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

Weak Lensing Dilution in A1689
30
28
Radial critical curve
κ=1 curve
26
24
θ [arcsec]
22
20
18
16
14
12
0 5 10 15 20 25 30
C Vir
Figure 2.20 – The curves shows how the radius of the radial critical curve, shown in
blue, varies with the concentration parameter of an NFW profile, where the model is normalized
to generate the observed Einstein radius of 47 ′′ for all values of the concentration
parameter, C vir . The radial critical curve shrinks as the mass profile becomes steeper.
This is also the case for the radius at which the distortion g T = 0, corresponding to the
radius where the surface density of matter is equal to the critical surface density (κ = 1),
here the degree of tangential and radial distortion is always equal, independent of the
form of the mass profile. We have marked the observed values of the radial critical curves
and the radius where the distortion is seen to be zero as measured independently in two
ways using the statistical distortion measurements (dotted lines) as described in § 2.4, and
the same values derived from the multiple image analysis presented in Broadhurst et al.
(2005a) (dashed lines). These differing measurements are consistent with each other and
by comparison with the model curves bracket intermediate values of concentration in the
range 5 < C vir < 15 for the inner strongly lensed region.