## 4. Dynamical friction in inhomogeneous systemsThe introduction of the notion of dynamical friction is due to CN43. In the stochastic formalism developed by CN43 the dynamical friction is discussed in terms of : and . As shown by CN43, the origin of dynamical friction is due to the asymmetry in the distribution of relative velocities. As previously told, if a test star moves with velocity in a spherical distribution of field stars, namely then we have that: The asymmetry in the distribution of relative velocities is conserved in the final Eq. (25). In fact from Eq. (25) we have: (CN43). This means that when then ; while when then . As a consequence, when has a positive component in the direction of , increases on average; while if has a negative component in the direction of , decreases on average. Moreover, the star suffers a greater amount of acceleration in the direction when than in the direction when . In other words the test star suffers, statistically, an equal number of accelerating and decelerating impulses. Being the modulus of deceleration larger than that of acceleration the star slows down. At this point we may show how dynamical friction changes due to
inhomogeneity. From Eq. (18) we see that
differs from that obtained in
homogeneus system only for the presence of a dependence on the
inhomogeneity parameter If we consider a homogeneous system, , the previous equation reduces to: In the case of an inhomogeneous system, , we see that: where As we show in Fig. 1, this last equation is an increasing function
of
In addition, by increasing © European Southern Observatory (ESO) 1999 Online publication: December 22, 1998 |