## Towards the optimal window for the 2MASS dipole

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Chodorowski, Michal

Coiffard, Jean-Baptiste

Bilicki, Maciej

Colombi, Stephane

Ciecielag, Pawel

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A comparison of the 2MASS flux dipole to the 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 nonlinear 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 five. 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% 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. (ABRIDGED)

Comment: 14 pages, 3 figures. Significantly expanded version, with added sections on shot noise and likelihood for beta, as well as an appendix with a derivation of the distribution for the misalignment angle relaxing the small-angle assumption

Comment: 14 pages, 3 figures. Significantly expanded version, with added sections on shot noise and likelihood for beta, as well as an appendix with a derivation of the distribution for the misalignment angle relaxing the small-angle assumption

##### Keywords

Astrophysics