New tools for studying planarity in galaxy satellite systems: Milky Way satellite
planes are consistent with $\Lambda$CDM
We combine positions and velocities of Milky Way (MW) satellites from the Gaia EDR3,
with new tools for describing planarity and the \textsc{NewHorizon} cosmological
simulation to (1) measure planarity in MW satellites and the extent to which planes
are kinematically supported and (2) explore the consequences of satellite planes
for the fidelity of the $\rm{\Lambda CDM}$ paradigm. We first show that past
approaches have some challenges, such as the requirement of an unreasonably wide
opening angle and the disproportionate fixing effect of position vectors on angular
momenta because they have much lower measurement errors than the velocities. We then
use our new tools to analyse planar structures in 3D space and to better describe
planarity in the MW. We show that the position vectors of the MW exhibit planarity
but the velocity vectors do not and that kinematic coherence cannot, therefore, be
confirmed from current observational data. We apply our tools to \textsc{NewHorizon},
in order to compare satellite planarity around mock galaxies in a $\rm{\Lambda CDM}$-based
model to those calculated from MW satellite data. We show that kinematically supported
planes are very common in the simulation and the planarity of MW satellites is,
therefore, not in tension with the standard $\rm{\Lambda CDM}$ paradigm.