Two-Dimensional Modelling of Optical HST and Infrared Tip-Tilt Images of Quasar Host Galaxies

A description is given of the method used to extract quasar host-galaxy parameters from the deep Hubble Space Telescope quasar images presented by McLure et al. (1999) and Dunlop et al. (2000). We then give the results of extensive testing of this technique on a wide range of simulated quasar+host combinations spanning the redshift range of our HST study (0.1 < z < 0.3). These simulations demonstrate that, when applied to our deep HST images, our method of analysis can easily distinguish the morphological type of a given host galaxy, as well as determining its scalelength, luminosity, axial ratio and position angle to within an accuracy of a few percent. We also present new infrared tip-tilt images of 4 of the most luminous quasars in our {\sc hst} sample, along with the outcome of modelling these data in a similar manner. The results provide further confidence in the accuracy of the derived host-galaxy scalelengths, and allow accurate determination of $R-K$ colours for this subset of sources. All 4 of these quasar host galaxies have very similar red colours, $R-K = 2.9 \pm 0.2$, indicative of a well-evolved stellar population.