The kinematics of the Local Group in a cosmological context

Recent observations constrained the tangential velocity of M31 with respect to the Milky Way (MW) to be v_tan<34.4 km/s and the radial velocity to be in the range v_rad=-109+/- 4.4 km/s (van der Marel et al. 2012). In this study we use a large volume high resolution N-body cosmological simulation (Bolshoi) together with three constrained simulations to statistically study this kinematics in the context of the LCDM. The comparison of the ensembles of simulated pairs with the observed LG at the 1-sigma level in the uncertainties has been done with respect to the radial and tangential velocities, the reduced orbital energy (e_tot), angular momentum (l_orb) and the dimensionless spin parameter, lambda. Our main results are: (i) the preferred radial and tangential velocities for pairs in LCDM are v_rad=-80+/-20 km/s, v_tan=50+/-10 km/s, (ii) pairs around that region are 3 to 13 times more common than pairs within the observational values, (iii) 15%to 24% of LG-like pairs in LCDM have energy and angular momentum consistent with observations while (iv) 9% to 13% of pairs in the same sample show similar values in the inferred dimensionless spin parameter. It follows that within current observational uncertainties the quasi-conserved quantities that characterize the orbit of the LG, i.e. e_tot, r_orb and lambda, do not challenge the standard LCDM model, but the model is in tension with regard to the actual values of the radial and tangential velocities. This might hint to a problem of the LCDM model to reproduce the observed LG.