The half mass radius of MaNGA galaxies. I. Effect of IMF gradients
  Gradients in the stellar populations of galaxies -- e.g., in age,
metallicity, IMF -- can result in gradients in the stellar mass to light ratio,
$M_*/L$. Such gradients imply that the distribution of the stellar mass and
light are different. For old stellar populations, such as those typical of
early-type galaxies at $z\sim 0$, the $M_*/L$ gradients are weak if driven by
variations in age and metallicity. However, if they are driven by variations in
the stellar Initial Mass Function (IMF), then they can be significantly larger.
An IMF-driven gradient which has $M_*/L$ decreasing outwards from the center
increases the estimated total stellar mass ($M_*$) and reduces the scale which
contains half this mass ($R_{e,*}$), compared to the values of mass and size
when the gradient is ignored. We estimate IMF-gradients from spatially resolved
spectra of early-type galaxies in the final release of the MaNGA survey,
showing that the fractional decrease in $R_{e,*}$ can be significantly larger
than the fractional $M_*$ increase, especially when the light is more centrally
concentrated. The $R_{e,*}-M_*$ correlation which results from the IMF-driven
$M_*/L$ gradients at $z\sim 0$ is offset by almost 0.3 dex to smaller sizes
compared to when these gradients are ignored. Comparison with higher redshift
samples is not straightforward. If it is fair to compare $z\sim 0$ `early-type'
galaxies with `quiescent' galaxies at higher-$z$, then one must be able to
consistently account for evolution in stellar population gradients (especially
age and IMF) as well as changes in the steepness of the light profile before
drawing conclusions about the evolution of the $R_{e,*}-M_*$ relation.
