The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter a binary system consisting of a Jupiter-sized planet revolving around a Sun-like star. To simplify the problem we assume coplanar orbits for the bound and the free-floating planet and an initially parabolic orbit for the free-floating planet. By calculating the uncertainty exponent, a quantity that measures the dependence of the final state of the system on small changes of the initial conditions, we show that the interaction process is a fractal classical scattering. The uncertainty exponent is in the range (0.2–0.3) and is a decreasing function of time. In this way we see that the statistical approach we follow to tackle the problem is justified. The possible final outcomes of this interaction are only four, namely flyby, planet exchange, capture or disruption. We give the probability of each outcome as a function of the incoming planet’s mass. We find that the probability of exchange or capture (in prograde as well as retrograde orbits and for very long times) is non-negligible, a fact that might explain the possible future observations of planetary systems with orbits that are either retrograde (see e.g. Queloz et al. Astron. Astrophys. 417, L1, 2010) or tight and highly eccentric.
Planetary systems Numerical methods Planet exchange Temporary capture
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Adams F.C., Proszkow E.M., Fatuzzo M., Myers P.C.: Early evolution of stellar groups and clusters: environmental effects on forming planetary systems. Astrophys. J. 641, 504–525 (2006)ADSCrossRefGoogle Scholar
Astakhov S.A., Farrelly D.: Capture and escape in the elliptic restricted three-body problem. Mon. Not. R. Astron. Soc. 354, 971–979 (2004)ADSCrossRefGoogle Scholar
Donnison J.R.: The stability of binary star systems during encounters with a third star. Mon. Not. R. Astron. Soc. 210, 915–927 (1984b)ADSzbMATHGoogle Scholar
Donnison J.R.: The Hill stability of a binary or planetary system during encounters with a third inclined body. Mon. Not. R. Astron. Soc. 369, 1267–1280 (2006)ADSCrossRefGoogle Scholar
Donnison J.R.: The Hill stability of a binary or planetary system during encounters with a third inclined body moving on a hyperbolic orbit. Planet. Space Sci. 56, 927–940 (2008)ADSCrossRefGoogle Scholar
Gayon-Markt J., Bois E.: On fitting planetary systems in counter-revolving configurations. Mon. Not. R. Astron. Soc. 399, 137–140 (2009)ADSCrossRefGoogle Scholar
Gear C.W.: Numerical Initial Value Problems in Ordinary Differential Equations, pp. 76–84. Prentice-Hall, Englewood Cliffs, N.J. (1971)zbMATHGoogle Scholar
Malmberg D., de Angeli F., Davies M.B., Church R.P., Mackey D., Wilkinson M.I.: Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood. Mon. Not. R. Astron. Soc. 378, 1207–1216 (2007)ADSCrossRefGoogle Scholar
Sumi T. et al.: Unbound or distant planetary mass population detected by gravitational microlensing. Nature 473, 349–352 (2011)ADSCrossRefGoogle Scholar
Zapatero Osorio M.R., Béjar V.J.S., Martín E.L., Rebolo R., Barrado y Navascués D., Bailer-Jones C.A.L., Mundt R.: Discovery of young, isolated planetary mass objects in the sigma Orionis star cluster. Science 290, 103–107 (2000)ADSCrossRefGoogle Scholar