This chapter deals with two effects of two-body encounters. In a general way this process was discussed in Chapter 14, but now we begin to study the effects on the system itself. Furthermore, the theory described there is applicable only to one of the two topics of this chapter. That theory describes the cumulative effects of many weak scatterings, and is perfectly adequate for an understanding of mass segregation. The escape of stars from an isolated stellar system, however, is controlled by single, more energetic encounters, and a better theory is necessary. The theory we shall describe is illustrative of a whole body of theory which improves on that of Chapter 14, though for most purposes (e.g. mass segregation) the improvements are unimportant.

Escape

We consider the case of an isolated stellar system. For this case, a star with speed ν will almost certainly escape if ν2/2 + φ > 0, where φ is the smoothed potential of the system at the location of the star, with the convention that φ → 0 at infinity. The exceptions are binary components (for which the true potential differs significantly from the smoothed potential), and an escaper which, on its way out, interacts with another star in such a way that its energy once again becomes negative. The latter possibility is rare in large systems (King 1959), precisely because two-body relaxation takes place on a much longer time scale than orbital motions (Chapter 14).