2. The distribution function in inhomogeneous systems
where is the velocity of the field particle relative to the test one.
The expression of is given following Markoff 's method by (CN43):
and is the probability that a star has velocity in the range , positions in and mass in .
where a is a constant that can be obtained from the normalization condition for , j a parameter (of dimensions of velocity-1), an arbitrary function, the velocity of a field star. In other words we assume, according to CN43 and Chandrasekhar & von Newmann (1942), that the distribution of velocities is spherical, i.e. the distribution function is , but differently from the quoted papers we suppose that the positions are not equally likely for stars, that is the stars are inhomogeneously distributed in space. A lenghty calculation leads us (see Appendix for a derivation and the meaning of simbols) to find the function :
This last equation introduced into Eq. (7) solves the problem of finding the distribution and makes it possible to find the moments of that give information regarding the dynamical friction.
© European Southern Observatory (ESO) 1999
Online publication: December 22, 1998