2024ApJ...976..253S

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 (σ_c/a ∼ 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.