Gravitational Lensing of Anisotropic Sources
  In strong gravitational lensing, the multiple images we see correspond to
light rays that leave the source in slightly different directions. If the
source emission is anisotropic, the images may differ from conventional lensing
predictions (which assume isotropy). To identify scales on which source
anisotropy may be important, we study the angle delta between the light rays
emerging from the source, for different lensing configurations. If the lens has
a power law profile M propto R^gamma, the angle delta initially increases with
lens redshift and then either diverges (for a steep profile gamma<1), remains
constant (for an isothermal profile gamma=1), or vanishes (for a shallow
profile gamma>1) as zl approaches zs. The scaling with lens mass is roughly
delta propto M^(1/(2-gamma)). The results for an NFW profile are qualitatively
similar to those for a shallow power law, with delta peaking at about half the
redshift of the source (not half the distance). In practice, beaming could
modify the statistics of beamed sources lensed by massive clusters: for an
opening angle theta_jet, there is a probability as high as P ~ 0.02-0.07
(theta_jet/{0.5} deg)^-1 that one of the lensed images may be missed (for 2 <
zs < 6). Differential absorption within Active Galactic Nuclei could modify the
flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters
could provide further constraints on the sizes of absorbing regions. Source
anisotropy is not likely to be a significant effect in galaxy-scale strong
lensing.
