  There is good evidence that the centers of massive early-type galaxies have a
bottom-heavy stellar initial mass function (IMF) compared to the IMF of the
Milky Way. Here we study the radial variation of the IMF within such galaxies,
using a combination of high quality Keck spectroscopy and a new suite of
stellar population synthesis models that cover a wide range in metallicity. As
in the previous studies in this series, the models are fitted directly to the
spectra and treat all elemental abundance ratios as free parameters. Using
newly obtained spectroscopy for six galaxies, including deep data extending to
~1Re for the galaxies NGC1407, NGC1600, and NGC2695, we find that the IMF
varies strongly with galactocentric radius. For all six galaxies the IMF is
bottom-heavy in the central regions, with average mass-to-light ratio
"mismatch" parameter a~2.5 at R=0. The IMF rapidly becomes more bottom-light
with increasing radius, flattening off near the Milky Way value (a~1.1) at
R>0.4Re. A consequence is that the luminosity-weighted average IMF depends on
the measurement aperture: within R=Re we find <a>=1.3-1.5, consistent with
recent lensing and dynamical results from SLACS and ATLAS-3D. Our results are
also consistent with several earlier studies that were based on analyses of
radial gradients of line indices. The observed IMF gradients support galaxy
formation models in which the central regions of massive galaxies had a
different formation history than their outer parts. Finally, we make use of the
high signal-to-noise central spectra of NGC1407 and NGC2695 to demonstrate how
we can disentangle IMF effects and abundance effects.
