  Observations indicate that intermediate mass stars, binary stars, and stellar
remnants often host planets; a complete explanation of these systems requires
an understanding of how planetary orbits evolve as their central stars lose
mass. Motivated by these dynamical systems, this paper generalizes in two
directions previous studies of orbital evolution in planetary systems with
stellar mass loss: [1] Many previous treatments focus on constant mass loss
rates and much of this work is carried out numerically. Here we study a class
of single planet systems where the stellar mass loss rate is time dependent.
The mass loss rate can be increasing or decreasing, but the stellar mass always
decreases monotonically. For this class of models, we develop analytic
approximations to specify the final orbital elements for planets that remain
bound after the epoch of mass loss, and find the conditions required for the
planets to become unbound. We also show that for some mass loss functions,
planets become unbound only in the asymptotic limit where the stellar mass
vanishes. [2] We consider the chaotic evolution for two planet systems with
stellar mass loss. Here we focus on a model consisting of analogs of Jupiter,
Saturn, and the Sun. By monitoring the divergence of initially similar
trajectories through time, we calculate the Lyapunov exponents of the system.
This analog solar system is chaotic in the absence of mass loss with Lyapunov
time in the range 5 - 10 Myr; we find that the Lyapunov time decreases with
increasing stellar mass loss rate, with a nearly linear relationship between
the two time scales. Taken together, the results of this paper help provide an
explanation for a wide range of dynamical evolution that occurs in solar
systems with stellar mass loss.
