These formula have been applied in several situations, such as the decay of globular cluster orbits around the Milky Way and the fate of the nearby Magellanic clouds. But the most intriguing applications have been in the area of galaxy cannibalism.
A small galaxy that passes through the envelope of a larger galaxy will experience the drag force from dynamical friction. The drag will cause the small galaxy to lose energy and spiral inward. Using the above acceleration formula, a typical timescale can be derived such that
where the timescale has been normalized to typical galaxy values for size and internal velocities. Since typical Coulomb logarithm values are 3, then a small galaxy will spiral to center in a fraction of a Hubble time.
When the small galaxy reaches the Roche limit, it is tidally disrupted and `cannibalized'. Thus, a galaxy located at the bottom of the cluster potential well begins to accrete mass by cannibalizing smaller galaxies that pass through its envelope.
The following simulations shows dynamical friction at work on a dwarf galaxy (white circle) passing near a disk galaxy.
Simulations of galaxy formation find that dynamical friction is very efficient and that all galaxies formed from the mergers of proto-galactic lumps that dropped out of the expanding Universe as shown in this galaxy formation movie.
These protogalaxies in rich environments would then evolve into clusters of galaxies, with the growth of a central dominant member by galaxy cannibalism as shown in this supergiant galaxy simulation.
So, at least in clusters of galaxies, dynamical evolution can actually dominate the luminosity changes due to passive color evolution. And galaxy cannibalism radically changes the shape of the luminosity function, where the small, faint galaxies are consumed and the central cD galaxies grows to enormous size and luminosity.
The next question is at what epoch does all this dynamical evolution occur? Was it fixed early on as simulations suggest? or is it still happening today? The answer lies in comparisons of the orientation of cD galaxies with the large-scale structure of the Universe.