On the nonlinear instability of Maclaurin stellar disk having a giant halo

The stability of a model galaxy, taken in the form of a Maclaurin rotating disk, with respect to nonradial ''affine'' perturbations in the presence of a non-oscillating giant halo with a homogeneous density distribution is discussed. The criterion of linear stability of the disk is defined. It is shown that the criterion remains in force in the nonlinear case only down a certain value of the critical angular velocity of rotation, after which the effect of nonlinear stabilization gradually falls behind of the linear stabilization effect. In case of the greatest angular velocity (i.e. in absence of the velocity dispersion) the disk is unstable even in the presence of a massive halo