From a sample of ~50000 early-type galaxies from the SDSS, we measured the
traditional Fundamental Plane in four bands. We then replaced luminosity with
stellar mass, and measured the "stellar mass" FP. The FP steepens slightly as
one moves from shorter to longer wavelengths: the orthogonal fit has slope 1.40
in g and 1.47 in z. The FP is thinner at longer wavelengths: scatter is 0.062
dex in g, 0.054 dex in z. The scatter is larger at small galaxy sizes/masses;
at large masses measurement errors account for essentially all of the observed
scatter. The FP steepens further when luminosity is replaced with stellar mass,
to slope ~ 1.6. The intrinsic scatter also reduces further, to 0.048 dex. Since
color and stellar mass-to-light ratio are closely related, this explains why
color can be thought of as the fourth FP parameter. However, the slope of the
stellar mass FP 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 as M_d^0.17. The face-on view of the stellar mass
kappa-space 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 ~ M_d^-4/3.
We also study how the estimated coefficients a and b of the FP are affected by
other selection effects (e.g. excluding small sigma biases a high; excluding
fainter L biases a low). These biases are seen in FPs 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. We show that the FP appears to curve
sharply downwards at the small mass end, and more gradually downwards towards
larger masses. Whereas the drop at small sizes is real, most of the latter
effect is due to correlated errors.Comment: 17 pages, 15 figures, MNRAS in press. Added appendix on possible
sample contamination by disk
