  Investigating the link between supermassive black hole and galaxy evolution
requires careful measurements of the properties of the host galaxies. We
perform simulations to test the reliability of a two-dimensional image-fitting
technique to decompose the host galaxy and the active galactic nucleus (AGN),
especially on images obtained using cameras onboard the Hubble Space Telescope
(HST), such as the Wide-Field Planetary Camera 2, the Advanced Camera for
Surveys, and the Near-Infrared Camera and Multi-Object Spectrometer. We
quantify the relative importance of spatial, temporal, and color variations of
the point-spread function (PSF). To estimate uncertainties in AGN-to-host
decompositions, we perform extensive simulations that span a wide range in
AGN-to-host galaxy luminosity contrast, signal-to-noise ratio, and host galaxy
properties (size, luminosity, central concentration). We find that realistic
PSF mismatches that typically afflict actual observations systematically lead
to an overestimate of the flux of the host galaxy. Part of the problem is
caused by the fact that the HST PSFs are undersampled. We demonstrate that this
problem can be mitigated by broadening both the science and the PSF images to
critical sampling without loss of information. Other practical suggestions are
given for optimal analysis of HST images of AGN host galaxies.
