Testing a proposed planarity tool for studying satellite systems: The alleged consistency of Milky Way satellite galaxy planes with ΛcDM

Context. The existence of planes of satellite galaxies has been identified as a long-standing challenge to ΛCDM cosmology because satellite systems in cosmological simulations that are as extremely flattened and as strongly kinematically correlated as the observed structures are rare. Aims. We investigate a recently proposed new metric for measuring the overall degree of planarity of a satellite system that was used to claim consistency between the Milky Way satellite plane and ΛCDM. Methods. We studied the behavior of the planarity metric under several features of anisotropy that are present in ΛCDM satellite systems but are not related to satellite planes. Specifically, we considered the impact of oblate or prolate distributions, the number of satellites, the clustering of satellites, and radial and asymmetric distributions (lopsidedness). We also investigated whether the metric is independent of the orientation of the studied satellite system. Results. We find that all of these features of anisotropy lead to the metric to infer an increased degree of planarity, even though none of them has any direct relation to satellite planes. The metric is also highly sensitive to the orientation of the studied system (or chosen coordinate system): There is almost no correlation between the reported degrees of planarity of the metric for identical random systems rotated by 90. Conclusions. Our results demonstrate that the new proposed metric is not suited for measuring the overall planarity in satellite systems. Consequently, no consistency of the observed Milky Way satellite plane with ΛCDM can be inferred using this metric.