Optimal Softening for Gravitational Force Calculations in N-body Dynamics

Abstract

Abstract The choice of the optimal value of the softening length (ϵ i ) of each particle dealing with N-body simulations has a profound impact on error values in the gravitational force calculation. A slight deviation from its exact optimal value may result in a large error in the calculation. In this paper we augment the accuracy of the existing gravitational force calculation methods by providing a new technique to calculate the individual optimal values of ϵ i for various configurations of the Plummer density model. We have proposed an expression that relates each particle by considering the average characteristic length (λ i ) and density (ρ i ), unlike previous studies that considered ϵ i as an exclusive function of ρ i . We have performed gravitational force calculations for each and every particle from the Plummer density model using compact as well as noncompact gravitational force methods based on smoothed particle hydrodynamics. We have tested our new equation for the entire range of numerical simulations performed during the study. It is found that the errors in our force calculations are not only lower than those estimated from previous studies but also remain flat for various considerations of nearest neighboring particles (N neigh). The adjusted expression of ϵ λ,i in our study has less dependence on N neigh in the Plummer sphere. Finally, based on the results obtained using the method proposed in this study, we find that it remarkably improves both the accuracy as well as the stability of the gravitational force calculation.