Galaxies in the Illustris simulation as seen by the Sloan Digital Sky
  Survey - II: Size-luminosity relations and the deficit of bulge-dominated
  galaxies in Illustris at low mass
  The interpretive power of the newest generation of large-volume
hydrodynamical simulations of galaxy formation rests upon their ability to
reproduce the observed properties of galaxies. In this second paper in a
series, we employ bulge+disc decompositions of realistic dust-free galaxy
images from the Illustris simulation in a consistent comparison with galaxies
from the Sloan Digital Sky Survey (SDSS). Examining the size-luminosity
relations of each sample, we find that galaxies in Illustris are roughly twice
as large and $0.7$ magnitudes brighter on average than galaxies in the SDSS.
The trend of increasing slope and decreasing normalization of size-luminosity
as a function of bulge-fraction is qualitatively similar to observations.
However, the size-luminosity relations of Illustris galaxies are quantitatively
distinguished by higher normalizations and smaller slopes than for real
galaxies. We show that this result is linked to a significant deficit of
bulge-dominated galaxies in Illustris relative to the SDSS at stellar masses
$\log\mathrm{M}_{\star}/\mathrm{M}_{\odot}\lesssim11$. We investigate this
deficit by comparing bulge fraction estimates derived from photometry
\emph{and} internal kinematics. We show that photometric bulge fractions are
systematically lower than the kinematic fractions at low masses, but with
increasingly good agreement as the stellar mass increases.
