Bulk flow and shear moments of the SFI++ survey

We find the nine bulk flow and shear moments from the SFI++ survey, as well as for subsamples of group and field galaxies. We constrain the velocity power spectrum shape parameter Γ in linear theory using these moments. A likelihood function for Γ was found after marginalizing over the power spectrum amplitude  σ₈Ω^0.6_m  using constraints obtained from comparisons between redshift surveys and peculiar velocity data. We have estimated the velocity noise  σ_*  from the data since without it our results may be biased. We also performed a statistical analysis of the difference between the field and group catalogues and found that the results from each reflect the same underlying large-scale flows. We found that we can constrain the power spectrum shape parameter to be  Γ= 0.15^+0.18_−0.08  for the groups catalogue and  Γ= 0.09^+0.04_−0.04  for the field galaxy catalogue in fair agreement with the value from Wilkinson Microwave Anisotropy Probe .