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Decomposing the host galaxy from high-z QSOs using principal component analysis

High resolution deep imaging from space and adaptive optics techniques with large ground-based facilities have enabled studies examining faint host galaxies of high redshift quasi-stellar objects (QSOs). However, the related image processing techniques, especially for a precise point-spread function (PSF) reconstruction and characterization of the host galaxy light profiles, have yet to be optimized. We present here the scientific performance of a principal component analysis (PCA) based PSF subtraction of the central bright point source of high redshift QSO images, as well as further characterization of the host galaxy profile by directly fitting a Sèrsic model to the residual image using the Markov Chain Monte Carlo (MCMC) algorithm. With a set of reference PSF star images which represent interleaving exposures between the QSO imaging, we can create an orthogonal basis of eigen-images and restore the PSF of QSO images by projecting the QSO images onto the basis. In this way, we can quantify the modes in which the PSF varies with time by a basis function that characterizes the temporal variations of the reference star as well as the QSO images. To verify the algorithm, we performed a simulation and applied this method to one of the high-z QSO targets from Mechtley et al. We demonstrate that the PCA-based PSF subtraction and further modeling of the galaxy’s light profile using MCMC fitting would sufficiently remove the effects from central dominating point sources, and improve characterization ability for the host galaxies of high-z QSOs to the background noise level which is much better than previous two-component fitting procedures.