The mass of the Local Group ( LG ) is a crucial parameter for galaxy formation theories .
However , its observational determination is challenging - its mass budget is dominated by dark matter which can not be directly observed .
To meet this end the posterior distributions of the LG and its massive constituents have been constructed by means of constrained and random cosmological simulations .
Two priors are assumed - the \Lambda CDM model that is used to set up the simulations and a LG model , which encodes the observational knowledge of the LG and is used to select LG-like objects from the simulations .
The constrained simulations are designed to reproduce the local cosmography as it is imprinted onto the Cosmicflows-2 database of velocities .
Several prescriptions are used to define the LG model , focusing in particular on different recent estimates of the tangential velocity of M31 .
It is found that ( a ) different v _ { tan } choices affect the peak mass values up to a factor of 2 , and change mass ratios of M _ { M 31 } to M _ { MW } by up to 20 % ; ( b ) constrained simulations yield more sharply peaked posterior distributions compared with the random ones ; ( c ) LG mass estimates are found to be smaller than those found using the timing argument ; ( d ) preferred MW masses lie in the range of ( 0.6 - 0.8 ) \times 10 ^ { 12 } { { M _ { \odot } } } whereas ( e ) M _ { M 31 } is found to vary between ( 1.0 - 2.0 ) \times 10 ^ { 12 } { { M _ { \odot } } } , with a strong dependence on the v _ { tan } values used .