An advanced N-body model for interacting multiple stellar systems

We construct an advanced model for interacting multiple stellar systems in which we compute all trajectories with a numerical N-body integrator, namely the Bulirsch--Stoer from the SWIFT package. We can then derive various observables: astrometric positions, radial velocities, minima timings (TTVs), eclipse durations, interferometric visibilities, closure phases, synthetic spectra, spectral-energy distribution, and even complete light curves. We use a modified version of the Wilson--Devinney code for the latter, in which the instantaneous true phase and inclination of the eclipsing binary are governed by the N-body integration. If one has all kinds of observations at disposal, a joint $\chi^2$ metric and an optimisation algorithm (a~simplex or simulated annealing) allows to search for a global minimum and construct very robust models of stellar systems. At the same time, our N-body model is free from artefacts which may arise if mutual gravitational interactions among all components are not self-consistently accounted for. Finally, we present a number of examples showing dynamical effects that can be studied with our code and we discuss how systematic errors may affect the results (and how to prevent this from happening).