Co-orbital terrestrial planets in exoplanetary systems: a formation scenario

Abstract

Aims. We study the formation of a hypothetical terrestrial-type body in the equilateral Lagrange points of a giant extrasolar planet. Starting from a swarm of planetesimals in stable tadpole orbits, we simulate its dynamical and collisional evolution under a wide range of different initial conditions and masses for both the Trojan population and its planetary companion. We also analyze the effects of gas drag from the interaction of the planetesimals with the nebular disk. Methods. The formation process is simulated with an N-body code that considers full gravitational interactions between the planetesimals and the giant planet. Gas interaction is modeled with Stokes and Epstein drags, where the drag coefficients are chosen following the results of full hydrodynamic simulations performed with the 2D public hydro-code FARGO. Results. In both gas-free and gas-rich scenarios, we have been able to obtain a single final terrestrial-type body in a stable tadpole orbit around one of the triangular Lagrange points of the system. However, due to gravitational instabilities within the swarm, the accretional process is not very efficient and the mass of the final planet never seems to exceed ∼0.6 Earth masses, even when the total mass of the swarm is five times this value. Finally, we also included an orbital decay of the giant planet due to a type II migration. Although the accretional process shows evidence of a lower efficiency, a small terrestrial planet is still able to form, and follows the giant planet towards the habitable zone of the hosting star.

Stability of librational motion in the spatial circular restricted three‐body problem for high inclinations and mass ratios

“…For the high mass ratio border the B 1:1 resonance limits the librational motion originating from the point (µ c , 0) (Danby 1964;Érdi et al 2007). A number of type A resonances appear in the low mass region, while the B 2:1 resonance (see Figure 3) is responsible for the large gap.…”

“…Besides the planetary (P-type) and satellite (S-type) motion around both respectively one of the components, T-type motion was considered as a third possibility. Not only the formation of Earth-mass planets directly in T-type orbits (about a migrating gas giant in a proto-planetary disk) was studied (Beaugé et al 2007), but also the possible capture of asteroids into Trojan orbits by the inner planets (Schwarz & Dvorak 2012 Funk et al (2012). Since extrasolar planets were also detected in binary star systems and systems consisting of a star and a sub-stellar companion, the dynamics of librational motion at high mass ratios is of interest, especially for the non-coplanar motion.…”

On the ultraviolet anomalies of the WASP-12 and HD 189733 systems: Trojan satellites as a plasma source

“…This makes the existence of one or two (in L4 and L5) Io-mass satellites possible. Beaugé et al (2007) also studied the type II migration of a giant planet assuming that its semimajor axis decayed on a time scale of 10 5 − 10 7 years. Their results showed that the Trojan satellite migrated together with the planet, and that the tadpole configuration close to L4 was maintained.…”

Orbital determination and dynamics of resonant extrasolar planetary systems

“…More recently, Goździewski and Konacki (2006) showed that two planets in stable co-orbital motion and non-coplanar orbits could yield similar radial velocity curves, albeit with significantly larger residuals. However, the existence of co-orbital giant planets is far from being established, and there is evidence that planetary bodies with masses larger than ∼ 0.7M ⊕ could not be accreted in the equilateral Lagrange points of giant exoplanets (Beaugé et al 2007). Even so, it is very curious how co-orbital bodies can mimic the radial velocity curve of two bodies in a 2/1 MMR.…”