The galaxy size - halo mass scaling relations and clustering properties
  of central and satellite galaxies
  In this work, we combine size and stellar mass measurements from the Sloan
Digital Sky Server (SDSS) with the group finder algorithm of Rodriguez \&
Merch\'an in order to determine the stellar and halo mass -- size relations of
central and satellite galaxies separately. We show that, while central and
satellite galaxies display similar stellar mass -- size relations, their halo
mass -- size relations differ significantly. As expected, more massive haloes
tend to host larger central galaxies. However, the size of satellite galaxies
depends only slightly on halo virial mass. We show that these results are
compatible with a remarkably simple model in which the size of central and
satellite galaxies scales as the cubic root of their host halo mass, with the
normalization for satellites being $\sim$ 30 \% smaller than that for central
galaxies, which can be attributed to tidal stripping. We further check that our
measurements are in excellent agreement with predictions from the IllustrisTNG
hydrodynamical simulation. In the second part of this paper, we analyse how the
clustering properties of central and satellite galaxies depend on their size.
We demonstrate that, independently of the stellar mass threshold adopted,
smaller galaxies are more tightly clustered than larger galaxies when either
the entire sample or only satellites are considered. The opposite trend is
observed on large scales when the size split is performed for the central
galaxies alone. Our results place significant constraints for halo-galaxy
connection models that link galaxy size with the properties of their hosting
haloes.
