The internal dynamics of very flattened normal galaxies: Stellar distribution functions for NGC 4697

Using the photometry and the kinematic data, part of which acquired with the NTT, we constructed a 2-integral and a 3-integral distribution function for NGC 4697. We detected a nuclear dust lane at ${3.4}^{\mathrm{\prime }\mathrm{\prime }}$ or 0.4 kpc from the centre. A comparison of the Lucy-deprojection method and the multi-gaussian expansion method showed that the latter offers a number of advantages, among which a qualitatively better fit and better controllable convergence. Futhermore, we show that a 2-integral model cannot be excluded for as far as the Satoh parameter $k$ is allowed to vary. The 3-integral model is based on a St"ackel third integral. The original potential is retained where appropriate, in order to minimise errors due to the St"ackel approximation. On the whole, the 3-integral model produces more satisfying results than the 2-integral model, and is better in handling some peculiarities in the kinematic data. For both models we show detailed contour plots for all deprojected moments up to order 2. The mass-to-light ratio appears to be a fairly well determined $(M\mathrm{/}L{)}_B=4.8h_{50}$, and is much better constrained than would be the case for spherical anisotropic models with comparable data.