  A standard method to study the mass distribution in galaxy clusters is
through strong lensing of background galaxies in which the positions of
multiple images of the same source constrain the surface mass distribution of
the cluster. However, current parametrized mass models can often only reproduce
the observed positions to within one or a few arcsec which is worse than the
positional measurement uncertainty. One suggested explanation for this
discrepancy is the additional perturbations of the path of the light ray caused
by matter density fluctuations along the line of sight. We investigate this by
calculating the statistical expectation value for the angular deflections
caused by density fluctuations, which can be done given the matter power
spectrum. We find that density fluctuations can, indeed, produce deflections of
a few arcsec. We also find that the deflection angle of a particular image is
expected to increase with source redshift and with the angular distance on the
sky to the lens. Since the light rays of neighbouring images pass through much
the same density fluctuations, it turns out that the images' expected
deflection angles can be highly correlated. This implies that line-of-sight
density fluctuations are a significant and possibly dominant systematic for
strong lensing mass modeling and set a lower limit to how well a cluster mass
model can be expected to replicate the observed image positions. We discuss how
the deflections and correlations should explicitly be taken into account in the
mass model fitting procedure.
