Elliptical galaxies: rotationally distorted, after all.

On the basis of earlier investigations on homeoidally striated Mac Laurin spheroids and Jacobi ellipsoids (Caimmi and Marmo 2005, Caimmi 2006a, 2007), different sequences of configurations are defined and represented in the ellipticity-rotation plane, ({O}hat{e}\u3c7_v^2). The rotation parameter, \u3c7_v^2, is defined as the ratio, E_{rot}/E_{res}, of kinetic energy related to the mean tangential equatorial velocity component, M(overline{v_\u3c6})^2/2, to kinetic energy related to tangential equatorial component velocity dispersion, M\u3c3_{\u3c6\u3c6}^2/2, and residual motions, M(\u3c3_{ww}^2+\u3c3_{33}^2)/2. Without loss of generality (above a threshold in ellipticity values), the analysis is restricted to systems with isotropic stress tensor, which may be considered as adjoint configurations to any assigned homeoidally striated density profile with anisotropic stress tensor, different angular momentum, and equal remaining parameters. The description of configurations in the ({O}hat{e}\u3c7_v^2) plane is extended in two respects, namely (a) from equilibrium to nonequilibrium figures, where the virial equations hold with additional kinetic energy, and (b) from real to imaginary rotation, where the effect is elongating instead of flattening, with respect to the rotation axis. An application is made to a subsample (N=16) of elliptical galaxies extracted from richer samples (N=25, N=48) of early type galaxies investigated within the SAURON project (Cappellari et al. 2006, 2007). Sample objects are idealized as homeoidally striated MacLaurin spheroids and Jacobi ellipsoids, and their position in the ({O}hat{e}\u3c7_v^2) plane is inferred from observations following a procedure outlined in an earlier paper (Caimmi 2009b). The position of related adjoint configurations with isotropic stress tensor is also determined. With a single exception (NGC 3379), slow rotators are characterized by low ellipticities (0 64 hat{e}<0.2), low anisotropy parameters (0 64\u3b4<0.15), and low rotation parameters (0 64\u3c7_v^2<0.15), while fast rotators show large ellipticities (0.2 64 hat{e}<0.65), large anisotropy parameters (0.15 64\u3b4<0.35), and large rotation parameters (0.15 64\u3c7_v^2