  Several independent lines of evidence suggest that the stellar initial mass
function (IMF) in early-type galaxies becomes increasingly `bottom-heavy' with
increasing galaxy mass and/or velocity dispersion, sigma. Here we consider
evidence for IMF variation in a sample of relatively compact early-type
galaxies drawn from the Sloan Digital Sky Survey. These galaxies are of
sufficiently high stellar density that a dark halo likely makes a minor
contribution to the total dynamical mass, Mdyn, within one effective radius. We
fit our detailed stellar population synthesis models to the stacked absorption
line spectra of these galaxies in bins of sigma and find evidence from
IMF-sensitive spectral features for a bottom-heavy IMF at high sigma. We also
apply simple `mass-follows-light' dynamical models to the same data and find
that Mdyn is significantly higher than what would be expected if these galaxies
were stellar dominated and had a universal Milky Way IMF. Adopting Mdyn M_*
therefore implies that the IMF is `heavier' at high sigma. Most importantly,
the quantitative amount of inferred IMF variation is very similar between the
two techniques, agreeing to within 0.1 dex in mass. The agreement between two
independent techniques, when applied to the same data, provides compelling
evidence for systematic variation in the IMF as a function of early-type galaxy
velocity dispersion. Any alternative explanations must reproduce both the
results from dynamical and stellar population-based techniques.
