Internal structure of globular clusters

For a typical cluster, the exchange of energy is sufficient for equilibrium within a radius R 12 pc, where about half the mass lies inside. From 2R on, the exchange becomes negligible. For the equilibrium region a method is given for obtaining the mass-luminosity relation and some information about the distribution of star masses. Space density-curves have been calculated for six models of central mass distribution. Under the assumption that all stars of the outer parts have been evaporated from the center, the density of the outer parts also could be given for different star masses. An investigation of the stability of globular clusters shows that only the tidal force of the galaxy is effective. Less massive clusters (104rn0) should have a limiting radius of about 30 pc. For M3 and M92, the space densities of stars of different magnitudes have been calculated from star counts of Sandage and Tayler. A correction for finice plate is given. The structures of both clusters are very similar. Their mass-luminosity relation is close to the form demanded by the theory of stellar evolution. The mass distribution from Luyten's luminosity function (with a steep cutoff at 1.2rn0) can be used to describe the observed space densities. Only at the very center are the observed densities too high. Therefore, there must be about a thousand stars more massive than the brightest ones, which could be white dwarfs or double stars. The density of the fainter stars in the outer region seems to be too high, thus indicating the remnants of an original density. But further proof is needed. For further observations, we recommend the use of comparison stars instead of counts to the limiting magnitude of the plate. The counts should reach as far out as possible (the field stars cancel out by the derivation leading to the space density). For comparison between theory and observation, the space density is more suitable than the projected density.