Gaussianization of peculiar velocities and bulk flow measurement

Abstract: The line-of-sight peculiar velocities are good indicators of the gravitational fluctuation of the density field. Techniques have been developed to extract cosmological information from the peculiar velocities in order to test the cosmological models. These techniques include measuring cosmic flow, measuring two-point correlation and power spectrum of the peculiar velocity fields, reconstructing the density field using peculiar velocities. However, some measurements from these techniques are biased due to the non-Gaussianity of the estimated peculiar velocities. Therefore, we use the 2MTF survey to explore a power transform that can Gaussianize the estimated peculiar velocities. We find a tight linear relation between the transformation parameters and the measurement errors of log-distance ratio. To show an example for the implement of the Gaussianized peculiar velocities in cosmology, we develop a bulk flow estimator and estimate bulk flow from the Gaussianized peculiar velocities. We use 2MTF mocks to test the algorithm, we find the algorithm yields unbiased measurements. We also find this technique gives smaller measurement errors compared to other techniques. Under the Galactic coordinates, at the depth of $30$ $h^{-1}$ Mpc, we measure a bulk flow of $332\pm27$ km s$^{-1}$ in the direction $(l,b)=(293\pm 5^{\circ}, 13\pm 4^{\circ})$. The measurement is consistent with the $\Lambda$CDM prediction.