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``Softened'' gravity is commonly used to model collisionless galactic systems. Modification of the $1/r^2$ force at short range diminishes two-body scattering and allows for larger time steps in computational experiments. But the effects of using a softened potential must be well understood when designing experiments and analyzing results of numerical runs. Some of the most basic results of Newtonian physics are modified as a consequence of changing the force law. For example, a spherical shell of matter produces a force in its interior.
This paper examines some of the dynamical effects of using softened gravity with the goal of determining under which circumstances the desired physics is being faithfully modeled. In particular the calculation of global quantities -- such as force fields, total energies and virial relationships -- are studied. It is shown that softening, introduced as a short range modification of gravity, can have global effects, e.g., the familiar form of the scalar virial theorem is no longer valid.
A simple physical system, a spherical galaxy undergoing global oscillations, is used to illustrate some of the effects. The dynamical behavior of the model is examined with different values of softening using both Particle Mesh (PM) grid and tree N-body codes.
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