Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk
  Flow, Shear and Octupole Moments
  The low order moments, such as the bulk flow and shear, of the large scale
peculiar velocity field are sensitive probes of the matter density fluctuations
on very large scales. In practice, however, peculiar velocity surveys are
usually sparse and noisy, which can lead to the aliasing of small scale power
into what is meant to be a probe of the largest scales. Previously, we
developed an optimal ``minimum variance'' (MV) weighting scheme, designed to
overcome this problem by minimizing the difference between the measured bulk
flow (BF) and that which would be measured by an ideal survey. Here we extend
this MV analysis to include the shear and octupole moments, which are designed
to have almost no correlations between them so that they are virtually
orthogonal. We apply this MV analysis to a compilation of all major peculiar
velocity surveys, consisting of 4536 measurements. Our estimate of the BF on
scales of ~ 100 Mpc/h has a magnitude of |v|= 416 +/- 78 km/s towards Galactic
l = 282 degree +/- 11 degree and b = 6 degree +/- 6 degree. This result is in
disagreement with LCDM with WMAP5 cosmological parameters at a high confidence
level, but is in good agreement with our previous MV result without an
orthogonality constraint, showing that the shear and octupole moments did not
contaminate the previous BF measurement. The shear and octupole moments are
consistent with WMAP5 power spectrum, although the measurement noise is larger
for these moments than for the BF. The relatively low shear moments suggest
that the sources responsible for the BF are at large distances.
