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Register a new userEccentricity generation in hierarchical triple systems: the planetary regime
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Nikolaos Georgakarakos Ph.D.
Publication date
2014
fields
Physics
and research's language is
English
Authors
Nikolaos Georgakarakos
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In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial setups (e.g. coplanar and non-coplanar orbits). However, the systems we examined had comparable masses. In the present paper, the validity of some of the formulae derived previously is tested by numerically integrating the full equations of motion for systems with smaller mass ratios (from ${10^{-3} hspace{0.2cm} mbox{to} hspace{0.2cm} 10^{3}}$, i.e. systems with Jupiter-sized bodies). There is also discussion about HD217107 and its planetary companions.
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In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well separated components, based on an expansion of the rate of change of the Runge-Lenz vector. Now, the same technique is extended to non-coplanar orbits. However, it can only be applied to systems with ${I_{0}<39.23^{circ}}$ or ${I_{0}>140.77^{circ}}$, where ${I}$ is the inclination of the two orbits, because of complications arising from the so-called Kozai effect. The theoretical model is tested against results from numerical integrations of the full equations of motion.
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and comparable masses. The derivation of short period terms is based on an expansion of the rate of change of the Runge-Lenz vector. Then, the short period terms are combined with secular terms, obtained by means of canonical perturbation theory. The validity of the theoretical equations is tested by numerical integrations of the full equations of motion.
Although our solar system features predominantly circular orbits, the exoplanets discovered so far indicate that this is the exception rather than the rule. This could have crucial consequences for exoplanet climates, both because eccentric terrestrial exoplanets could have extreme seasonal variation, and because giant planets on eccentric orbits could excite Milankovitch-like variations of a potentially habitable terrestrial planet,A^os eccentricity, on timescales of thousands-to-millions of years. A particularly interesting implication concerns the fact that the Earth is thought to have gone through at least one globally frozen, snowball state in the last billion years that it presumably exited after several million years of buildup of greenhouse gases when the ice-cover shut off the carbonate-silicate cycle. Water-rich extrasolar terrestrial planets with the capacity to host life might be at risk of falling into similar snowball states. Here we show that if a terrestrial planet has a giant companion on a sufficiently eccentric orbit, it can undergo Milankovitch-like oscillations of eccentricity of great enough magnitude to melt out of a snowball state.
Field stars are frequently formed in pairs, and many of these binaries are part of triples or even higher-order systems. Even though, the principles of single stellar evolution and binary evolution, have been accepted for a long time, the long-term evolution of stellar triples is poorly understood. The presence of a third star in an orbit around a binary system can significantly alter the evolution of those stars and the binary system. The rich dynamical behavior in three-body systems can give rise to Lidov-Kozai cycles, in which the eccentricity of the inner orbit and the inclination between the inner and outer orbit vary periodically. In turn, this can lead to an enhancement of tidal effects (tidal friction), gravitational-wave emission and stellar interactions such as mass transfer and collisions. The lack of a self-consistent treatment of triple evolution, including both three-body dynamics as well as stellar evolution, hinders the systematic study and general understanding of the long-term evolution of triple systems. In this paper, we aim to address some of these hiatus, by discussing the dominant physical processes of hierarchical triple evolution, and presenting heuristic recipes for these processes. To improve our understanding on hierarchical stellar triples, these descriptions are implemented in a public source code TrES which combines three-body dynamics (based on the secular approach) with stellar evolution and their mutual influences. Note that modeling through a phase of stable mass transfer in an eccentric orbit is currently not implemented in TrES , but can be implemented with the appropriate methodology at a later stage.
Previous work concerning planet formation around low-mass stars has often been limited to large planets and individual systems. As current surveys routinely detect planets down to terrestrial size in these systems, a more holistic approach that reflects their diverse architectures is timely. Here, we investigate planet formation around low-mass stars and identify differences in the statistical distribution of planets. We compare the synthetic planet populations to observed exoplanets. We used the Generation III Bern model of planet formation and evolution to calculate synthetic populations varying the central star from solar-like stars to ultra-late M dwarfs. This model includes planetary migration, N-body interactions between embryos, accretion of planetesimals and gas, and long-term contraction and loss of the gaseous atmospheres. We find that temperate, Earth-sized planets are most frequent around early M dwarfs and more rare for solar-type stars and late M dwarfs. The planetary mass distribution does not linearly scale with the disk mass. The reason is the emergence of giant planets for M*>0.5 Msol, which leads to the ejection of smaller planets. For M*>0.3 Msol there is sufficient mass in the majority of systems to form Earth-like planets, leading to a similar amount of Exo-Earths going from M to G dwarfs. In contrast, the number of super-Earths and larger planets increases monotonically with stellar mass. We further identify a regime of disk parameters that reproduces observed M-dwarf systems such as TRAPPIST-1. However, giant planets around late M dwarfs such as GJ 3512b only form when type I migration is substantially reduced. We quantify the stellar mass dependence of multi-planet systems using global simulations of planet formation and evolution. The results compare well to current observational data and predicts trends that can be tested with future observations.
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