  The Rotten Egg Nebula has at its core a binary composed of a Mira star and an
A-type companion at a separation >10 au. It has been hypothesized to have
formed by strong binary interactions between the Mira and a companion in an
eccentric orbit during periastron passage ~800 years ago. We have performed
hydrodynamic simulations of an asymptotic giant branch star interacting with
companions with a range of masses in orbits with a range of initial
eccentricities and periastron separations. For reasonable values of the
eccentricity, we find that Roche lobe overflow can take place only if the
periods are <<100 years. Moreover, mass transfer causes the system to enter a
common envelope phase within several orbits. Since the central star of the
Rotten Egg nebula is an AGB star, we conclude that such a common envelope phase
must have lead to a merger, so the observed companion must have been a tertiary
companion of a binary that merged at the time of nebula ejection. Based on the
mass and timescale of the simulated disc formed around the companion before the
common envelope phase, we analytically estimate the properties of jets that
could be launched. Allowing for super-Eddington accretion rates, we find that
jets similar to those observed are plausible, provided that the putative lost
companion was relatively massive.
