Exploring the Brighter-fatter Effect with the Hyper Suprime-Cam

The brighter-fatter effect has been postulated to arise due to the build up of a transverse electric field, produced as photocharges accumulate in the pixels' potential wells. We investigate the brighter-fatter effect in the Hyper Suprime-Cam by examining flat fields and moments of stars. We observe deviations from the expected linear relation in the photon transfer curve (PTC), luminosity-dependent correlations between pixels in flat-field images, and a luminosity-dependent point-spread function (PSF) in stellar observations. Under the key assumptions of translation invariance and Maxwell's equations in the quasi-static limit, we give a first-principles proof that the effect can be parameterized by a translationally invariant scalar kernel. We describe how this kernel can be estimated from flat fields and discuss how this kernel has been used to remove the brighter-fatter distortions in Hyper Suprime-Cam images. We find that our correction restores the expected linear relation in the PTCs and significantly reduces, but does not completely remove, the luminosity dependence of the PSF over a wide range of magnitudes.