  We analyze the fundamental plane projections of elliptical galaxies as a
function of luminosity, using a sample of approximately 80,000 galaxies drawn
from Data Release 4 (DR4) of the Sloan Digital Sky Survey (SDSS). We separate
brightest cluster galaxies (BCGs) from our main sample and reanalyze their
photometry due to a problem with the default pipeline sky subtraction for BCGs.
The observables we consider are effective radius (R_e), velocity dispersion
(sigma), dynamical mass (M_dyn ~ R_e sigma2), effective density (sigma2/R_e2),
and effective surface brightness (mu_e). With the exception of the L-M_dyn
correlation, we find evidence of variations in the slope (i.e. the power-law
index) of the fundamental plane projections with luminosity for our normal
elliptical galaxy population. In particular, the radius-luminosity and
Faber-Jackson relations are steeper at high luminosity relative to low
luminosity, and the more luminous ellipticals become progressively less dense
and have lower surface brightnesses than lower luminosity ellipticals. These
variations can be understood as arising from differing formation histories,
with more luminous galaxies having less dissipation. Data from the literature
and our reanalysis of BCGs show that BCGs have radius-luminosity and
Faber-Jackson relations steeper than the brightest non-BCG ellipticals in our
sample, consistent with significant growth of BCGs via dissipationless mergers.
The variations in slope we find in the Faber-Jackson relation of non-BCGs are
qualitatively similar to that reported in the black hole mass-velocity
dispersion (M_BH-sigma) correlation. This similarity is consistent with a
roughly constant value of M_BH/M_star over a wide range of early type galaxies,
where M_star is the stellar mass.
