Sampling Effects on Cosmological Dipoles
We use numerical simulations to investigate the behaviour of the dipole moment of the spatial distribution of different kinds of mass tracers. We select density peaks of the simulated matter distribution with mean separations of 38 and 30 $h^{-1}$ Mpc to represent two samples of rich clusters of galaxies. We extract, from the same simulations, samples selected to mimic the full 3D galaxy distribution of IR galaxies, and the flux--limited IRAS and QDOT galaxy samples. We compare the dipole moments of these ``galaxy'' and ``cluster'' samples in order to assess the effects of sampling uncertainties and shot--noise on the relationship between the ``true'' underlying galaxy dipole and the dipoles obtained for clusters and for the flux--limited galaxy samples. The results of this analysis demonstrate that the dipoles of both the IRAS and QDOT--like catalogues should trace the full 3D dipole shape fairly accurately, with the loss however of about 15--20$\%$ of the total 3D dipole amplitude. Furthermore, using a simple argument based on linear perturbation theory, on the linear biasing assumption and on the amplitude of the cluster dipole relative to that of galaxies, we can estimate their relative biasing factors quite accurately and in agreement with results obtained by other methods.