The Proposed Quadruple System SZ Herculis: Revised LITE Model and Orbital Stability Study

TL;DR

This study critically examines the proposed quadruple system around SZ Herculis, finding that the suggested orbital configuration is dynamically unstable and likely cannot exist, thus challenging previous interpretations of the observed timing variations.

Contribution

The paper provides a dynamical stability analysis of the proposed system, demonstrating its instability and proposing alternative explanations for the observed timing variations.

Findings

The proposed system exhibits short-term dynamical instability.

Monte Carlo analysis suggests a different, more stable orbital configuration.

The system as proposed cannot exist under Newtonian dynamics.

Abstract

In a recent study, Lee et al. presented new photometric follow-up timing observations of the semi-detached binary system SZ Herculis and proposed the existence of two hierarchical cirumbinary companions. Based on the light-travel time effect, the two low-mass M-dwarf companions are found to orbit the binary pair on moderate to high eccentric orbits. The derived periods of these two companions are close to a 2:1 mean-motion orbital resonance. We have studied the stability of the system using the osculating orbital elements as presented by Lee et al. Results indicate an orbit-crossing architecture exhibiting short-term dynamical instabilities leading to the escape of one of the proposed companions. We have examined the system's underlying model parameter-space by following a Monte Carlo approach and found an improved fit to the timing data. A study of the stability of our best-fitting orbits also indicates that the proposed system is generally unstable. If the observed anomalous timing variations of the binary period is due to additional circumbinary companions, then the resulting system should exhibit a long-term stable orbital configuration much different from the orbits suggested by Lee et al. We, therefore, suggest that based on Newtonian-dynamical considerations, the proposed quadruple system cannot exist. To uncover the true nature of the observed period variations of this system, we recommend future photometric follow-up observations that could further constrain eclipse-timing variations and/or refine light-travel time models.