Density waves in the shearing sheet III. Disc heating

The problem of dynamical heating of galactic discs by spiral density waves is discussed using the shearing sheet model. The secular evolution of the disc is described quantitatively by a diffusion equation for the distribution function of stars in the space spanned by integrals of motion of the stars, in particular the radial action integral and an integral related to the angular momentum. Specifically, disc heating by a succession of transient, `swing amplified' density waves is studied. It is shown that such density waves lead predominantly to diffusion of stars in radial action space. The stochastical changes of angular momenta of the stars and the corresponding stochastic changes of the guiding centre radii of the stellar orbits induced by this process are much smaller.