Numerical Experiments on Collective Effects in Stellar Dynamics.

Abstract

Recently several authors have used one-dimensional models to investigate plasma theory. We have used such a model to investigate a gas of stars. Since the model is one dimensional, the stars can be represented by a large number of mass sheets. The motion of such sheets is easily followed on a high-speed electronic computer. Since irregular forces due to stellar encounters can be neglected, a self-consistent Vlasov model will describe the system. We have found that systems which are initially equivalent but have different graininess (that is, different numbers of stars) display identical time behavior. Therefore, the only difference between our one-dimensional sheet model and a three-dimensional point model is that of solving the Vlasov equation in one instead of three dimensions. We have performed "numerical experiments" to investigate the time development of instabilities and/or the approach to equilibrium of systems of stars. We have found that the time behavior depends mainly on the initial ratio of T/P, where T is the kinetic energy and P is the potential energy of the system. For initial values of T/P of the order of 0.5 (the equilibrium value), collective damping will force the gas to its equilibrium state in a few plasma periods [2ir (4irGmn) -~]. In the steady state the dimension of the system is then found to be of the order of a Debye length [VT (4~Gmn)-~]. If the initial value of T/P is much larger or much smaller than the equilibrium value, the system will break up into smaller clusters. Analysis of the individual particle traj ectories indicates that the initial break up is due to a phase instability of the individual particle orbits. The conection of our results with the usual Rayleigh- Jeans instability is discussed.