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Register a new userPlanet formation, orbital evolution and planet-star tidal interaction
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D.N.C. Lin
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We consider several processes operating during the late stages of planet formation that can affect observed orbital elements. Disk-planet interactions, tidal interactions with the central star, long term orbital instability and the Kozai mechanism are discussed.
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In this article we present results from three on-going projects related to the formation of protoplanets in protostellar discs. We present the results of simulations that model the interaction between embedded protoplanets and disc models undergoing MHD turbulence. We review the similarities and differences that arise when the disc is turbulent as opposed to laminar (but viscous), and present the first results of simulations that examine the tidal interaction between low mass protoplanets and turbulent discs. We describe the results of simulations of Jovian mass protoplanets forming in circumbinary discs, and discuss the range of possible outcomes that arise in hydrodynamic simulations. Finally, we report on some preliminary simulations of three protoplanets of Jovian mass that form approximately coevally within a protostellar disc. We describe the conditions under which such a system can form a stable three planet resonance.
We have investigated i) the formation of gravitationally bounded pairs of gas-giant planets (which we call binary planets) from capturing each other through planet-planet dynamical tide during their close encounters and ii) the following long-term orbital evolution due to planet-planet and planet-star {it quasi-static} tides. For the initial evolution in phase i), we carried out N-body simulations of the systems consisting of three jupiter-mass planets taking into account the dynamical tide. The formation rate of the binary planets is as much as 10% of the systems that undergo orbital crossing and this fraction is almost independent of the initial stellarcentric semi-major axes of the planets, while ejection and merging rates sensitively depend on the semi-major axes. As a result of circularization by the planet-planet dynamical tide, typical binary separations are a few times the sum of the physical radii of the planets. After the orbital circularization, the evolution of the binary system is governed by long-term quasi-static tide. We analytically calculated the quasi-static tidal evolution in later phase ii). The binary planets first enter the spin-orbit synchronous state by the planet-planet tide. The planet-star tide removes angular momentum of the binary motion, eventually resulting in a collision between the planets. However, we found that the binary planets survive the tidal decay for main-sequence life time of solar-type stars (~10Gyrs), if the binary planets are beyond ~0.3 AU from the central stars. These results suggest that the binary planets can be detected by transit observations at >0.3AU.
During the process of planet formation, the planet-discs interactions might excite (or damp) the orbital eccentricity of the planet. In this paper, we present two long ($tsim 3times 10^5$ orbits) numerical simulations: (a) one (with a relatively light disc, $M_{rm d}/M_{rm p}=0.2$) where the eccentricity initially stalls before growing at later times and (b) one (with a more massive disc, $M_{rm d}/M_{rm p}=0.65$) with fast growth and a late decrease of the eccentricity. We recover the well-known result that a more massive disc promotes a faster initial growth of the planet eccentricity. However, at late times the planet eccentricity decreases in the massive disc case, but increases in the light disc case. Both simulations show periodic eccentricity oscillations superimposed on a growing/decreasing trend and a rapid transition between fast and slow pericentre precession. The peculiar and contrasting evolution of the eccentricity of both planet and disc in the two simulations can be understood by invoking a simple toy model where the disc is treated as a second point-like gravitating body, subject to secular planet-planet interaction and eccentricity pumping/damping provided by the disc. We show how the counterintuitive result that the more massive simulation produces a lower planet eccentricity at late times can be understood in terms of the different ratios of the disc-to-planet angular momentum in the two simulations. In our interpretation, at late times the planet eccentricity can increase more in low-mass discs rather than in high-mass discs, contrary to previous claims in the literature.
We present high-spatial resolution HST and adaptive optics observations, and high-sensitivity ISO (ISOCAM & ISOPHOT) observations of a sample of X-ray selected weak-line (WTTS) and post (PTTS) T Tauri stars located in the nearby Chamaeleon T and Scorpius-Centaurus OB associations. HST/NICMOS and adaptive optics observations aimed at identifying substellar companions at separations >=30 A.U. from the primary stars. No such objects were found within 300 A.U. of any of the target stars, and a number of faint objects at larger separations can very likely be attributed to a population of background stars. ISOCAM observations of 5 to 15 Myr old WTTS and PTTS in ScoCen reveal infrared excesses which are clearly above photospheric levels, and which have a spectral index intermediate between that of younger (1 to 5 Myr) T Tauri stars in Cha and that of pure stellar photospheres. The difference in the spectral index of the older PTTS in ScoCen compared to the younger classical and WTTS in Cha can be attributed to a deficiency of smaller size (0.1 to 1mu) dust grains relative to larger size (~5mu) dust grains in the disks of the PTTS. The lack of small dust grains is either due to the environment (effect of nearby O stars and supernova explosions) or due to disk evolution. If the latter is the case, it would hint that circumstellar disks start to get dust depleted at an age between 5 to 15 Myr. Dust depletion is very likely related to the build-up of larger particles (ultimately rocks and planetesimals) and thus an indicator for the onset of the period of planet formation.
We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this configuration is confirmed, but the motion of planets is found to be chaotic. The eccentricity values are found to vary within finite ranges. The rates of tidal dissipation and tidal evolution of orbits are estimated, assuming an Earth-like rheology for the planets. We find that under this assumption the planets b, d, e were captured in the 3:2 or higher spin-orbit resonances during the initial spin-down but slipped further down into the 1:1 resonance. Dependent on its rheology, the innermost planet b may be captured in a stable pseudosynchronous rotation. Non-synchronous rotation ensures higher levels of tidal dissipation and internal heating. The positive feedback between the viscosity and the dissipation rate -- and the ensuing runaway heating -- are terminated by a few self-regulation processes. When the temperature is high and the viscosity is low enough, the planet spontaneously leaves the 3:2 resonance. Further heating is stopped either by passing the peak dissipation or by the emergence of partial melt in the mantle. In the post-solidus state, the tidal dissipation is limited to the levels supported by the heat transfer efficiency. The tides on the host star are unlikely to have had a significant dynamical impact. The tides on the synchronized inner planets tend to reduce these planets orbital eccentricity, possibly contributing thereby to the systems stability.
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