Tidal interactions of disc galaxies

In this paper we develop general analytic expressions for the energy and angular momentum transferred between a cold disc galaxy and a perturbing mass, for the case when the perturber is in a parabolic, coplanar orbit about the disc. Analogous expressions are developed for the case of flat hot discs. The equations for the zero velocity dispersion case were integrated for a disc with constant rotational velocity, and the results were explored for a range of the parameters. It was found that for slow, direct encounters the n = 2 inner Lindblad resonance dominates and so transfers energy and angular momentum from the disc to the perturber's orbit. This is the opposite result from what one would get by using the impulse approximation. For a retrograde encounter the energy of the disc increases, and the angular momentum decreases. However, these effects are small. It is shown, therefore, that tidal capture of galaxies cannot take place unless the galaxies actually collide. In the case of hot discs, however, if the distribution function is isotropic, it is shown that the change in energy of the disc is always positive, in spite of the details of the encounter. (author)