Accuracy of Analytic Potentials for Orbits of Satellites Around a Milky Way-like Galaxy: Comparison with N-Body Simulations

To study the orbits of satellites, a galaxy can be modeled either by means of a static gravitational potential or by live N-body particles. Analytic potentials allow for fast calculations but are idealized and non-responsive. On the other hand, N-body simulations are more realistic but demand higher computational cost. Our goal is to characterize the regimes in which analytic potentials provide a sufficient approximation and those where N-bodies are necessary. We perform two sets of simulations, using both Gala and Gadget, in order to closely compare the orbital evolution of satellites around a Milky Way-like galaxy. Focusing on the periods when the satellite has not yet been severely disrupted by tidal forces, we find that the orbits of satellites up to 108M⊙ can be reliably computed with analytic potentials to within 5% error if they are circular or moderately eccentric. If the satellite is as massive as 109M⊙ then errors of 9% are to be expected. However, if the orbital radius is smaller than 30 kpc then the results may not be relied upon with the same accuracy beyond 1–2 Gyr.