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

We investigate the well-known correlations between the dynamical mass-to-light ratio (M/L) and other global observables of elliptical (E) and lenticular (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 to about one effective (half-light) radius R_e. They have well-calibrated I-band Hubble Space Telescope WFPC2 and large-field ground-based photometry, accurate surface brightness fluctuation distances, and their observed kinematics is consistent with an axisymmetric intrinsic shape. All these factors result in an unprecedented accuracy in the M/L measurements. We find a tight correlation of the form (M/L) = (3.80 +/- 0.14) × (σ_e/200kms^-1)^0.84+/-0.07 between the M/L (in the I band) measured from the dynamical models and the luminosity-weighted second moment σ_e of the LOSVD within R_e. The observed rms scatter in M/L for our sample is 18 per cent, while the inferred intrinsic scatter is ~13 per cent. The (M/L)-σ_e relation can be included in the remarkable series of tight correlations between σ_e 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, describing the deviation of the FP from the virial relation, is almost exclusively due to a real M/L variation, while structural and orbital non-homology have a negligible effect. When the photometric parameters are determined in the `classic' way, using growth curves, and the σ_e is measured in a large aperture, the virial mass appears to be a reliable estimator of the mass in the central regions of galaxies, and can be safely used where more `expensive' models are not feasible (e.g. in high-redshift studies). In this case the best-fitting virial relation has the form (M/L)_vir= (5.0 +/- 0.1) ×R_eσ²_e/(LG), in reasonable agreement with simple theoretical predictions. We find no difference between the M/L of the galaxies in clusters and in the field. 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 per cent of the total mass inside one R_e, in broad agreement with previous studies, and it also shows that the stellar initial mass function varies little among different galaxies. Our results suggest a variation in M/L at constant (M/L)_pop, which seems to be linked to the galaxy dynamics. We speculate that fast-rotating galaxies have lower dark matter fractions than the slow-rotating and generally more-massive ones. If correct, this would suggest a connection between the galaxy assembly history and the dark matter halo structure. The tightness of our correlation provides some evidence against cuspy nuclear dark matter profiles in galaxies.