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

3.6 Weak lensing analysis
3.6 Weak lensing analysis
We use the IMCAT package developed by N. Kaiser 3 to perform object detection
and shape measurements, following the formalism outlined in Kaiser,
Squires, & Broadhurst (1995, hereafter KSB). Our analysis pipeline is described
in Umetsu et al. (2010). We have tested our shape measurement and
object selection pipeline using STEP (Heymans et al. 2006) data of mock
ground-based observations (see Umetsu et al. 2010, § 3.2). Full details of
the methods are presented in Umetsu & Broadhurst (2008), Umetsu et al.
(2009) and Umetsu et al. (2009). In short, we find that we can recover the
weak lensing signal with good precision, typically, m ∼ 5% of the shear
calibration bias, and c ∼ 10 −3 of the residual shear offset which is about
one-order of magnitude smaller than the weak-lensing signal in the cluster
outskirts (|g| ∼ 10 −2 ). We emphasize that this level of calibration bias is subdominant
compared to the statistical uncertainty (∼ 15%) in the mass due
to the intrinsic scatter in galaxy shapes. Rather, the most critical source of
systematic uncertainty in cluster weak lensing is dilution of the distortion signal
due to the inclusion of unlensed foreground and cluster member galaxies,
which can lead to an underestimation of the true signal for R < 400 h −1 kpc
by a factor of 2−5, as demonstrated in Broadhurst et al. (2005b), Medezinski
et al. (2007) and here.
The shape distortion of an object is described by the complex reducedshear,
g = g 1 + ig 2 , where the reduced-shear is defined as:
g α ≡ γ α /(1 − κ). (3.1)
The tangential component of the reduced-shear, g T , is used to obtain the
azimuthally averaged distortion due to lensing, and computed from the distortion
coefficients g 1 , g 2 :
g T = −(g 1 cos 2θ + g 2 sin 2θ), (3.2)
3 http://www.ifa.hawaii.edu/ kaiser/imcat
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