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

Mass and Light of A1703, A370 & RXJ1347-11
our CC selection.
3.7 Weak lensing dilution
We can now estimate the fraction of cluster galaxies by taking the ratio of
the WL signal between the green sample and the background sample, with
the background including both red and blue galaxies as explained in § 3.3.
For a given radial bin (r n ) containing objects in the green sample (§ 3.2),
the mean value of g (G)
T
(eq. 3.3) is an average of the signal over cluster members
and some background galaxies. Thus, its mean value 〈g (G)
T
〉 will be lower
than the true background level denoted by 〈g (B) 〉 (Fig. 3.6) in proportion to
T
the fraction of unlensed galaxies in the bin that lie in the cluster (rather
than in the background), since the cluster members on average will add no
net tangential signal. Therefore,
f cl (r n ) ≡
N cl
= 1 − 〈g T (r n ) (G) 〉
N Green 〈g T (r n ) (B) 〉
〈D (B) 〉
〈D (G) 〉
(3.5)
is the cluster membership fraction of the green sample, where 〈D (B) 〉 and
〈D (G) 〉 are the mean lensing depths, D ds /D s , of the background and green
galaxy samples, respectively, derived in § 3.5 (see full derivation in the appendix
of Medezinski et al. 2007).
In Fig. 3.7 we show this ratio for each of our new clusters. In our previous
analysis of A1689, where only color-magnitude selection was done, many
background galaxies were present in the green sample, so that only in the first
radial bins the fraction of cluster galaxies was high, and gradually declined
with radius (due to increasing fraction of background galaxies) at larger
radii. Here, since we select a tight region around the cluster in CC and are
able to better resolve it, our results show that the fraction is close to unity
throughout the radial range of the cluster. Only in the outer bins, usually
at r > 5 ′ − 10 ′ does the fraction decline, and we see a smaller percentage of
cluster members. Large errorbars are introduced at outer radii since there
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