In Fig. 1.1 we see a picture of the globular cluster M15, taken with the Hubble Space Telescope. This cluster contains roughly a million stars. In the central region typical distances between neighboring stars are only a few hundredth of a light year, more than a hundred times smaller than those in the solar neighborhood. This implies a stellar density that is more than a million times larger than that near the sun. Since the typical relative velocities of stars in M15 are comparable to that of the sun and its neighbors, a few tens of km/sec, collision times scale with the density, leading to a central time between collisions of less than years. With globular clusters having an age of more than years, a typical star near the center already has a chance of more than a percent to have undergone a collision in the past.
In fact, the chances are much higher than this rough estimate indicates. One reason is the stars spend some part of their life time in a much more extended state. A star like the sun increases its diameter by more than a factor of one hundred toward the end of its life, when they become a red giant. By presenting a much larger target to other stars, they increase their chance for a collision during this stage (even though this increase is partly offset by the fact that the red giant stage lasts shorter than the so-called main-sequence life time of a star, during which they have a normal appearance and diameter). The other reason is that many stars are part of a double star system, a type of dynamic spider web that can catch a third star, or another double star, into a temporary three- or four-body dance. Once engaged in such a dance, the local stellar crowding is enormously enhanced, and the chance for collisions is greatly increased.
A detailed analysis of all these factors predicts that a significant fraction of stars in the core of a dense globular cluster such as M15 has already undergone at least one collision in its life time. This analysis, however, is quiet complex. To study all of the important channels through which collisions may occur, we have to analyze encounters between a great variety of single and double stars, and occasional bound triples and larger bound multiples of stars. Since each star in a bound subsystem can be a normal main-sequence star, a red giant, a white dwarf, a neutron star or even a black hole, as well as an exotic collision product itself, the combinatorial richness of flavors of double stars and triples is enormous. If we want to pick a particular double star, we not only have to choose a star type for each of its members, but in addition we have to specify the mass of each star, and the parameters of its orbit, such as the semimajor axis (a measure for the typical separation of the two stars) as well as the orbital eccentricity.
The goal of our book series is to develop the software tools to make it possible to simulate an entire star cluster like M15, and to analyze the resulting behavior both locally and globally.