New light-travel time models and orbital stability study of the proposed planetary system HU Aquarii

In this work we propose a new orbital architecture for the two proposed circumbinary planets around the polar eclipsing binary HU Aquarii. We base the new two-planet, light-travel time model on the result of a Monte Carlo simulation driving a least-squares LevenbergMarquardt minimization algorithm on the observed eclipse egress times. Our best-fitting model with resulted in high final eccentricities for the two companions leading to an unstable orbital configuration. From a large ensemble of initial guesses, we examined the distribution of final eccentricities and semimajor axes for different parameter intervals and encountered qualitatively a second population of best-fitting parameters. The main characteristic of this population is described by low-eccentric orbits favouring long-term orbital stability of the system. We present our best-fitting model candidate for the proposed two-planet system and demonstrate orbital stability over one million years using numerical integrations.