A New View of the Size-Mass Distribution of Galaxies: Using $r_{20}$ and
  $r_{80}$ instead of $r_{50}$
  When investigating the sizes of galaxies it is standard practice to use the
half-light radius, $r_{50}$. Here we explore the effects of the size definition
on the distribution of galaxies in the size -- stellar mass plane.
Specifically, we consider $r_{20}$ and $r_{80}$, the radii that contain 20% and
80% of a galaxy's total luminosity, as determined from a Sersic profile fit,
for galaxies in the 3D-HST/CANDELS and COSMOS-DASH surveys. These radii are
calculated from size catalogs based on a simple calculation assuming a Sersic
profile. We find that the size-mass distributions for $r_{20}$ and $r_{80}$ are
markedly different from each other and also from the canonical $r_{50}$
distribution. The most striking difference is in the relative sizes of star
forming and quiescent galaxies at fixed stellar mass. Whereas quiescent
galaxies are smaller than star forming galaxies in $r_{50}$, this difference
nearly vanishes for $r_{80}$. By contrast, the distance between the two
populations increases for $r_{20}$. Considering all galaxies in a given stellar
mass and redshift bin we detect a significant bimodality in the distribution of
$r_{20}$, with one peak corresponding to star forming galaxies and the other to
quiescent galaxies. We suggest that different measures of the size are tracing
different physical processes within galaxies; $r_{20}$ is closely related to
processes controlling the star formation rate of galaxies and $r_{80}$ may be
sensitive to accretion processes and the relation of galaxies with their halos.
