A statistical look on kinematic planes of satellite galaxies II: The physics behind their early formation in TNG50 MW/M31-like galaxies

Abstract: We investigate the physical origin of kinematically persistent planes (KPPs) of satellite galaxies in a sample of 190 Milky Way (MW)/M31-like host-satellite systems drawn from the TNG50 simulation. Building on the identification of 46 early KPPs in a previous work, we analyse their formation in the context of the high-redshift evolution of the local Cosmic Web by tracking the deformation of the so-called Lagrangian Volumes (LVs) surrounding each system. Using a reduced tensor-of-inertia analysis, we characterise the time evolution of the principal directions of collapse and relate them to the clustering of satellite orbital poles. We find that in approximately 67\% of KPPs satellite orbital poles align with the LV direction of strongest collapse, $\vec{e}<em>3$, while a smaller fraction ($\sim20\%$) align with the intermediate axis, $\vec{e}_2$; alignments with the major axis are rare. These alignments are statistically distinct from random expectations and reflect the confinement of satellites to planar configurations normal to the corresponding LV principal directions. We perform a kinematic analysis of satellite motion within KPPs, finding that vertical and radial motions relative to these KPPs decay early, leading to rotation-dominated, ``disky'' configurations. The characteristic timescales for satellites to settle onto a common orbital plane, for satellite orbital pole clustering, and for LV shape evolution are found to be quasi-coeval, peaking at a Universe age T$</em>{\rm uni}\sim4$~Gyr, during the fast mass assembly phase of the host halo. These results support a scenario in which early KPPs are fossil remnants of high-redshift, anisotropic mass collapse driven by the local Cosmic Web formation process in $Λ$CDM.