Global instability of stellar discs in presence of dark matter halos

Since the 1970s, numerical studies have shown that highly flattened rotationally supported galactic discs are globally unstable: in particular, they are subject to large-scale bar-like instabilities. Ostriker and Peebles (1973) proposed a global stability criterion through the ratio t_OP=T/|W| between the total kinetic energy of rotation of the system T and its total gravitational energy W. Even though t_OP is widely used as a global stability parameter, its applicability has been questioned from both theoretical and numerical perspectives. Efstathiou, Lake and Negroponte (1982) presented an alternative criterion based on the parameter t^*=T_d/[(1+f_ext)^2|W_D|], where T_d represents the stellar kinetic energy of rotation, W_D is the gravitational energy related to the stars in the total disc-halo potential and f_ext=W_dh/W_d is the ratio of the gravitational energy of the stars due to the halo potential and the self-energy of the stellar disc. In this master thesis we have studied the behaviour of t_OP and t^* and their relationship with global instability through N-body simulations with the FVFPS code (Londrillo et al. 2003). Together with t_OP and t^*, we also present and study a new global stability parameter t_W=T_d/|W_D|. At the beginning of the simulations, the disc particles move around circular orbits in the disc-halo potential, where the dark matter halo is rigid, non-rotating and modelled by a Hernquist (1990) profile. In the subsequent part of the thesis, we perform N-body simulations using the FVFPS code for the initial disc-halo systems. In a diagnostic phase, the results of the numerical simulations are analysed. The main results of this work are the following: i) we have found unstable systems even though T_d=0 (i.e. t_OP=t^*=0), which are thus counterexamples of Ostriker and Peebles's and Efstathiou, Lake and Negroponte's criteria; ii) the t_W parameter has some problems too: in all the simulations it is not sensitive to the presence of the halo.