R-layer Mode Theory (RLMT) XLI‑Q: R-layer Potential Model for Prograde–Retrograde Bifurcation of Accreted Stars

This volume XLI‑Q develops a minimal, analytically tractable R-layer potential model that explains the observed prograde–retrograde bifurcation of the accreted stellar group “Loki.” A single infalling dwarf galaxy, interacting with an early-time R-layer torsional mode, naturally produces both prograde and retrograde debris without requiring fine-tuned scattering or multiple mergers. The model introduces a sign-dependent coupling between the R-layer mode and stellar angular momentum, derives the resulting equations of motion, and implements a numerical scheme that reproduces the observed Lz distribution and the narrow E–Lz band of the Loki sample.