Harry Varvoglis, Vasiliki Sgardeli, Kleomenis Tsiganis
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 the existence of exoplanets 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. 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 also give the final %elements of the orbits of both
planets as functions of the masses %and the elements of the orbit of the
initially bound planet. 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 either retrograde or tight and highly eccentric.
View original:
http://arxiv.org/abs/1201.1385
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