A Detection of the Environmental Dependence of the Sizes and Stellar
  Haloes of Massive Central Galaxies
  We use ~100 square deg of deep (>28.5 mag arcsec$^{-2}$ in i-band),
high-quality (median 0.6 arcsec seeing) imaging data from the Hyper Suprime-Cam
(HSC) survey to reveal the halo mass dependence of the surface mass density
profiles and outer stellar envelopes of massive galaxies. The i-band images
from the HSC survey reach ~4 magnitudes deeper than Sloan Digital Sky Survey
and enable us to directly trace stellar mass distributions to 100 kpc without
requiring stacking. We conclusively show that, at fixed stellar mass, the
stellar profiles of massive galaxies depend on the masses of their dark matter
haloes. On average, massive central galaxies with $\log M_{\star, 100\
\mathrm{kpc}}>11.6$ in more massive haloes at 0.3 < z < 0.5 have shallower
inner stellar mass density profiles (within ~10-20 kpc) and more prominent
outer envelopes. These differences translate into a halo mass dependence of the
mass-size relation. Central galaxies in haloes with $\log M_{\rm{Halo}}>14.0$
are ~20% larger in $R_{\mathrm{50}}$ at fixed stellar mass. Such dependence is
also reflected in the relationship between the stellar mass within 10 and 100
kpc. Comparing to the mass--size relation, the $\log M_{\star, 100\
\rm{kpc}}$-$\log M_{\star, 10\ \rm{kpc}}$ relation avoids the ambiguity in the
definition of size, and can be straightforwardly compared with simulations. Our
results demonstrate that, with deep images from HSC, we can quantify the
connection between halo mass and the outer stellar halo, which may provide new
constraints on the formation and assembly of massive central galaxies.
