Nicholas Rowell, Michael Davidson, Nigel C. Hambly, Lennart Lindegren, Javier Castañeda, Claus Fabricius, Jose Hernández, Dafydd W. Evans

An accurate model of the point spread function is required in order to estimate positions and brightnesses of stars in digitized images. The PSF of the Gaia space telescope is unusual due to the use of drift-scan mode and time-delayed integration, in which the satellite spins and precesses while images are captured. This induces several systematic and periodic distortions in the PSF that are unique to Gaia. These include systematic variations in the stellar image drift rate with respect to the charge transfer rate, and spatial variations in the CCD response that are, contrary to expectations, not marginalised by the use of TDI mode. These must be incorporated into the PSF model in order to reduce systematic errors in Gaia's data products. We have developed a semi-analytic model of the PSF, in which the blurring effects of along- and across-scan stellar image motion are modelled analytically, and dependences of the PSF shape on source colour and position within the CCD are calibrated empirically. Constraints on the PSF origin are introduced in order to break a degeneracy with the geometric instrument calibration. Our new PSF model leads to significant improvements in the modelling of observations, particularly around the 11-13 magnitude range in G. This will contribute to reductions in the astrometric and photometric uncertainties in the derived data products. Our PSF model was deployed in the Gaia cyclic data processing systems and used in the production of the forthcoming Data Release 4. The linear part of Gaia's PSF is now well understood. Future development work will focus on the handling of several nonlinear effects that depend on the signal level, including charge transfer inefficiency and the brighter-fatter effect. This work will provide a useful reference for users of Gaia data and for other missions that use the same observing principles, such as the proposed GaiaNIR mission.