## 3. Evalutation ofAs we stressed in the introduction, the study of the dynamical friction is possible when we know the first moment of . This calculation can be done using the components of () in the system of coordinates previously introduced. We have that: and similar equations for the other components of the force. The distribution function , giving the number of stars subject to a force , can be calculated as follows: This equation gives the generalized Holtsmark distribution obtained by Kandrup (1980a - Eq. 4.17) and provides the probability that a star is subject to a force in a inhomogeneous system. As previously stressed, to calculate the first moment of we need only an approximated form for : Using this last expression for and Eq. (A36), Eq. (A37), Eq. (14), Eq. (16), Eq. (17) and performing a calculation similar to that by CN43 the first moment of is given by: this last expression can also be written as: In this way we can written Eq. (20) as: this last equation coincides with Eq. (105) by CN43. The results obtained by us for an inhomogeneus system are different
[see Eq. (18)], as expected, from that obtained by CN43 for a
homogeneous system (CN43 - Eq. 105). At the same time it is very
interesting to note that for
(homogeneous system) our result coincides, as obvious, with the
results obtained by CN43. In a inhomogeneous system, in a similar way
to what happens in a homogeneus system,
depends on
,
and (the angle between
and
) while differently from homogeneous
systems, is a function of the
inhomogeneity parameter © European Southern Observatory (ESO) 1999 Online publication: December 22, 1998 |