SDSS-IV MaNGA: The Spatially Resolved Stellar Initial Mass Function in
  $\sim$400 Early-Type Galaxies
  MaNGA provides the opportunity to make precise spatially resolved
measurements of the IMF slope in galaxies owing to its unique combination of
spatial resolution, wavelength coverage and sample size. We derive radial
gradients in age, element abundances and IMF slope analysing optical and
near-infrared absorption features from stacked spectra out to the half-light
radius of 366 early-type galaxies with masses $9.9 - 10.8\;\log M/M_{\odot}$.
We find flat gradients in age and [$\alpha$/Fe] ratio, as well as negative
gradients in metallicity, consistent with the literature. We further derive
significant negative gradients in the [Na/Fe] ratio with galaxy centres being
well enhanced in Na abundance by up to 0.5 dex. Finally, we find a gradient in
IMF slope with a bottom-heavy IMF in the centre (typical mass excess factor of
1.5) and a Milky Way-type IMF at the half-light radius. This pattern is
mass-dependent with the lowest mass galaxies in our sample featuring only a
shallow gradient around a Milky Way IMF. Our results imply the local
IMF-$\sigma$ relation within galaxies to be even steeper than the global
relation and hint towards the local metallicity being the dominating factor
behind the IMF variations. We also employ different stellar population models
in our analysis and show that a radial IMF gradient is found independently of
the stellar population model used. A similar analysis of the Wing-Ford band
provides inconsistent results and further evidence of the difficulty in
measuring and modelling this particular feature.
