We performed an extended analysis of the parameter space for the interaction of the Magellanic System with the Milky Way ( MW ) .
The varied parameters cover the phase space parameters , the masses , the structure , and the orientation of both Magellanic Clouds , as well as the flattening of the dark matter halo of the MW .
The analysis was done by a specially adopted optimization code searching for the best match between numerical models and the detailed H I map of the Magellanic System by Brüns et al .
( [ 2005 ] ) .
The applied search algorithm is a genetic algorithm combined with a code based on the fast , but approximative restricted N–body method .
By this , we were able to analyze more than \mathrm { 10 ^ { 6 } } models , which makes this study one of the most extended ones for the Magellanic System .
Here we focus on the flattening q of the axially symmetric MW dark matter halo potential , that is studied within the range 0.74 \leq q \leq 1.20 .
We show that creation of a trailing tail ( Magellanic Stream ) and a leading stream ( Leading Arm ) is quite a common feature of the Magellanic System–MW interaction , and such structures were modeled across the entire range of halo flattening values .
However , important differences exist between the models , concerning density distribution and kinematics of H I , and also the dynamical evolution of the Magellanic System .
Detailed analysis of the overall agreement between modeled and observed distribution of neutral hydrogen shows that the models assuming an oblate ( q < 1.0 ) dark matter halo of the Galaxy allow for better satisfaction of H I observations than models with other halo configurations .