The SAURON project - X. The orbital anisotropy of elliptical and lenticular galaxies: revisiting the (V/ ,  ) diagram with integral-field stellar kinematics

We analyse the orbital distribution of elliptical (E) and lenticular (S0) galaxies using SAURON integral-field stellar kinematics within about one effective (half light) radius. We construct the anisotropy diagram, which relates the ratio of the ordered and random motion in a galaxy (V/σ), to its observed ellipticity (ε), for the 48 E/S0 galaxies from the SAURON survey. For a subsample of 24 galaxies consistent with axisymmetry, we use three-integral axisymmetric Schwarzschild dynamical models to recover the detailed orbital distribution and we find good agreement with the anisotropy derived from the (V/σ, ε) diagram. In the companion Paper IX we show that the early-type galaxies can be subdivided into two classes of systems with or without a significant amount of specific stellar angular momentum. Here we show that the two classes have different distributions on the (V/σ, ε) diagram. The slow rotators are more common among the most massive systems and are generally classified as E from photometry