Non-linear coupling of spiral waves in disk galaxies: a numerical study

We present the results of two-dimensional numerical simulations of stellar galactic disks, aimed at studying the non-linear coupling between bar and spiral waves and modes, in disks with realistically peaked rotation profiles. The power spectrum analysis of the perturbed density in the disk, for azimuthal numbers ranging from m=0 to m=4, shows an unambiguous signature of non-linear coupling between the bar and spiral waves, or between spiral waves only, with a very sharp selection of the frequencies which optimize the coupling efficiency. It turns out that non-linear coupling can be quite efficient, and even more relevant than the Swing mechanism to account for the dynamics of the galaxy beyond the corotation of the bar. Non-linear coupling is also responsible for a number of other behaviors observed in our runs, such as harmonic or sub-harmonic excitation, and the excitation of m=1 spiral waves.