SELF-CONSISTENT, AXISYMMETRICAL 2-INTEGRAL MODELS OF ELLIPTIC GALAXIES WITH EMBEDDED NUCLEAR DISCS

Ionized gas discs in the nuclei of ellipticals have proven to be excel lent tools for the determination of the central mass density in these galaxies. The recent discovery with the Hubble Space Telescope of smal l stellar discs embedded in the nuclei of a number of ellipticals and SOs might be of similar importance. We construct two-integral axisymme tric models for such systems. The models consist of a spheroidal bulge with a central density cusp, and a disc described by a strongly flatt ened exponential spheroid. We use the Hunter & Qian method to calculat e the even part of the phase-space distribution function (DF), and spe cify the odd part by means of a simple parametrization. We consider lo cal stability against axisymmetric perturbations, as well as global st ability against bar-forming modes, and find that our models are stable as long as the discs are not too flat and/or compact. The margin of s tability is derived as a function of disc scalelength and central surf ace density. Its location agrees well with the observed values of thes e disc parameters. This suggests that discs build up their mass until they become marginally stable. We investigate the photometric as well as the kinematic signatures of nuclear discs, including their velocity profiles (VPs), and study the influence of seeing convolution. In par ticular, we study to what extent these kinematic signatures can be use d to determine the central density of the galaxy, and to test for the presence of massive black holes. We consider nuclear discs that are ei ther dynamically coupled to or decoupled from the host elliptical, inc luding counter-rotating discs. The latter are models for the counter-r otating cores observed in a number of galaxies, which are often found to exhibit discy isophotes in the central region. The counter-rotation is only detectable when the disc light contributes significantly to t he central velocity profiles. We find that in this case the observed v elocity dispersion will show a central decrease. The rotation curve of a nuclear disc gives an excellent measure of the central mass-to-ligh t ratio whenever the VPs clearly reveal the narrow, rapidly rotating c omponent associated with the nuclear disc. Steep cusps and seeing conv olution both result in central Ws that are dominated by the bulge ligh t, and these VPs barely show the presence of the nuclear disc, impedin g measurements of the central rotation velocities of the disc stars. H owever, if a massive black hole is present, the disc component of the VP can be seen in the wing of the bulge part, and measurements of its mean rotation provide a clear signature of the presence of the black h ole. This signature is insensitive to the uncertainties in the velocit y anisotropy, which often lead to ambiguity in the interpretation of a central rise in velocity dispersion as due to a central black hole.