  Some bright cD galaxies in cluster cooling flows have Thomson optical depths
exceeding 0.01. A few percent of their luminosity is scattered and appears as
diffuse polarized emission. We calculate the scattering process for different
geometric combinations of luminosity sources and scattering media. We apply our
results to galaxies, with and without active nuclei, immersed in cooling flows.
We model observations of NGC 1275 and M87 (without active nuclei) in the
presence of sky and galactic background fluxes which hinder the measurement of
the scattered light at optical wavelengths. Current instruments are unable to
detect the scattered light from such objects. However, when a galaxy has an
active nucleus of roughly the same luminosity as the remainder of the galaxy in
V, both the total and polarized scattered intensity should observable on large
scales (5--30kpc), meaning intensity levels greater than 1% of the background
level. For typical AGN and galaxy spectral distributions, the scattering is
most easily detected at short (U) wavelengths. We point out that a number of
such cases will occur. We show that the radiation pattern from the central
nuclear region can be mapped using the scattering. We also show that the
scattered light can be used to measure inhomogeneities in the cooling flow.
