On the structure of stellar clusters after relaxation

The evolution of globular clusters is studied by means of N -body problem calculations with 16 and 25 stars for time intervals up to 40 times of relaxation. It is found that within two to four times of relaxation all clusters with different starting conditions approach an isothermal polytrope and a Maxwellian distribution of velocities. In much longer times the deviations from an isothermal polytrope and a Maxwellian distribution of velocities become very important. A cusp is formed near the center of the cluster, but no central core can be distinguished. There is an excess of small and large velocities; the excess of high velocities is due to the formation of close pairs near the center. The escaping stars are fewer by a factor of 5. The virial theorem and Chandrasekhar's time of relaxation are approximately verified. Some other results are also discussed.