The validity of statistical results from Nbody calculations.
Abstract
A differential approach is used to investigate the effects of truncation and roundoff errors in numerical integration of the Nbody equations of motion. For this purpose, the six N equations of motion are integrated by a standard technique without regularization for ensembles of Nbody systems with N = 16; all systems initially satisfy the virial theorem, and the members of each ensemble differ among themselves only in the randomly assigned positions and velocities of the N particles. Deviations and errors are defined, the relevant statistical quantities are identified, and various correlations among the statistical quantities are examined. The results indicate that there are three phases in the development of integration errors with calculated Nbody systems, that the magnitude of deviations in individual coordinates does not increase linearly with time in all cases, and that the efolding time increases considerably. It is concluded that significant distortions of the statistical quantities describing Nbody systems appear only when the calculated system diverges and that this divergence is readily identifiable through a strong violation of energy conservation.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1977
 Bibcode:
 1977A&A....61..305S
 Keywords:

 Many Body Problem;
 Star Clusters;
 Statistical Mechanics;
 Stellar Motions;
 Astronomical Models;
 Equations Of Motion;
 Numerical Integration;
 Astronomy