Abstract
I conduct an analytical study of the interaction of jets, or a collimated fast wind (CFW), with a previously blown asymptotic giant branch (AGB) slow wind. Such jets (or CFWs) are supposedly formed when a compact companion, a main-sequence star, or a white dwarf accretes mass from the AGB star, forms an accretion disk, and blows two jets. This type of flow, which I think shapes bipolar planetary nebulae (PNs), requires three-dimensional gasdynamical simulations, which are limited in the parameter space they can cover. By imposing several simplifying assumptions, I derive simple expressions which reproduce some basic properties of lobes in bipolar PNs and which can be used to guide future numerical simulations. I quantitatively apply the results to two proto-PNs. I show that the jet interaction with the slow wind can form lobes which are narrow close to, and far away from, the central binary system, and which are wider somewhere in between. Jets that are recollimated and have constant cross section can form cylindrical lobes with constant diameter, as observed in several bipolar PNs. Close to their source, jets blown by main-sequence companions are radiative; only further out they become adiabatic, i.e., they form high-temperature, low-density bubbles that inflate the lobes.
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