Mounting discoveries of extrasolar planets orbiting post‐main‐sequence stars motivate studies to understand the fate of these planets. In the traditional ‘adiabatic’ approximation, a secondary’s eccentricity remains constant during stellar mass‐loss. Here, we remove this approximation, investigate the full two‐body point‐mass problem with isotropic mass‐loss, and illustrate the resulting dynamical evolution. The magnitude and duration of a star’s mass‐loss combined with a secondary’s initial orbital characteristics might provoke ejection, modest eccentricity pumping, or even circularization of the orbit. We conclude that Oort Clouds and wide‐separation planets may be dynamically ejected from 1–7 M⊙ parent stars during AGB evolution. The vast majority of planetary material that survives a supernova from a 7–20 M⊙ progenitor will be dynamically ejected from the system, placing limits on the existence of first‐generation pulsar planets. Planets around >20 M⊙ black hole progenitors may easily survive or readily be ejected depending on the core collapse and superwind models applied. Material ejected during stellar evolution might contribute significantly to the free‐floating planetary population.

The search for planets around White Dwarf stars, and evidence for dynamical instability around them in the form of atmospheric pollution and circumstellar discs, raises questions about the nature of planetary systems that can survive the vicissitudes of the Asymptotic Giant Branch (AGB). We study the competing effects, on planets at several AU from the star, of strong tidal forces arising from the star's large convective envelope, and of the planets' orbital expansion due to stellar mass loss. We, for the first time, study the evolution of planets while following each thermal pulse on the AGB. For Jovian planets, tidal forces are strong, and can pull into the envelope planets initially at ∼ 3 AU for a 1 M ⊙ star and ∼ 5 AU for a 5 M ⊙ star. Lower-mass planets feel weaker tidal forces, and Terrestrial planets initially within 1.5 − 3 AU enter the stellar envelope. Thus, low-mass planets that begin inside the maximum stellar radius can survive, as their orbits expand due to mass loss. The inclusion of a moderate planetary eccentricity slightly strengthens the tidal forces experienced by Jovian planets. Eccentric Terrestrial planets are more at risk, since their eccentricity does not decay and their small pericentre takes them inside the stellar envelope. We also find the closest radii at which planets will be found around White Dwarfs, assuming that any planet entering the stellar envelope is destroyed. Planets are in that case unlikely to be found inside ∼ 1.5 AU of a White Dwarf with a 1 M ⊙ progenitor and ∼ 10 AU of a White Dwarf with a 5 M ⊙ progenitor.

Close-in planets are in jeopardy as their host stars evolve off the main sequence to the subgiant and red giant phases. In this paper, we explore the influences of the stellar mass (in the range 1.5-2M ⊙ ), mass-loss prescription, planet mass (from Neptune up to 10 Jupiter masses), and eccentricity, on the orbital evolution of planets as their parent stars evolve to become subgiants and Red Giants. We find that planet engulfment during the Red Giant Branch is not very sensitive to the stellar mass or mass-loss rates adopted in the calculations, but quite sensitive to the planetary mass. The range of initial separations for planet engulfment increases with decreasing mass-loss rates or stellar mass and increasing planetary masses. Regarding the planet's orbital eccentricity, we find that as the star evolves into the red giant phase, stellar tides start to dominate over planetary tides. As a consequence, a transient population of moderately eccentric close-in Jovian planets is created, that otherwise would have been expected to be absent from main sequence stars. We find that very eccentric and distant planets do not experience much eccentricity decay, and that planet engulfment is primarily determined by the pericenter distance and the maximum stellar radius.

Detectable debris discs are thought to require dynamical excitation (`stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semi-major axes to precess at different rates, and after some time t_cross initially non-intersecting orbits begin to cross. We show that t_cross is proportional to a_disc^(9/2)/(m_pl e_pl a_pl^3), where m_pl, e_pl and a_pl are the mass, eccentricity, and semi-major axis of the planet, and a_disc is the semi-major axis of the disc. This time-scale can be faster than that for the growth of planetesimals to Pluto's size within the outer disc. We also calculate the magnitude of the relative velocities induced amongst planetesimals and infer that a planet's perturbations can typically cause destructive collisions out to 100's of AU. Recently formed planets can thus have a significant impact on planet formation in the outer disc which may be curtailed by the formation of giant planets much closer to the star. The presence of an observed debris disc does not require the presence of Pluto-sized objects within it, since it can also have been stirred by a planet not in the disc. For the star epsilon Eridani, we find that the known RV planet can excite the planetesimal belt at 60 AU sufficiently to cause destructive collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.Comment: 13 pages, 14 figures. Accepted to MNRAS. v2: corrected typo