Numerical irreversibility in self-gravitating small N-body systems

Numerical irreversibility due to round-off errors appearing in self-gravitating N-body systems is investigated by means of molecular dynamics methods. As a typical self-gravitating system, a closed spherical system consisting of N point-particles, which are interacting through the Plummer softened potential, is considered. In order to examine the numerical irreversibility, time-reversible simulations are executed: that is, a velocity inversion technique for a time-reversal operation is applied at a certain time during the evolution of the system. Through the simulations with various energy states, it is found that, under a restriction of constant initial potential energy, numerical irreversibility prevails more rapidly with decreasing initial kinetic energy. In other words, the lower the initial kinetic energy (or the lower the total energy), the earlier the memory of the initial conditions is lost. Moreover, an influence of integration step sizes (i.e., time increments Δt) on numerical irreversibility is examined. As a result, even a small time increment could not improve reversibility of the present self-gravitating system, although the small time increment reduces global errors in total energy.