Modelling Tidal Streams from Galactic Satellites

Astrophysical simulations are very useful for understanding the physical phenomena of the stellar systems. In this simulation, the computational cost is one of the main concern. To tackle this issue, a choice of the time-step criterion is crucial. In this thesis, I study the efficiency of the time-step depending on the tidal force. This quantity follows gauge invariance under adding a constant acceleration where this property is not owned by conventional time-step criteria. Time step function based on the tidal force is more efficient than other time-step criteria. The observed tidal streams are very important to constrain the Galactic potential and the distribution of sub-haloes structure in the Milky-Way. In this thesis, I present a restricted N-body model for tidal debris to simulate the formation of tidal streams from Galactic satellites. If the satellite orbits are close to a Galactic disc, the structures of tidal debris do not spread in one dimension like the conventional streams but form two dimensions structures like a ribbon. This phenomenon can be explained analytically by action-angle variables and Hamiltonian formalism. This restricted N-body method has fewer ad-hoc assumptions and is more accurate than the alternative (and popular) particle sprinkling techniques at only a modest increase of the computational expense.