On the recovery of Local Group motion from galaxy redshift surveys
  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.
