Galaxy-Galaxy Lensing by Non-Spherical Haloes I:Theoretical
  Considerations
  We use Monte Carlo simulations to investigate the theory of galaxy-galaxy
lensing by non-spherical dark matter haloes. The simulations include a careful
accounting of the effects of multiple deflections. In a typical data set where
the mean tangential shear of sources with redshifts zs ~ 0.6 is measured with
respect to the observed symmetry axes of foreground galaxies with redshifts zl
~ 0.3, the signature of anisotropic galaxy-galaxy lensing differs substantially
from the expectation that one would have in the absence of multiple
deflections. The observed ratio of the mean tangential shears, g+/g-, is
strongly suppressed compared to the function that one would measure if the
intrinsic symmetry axes of the foreground galaxies were known. Depending upon
the characteristic masses of the lenses, the observed ratio of the mean
tangential shears may be consistent with an isotropic signal (despite the fact
that the lenses are non-spherical), or it may even be reversed from the
expected signal (i.e., the mean tangential shear for sources close to the
observed minor axes of the lenses may exceed the mean tangential shear for
sources close to the observed major axes of the lenses). These effects are
caused primarily by the fact that the lens galaxies have, themselves, been
lensed and therefore the observed symmetry axes of the lenses differ from their
intrinsic symmetry axes. The effects of lensing of the foreground galaxies on
the observed function g+/g- cannot be eliminated by the rejection of foreground
galaxies with small image ellipticities, nor by focusing the analysis on
sources that are located very close to the observed symmetry axes of the
foreground galaxies. We conclude that any attempt to use a measurement of g+/g-
to constrain the shapes of dark matter galaxy haloes must include Monte Carlo
simulations that take multiple deflections properly into account.
