The Apsidal Alignment of the HD 82943 System

We perform numerical simulations to explore the dynamical evolution of the HD 82943 planetary system. By simulating diverse planetary configurations, we find two mechanisms to maintain the stability of the system: the 2:1 mean motion resonance between the planets can act as the first mechanism for all stable orbits. The second mechanism is the apsidal alignment and we find that the difference of the apsidal longitudes $\theta_{3}$ librates about $180^{\circ}$ in the simulations. We also use the analytical model to explain the numerical results for the system.