Astronomisches Rechen-Institut Heidelberg

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ARI-Heidelberg Mitteilungen Serie A, No. 14

Author(s): von Hoerner, S.
Title: Die numerische Integration des n-Körper-Problemes für Sternhaufen. I
Source: Z. Astrophys. 50, 184-214
Year: 1960
Abstract: A method is proposed to approach the theory of stellar dynamics by integrating the equations of motion of a random cluster with few stars. The variable time-step is always governed by the closest pair of stars, and a special definition of the relaxation time is given. The accuracy of the calculation is adjusted to keep the relative energy error smaller than 5*10-4 per relaxation time. A satisfactory degree of reliability of the results is reached by taking the average over a number of examples and of relaxation times. Only the first phase of development has been calculated. The relaxation time for n = 4, 8, 12, 16 agrees very closely with CHANDRASEKHAR's formula.For n = 8, 12, 16, after 2 to 3 relaxation times, an internal structure is approached which shows no appreciable change within the next 10 relaxation times. The only exception is the density at great distance, which increases steadily due to stars escaping from the center. This might be used for an estimate of cluster ages. The density distribution of the inner region agrees with an isothermal polytrope, but deviations of 25% could be real. The velocity distribution is maxwellian within 17%, but shows a remarkable excess of higher velocities. These are due to close pairs and have nothing to do with escaping stars. Therefore, the velocity distribution does not seem to give an adequate description and should be replaced by the distribution of the total energies (kinetic plus potential) of the stars. Compared with theory, the production of stars with higher energies is too small by a factor of about 5. A rediscussion of the theory is suggested.
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