & Postman, the
M-log re 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 toward
l=203 deg , b=-29 deg (+/- 32 deg ) is obtained when using
the entire sample
of 119 BCG. This differs from the Local Group velocity inferred by the CMB
dipole, implying that the ACIF has a bulk flow of 738 +/- 158 km/s
toward l=330 deg , b=+45 deg (+/- 26 deg ). Both vectors
are consistent with those derived by Lauer & Postman.
The BCG studied are shown to be a very homogeneous set of objects, with their
radial-size corrected magnitudes having a scatter of only 0.26 magnitudes,
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 
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
revealed that use of the M-
relation is to be preferred over the
M-log re relation in this type of analysis of bulk flow motion, as it
results in considerably tighter flow constraints.