During the last ten years, enormous progress has been achieved in globular cluster dynamics. We now understand the phenomena of core collapse and post-collapse gravothermal oscillations, as well as the important role that primordial binaries play. Since there are various recent reviews that cover these topics (e.g. Goodman 1992, Hut 1992, Hut et al. 1992), I will simply outline the basic physical principles of cluster stellar dynamics here, before discussing the connections with stellar evolution.
Double stars play a central role in cluster dynamics. If their orbital speed exceeds that of the velocity dispersion of the single stars, the tendency toward energy equipartition during encounters will transfer some of the internal kinetic energy to passing stars. Doing so, energy conservation causes them to shrink, while the negative heat capacity of self-gravitating systems causes them to heat up further, to higher orbital speeds (Lynden-Bell's `donkey effect': trying to slow down particles in a Kepler orbit speeds them up, and vice versa).
The `gravitational fusion' of single stars into double stars is thus one mechanism that can heat a cluster, in order to balance the energy losses due to the evaporation of stars and the heat flow through the cluster toward the colder halo. Some of the analogies with nuclear fusion in stars, as well as a derivation of binary distribution functions as the classical limit of the hydrogen atom, are reviewed by Hut (1985). Some of the most detailed studies of gravitational scattering, the mechanism of gravitational fusion, can be found in Heggie &Hut (1993) and Goodman &Hut (1993) and references therein.
Energy Generation and Energy Budgets
Other mechanisms can play a role as well in fueling the central heat engine needed to balance the heat flow from the core to the cluster halo. Mass loss through stellar evolution (especially the much more rapid stellar evolution of merger remnants) can indirectly heat a cluster through the paradoxical effect of carrying off kinetic energy - simply because the potential energy carried off per unit mass is much larger, and tilts the balance towards an effective heating. Similarly, the formation of a modest black hole can also cause a heating of the cluster, through the selective eating of stars on low-energy orbits near the hole (for both mechanisms, see the review by Goodman 1992).
It is far from clear to what extent these various heating mechanisms compete with each other in actual globular cluster cores. Order-of-magnitude estimates indicate that they all can be significant, depending on the precise conditions in the cores, as well as on the nature of the stars. For example, white dwarfs, neutron stars and stellar-mass black holes are likely to produce energy by dynamical binary formation and hardening, while main-sequence stars and giants are likely to suffer physical collisions while attempting to do so.
Whatever the detailed mix of energy sources in individual clusters may turn out to be, binaries play a central role in the energy budget of a globular cluster. For example, observations of primordial binaries in globular clusters indicate that the binary abundance in globular clusters is not much smaller than that in the Galactic disk and halo (as reviewed recently by Hut et al. 1992; see also Kaluzny &Krzeminski 1993 for additional binary detections in NGC 4372). This suggests that %of the stellar objects in a cluster may be binaries with an orbit of A.U., which implies a average binding energy per binary of times that of the average kinetic energy of single cluster stars.
This simple reasoning leads to the astonishing conclusion that the internal energy reservoir in binary binding energies may well exceed the total amount of kinetic energy in the cluster as a whole (in the form of center-of-mass motion of single stars and binaries).
The dominant role played by the internal degrees of freedom of binaries in the overall energy budget already suggests that we'd better provide an accurate treatment of binary star evolution, if we want our overall cluster evolution to be believable. This is the topic of the next section.