Towards the optimal window for the 2MASS dipole

A comparison of the Two Micron All Sky Survey (2MASS) flux dipole to the cosmic microwave background (CMB) dipole can serve as a method to constrain a combination of the cosmological parameter Omega(m) and the luminosity bias of the 2MASS survey. For this constraint to be as tight as possible, it is necessary to maximize the correlation between the two dipoles. This can be achieved by optimizing the survey window through which the flux dipole is measured. Here we explicitly construct such a window for the 2MASS survey. The optimization in essence reduces to excluding from the calculation of the flux dipole galaxies brighter than some limiting magnitude K-min of the near-infrared K-s band. This exclusion mitigates non-linear effects and shot noise from small scales, which decorrelate the 2MASS dipole from the CMB dipole. Under the assumption of negligible shot noise we find that the optimal value of K-min is about 5. Inclusion of shot noise shifts the optimal K-min to larger values. We present an analytical formula for shot noise for the 2MASS flux dipole, to be used in follow-up work with 2MASS data. The misalignment angle between the two dipoles is a sensitive measure of their correlation: the higher the correlation, the smaller the expectation value of the angle. A minimum of the misalignment is thus a sign of the optimal gravity window. We model analytically the distribution function for the misalignment angle and show that the misalignment estimated by Maller et al. is consistent with the assumed underlying model (though it is greater than the expectation value). We predict with about 90 per cent confidence that the misalignment will decrease if 2MASS galaxies brighter than K-min = 5 mag are excluded from the calculation of the flux dipole. This prediction has been indirectly confirmed by the results of Erdogdu et al. The measured misalignment constitutes thus an alternative way of finding the optimal value of K-min: the latter corresponds to a minimum of the former.