Test‐Bed Simulations of Collisionless, Self‐Gravitating Systems Using the Schrodinger Method

Abstract

The Schrödinger method is a novel approach for modeling numerically self-gravitating, collisionless systems that may have certain advantages over N-body and phase-space methods. In particular, smoothing is part of the dynamics and not just the force calculation. This paper describes test-bed simulations which illustrate the viability of the Schrödinger method. We develop the techniques necessary to handle "hot" systems as well as spherically symmetric systems. A number of experiments are performed, and direct comparisons are made to results obtained using a simple shell code. We demonstrate that the method can adequately model a stable, equilibrium star cluster by constructing and then evolving a Plummer sphere. We also follow the evolution of a system from nonequilibrium initial conditions as it attempts to reach a state of virial equilibrium. Finally, we make a few remarks concerning the dynamics of axions and other bosonic dark matter candidates. The Schrödinger method, in principle, provides an exact treatment of these fields. However, such "scalar field" simulations are feasible and warranted only if the de Broglie wavelength of the particle is comparable to the size of the system of interest, a situation that is almost certainly not the case for axions in the Galaxy. The dynamics of axions is therefore no different from that of any other system of collisionless particles. We challenge recent claims in the literature that axions in the Galaxy form soliton stars.