## 3. Formation mechanismOur computations show that high eccentricities can be generated during multi-star gravitational interactions. The main mechanism is connected with the formation of a hierarchical triple or quadruple system. In order to identify stable configurations we use the stability criterion of Mardling and Aarseth (1997a). By using this criterion we select the stable hierarchical configuration to apply the Heggie and Rasio theory to the inner (planetary) orbit. The critical ratio of the outer periastron distance of the mass to the inner apastron distance of is given by where are the outer and inner eccentricities respectively, , = 2.8, and = 2. This criterion has been verified (for mass ratios in range 0.01-100 of the outer body and wide range of values for ) by systematic calculations (Mardling & Aarseth 1997b). The characteristic time-scale on which a single star is captured by a mono-planetary system (hereafter MPS) is given approximately by where
is the probability that a fourth star (single
in this case) also lies within a given distance where
is the mass of the MPS and where
is the number of single star (without planets)
and where
, and From the calculations these systems only form in the cluster core
so we must use the core parameters in Eq.
(6). This equation gives
for the typical values of the parameters found
in our calculations. The frequency of hierarchical system formation
for a cluster with © European Southern Observatory (ESO) 1997 Online publication: April 8, 1998 |