The Dependence of Halo Mass on Galaxy Size at Fixed Stellar Mass Using
  Weak Lensing
  Stellar mass has been shown to correlate with halo mass, with non-negligible
scatter. The stellar mass-size and luminosity-size relationships of galaxies
also show significant scatter in galaxy size at fixed stellar mass. It is
possible that, at fixed stellar mass and galaxy colour, the halo mass is
correlated with galaxy size. Galaxy-galaxy lensing allows us to measure the
mean masses of dark matter haloes for stacked samples of galaxies. We extend
the analysis of the galaxies in the CFHTLenS catalogue by fitting single
S\'{e}rsic surface brightness profiles to the lens galaxies in order to recover
half-light radius values, allowing us to determine halo masses for lenses
according to their size. Comparing our halo masses and sizes to baselines for
that stellar mass yields a differential measurement of the halo mass-galaxy
size relationship at fixed stellar mass, defined as $M_{h}(M_{*}) \propto
r_{\mathrm{eff}}^{\eta}(M_{*})$. We find that on average, our lens galaxies
have an $\eta = 0.42\pm0.12$, i.e. larger galaxies live in more massive dark
matter haloes. The $\eta$ is strongest for high mass luminous red galaxies
(LRGs). Investigation of this relationship in hydrodynamical simulations
suggests that, at a fixed $M_{*}$, satellite galaxies have a larger $\eta$ and
greater scatter in the $M_{\mathrm{h}}$ and $r_{\mathrm{eff}}$ relationship
compared to central galaxies.
