## 7. Special forms of the velocity distribution## 7.1. Maxwell distributionA distribution implies and for and one has from Eqs. (42) and (43) For and separation of the spatial distribution and velocity distribution, these equations read Examples for these distributions are shown in Sect. 8, where the galactic halo is discussed. ## 7.2. Fixed velocityA model with a fixed velocity corresponds to It follows that and
does not depend on with With Eq. (42), follows as With the substitution one gets The argument of the -function is zero for so that This yields for Note that does not depend on Since there exist (real) solutions for is restricted by for , or by for , where Since , the critical value of which is a maximum for and a minimum for . The distribution of which yields the probability density and for one gets the probability density Since is given by © European Southern Observatory (ESO) 1998 Online publication: January 27, 1998 |