Dark matter halo and albedo effects on equilibrium points and non-linear stability zones

Abstract

This study investigates the non-linear dynamical behavior of small space objects (e.g. asteroids, spacecraft, satellites, comets etc.) under the frame of the restricted three-body problem (RTBP), influenced by a dark matter halo and albedo effect from an oblate secondary. The dark matter halo is characterized by an inner density slope parameter \(\gamma \in [0,\,3)\), which enables representation of both cored and cuspy halo structures. The incorporation of albedo force introduces additional non-gravitational perturbations that enrich the system’s utility. The equilibria configurations are analyzed and a linear stability test is performed up to third order resonance, consequently stability range is obtained. It is observed that both the dark matter halo and albedo significantly influence the positions of equilibrium points and modify the topology of their stability regions. Again, non-linear stability zone and Poincaré surface of section around a linearly stable equilibrium is estimated using long-term numerical integration based on the fourth order Runge-Kutta method. The obtained results indicate that the halo parameters (\(M_h\), \(\gamma \)) enhance stability domains, whereas radiation pressure, albedo, luminosity ratio and oblateness reduce them. Numerical simulations reveal that the non-linear stability zone is highly sensitive to the oblateness coefficient \(A_2\) and increments in the radiation pressure broadens the librational region, while greater halo concentration or geometric asymmetry constricts it. The study extends the classical RTBP to a more realistic astrophysical regime, providing new insights into the interplay of gravitational, radiative, and halo-induced perturbations in governing orbital stability within halo-dominated galactic systems.