A Halo Expansion (HEX) Technique for Approximating Simulated Dark

We apply a basis function expansion method to create a time-evolving den-sity/potential approximation of the late growth of simulated N-body dark matter haloes. We demonstrate how the potential of a halo from the Aquarius Project can be accurately represented by a small number of basis functions, and show that the halo expansion (HEX) method provides a way to replay simulations. We explore the level of accuracy of the technique as well as some of its limitations. We find that the number of terms included in the expansion must be large enough to resolve the large-scale distribution and shape of the halo but, beyond this, additional terms result in little further improvement. Particle and subhalo orbits can be integrated in this real-istic, time-varying halo potential approximation, at much lower cost than the original simulation, with high fidelity for many individual orbits, and a good match to the distributions of orbital energy and angular momentum. Statistically, the evolution of structural subhalo properties, such as mass, half-mass radius and characteristic circu-lar velocity, are very well reproduced in the halo expansion approximation over several gigayears. We demonstrate an application of the technique by following the evolution of an orbiting subhalo at much higher resolution than can be achieved in the origi-nal simulation. Our method represents a significant improvement over commonly used techniques based on static analytical descriptions of the halo potential