New Light-Travel Time Models and Orbital Stability Study of the Proposed Planetary System HU Aquarii

TL;DR

This paper proposes a new orbital model for the proposed planets around HU Aquarii, emphasizing the importance of orbital stability and presenting a candidate model that remains stable over a million years.

Contribution

The study introduces a novel light-travel time model based on Monte Carlo simulations and identifies stable orbital configurations for the proposed planets.

Findings

Best-fitting model with high eccentricities is unstable.

Low-eccentricity orbits are more stable over long timescales.

Numerical integrations confirm stability over one million years.

Abstract

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 Levenberg-Marquardt minimisation algorithm on the observed eclipse egress times. Our best-fitting model with $\chi_{r}^2=1.43$ 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 semi-major axes for different $\chi_{r}^2$ 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.