An Inconsistency in standard Maximum Likelihood Estimation of Bulk Flows
  Maximum Likelihood estimation of the bulk flow from radial peculiar motions
of galaxies, generally assumes a constant velocity field inside the survey
volume. The assumption is inconsistent with the definition of the bulk flow as
the average of the peculiar velocity field over the relevant volume. This
follows from a straightforward mathematical relation between the bulk flow of a
sphere and the velocity potential on its surface. The inconsistency exists also
for ideal data with exact radial velocities and full spatial coverage.
  Based on the same relation we propose a simple modification to correct for
this inconsistency.
