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Astron. Astrophys. 326, L21-L24 (1997)

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2. Planet population evolution

Planets in our solar system show small eccentricities except Pluto and Mercury. Since the eccentricity of the Giant planets in our solar system is small (0.048, 0.056, 0.047, 0.009, respectively, for Jupiter, Saturn, Uranus and Neptune), we have generated a giant planet population orbiting cluster stars with an initial eccentricity of 0.010, semi-major axis in the range [6.3, 10.3] AU, and masses uniformly distributed in the range 1-6 [FORMULA]. All the planetary systems in a given model have the same value of the semi-major axis; i.e. there is no semi-major axis distribution. These are arbitrary but plausible values for newly formed giant planets. They could form by any of the two major giant planet origin mechanisms (Bodenheimer 1982): gravitational collapse of a gaseous sub-condensation until a stage at which a solid core may form; or solid core formation by accumulation of planetesimals, followed by accretion of gas onto the core until collapse instability.

Recently, it has been suggested that most of the stars form in small star clusters (Kroupa 1995a, b, c; de la Fuente Marcos 1997). In this work we consider models with populations in the range [100, 500] stars; the percentage of stars with giant planetary companions is in the range 10-50%. The clusters are situated in the solar neighbourhood. Most of the models have only single stars (except the planetary companions) but two additional models have also very hard (a = 6.4 AU) primordial binaries (binary fraction = 1/3). Double stars do not alter the results significantly. We have studied 500 mono-planetary systems in total.

In spite of the fact that almost circular orbits are harder to perturb, our computations show that both an increase and a diminution of orbital eccentricity is achievable. The eccentricity variations are associated with gravitational encounters. Gravitational circularization events are related to two-body interactions and the eccentricity decrement is in the range 10-40%. The percentage of systems which suffer this process is about 2%. Increase of eccentricity is observed in about 8% of systems with 38% in the range 0.06-0.99. The lowest increments come from simple two-body encounters but for higher increments, complex multi-body interactions are involved. All the largest increments are generated inside hierarchical retrograde configurations. The largest inner eccentricity is computed by using an analytical perturbation equation (Heggie & Rasio 1996) during the evolution of the hierarchical system. The life-time of these hierarchical systems could be greater than 100 Myr and all were formed inside the cluster core. Disintegration of hierarchical systems produce a single star and an EGP; very rarely the planet is ejected after disintegration.

Fig. 1 shows the systems whose eccentricities have changed due to dynamical interactions. It seems that the highest variations are restricted to stellar masses heavier than 0.3  [FORMULA]. For stars with masses in the range 0.5-1.0  [FORMULA] the biggest number of variations is observed. Only about 2% of systems are disrupted before escaping from the cluster and almost 90% leave the cluster without any major change in their dynamical parameters.

[FIGURE] Fig. 1. The relationship between eccentricity and mass of the primary for the systems which changed their initial eccentricity (0.010) after close encounters. The highest eccentricities are produced by four-body interactions (planet-star+two single stars) generating temporary stable hierarchical triple systems.
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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998