H0LiCOW. VI. Testing the fidelity of lensed quasar host galaxy reconstruction

The empirical correlation between the mass of a supermassive black hole (M_BH) and its host galaxy properties is widely considered to be an evidence of their co-evolution. A powerful way to test the co-evolution scenario and learn about the feedback processes linking galaxies and nuclear activity is to measure these correlations as a function of redshift. Unfortunately, currently M_BH can only be estimated in active galaxies at cosmological distances. At these distances, bright active galactic nuclei (AGNs) can outshine the host galaxy, making it extremely difficult to measure the host's luminosity. Strongly lensed AGNs provide in principle a great opportunity to improve the sensitivity and accuracy of the host galaxy luminosity measurements as the host galaxy is magnified and more easily separated from the point source, provided the lens model is sufficiently accurate. In order to measure the M_BH-L correlation with strong lensing, it is necessary to ensure that the lens modelling is accurate, and that the host galaxy luminosity can be recovered to at least a precision and accuracy better than that of the typical M_BH measurement. We carry out extensive and realistic simulations of deep Hubble Space Telescope observations of lensed AGNs obtained by our collaboration. We show that the host galaxy luminosity can be recovered with better accuracy and precision than the typical uncertainty in MBH(~0.5 dex) for hosts as faint as 2-4 mag dimmer than the AGN itself. Our simulations will be used to estimate bias and uncertainties in the actual measurements to be presented in a future paper.