Early-type galaxies -- slow and fast rotating ellipticals (E-SRs and E-FRs)
and S0s/lenticulars -- define a Fundamental Plane (FP) in the space of
half-light radius Re, enclosed surface brightness Ie and velocity
dispersion σe. Since Ie and σe are distance-independent
measurements, the thickness of the FP is often expressed in terms of the
accuracy with which Ie and σe can be used to estimate sizes Re.
We show that: 1) The thickness of the FP depends strongly on morphology. If the
sample only includes E-SRs, then the observed scatter in Re is ∼16%,
of which only ∼9% is intrinsic. Removing galaxies with
M∗<1011M⊙ further reduces the observed scatter to ∼13% (∼4% intrinsic). The observed scatter increases to the ∼25% usually
quoted in the literature if E-FRs and S0s are added. If the FP is defined using
the eigenvectors of the covariance matrix of the observables, then the E-SRs
again define an exceptionally thin FP, with intrinsic scatter of only 5%
orthogonal to the plane. 2) The structure within the FP is most easily
understood as arising from the fact that Ie and σe are nearly
independent, whereas the Re−Ie and Re−σe correlations are nearly
equal and opposite. 3) If the coefficients of the FP differ from those
associated with the virial theorem the plane is said to be `tilted'. If we
multiply Ie by the global stellar mass-to-light ratio M∗/L and we account
for non-homology across the population by using S\'ersic photometry, then the
resulting stellar mass FP is less tilted. Accounting self-consistently for
M∗/L gradients will change the tilt. The tilt we currently see suggests that
the efficiency of turning baryons into stars increases and/or the dark matter
fraction decreases as stellar surface brightness increases.Comment: 13 pages, 9 figures, 3 tables, accepted for publication in MNRA