A ballistic model for a precessing and orbiting jet with a time-dependent ejection velocity

Abstract

We have found that the ballistic trajectory of a precessing, orbiting and time-dependent velocity jet has a semi-analytical solution. Bipolar, multipolar and S-like morphologies, which are observed in young protoplanetary and planetary nebula (PPN and PN, respectively), can be reproduced by setting different values for the ratio between dynamical time and precession periods, the ratio between the precession and orbital periods, and the jet velocity variability period. We have also computed numerical simulations and find a good agreement with the semi-analytical solution for a jet 103 times denser than the surrounding environment.