Distributions of the probability density (PD) of the spherical standard distance Δsph of the six most closely aligned angular momentum vectors out of eight different, randomly drawn angular momentum vectors. In the first eight panels, the angular momentum vectors are drawn from the subhalo angular momentum vectors of the Aquarius simulations presented by L11 and from the Via Lactea simulations by D07 and D08. The last four panels show the distribution that results when drawing angular momentum vectors from the particles in calculations of galaxy interactions by P11. They each contain three distributions showing the time evolution of each model. The thin, light grey histogram illustrates the situation at 5 Gyr after the start of the calculation, the dark grey histogram at 7.5 Gyr and the thick black histogram at 10 Gyr. The case of an isotropic sample of angular momenta is included as the thin black line in all panels for comparison. The spherical standard distance for the six best-fitting orbital poles in the MW, 35.°4, is indicated by the vertical dashed lines. To fulfil the clustering criterion, a realization has to fall to the left of this line, this allowed region being highlighted by a shading. The distributions resulting from the cosmological simulations are nearly indistinguishable from the isotropic case. The vast majority of determined spherical standard distances is significantly larger than the observed one. This is completely different for the most examples of tidal material, which show very strongly concentrated distributions of angular momentum directions, in agreement with the distribution inferred from the MW satellite galaxies.
