According to the standard model of cosmology, galaxies are embedded in dark matter halos which are made of particles beyond the standard model of particle physics, thus extending the mass and the size of the visible baryonic matter by typically two orders of magnitude. The observed gas distribution throughout the nearby M81 group of galaxies shows evidence for past significant galaxy--galaxy interactions but without a merger having occurred. This group is here studied for possible dynamical solutions within the dark-matter standard model. In order to cover a comprehensive set of initial conditions, the inner three core members M81, M82 and NGC3077 are treated as a three-body model based on Navarro-Frenk-White profiles. The possible orbits of these galaxies are examined statistically taking into account dynamical friction. Long living, non-merging initial constellations which allow multiple galaxy-galaxy encounters comprise unbound galaxies only, which are arriving from a far distance and happen to simultaneously encounter each other within the recent 500 Myr. Our results are derived by the employment of two separate and independent statistical methods, namely a Markov chain Monte Carlo method and the genetic algorithm using the SAP system environment. The conclusions reached are confirmed by high-resolution simulations of live self-consistent systems (N-body calculations). Given the observed positions of the three galaxies the solutions found comprise predictions for their proper motions.
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