Evidence for a non-universal stellar initial mass function in
  low-redshift high-density early-type galaxies
  We determine an absolute calibration of stellar mass-to-light ratios for the
densest \simeq 3% of early-type galaxies in the local universe (redshift
z\simeq 0.08) from SDSS DR7. This sample of \sim 4000 galaxies has, assuming a
Chabrier IMF, effective stellar surface densities, Sigma_e > 2500 M_sun/pc^2,
stellar population synthesis (SPS) stellar masses log_10(M_sps/M_sun)<10.8, and
aperture velocity dispersions of sigma_ap=168^{+37}_{-34} km/s (68% range). In
contrast to typical early-type galaxies, we show that these dense early-type
galaxies follow the virial fundamental plane, which suggests that
mass-follows-light. With the additional assumption that any dark matter does
not follow the light, the dynamical masses of dense galaxies provide a direct
measurement of stellar masses. Our dynamical masses (M_dyn), obtained from the
spherical Jeans equations, are only weakly sensitive to the choice of
anisotropy (\beta) due to the relatively large aperture of the SDSS fiber for
these galaxies: R_ap \simeq 1.5 R_e. Assuming isotropic orbits (\beta=0) we
find a median log_{10} (M_dyn/M_sps) = 0.233 \pm 0.003, consistent with a
Salpeter IMF, while more bottom heavy IMFs and standard Milky-Way IMFs are
strongly disfavored. Our results are consistent with, but do not require, a
dependence of the IMF on dynamical mass or velocity dispersion. We find
evidence for a color dependence to the IMF such that redder galaxies have
heavier IMFs with M_dyn/M_sps \propto (g-r)^{1.13\pm0.09}. This may reflect a
more fundamental dependence of the IMF on the age or metallicity of a stellar
population, or the density at which the stars formed.
