The rings around the Egg Nebula

We present an eccentric binary model for the formation of the proto-planetary nebula CRL 2688 (the Egg Nebula) that exhibits multiple concentric shells. Given the apparent regularity of the structure in the Egg Nebula, we postulate that the shells are caused by the periodic passages of a companion star. Such an orbital period would have to lie in the range of 100-500 yr, the apparent time that corresponds to the spacing between the rings. We assume, in this model, that an asymptotic giant branch (AGE) star, which is the origin of the matter within the planetary nebula, loses mass in a spherically symmetric wind. We further suppose that the AGE star has an extended atmosphere (out to similar to 10 stellar radii) in which the outflow speed is less than the escape speed; still farther out, grains form and radiation pressure accelerates the grains along with the trapped gas to the escape speed. Once escape speed has been attained, the presence of a companion star will not significantly affect the trajectories of the matter leaving in the wind and the mass loss will be approximately spherically symmetric. On the other hand, if the companion star is sufficiently close that the Roche lobe of the AGE star moves inside the extended atmosphere, then the slowly moving material will be forced to flow approximately along the critical potential surface (i.e., the Roche lobe) until it flows into the potential lobe of the companion star. Therefore, in our model, the shells are caused by periodic cessations of the isotropic wind rather than by any periodic enhancement in the mass-loss process. We carry out detailed binary evolution calculations within the context of this scenario, taking into account the nuclear evolution and stellar wind losses of the giant as well as the effects of mass loss and mass transfer on the evolution of the eccentric binary orbit. From the initial binary parameters that we find are required to produce a multiple concentric shell nebula and the known properties of primordial binaries, we conclude that similar to 0.3% of all planetaries should go through a phase with multiple concentric shells.