  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.
