Peculiar Hubble Flows in Our Local Universe

A formalism that simultaneously searches for the monopolar and dipolarpeculiar velocities is presented. The formalism is applied to (1) the Mark IIIcatalogue, (2) Lauer and Postman's Abell cluster catalogue, and (3) Riess etal.'s Type Ia supernova sample. The emphasis is drawn to the monopolar peculiarvelocities, i.e., peculiar Hubble flows, within these samples. The samples showinconsistent peculiar Hubble flows within a depth of $\sim 60h^{-1}$ Mpc.Beyond a depth of $\sim 80h^{-1}$ Mpc, the Hubble flows of all samples convergeto the global Hubble flow to better than 10% at the $2\sigma$ level. Theresults are compared with theoretical predictions. They at face value disfavormodels predicting smaller peculiar velocities such as the tilted Cold DarkMatter model. Limitations of the catalogues are discussed, so are ways toimprove the catalogues so that an accurate map of Hubble flows in our localuniverse can be drawn and be compared with theoretical predictions.Comment: 20 latex pages and 8 figures. Final versio