Is the 2MASS clustering dipole convergent

There is a long-standing controversy about the convergence of the dipole moment of the galaxy angular distribution (the so-called clustering dipole). We study the growth of the clustering dipole of galaxies as a function of the limiting flux of the sample from the Two Micron All Sky Survey (2MASS). Contrary to some earlier claims, we find that the dipole does not converge before the completeness limit of the 2MASS Extended Source Catalog, i.e. up to 13.5 mag in the near-infrared K_s band (equivalent to an effective distance of 300 Mpc/h). We compare the observed growth of the dipole with the theoretically expected, conditional one (i.e., given the velocity of the Local Group relative to the CMB), for the LambdaCDM power spectrum and cosmological parameters constrained by WMAP. The observed growth turns out to be within 1-sigma confidence level of its theoretical counterpart once the proper observational window of the 2MASS flux-limited catalog is included. For a contrast, if the adopted window is a top-hat, then the predicted dipole grows significantly faster and converges to its final value for a distance of about 300 Mpc/h. By comparing the observational windows, we show that for a given flux limit and a corresponding distance limit, the 2MASS flux-weighted window passes less large-scale signal than the top-hat one. We conclude that the growth of the 2MASS dipole for effective distances greater than 200 Mpc/h is only apparent. On the other hand, for a distance of 80 Mpc/h (mean depth of the 2MASS Redshift Survey) and the LambdaCDM power spectrum, the true dipole is expected to reach only ~80% of its final value. Eventually, since for the window function of 2MASS the predicted growth is consistent with the observed one, we can compare the two to evaluate beta = (Omega_m)^0.55 / b. The result is beta = 0.38+-0.04, which leads to an estimate of the density parameter Omega_m = 0.20+-0.08.