Hamiltonian model of capture into mean motion resonance

Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. Full details can be found in \cite{2010submitted}. (Abridged)Comment: 4 pages, Proceedings of IAUS276 "The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution

Circularizing Planet Nine through dynamical friction with an extended, cold planetesimal belt

Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical "Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from the giant-planet region could be lifted to an orbit similar to the one suggested for Planet Nine through dynamical friction with a cold, distant planetesimal belt. Recent simulations of planetesimal formation via the streaming instability suggest that planetesimals can readily form beyond 100au. We explore this circularisation by dynamical friction with a set of numerical simulations. We find that a planet that is scattered from the region close to Neptune onto an eccentric orbit has a 20-30% chance of obtaining an orbit similar to that of Planet Nine after 4.6Gyr. Our simulations also result in strong or partial clustering of the planetesimals; however, whether or not this clustering is observable depends on the location of the inner edge of the planetesimal belt. If the inner edge is located at 200au the degree of clustering amongst observable objects is significant.Comment: Accepted to MNRA

The destruction of inner planetary systems during high-eccentricity migration of gas giants

Hot Jupiters are giant planets on orbits a few hundredths of an AU. They do not share their system with low-mass close-in planets, despite these latter being exceedingly common. Two migration channels for hot Jupiters have been proposed: through a protoplanetary gas disc or by tidal circularisation of highly-eccentric planets. We show that highly-eccentric giant planets that will become hot Jupiters clear out any low-mass inner planets in the system, explaining the observed lack of such companions to hot Jupiters. A less common outcome of the interaction is that the giant planet is ejected by the inner planets. Furthermore, the interaction can implant giant planets on moderately-high eccentricities at semimajor axes $<1$ AU, a region otherwise hard to populate. Our work supports the hypothesis that most hot Jupiters reached their current orbits following a phase of high eccentricity, possibly excited by other planetary or stellar companions.Comment: Replaced with accepted versio

The effects of external planets on inner systems: multiplicities, inclinations, and pathways to eccentric warm Jupiters

We study how close-in systems such as those detected by Kepler are affected by the dynamics of bodies in the outer system. We consider two scenarios: outer systems of giant planets potentially unstable to planet--planet scattering, and wide binaries that may be capable of driving Kozai or other secular variations of outer planets' eccentricities. Dynamical excitation of planets in the outer system reduces the multiplicity of Kepler-detectable planets in the inner system in $\sim20-25\%$ of our systems. Accounting for the occurrence rates of wide-orbit planets and binary stars, $\approx18\%$ of close-in systems could be destabilised by their outer companions in this way. This provides some contribution to the apparent excess of systems with a single transiting planet compared to multiple, however, it only contributes at most $25\%$ of the excess. The effects of the outer dynamics can generate systems similar to Kepler-56 (two coplanar planets significantly misaligned with the host star) and Kepler-108 (two significantly non-coplanar planets in a binary). We also identify three pathways to the formation of eccentric warm Jupiters resulting from the interaction between outer and inner systems: direct inelastic collision between an eccentric outer and an inner planet, secular eccentricity oscillations that may "freeze out" when scattering resolves in the outer system; and scattering in the inner system followed by "uplift", where inner planets are removed by interaction with the outer planets. In these scenarios, the formation of eccentric warm Jupiters is a signature of a past history of violent dynamics among massive planets beyond $\sim1$ au.Comment: 24 pages, 19 figures. Accepted to MNRA

Foretellings of Ragnarök: World-engulfing asymptotic giants and the inheritance of white dwarfs

The Astrophysical Journal 761.2 (2012): 21, reproduced by permission of the AASThe search for planets around white dwarf stars, and evidence for dynamical instability around them in the form of atmospheric pollution and circumstellar disks, 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 study, for the first time, 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 pericenter 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.This work is funded by the Spanish National Plan of R&D grant AYA2010-20630, “Planets and stellar evolution.” E.V. also acknowledges the support provided by the Marie Curie grant FP7-People-RG268111

Hot Jupiters and Cool Stars

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--2\Mso ), 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.Comment: 38 pages, 15 figures, accepted for publication in Ap

Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution

Exoplanets have been observed at many stages of their host star's life, including the main sequence (MS), subgiant and red giant branch stages. Also, polluted white dwarfs (WDs) likely represent dynamically active systems at late times. Here, we perform 3-body simulations which include realistic post-MS stellar mass loss and span the entire lifetime of exosystems with two massive planets, from the endpoint of formation to several Gyr into the WD phase of the host star. We find that both MS and WD systems experience ejections and star-planet collisions (Lagrange instability) even if the planet-planet separation well-exceeds the analytical orbit-crossing (Hill instability) boundary. Consequently, MS-stable planets do not need to be closely-packed to experience instability during the WD phase. This instability may pollute the WD directly through collisions, or, more likely, indirectly through increased scattering of smaller bodies such as asteroids or comets. Our simulations show that this instability occurs predominately between tens of Myr to a few Gyrs of WD cooling.Comment: Accepted for publication in MNRAS; 24 pages, 19 figure

Fly-by encounters between two planetary systems I: solar system analogues

Stars formed in clusters can encounter other stars at close distances. In typical open clusters in the Solar neighbourhood containing hundreds or thousands of member stars, ten to twenty per cent of Solar-mass member stars are expected to encounter another star at distances closer than 100 au. These close encounters strongly perturb the planetary systems, directly causing ejection of planets or their capture by the intruding star, as well as exciting the orbits. Using extensive $N$-body simulations, we study such fly-by encounters between two Solar System analogues, each with four giant planets from Jupiter to Neptune. We quantify the rates of loss and capture immediately after the encounter, e.g., the Neptune analogue is lost in one in four encounters within 100 au, and captured by the flying-by star in one in twelve encounters. We then perform long-term (up to 1 Gyr) simulations investigating the ensuing post-encounter evolution. We show that large numbers of planets are removed from systems due to planet--planet interactions and that captured planets further enhance the system instability. While encounters can initially leave a planetary system containing more planets by inserting additional ones, the long-term instability causes a net reduction in planet number. A captured planet ends up on a retrograde orbit in half of the runs in which it survives for 1 Gyr; also, a planet bound to its original host star but flipped during the encounter may survive. Thus, encounters between planetary systems are a channel to create counter-rotating planets, This would happen in around 1% of systems, and such planets are potentially detectable through astrometry or direct imaging.Comment: accepted to MNRA

Fly-by encounters between two planetary systems II: Exploring the interactions of diverse planetary system architectures

Planetary systems formed in clusters may be subject to stellar encounter flybys. Here we create a diverse range of representative planetary systems with different orbital scales and planets' masses and examine encounters between them in a typical open cluster. We first explore the close-in multi-super earth systems $\lesssim0.1$ au. They are resistant to flybys in that only ones inside a few au can destabilise a planet or break the resonance between such planets. But these systems may capture giant planets onto wide orbits from the intruding star during distant flybys. If so, the original close-in small planets' orbits may be tilted together through Kozai--Lidov mechanism, forming a ``cold'' system that is significantly inclined against the equator of the central host. Moving to the intermediately-placed planets around solar-like stars, we find that the planets' mass gradient governs the systems' long-term evolution post-encounter: more massive planets have better chances to survive. Also, a system's angular momentum deficit, a quantity describing how eccentric/inclined the orbits are, measured immediately after the encounter, closely relates to the longevity of the systems -- whether or not and when the systems turn unstable in the ensuing evolution millions of years post-encounter. We compare the orbits of the surviving planets in the unstable systems through (1) the immediate consequence of the stellar fly or (2) internal interplanetary scattering long post-encounter and find that those for the former are systematically colder. Finally, we show that massive wide-orbit multi-planet systems like that of HR 8799 can be easily disrupted and encounters at a few hundreds of au suffice.Comment: to appear in MNRA