The luminosity and stellar mass Fundamental Plane of early-type galaxies

From a sample of similar to 50 000 early-type galaxies from the Sloan Digital Sky Survey, we measured the traditional Fundamental Plane in the g, r, i and z bands. We then replaced luminosity with stellar mass, and measured the 'stellar mass' Fundamental Plane. The Fundamental Plane, R alpha sigma(a)/I(B), steepens slightly as one moves from shorter to longer wavelengths: the orthogonal fit has slope a = 1.40 in the g band and 1.47 in z, with a statistical random error of similar to 0.02. However, systematic effects can produce larger uncertainties, of the order of similar to 0.05. The Fundamental Plane is thinner at longer wavelengths: it has an intrinsic scatter of 0.062 dex in g and 0.054 dex in z. We have clear evidence that the scatter is larger at small galaxy sizes/masses; at large masses, measurement errors account for essentially all of the observed scatter (about 0.04 dex), suggesting that the Plane is rather thin for the very massive galaxies. The Fundamental Plane steepens further when luminosity is replaced with stellar mass to 1.54 or 1.63 when stellar masses are estimated from broad-band colours or from spectra, respectively. The intrinsic scatter also reduces further to 0.048 dex on average. Since colour and stellar-mass-to-light ratio are closely related, this explains why colour can be thought of as the fourth Fundamental Plane parameter. However, the slope of the stellar mass Fundamental Plane remains shallower than the value of 2 associated with the virial theorem. This is because the ratio of dynamical to stellar mass increases at large masses: M(dyn)/M(*) alpha M(dyn)(0.17 +/- 0.01). This scaling is the edge-on projection of the stellar mass kappa-space. The face-on view suggests that there is an upper limit to the stellar density for a given dynamical mass, and this decreases at large masses: M(*)/R(e)(3) alpha M(dyn)(-4/3) . All these trends can be used to constrain early-type galaxy formation models. We also study how the estimated coefficients a and B of the Plane are affected by other selection effects, whether in apparent or in absolute quantities. For example, if low-luminosity objects are missing from the sample, and one does not account for this, then a and B are both biased low from their true values. If objects with small velocity dispersions are missing, then a is biased high, although this matters more for the orthogonal than the direct-fitted quantities. These biases are seen in Fundamental Planes which have no intrinsic curvature, so the observation that a and B scale with L and sigma is not, by itself, evidence that the Plane is warped. On the other hand, we show that the Plane appears to curve sharply downwards at the small-size/mass end, and more gradually downwards as one moves towards larger sizes/masses. Whereas the drop at small sizes is real, most of the latter effect is due to correlated errors.