0 A ug 1 99 9 What can we learn from the fluxes of the 1 . 2 Jy IRAS sample ?

We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the lumi-nosity function of the sources as a distance indicator. The method is characterized by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover the inclusion of additional observables, such for example the one carrying the Tully-Fisher information, is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model is herein tested using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. The results suggest that this model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales. 1. The method The application of the method is restricted to samples strictly complete up to a given magnitude limit m lim , i.e. the selection function in apparent magnitude is well described by a sharp cutoff ψ(m) = θ(m lim − m) with θ(x) the Heaveside function. The probability density of the sample may be written in this case as dP = 1 A h(µ, l, b) cos b dldbdµ f (M)dM θ(m lim − m) (1) where µ = m − M is the distance modulus, h(µ, l, b) the line-of-sight distribution function, f (M) the luminosity function and A is the normalisation factor warranting dP = 1. The milestone of the method consists in defining the random variable ζ as follows ζ = F (M) F (M lim) ; dζ = f (M) F (M lim) dM (2) where F (M) = M −∞ f (x)dx stands for the cumulative distribution function in M and M lim ≡ M lim (µ) is the maximum absolute magnitude for which a galaxy at distance µ would be visible in the sample (e.g. M lim (µ) = m lim − µ if the k-correction is neglected). By definition, the random variable ζ for a sampled galaxy belongs to the interval [0, 1]. The probability density of Eq. (1) reduces to dP = 1 A h(µ, l, b) F (M lim (µ)) cos b dldbdµ × θ(ζ) θ(1 − ζ) dζ (3)