Optimal Softening for N-Body Halo Simulations

We propose to determine the optimal softening length in N-body halo simulations by minimizing the ensemble-average acceleration error at a small radius r0. This strategy ensures that the error never exceeds the optimal value beyond r0. Furthermore, we derive semi-analytic formulae for calculating the acceleration error due to the discreteness of particles and softened gravity, which are validated by direct N-body force calculations. We estimate that current state-of-the-art halo simulations suffer >~6% acceleration error at 1% of the halo virial radius. The error grows rapidly toward the center and could contribute significantly to the uncertainties of inner halo properties.