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 .