Abstract
We perform numerical simulations to investigate tidal evolution of two single-planet systems, that is, WASP-50 and GJ 1214 and a two-planet system CoRoT-7. The results of orbital evolution show that tidal decay and circularization may play a significant role in shaping their final orbits, which is related to the initial orbital data in the simulations. For GJ 1214 system, different cases of initial eccentricity are also considered as only an upper limit of its eccentricity (0.27) is shown, and the outcome suggests a possible maximum initial eccentricity (0.4) in the adopted dynamical model. Moreover, additional runs with alternative values of dissipation factor Q′1 are carried out to explore tidal evolution for GJ 1214b, and these results further indicate that the real Q′1 of GJ 1214b may be much larger than its typical value, which may reasonably suggest that GJ 1214b bears a present-day larger eccentricity, undergoing tidal circularization at a slow rate. For the CoRoT-7 system, tidal forces make two planets migrating towards their host star as well as producing tidal circularization, and in this process tidal effects and mutual gravitational interactions are coupled with each other. Various scenarios of the initial eccentricity of the outer planet have also been done to investigate final planetary configuration. Tidal decay arising from stellar tides may still work for each system as the eccentricity decreases to zero, and this is in association with the remaining lifetime of each planet used to predict its future.
Similar content being viewed by others
References
Murray C D, Dermott S F. Solar System Dynamics. New York: Cambridge Univ Press, 1999
Jackson B, Barnes R, Greenberg R. Observation evidence for tidal destruction of exoplanets. Astrophys J, 2009, 698: 1357–1366
Lanza A F. Hot Jupiters and the evolution of stellar angular momentum. Astron Astrophys, 2010, 512: 77–91
Lissauer J J. Planet formation. Ann Rev Astron Astrophys, 1993, 31: 129–174
Rasio F A, Ford E B. Dynamical instabilities and the formation of extrasolar planetary systems. Science, 1996, 274: 954–956
Zhou J L, Aarseth S J, Lin D N C, et al. Origin and ubiquity of shortperiod earth-like planets: evidence for the sequential accretion theory of planet of formation. Astrophys J, 2005, 631: L85–L88
Ji J H, Jin S, Tinney C G. Forming close-in earth-like planets via a collision-merger mechanism in late-stage planet formation. Astrophys J, 2011, 727: L5–L8
Jin S, Ji J H. Terrestrial planet formation in inclined systems: application to the OGLE-2006-BLG-109L system. Mon Not Roy Astron Soc, 2011, 418: 1335–1345
Lin D, Bodenheimer P, Richardson D. Orbital migration of the planetary companion of 51 Pegasi to its present location. Nature, 1996, 380: 606–607
Goldreich P. Disk-satellite interactions. Astrophys J, 1980, 241: 425–441
Fabrycky D, Tremaine S. Shrinking Binary and Planetary Orbits by Kozai Cycles with Tidal Friction. Astrophys J, 2007, 669: 1298–1315
Ford E B, Rasio F A. on the relation between hot Jupiters and the Roche limit. Astrophys J, 2006, 638: L45–L48
Rasio F A, Tout C A, Lubow S H, et al. Tidal decay of close planetary orbits. Astrophys J, 1996, 470: 1187–1191
Zhou J L, Lin D N C. Migration and Final Location of Hot Super Earths in the Presence of Gas Giants. In: IAU Symp. 249, Exoplanets: Detection, Formation and Dynamics. ed. Sun Y S, Ferraz-Mello S, Zhou J L, eds. Suzhou, China, 2008, 319. 285–289
Rodrıguez A, Ferraz-Mello S, Michtchenko T A, et al. Tidal decay and orbital circularization in close-in two-planet systems. Mon Not Roy Astron Soc, 2011, 415: 2349–2358
Dobbs-Dixon I, Lin D N C, Mardling R A. Spin-Orbit Evolution of Short-Period Planets. Astrophys J, 2004, 610: 464–476
Beutler G. Methods of Celestial Mechanics. Vol. I: Physical, mathematical, and numerical principles. Berlin: Springer, 2005
Mignard F. The evolution of the lunar orbit revisited. I. Earth Moon Planets, 1979, 20: 301–315
Mardling R A, Lin D N C. Calculating the tidal, spin, and dynamical evolution of extrasolar planetary systems. Astrophys J, 2002, 573: 829–844
Chambers J E. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon Not Roy Astron Soc, 1999, 304: 793–799
Stoer J, Bulirsch R. Introduction to Numerical Analysis. New York: Springer Verlag, 1980 Soc, 1999, 304: 793–799
Gillon M, Doyle A P, Lendl M, et al. WASP-50b: a hot Jupiter transiting a moderately active solar-type star. Astron Astrophys, 2011, 533: 88–95
Goldreich P, Soter S. Q in the Solar System. Icarus, 1966, 5: 375–389
Levrard B, Winisdoerffer C, Chabrier G. Falling transiting extrasolar giant planets. Astrophys J, 2009, 692: L9–L13
Charbonneau D, Berta Z K, Irwin J. A super-Earth transiting a nearby low-mass star. Nature, 2009, 462: 891–894
Carter J A, Winn J N, Holman M J, et al. The transit light curve project, XIII. sixteen transits of he super-earth GJ 1214b. Astrophys J, 2011, 730: 82–91
Léger A, Rouan D, Schneider J, et al. Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first super-Earth with measured radius. Astron Astrophys, 2009, 506: 287–302
Queloz D, Bouchy F, Moutou C, et al. The CoRoT-7 planetary system: two orbiting super-Earths. Astron Astrophys, 2009, 506: 303–319
Ferraz-Mello S, Tadeu D S M, Beaugé C, et al. On the mass determination of super-Earths orbiting active stars: the CoRoT-7 system. Astron Astrophys, 2011, 531: 161–171
Mardling R A. Long-term tidal evolution of short-period planets with companions. Mon Not Roy Astron Soc, 2007, 382: 1768–1790
Huang C, Liu L. Analytical solutions to the four post-Newtonian effects in a near-earth satellite orbit. Celest Mech Dyn Astr, 1992, 53: 293–307
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dong, Y., Ji, J. Tidal evolution of exo-planetary systems: WASP-50, GJ 1214 and CoRoT-7. Sci. China Phys. Mech. Astron. 55, 872–879 (2012). https://doi.org/10.1007/s11433-012-4707-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-012-4707-8