Point spread function errors for weak lensing – density cross-correlations

Aims. Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for quantifying PSF-induced systematics as diagnostics for cross-correlation measurements of weak lensing with density tracers; for example, galaxy-galaxy lensing. We show how those systematics propagate to physical parameters of the density tracers. Those diagnostics only require a shape catalog of PSF stars and foreground galaxy positions. Methods. We considered the PSF-induced multiplicative bias, and introduced three second-order statistics as additive biases. We computed both biases for the weak-lensing derived halo mass of spectroscopic foreground galaxy samples; in particular, their effect on the tangential shear and fit halo mass as a function of stellar mass. In addition, we assessed their impact on the recently published black-hole – halo-mass relation for type I active galactic nuclei (AGNs). Results. Using weak-lensing catalogs from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) and the Dark Energy Survey (DES), we find the multiplicative biases in the tangential shear to be less than 0.5%. No correlations between additive bias and galaxy properties of the foreground sample are detected. The combined PSF systematics affect low-mass galaxies and small angular scales; halo mass estimates can be biased by up to 18% for a sample of central galaxies in the stellar mass range of 9.0 ≤ log M*/M⊙ < 9.5. Conclusions. The PSF-induced multiplicative bias is a subdominant contribution to current studies of weak-lensing – density cross-correlations, but might become significant for upcoming stage IV surveys. For samples with a low tangential shear, additive PSF systematics can induce a significant bias on derived properties such as the halo mass.