The role of binaries in the dynamical evolution of the core of a globular cluster

The size of the core is one of the main diagnostics of the evolutionary state of a globular cluster. Much has been learned over the last few years about the behavior of the core radius during and after core collapse, under a variety of different conditions related to the presence or absence of large numbers of binaries. An overview is presented of the basic physical principles that can be used to estimate the core radius. Four different situations are discussed, and expressions are presented for the ratio r(c)/r(h) of core radius to half mass radius. The regimes are: deep collapse in the absence of primordial binaries; steady post-collapse evolution after primordial binaries have been burned up; chaotic post-collapse evolution under the same conditions; and post-collapse evolution in the presence of primordial binaries. In addition, modifications to all of these cases are indicated for the more realistic situation where effects of the galactic tidal field are taken into account.