A METHOD FOR SOLVING THE LINEARIZED BOLTZMANN-EQUATION FOR ALMOST UNIFORMLY ROTATING STELLAR DISKS

We construct analytical phase-space solutions for perturbations of fla t disks by performing a power series expansion for the radius and the velocity coordinates. We show that this approach translates into an el egant mathematical formulation which is easy to use for a wide variety of distribution functions, for as far as resonances do not play a rol e, such as is the case for potentials which are close to quadratic. As a testcase, the method is applied on the Kalnajs disks. The results o btained are in full agreement with the analytical solutions of the mod e analysis. The strongest advantages of this method are its independen ce of the mathematical complexity of the unperturbed distribution, the degree of detail with which the solutions can be calculated and its c omputational straightforwardness. On the contrary, power series soluti ons are not suitable for describing regions where resonant orbits occu r, which we therefore exclude in this paper. We used the technique to analyse perturbations in the central regions of a galaxy, tracking the dynamical consequences of a Galactic bar on the kinematics of the sol ar neighbourhood (Hipparcos). We showed how the orientation and streng th of the bar is related to the properties of the velocity ellipsoid i n our model.