On the recovery of Local Group motion from galaxy redshift surveys

Abstract

There is a $\sim 150 km s^{-1}$ discrepancy between the measured motion of the Local Group of galaxies (LG) with respect to the CMB and the linear theory prediction based on the gravitational force field of the large scale structure in full-sky redshift surveys. We perform a variety of tests which show that the LG motion cannot be recovered to better than $150-200 km s^{-1}$ in amplitude and within a $\approx10^\circ$ in direction. The tests rely on catalogs of mock galaxies identified in the Millennium simulation using semi-analytic galaxy formation models. We compare these results to the $K_s=11.75$ Two-Mass Galaxy Redshift Survey, which provides the deepest, widest and most complete spatial distribution of galaxies available so far. In our analysis we use a new, concise relation for deriving the LG motion and bulk flow from the true distribution of galaxies in redshift space. Our results show that the main source of uncertainty is the small effective depth of surveys like the 2MRS that prevents a proper sampling of the large scale structure beyond $\sim100 h^{-1} Mpc$. Deeper redshift surveys are needed to reach the "convergence scale" of $\approx 250 h^{-1}Mpc $ in a $\Lambda$CDM universe. Deeper survey would also mitigate the impact of the "Kaiser rocket" which, in a survey like 2MRS, remains a significant source of uncertainty. Thanks to the quiet and moderate density environment of the LG, purely dynamical uncertainties of the linear predictions are subdominant at the level of $\sim 90 km s^{-1}$. Finally, we show that deviations from linear galaxy biasing and shot noise errors provide a minor contribution to the total error budget.