Astron. Astrophys. 350, 685-693 (1999)

4. Parameters used in the simulation

To calculate the effects of dynamical friction, introduced in the previous section, on a disc-like structure as KB, we cannot use the classical Chandrasekhar (1943) theory but we need equations specified for distributions like KB. These equations were written in the previous section (Eqs. 8 - 11). To calculate the effect of dynamical friction on the orbital evolution of the largest bodies we suppose that and are constants and that =. We need also the mass density distribution in the disc. We assume a heliocentric (R) distribution in surface mass density and a total primordial mass, in the region (Stern & Colwell 1997b). To evaluate the dynamical friction force we need the spatial distribution of the field objects, . To reproduce the quoted surface density we need a number density decreasing as a function of distance from the Sun, R, to the third power (Levison & Duncan 1990):

We remember also that the KB is a disc and then we use the mass distribution given by a Myiamoto-Nagai disc (Binney & Tremaine 1987; Wiegert & Tremaine 1997):

which in the disc plane reproduces the quoted surface density and Eq. (15) . Here M is the disc mass, a and b are parameters describing the disc characteristic radius and thickness. Because there is presently no information on the way in which ensemble-averaged inclinations () and eccentricities () vary in the KB, we adopt a disc with a width (Stern 1996b). The equations of motion were integrated in heliocentric coordinates using the Bulirsch-Stoer method.

© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999
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