The Evolution of Planetary Systems with Time-dependent Stellar Mass Loss Rates

Observations indicate that intermediate mass stars, binary stars, and stellar remnants often host planets; a full 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 previous studies of orbital evolution in planetary systems with stellar mass loss, with a focus on two issues: [1] Whereas most previous treatments consider constant mass loss rates, we consider 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 is always monotonically decreasing. We show that the qualitative behavior found previously for constant mass loss rates often occurs for this generalized case, and we find general conditions required for the planets to become unbound. However, for some mass loss functions, where the mass loss time scale increases faster than the orbital period, 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 simple 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 τ0 ≈ 5 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, results [1] and [2] help provide an explanation for a wide range of dynamical evolution that occurs in solar systems with stellar mass loss. Subject headings: planets and satellites: dynamical evolution and stability — planet-star interactions — stars: evolution — stars: mass loss — white dwarfs