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.
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