Principal Component Analysis of the Time- and Position-Dependent Point Spread Function of the Advanced Camera for Surveys

We describe the time- and position-dependent point spread function (PSF) variation of the Wide Field Channel (WFC) of the Advanced Camera for Surveys (ACS) with the principal component analysis (PCA) technique. The time-dependent change is caused by the temporal variation of the $HST$ focus whereas the position-dependent PSF variation in ACS/WFC at a given focus is mainly the result of changes in aberrations and charge diffusion across the detector, which appear as position-dependent changes in elongation of the astigmatic core and blurring of the PSF, respectively. Using >400 archival images of star cluster fields, we construct a ACS PSF library covering diverse environments of the $HST$ observations (e.g., focus values). We find that interpolation of a small number ($\sim20$) of principal components or ``eigen-PSFs'' per exposure can robustly reproduce the observed variation of the ellipticity and size of the PSF. Our primary interest in this investigation is the application of this PSF library to precision weak-lensing analyses, where accurate knowledge of the instrument's PSF is crucial. However, the high-fidelity of the model judged from the nice agreement with observed PSFs suggests that the model is potentially also useful in other applications such as crowded field stellar photometry, galaxy profile fitting, AGN studies, etc., which similarly demand a fair knowledge of the PSFs at objects' locations. Our PSF models, applicable to any WFC image rectified with the Lanczos3 kernel, are publicly available.