Power Spectrum Shape from Peculiar Velocity Data

We constrain the velocity power spectrum shape parameter $\Gamma$ in linear theory using the nine bulk-flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for $\Gamma$ was found after marginalizing over the power spectrum amplitude $\sigma_8\Omega_m^{0.6}$ using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise $\sigma_*$ was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint $\Gamma=0.13^{+0.09}_{-0.05}$. This value is lower than, but consistent with, values obtained using redshift surveys and CMB data.