The stellar dynamical term ‘stellar collision’ is not limited to the case of actual physical contact between stars, but refers to any gravitational interaction where the stars exchange momentum or energy. The dynamical processes in a gravitating stellar system can be summarized by classifying stellar collisions according to their distance scale. The reader is referred to Binney and Tremaine (1987) for a detailed treatment of this subject.

On the largest scale, the motion of a star is determined by the sum of interactions with all the other stars, that is, by the smooth gravitational potential of the system. Two body interactions occur on a shorter length scale, when two stars approach each other to the point where their mutual interaction dominates over that of the smoothed potential. Two body interactions randomize the stellar motions and lead to the relaxation of the system. In the course of relaxation, the stars, whose mass range spans two to three orders of magnitude, are driven towards equipartition. However, equipartition cannot be achieved in the presence of a central concentration of mass (in particular a central MBH). When two stars, which are initially on the same orbit (and therefore have the same velocity) interact, the massive one will slow down and the lighter one will speed up. Since the radius of the orbit depends only on the star's specific energy, and not its total energy, the massive star will sink to the center, while the lighter star will drift outwards. Over time, this process leads to ‘mass segregation’ the more massive stars are concentrated near the MBH and the lighter stars are pushed out of the inner region.

Occasionally, two-body interactions will eject a star out of the system altogether, thereby taking away positive energy from the system. The system will then become more bound and compact, the collision rate will increase, more stars will be ejected, and the result will be a runaway process. This process is called the ‘gravothermal catastrophe’, or ‘core collapse’, and is linked to the fact that self-gravitating systems have a negative heat capacity they become hotter when energy is taken out. Core collapse, if unchecked, will lead to the formation of an extremely dense stellar core surrounded by a diffuse extended halo. Once the density becomes high enough, very short range inelastic collisions are no longer extremely rare, and the fact that the stars are not point masses but have internal degrees of freedom starts to play a role. In such collisions energy is extracted from the orbit and invested in the work required to raise stellar tides, or strip stellar mass. The tidal energy is eventually dissipated in the star and radiated away. If the collision is slow, as it is in the core of a globular cluster where there is no MBH (but see Gebhardt et al 2002 for evidence for a black hole in a globular cluster), then the typical initial orbit is just barely unbound. In this case, the tidal interaction may extract enough orbital energy for ‘tidal capture’, and lead to the formation of a tightly bound, or ‘hard’ binary (tight, because tidal forces become effective only when the two stars are very close to each other). Hard binaries are a heat source for the cluster and play a crucial role in arresting core collapse. When a third star collides with a hard binary, it will tend to gain energy from the binary, thereby injecting positive energy into the cluster, while the binary becomes harder still.

When the stars orbit a central MBH, the collisions are fast (the Keplerian velocity near the MBH exceeds the escape velocity from the star) and the initial orbits are very unbound (hyperbolic). Even very close fly-bys cannot take enough energy from the orbit to bind the two stars, and so they continue on their way separately after having extracted energy and angular momentum from the orbit. The stars can radiate away the excess heat on a timescale shorter than the mean time between collisions, but it is harder to get rid of the excess angular momentum. Magnetic braking (the torque applied to a star when the stellar wind resists being swept by the rotating stellar magnetic field) typically operates on timescales similar to the stellar lifetime. It is therefore likely that high rotation is the longest lasting dynamical after effect of a close hyperbolic encounter, and that stars in a high density cusp are spun up stochastically by repeated collisions. Finally, at zero range, almost head on stellar collisions can lead to the stripping of stellar envelopes, the destruction of stars, or to mergers that result in the creation of ‘exotic stars’. These are stars that cannot be formed in the course of normal stellar evolution, such as a Thorne-Zytkow object, which is an accreting neutron star embedded in a giant envelope (Thorne and Zytkow 1975).