  In 2009, the discovery of two planets orbiting the evolved binary star system
HW Virginis was announced, based on systematic variations in the timing of
eclipses between the two stars. The planets invoked in that work were
significantly more massive than Jupiter, and moved on orbits that were mutually
crossing - an architecture which suggests that mutual encounters and strong
gravitational interactions are almost guaranteed. In this work, we perform a
highly detailed analysis of the proposed HW Vir planetary system. First, we
consider the dynamical stability of the system as proposed in the discovery
work. Through a mapping process involving 91,125 individual simulations, we
find that the system is so unstable that the planets proposed simply cannot
exist, due to mean lifetimes of less than a thousand years across the whole
parameter space. We then present a detailed re-analysis of the observational
data on HW Vir, deriving a new orbital solution that provides a very good fit
to the observational data. Our new analysis yields a system with planets more
widely spaced, and of lower mass, than that proposed in the discovery work, and
yields a significantly greater (and more realistic) estimate of the uncertainty
in the orbit of the outermost body. Despite this, a detailed dynamical analysis
of this new solution similarly reveals that it also requires the planets to
move on orbits that are simply not dynamically feasible. Our results imply that
some mechanism other than the influence of planetary companions must be the
principal cause of the observed eclipse timing variations for HW Vir. If the
sys- tem does host exoplanets, they must move on orbits differing greatly from
those previously proposed. Our results illustrate the critical importance of
performing dynamical analyses as a part of the discovery process for
multiple-planet exoplanetary systems.
