  We study the variation of the dark matter mass fraction of elliptical
galaxies as a function of their luminosity, stellar mass, and size using a
sample of 29,469 elliptical galaxies culled from the Sloan Digital Sky Survey.
We model ellipticals as a stellar Hernquist profile embedded in an
adiabatically compressed dark matter halo. This model allows us to estimate a
dynamical mass ($M_{dynm}$) at the half-light radius from the velocity
dispersion of the spectra, and to compare these to the stellar mass estimates
($M_{*}$) from Kauffmann et al (2003). We find that $M_{*}/L$ is independent of
luminosity, while $M_{dynm}/L$ increases with luminosity, implying that the
dark matter fraction increases with luminosity. We also observe that at a fixed
luminosity or stellar mass, the dark matter fraction increases with increasing
galaxy size or, equivalently, increases with decreasing surface brightness:
high surface brightness galaxies show almost no evidence for dark matter, while
in low surface brightness galaxies, the dark matter exceeds the stellar mass at
the half light radius. We relate this to the fundamental plane of elliptical
galaxies, suggesting that the tilt of this plane from simple virial predictions
is due to the dark matter in galaxies. We find that a simple model where
galaxies are embedded in dark matter halos and have a star formation efficiency
independent of their surface brightness explains these trends. We estimate the
virial mass of ellipticals as being approximately 7-30 times their stellar
mass, with the lower limit suggesting almost all of the gas within the virial
radius is converted into stars.
