  The brighter fatter effect has been postulated to arise due to the build up
of a transverse electric field, produced as photo-charges accumulate in the
pixels' potential wells. We investigate the brighter fatter effect in Hyper
Suprime-Cam by examining flat fields and moments of stars. We observe
deviations from the expected linear relation in the photon transfer curve,
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
parametrized 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 photon
transfer curves and significantly reduces, but does not completely remove, the
luminosity dependence of the PSF over a wide range of magnitudes.
