Galactic Dynamics: newtonian gravity & modified gravity

Dynamics of gravitational systems is traditionally based on Newton's physics. At galactic scale, the Newtonian gravity imposes a special matter to exist: the dark matter. Nowadays, this matter is invisible. If this model ($\Lambda$ Cold Dark Matter) is successful at large scales, some difficulties appear at galactic scale. In my thesis, I use numerical simulations to explore an alternative to the Newtonian gravity: MOND (Modified Newtonian Dynamics), where the modification of the gravity follows an acceleration scaling law, without invoking any dark matter. This gravity is non linear and needs specific methods than those which are used for the Newtonian gravity with dark matter. I wrote a code able to solve the two gravity models, to compare each other. Then, I tested the evolution of isolated galaxies and interacting galaxies. These simulations take into account the dissipation of cold gas and the star formation. They have shown that galaxies are less stable in modified gravity than in Newtonian gravity, the bars form faster in MOND. These simulations have revealed some important differences concerning the angular momuntum exchange during the bar formation and dynamical friction effects which slow down the bars. A simulation of interacting galaxies like the Antennae is feasible for the first time in modified gravity. Again, the dynamical friction effects play a major role about the fusion time-scale, longer in modified gravity. New horizons toward cosmological simulations are opened and could valorized a model by studing hierarchical structure formation starting from primordial fluctuation. Moreover, modelisation of galaxy kinematic (dwarves, spirales, elliptics) is deepened. In particular, the analysis of rotation curves shows that spiral galaxies could contain a molecular gas component two times heavier than the atomic component.