Low-energy ring particle accretion as the origin of Pan's equatorial ridge
Pan is a small Saturnian satellite embedded within the planet's A ring, characterized by a polygonal equatorial ridge whose formation mechanism remains debated. A proposed explanation is ring particle accretion, yet previous simplified models could not address the ridge's complex multi-lobed morphology without ad hoc assumptions, and the cause of its latitudinal spread remains unclear. This work studies the complex low-energy dynamics around Pan to verify whether the ring particle accretion paths are consistent with the observed ridge morphology. We model particle motion using a CR3BP with spherical harmonic perturbations. Accretion paths are analyzed via grid-search simulations of trajectories transiting the $L_1$ and $L_2$ necks, using backward propagation from Pan's surface to determine the impacting material's original orbital characteristics. Asymmetric accreting particle populations, with inner-ring particles located closer to Pan and contributing more significantly to the impact flux, produce impact distributions that correlate with the ridge structure, especially for the Saturn-facing hemisphere. The ridge latitudinal spread is recovered only when the out-of-plane position and velocity of the accreting particles are strictly limited, consistent with accretion from a thin disk such as Saturn's rings. Furthermore, analysis of the particles' impact conditions revises the previously estimated minimum accretion duration downward by an order of magnitude, to $10^4$ yr, while accreting material is shown to originate from ring particles that once populated the Encke Gap. By systematically sampling admissible low-energy trajectories near Pan, our grid-search approach resolves the complex accretion dynamics that previous simplified narrow-stream models do not capture, revealing that the ridge's main morphological features emerge naturally from the local low-energy dynamical environment.