  Charge-coupled devices (CCDs) are widely used in astronomy to carry out a
variety of measurements, such as for flux or shape of astrophysical objects.
The data reduction procedures almost always assume that ther esponse of a given
pixel to illumination is independent of the content of the neighboring pixels.
We show evidence that this simple picture is not exact for several CCD sensors.
Namely, we provide evidence that localized distributions of charges (resulting
from star illumination or laboratory luminous spots) tend to broaden linearly
with increasing brightness by up to a few percent over the whole dynamic range.
We propose a physical explanation for this "brighter-fatter" effect, which
implies that flatfields do not exactly follow Poisson statistics: the variance
of flatfields grows less rapidly than their average, and neighboring pixels
show covariances, which increase similarly to the square of the flatfield
average. These covariances decay rapidly with pixel separation. We observe the
expected departure from Poisson statistics of flatfields on CCD devices and
show that the observed effects are compatible with Coulomb forces induced by
stored charges that deflect forthcoming charges. We extract the strength of the
deflections from the correlations of flatfield images and derive the evolution
of star shapes with increasing flux. We show for three types of sensors that
within statistical uncertainties,our proposed method properly bridges
statistical properties of flatfields and the brighter-fatter effect.
