Charlton, Paul2017-04-242017-04-242017-04-242017-04-11http://hdl.handle.net/10012/11727Stellar mass has been shown to correlate with halo mass, but with significant scatter. The stellar mass-size and luminosity-size relationships of galaxies also show significant scatter in galaxy sizes for a fixed stellar mass. Investigating potential links between dark matter halo mass and properties of the baryons, like size, allows us to develop physical explanations for the observed variation in terms of how the baryons and dark matter interact. Galaxy-galaxy lensing allows us to probe the dark matter halos for stacked samples of galaxies, giving us an observational tool for finding halo masses. 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 allows us to do a differential measurement of the halo mass-galaxy size relationship at fixed stellar mass, defined as: $M_{h}(M_{*}) \propto r_{\mathrm{eff}}^{\eta}(M_{*})$, and compare $\eta$($M_{*}$) over the mass range of our sample. 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 trend is weakest for low mass blue galaxies and strongest for high mass large red galaxies (LRGs). This suggests that different processes are responsible for the strength of the observed trend over our range of stellar mass bins. Investigation of this relationship in hydrodynamical simulations suggests that this effect is strongest in satellite galaxies, and that the trend we observe in our data should be driven primarily by the fraction of satellite galaxies.encosmology: observationsgravitational lensing: weakdark mattergalaxies: haloesgalaxies: structureMaster Thesis