Mass and Light distributions in Clusters of Galaxies - Henry A ...

1.2 Gravitational Lensing
effects can range from slight biases arising from triaxiality of clusters, to large
uncertainties in the mass estimates due to line-of-sight mergers of clusters of
comparable sizes.
1.2.4.2.2 Mass-Sheet Degeneracy Adding a constant mass sheet to
κ does not affect the image ellipticities, since it causes only an isotropic
expansion of the images. This transformations is equivalent to scaling the
Jacobian matrix A by some scalar multiple λA, resulting in
A ′ = λA = λ
(
)
1 − κ − γ 1 −γ 2
−γ 2 1 − κ + γ 1
which is equivalent to the following transformations of κ and γ,
, (1.49)
1 − κ ′ = λ(1 − κ), γ ′ = λγ. (1.50)
This transformation evidently leaves the reduced shear g = γ/(1 − κ) invariant
under this scaling. This invariance ambiguity is referred to as the
mass-sheet degeneracy. It was originally discovered by Falco et al. (1985)
and further highlighted by Schneider & Seitz (1995). The ambiguity can
be broken by measuring the magnification effect, because µ is not invariant
under the transformation, as
µ( ⃗ θ) → λ 2 µ( ⃗ θ). (1.51)
Measuring the magnification bias has been suggested by Broadhurst et al.
(1995) using galaxy number-counts. Another approach is the use of wide-field
imaging with field-of-view larger than the clusters, in which case the lensing
effect vanishes at the boundaries of the field, thus breaking the degeneracy.
1.2.4.2.3 PSF Effects The main difficulty of weak lensing measurements
is due to point-spread function (PSF) effects, arising from the telescope/CCD
response and/or atmospheric seeing. The atmospheric seeing,
which is a term describing the result of atmospheric turbulence, causes smear-
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