The Dearth of Difference between Central and Satellite Galaxies III.
  Environmental Dependence of Mass-Size and Mass-Structure Relations
  As demonstrated in Paper I, the quenching properties of central and satellite
galaxies are quite similar as long as both stellar mass and halo mass are
controlled. Here we extend the analysis to the size and bulge-to-total light
ratio (B/T) of galaxies. In general central galaxies have size-stellar mass and
B/T-stellar mass relations different from satellites. However, the differences
are eliminated when halo mass is controlled. We also study the dependence of
size and B/T on halo-centric distance and find a transitional stellar mass
(M$_{*,t}$) at given halo mass (M$_h$), which is about one fifth of the mass of
the central galaxies in halos of mass M$_h$. The transitional stellar masses
for size, B/T and quenched fraction are similar over the whole halo mass range,
suggesting a connection between the quenching of star formation and the
structural evolution of galaxies. Our analysis further suggests that the
classification based on the transitional stellar mass is more fundamental than
the central-satellite dichotomy, and provide a more reliable way to understand
the environmental effects on galaxy properties. We compare the observational
results with the hydro-dynamical simulation, EAGLE and the semi-analytic model,
L-GALAXIES. The EAGLE simulation successfully reproduces the similarities of
size for centrals and satellites and even M$_{*,t}$, while L-GALAXIES fails to
recover the observational results.
