Testing isotropy in the Two Micron All-Sky redshift survey with information entropy

We use information entropy to test the isotropy in the nearby galaxy distribution mapped by the Two Micron All-Sky redshift survey (2MRS). We find that the galaxy distribution is highly anisotropic on small scales. The radial anisotropy gradually decreases with increasing length scales and the observed anisotropy is consistent with that expected for an isotropic Poisson distribution beyond a length scale of $90 \, h^{-1}\, {\rm Mpc}$. Using mock catalogues from N-body simulations, we find that the galaxy distribution in the 2MRS exhibits a degree of anisotropy compatible with that of the $\Lambda$CDM model after accounting for the clustering bias of the 2MRS galaxies. We also quantify the polar and azimuthal anisotropies and identify two directions $(l,b)=(150^{\circ}, -15^{\circ})$, $(l,b)=(310^{\circ},-15^{\circ})$ which are significantly anisotropic compared to the other directions in the sky. We suggest that their preferential orientations on the sky may indicate a possible alignment of the Local Group with two nearby large scale structures. Despite the differences in the degree of anisotropy on small scales, we find that the galaxy distributions in both the 2MRS and the $\Lambda$CDM model are isotropic on a scale of $90 \, h^{-1}\, {\rm Mpc}$.