A New Rarity Assessment of the "Disk of Satellites": The Milky Way System Is the Exception Rather Than the Rule in the ΛCDM Cosmology

The majority of satellite galaxies around the Milky Way (MW) show disk-like distributions (the disk of satellites; DoS), which is a small-scale problem of the lambda cold dark matter cosmology. The conventional definition of the MW-like DoS is a satellite system with a minor-to-major axis ratio (c/a) lower than the MW's c/a value of 0.181. Here, we question the validity of the c/a-based DoS rarity assessment and propose an alternative approach. How satellites are placed around a galaxy is dictated mainly by two factors: the distributions of the satellites' orbital poles and their distances from the host. Based on this premise, we construct the "satellite distribution generator" code and generate 105 spatially and kinematically analogous systems (SKASs) sharing these two factors. The SKAS can disclose the intrinsic, underlying c/a probability distribution function (PDF), from which a present-day c/a value is fortuitously determined. We find that the c/a PDF of the MW DoS defined by 11 classical satellites is quite broad (sigma c/a similar to 0.105), implying that a simple present-day c/a value, combined with its highly time-variable nature, cannot fully represent the degree of flatness. Moreover, based on the intrinsic c/a PDF, we reevaluate the rarity of the MW DoS by comparing it with Illustris TNG50-1 host-satellite systems and find that even with the new measure, the MW DoS remains rare (0.00%-3.40%). We show that the reason behind the rareness is that both orbital poles and distances of the 11 MW satellites are far more plane-friendly than those of simulated host-satellite systems, challenging the current structure and galaxy formation model.