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Register a new userAvoiding resonance capture in multi-planet extrasolar systems
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Authors
Margaret Pan
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A commonly noted feature of the population of multi-planet extrasolar systems is the rarity of planet pairs in low-order mean-motion resonances. We revisit the physics of resonance capture via convergent disk-driven migration. We point out that for planet spacings typical of stable configurations for Kepler systems, the planets can routinely maintain a small but nonzero eccentricity due to gravitational perturbations from their neighbors. Together with the upper limit on the migration rate needed for capture, the finite eccentricity can make resonance capture difficult or impossible in Sun-like systems for planets smaller than ~Neptune-sized. This mass limit on efficient capture is broadly consistent with observed exoplanet pairs that have mass determinations: of pairs with the heavier planet exterior to the lighter planet -- which would have been undergoing convergent migration in their disks -- those in or nearly in resonance are much more likely to have total mass greater than two Neptune masses than to have smaller masses. The agreement suggests that the observed paucity of resonant pairs around sun-like stars may simply arise from a small resonance capture probability for lower-mass planets. Planet pairs that thereby avoid resonance capture are much less likely to collide in an eventual close approach than to simply migrate past one another to become a divergently migrating pair with the lighter planet exterior. For systems around M stars we expect resonant pairs to be much more common, since there the minimum mass threshhold for efficient capture is about an Earth mass.
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We present a series of dynamical maps for fictitious 3-planets systems in initially circular coplanar orbits. These maps have unveiled a rich resonant structure involving two or three planets, as well as indicating possible migration routes from secular to double resonances or pure 3-planet commensurabilities. These structures are then compared to the present-day orbital architecture of observed resonant chains. In a second part of the paper we describe N-body simulations of type-I migration. Depending on the orbital decay timescale, we show that 3-planet systems may be trapped in different combinations of independent commensurabilities: (i) double resonances, (ii) intersection between a 2-planet and a first-order 3-planet resonance, and (iii) simultaneous libration in two first-order 3-planet resonances. These latter outcomes are found for slow migrations, while double resonances are almost always the final outcome in high-density disks. Finally, we discuss an application to the TRAPPIST-1 system. We find that, for low migration rates and planetary masses of the order of the estimated values, most 3-planet sub-systems are able to reach the observed double resonances after following evolutionary routes defined by pure 3-planet resonances. The final orbital configuration shows resonance offsets comparable with present-day values without the need of tidal dissipation. For the 8/5 resonance proposed to dominate the dynamics of the two inner planets, we find little evidence of its dynamical significance; instead, we propose that this relation between mean motions could be a consequence of the interaction between a pure 3-planet resonance and a 2-planet commensurability between planets c and d.
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We present high-precision radial-velocity measurements of three solar-type stars: HD 13908, HD 159243, and HIP 91258. The observations were made with the SOPHIE spectrograph at the 1.93-m telescope of Observatoire de Haute-Provence (France). They show that these three bright stars host exoplanetary systems composed of at least two companions. HD 13908 b is a planet with a minimum mass of 0.865+-0.035 Mjup, on a circular orbit with a period of 19.382+-0.006 days. There is an outer massive companion in the system with a period of 931+-17 days, e = 0.12+-0.02, and a minimum mass of 5.13+-0.25 Mjup. The star HD 159243, also has two detected companions with respective masses, periods, and eccentricities of Mp = 1.13+-0.05 and 1.9+-0.13 Mjup, $P$ = 12.620+-0.004 and 248.4+-4.9 days, and e = 0.02+-0.02 and 0.075+-0.05. Finally, the star HIP 91258 has a planetary companion with a minimum mass of 1.068+-0.038 Mjup, an orbital period of 5.0505+-0.0015 days, and a quadratic trend indicating an outer planetary or stellar companion that is as yet uncharacterized. The planet-hosting stars HD 13908, HD 159243, and HIP 91258 are main-sequence stars of spectral types F8V, G0V, and G5V, respectively, with moderate activity levels. HIP 91258 is slightly over-metallic, while the two other stars have solar-like metallicity. The three systems are discussed in the frame of formation and dynamical evolution models of systems composed of several giant planets.
Many planets are observed in stellar binary systems, and their frequency may be comparable to that of planetary systems around single stars. Binary stellar evolution in such systems influences the dynamical evolution of the resident planets. Here we study the evolution of a single planet orbiting one star in an evolving binary system. We find that stellar evolution can trigger dynamical instabilities that drive planets into chaotic orbits. This instability leads to planet-star collisions, exchange of the planet between the binary stars (star-hoppers), and ejection of the planet from the system. The means by which planets can be recaptured is similar to the pull-down capture mechanism for irregular solar system satellites. Because planets often suffer close encounters with the primary on the asymptotic giant branch, captures during a collision with the stellar envelope are also possible. Such capture could populate the habitable zone around white dwarfs.
Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the Laplace-Lagrange secular approximation for coplanar systems with two planets by including (near-)resonant harmonics, and realize an expansion at high order in the eccentricities of the resonant Hamiltonian both at orders one and two in the masses. We show that the expansion at first order in the masses gives a qualitative good approximation of the dynamics of resonant extrasolar systems with moderate eccentricities, while the second order is needed to reproduce more accurately their orbital evolutions. The resonant approach is also required to correct the secular frequencies of the motion given by the Laplace-Lagrange secular theory in the vicinity of a mean-motion resonance. The dynamical evolutions of four (near-)resonant extrasolar systems are discussed, namely GJ 876 (2:1 resonance), HD 60532 (3:1), HD 108874 and GJ 3293 (close to 4:1).
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