The relation between the virial theorem and the fundamental plane of elliptical galaxies

The analysis of the properties of a sample of elliptical galaxies for which the kinetic energy of both random and rotational motions are consistently defined, shows that more than half of the so-called ‘tilt’ of the fundamental plane of elliptical galaxies is accounted for by the non-homology in the dynamical structure of the systems. We find that the kinetic energy of random motions is proportional to σ1.6 0 instead of σ 2 0. We also confirm that some fraction of the tilt is accounted for by the rotation. The remaining 30% of the tilt, on the other hand, can be easily explained by stellar population effects and, possibly, by spatial non-homology.We find that, in the present sample, there is no correlation betweenmass-to-light ratio and luminosity.We are thus led to conclude that the existence of the fundamental plane can be consistently explained by the virial theorem, or, in other words, that elliptical galaxies are non-homologous virialized systems. The presence of the dynamical non-homology casts some doubts on the use of the FP as a distance indicator.