Determination of the orbital parameters of the M 51 system using a genetic algorithm

Using an efficient method based on genetic algorithms, we have searched for an optimum set of parameters for the interaction between NGC 5194 (M 51) and NGC 5195. The preferred model is one where the time of closest passage was 900 Myr ago. The orbit of NGC 5195 is almost perpendicular to the plane of the sky, and is slightly hyperbolic. The results from the search among non-self-gravitating models are confirmed by a fully self-gravitating simulation. Our model, which is limited to the outer regions of NGC 5194, reproduces the density distribution of the giant Hi arm of NGC 5194 accurately, but is not able to find a perfect representation of the velocity field. We argue that this is caused by deficiencies in the initial disc model used for NGC 5194, rather than a failure of our search method. In general, we argue that genetic algorithms are ideally suited for investigations of tidally interacting galaxies, where a large number of parameters need to be determined, and the goodness of fit for models contains a significant irregular component, with several local optima.