A robust method for fitting peculiar velocity field models

We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator. The method is characterised by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover, selection effects in redshift are allowed. Furthermore the inclusion of additional observables correlated with the absolute magnitude – such as for example rotation velocity information as described by the Tully-Fisher relation – is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model characterised by the density parameter β is tested on two samples. The application of our method to the Tully-Fisher MarkIII MAT sample leads to a value of β = 0.6± 0.125, fully consistent with the results obtained previously by the VELMOD and ITF methods on similar datasets. Unlike these methods however, we make a very conservative use of the Tully-Fisher information. Specifically, we require to assume neither the linearity of the Tully-Fisher relation nor a gaussian distribution of its residuals. Moreover, the robustness of the method implies that no Malmquist corrections are required. A second application is carried out, using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. In this case the effective depth of the volume in which the velocity model is compared to the data is almost twice the effective depth of the MarkIII MAT sample. The results suggest that the predicted IRAS velocity model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales.