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The SAURON project - IV. The mass-to-light ratio, the virial mass estimator and the fundamental plane of elliptical and lenticular galaxies

We investigate with unprecedented accuracy the correlations between the dynamical mass-to-light ratio M/L and other global observables of E and S0 galaxies. We construct two-integral Jeans and three-integral Schwarzschild dynamical models for a sample of 25 E/S0 galaxies with SAURON integral-field stellar kinematics. We find a tight correlation of the form (M/L)=(3.80+/-0.14)*(sigma/200 km/s)^(0.84+/-0.07) between the dynamical M/L (in the I-band) and the luminosity-weighted second moment (sigma) of the line-of-sight velocity-distribution within Re. The observed rms scatter in M/L for our sample is 18%, while the inferred intrinsic scatter is ~13%. The (M/L)-sigma relation can be included in the remarkable series of tight correlations between sigma and other galaxy global observables. The comparison of the observed correlations with the predictions of the Fundamental Plane (FP), and with simple virial estimates, shows that the `tilt' of the FP of early-type galaxies, is due to a real M/L variation, while structural and orbital non-homology have a negligible effect. The virial mass is a reliable estimator of the mass in the central regions of galaxies. The best-fitting virial relation has the form (M/L)_vir=(5.0+/-0.1)*Re*sigma^2/(L*G). The comparison of the dynamical M/L with the (M/L)_pop inferred from the analysis of the stellar population, indicates a median dark matter fraction in early-type galaxies of ~30% of the total mass inside one Re. (Abridged)