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The bodies in any N-body system can change. The most changeable bodies are stars. In order to fully model the evolution of a cluster of stars, we need to know how they interact with their environment, particularly how much mass they lose, and how they interact with each other. Is their evolution affected by a companion or close encounter? In this chapter we describe the physics and the mathematical formulation that we use to describe it. If we could we would evolve each star in every detail (Church, Tout & Aarseth 2007) but up to now, in practice, we have had to approximate the detailed evolution by empirical models (Hurley, Tout & Pols 2000). [ABSTRACT FROM AUTHOR]

In clusters there are both primordial binary stars and binaries created by dynamical interactions. Occasionally, a new binary system can be formed (Fabian, Pringle & Rees 1975) but more often new systems are the result of exchanges. In Chap. 12 Hurley describes an algorithm for including the interaction of the components of a binary star in N-body simulations. In this chapter we investigate the underlying physics and note that, though we have a good qualitative idea of what goes on, there is still much to be determined fully quantitatively. [ABSTRACT FROM AUTHOR]

The observed distribution of optical afterglows with respect to their host galaxies may suggest that some gamma-ray bursts (GRBs) are associated with star forming regions, and therefore with the explosions of massive stars rather than with merging neutron stars. We construct a simple computational scheme to explore the expected contribution of the presupernova ejecta of single Wolf-Rayet (WR) stars to the circumstellar environment. We make specific predictions for the interaction of the relativistic blast wave with the density bumps that arise when the progenitor star rapidly loses a large fraction of its initial mass or when the ejected wind interacts with the external medium and decelerates. A re-brightening of the afterglow with a spectrum redder than the typical synchrotron spectrum (as seen in GRB 970508 and GRB 980326) is predicted. [ABSTRACT FROM AUTHOR]