We are not the 99 percent: quantifying asphericity in the distribution
  of Local Group satellites
  We use simulations to build an analytic probability distribution for the
asphericity in the satellite distribution around Local Group (LG) type galaxies
in the Lambda Cold Dark Matter (LCDM) paradigm. We use this distribution to
estimate the atypicality of the satellite distributions in the LG even when the
underlying simulations do not have enough systems fully resembling the LG in
terms of its typical masses, separation and kinematics. We demonstrate the
method using three different simulations (Illustris-1, Illustris-1-Dark and
ELVIS) and a number of satellites ranging from 11 to 15. Detailed results
differ greatly among the simulations suggesting a strong influence of the
typical DM halo mass, the number of satellites and the simulated baryonic
effects. However, there are three common trends. First, at most $2\%$ of the
pairs are expected to have satellite distributions with the same asphericity as
the LG; second, at most $80\%$ of the pairs have a halo with a satellite
distribution as aspherical as in M31; and third, at most $4\%$ of the pairs
have a halo with satellite distribution as planar as in the MW. These
quantitative results place the LG at the level of a $3\sigma$ outlier in the
LCDM paradigm. We suggest that understanding the reasons for this atypicality
requires quantifying the asphericity probability distribution as a function of
halo mass and large scale environment. The approach presented here can
facilitate that kind of study and other comparisons between different numerical
setups and choices to study satellites around LG pairs in simulations.
