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

Weak Lensing Dilution in A1689
0.86
0.84
0.82
Cluster V−i [mag]
0.8
0.78
0.76
0.74
0.72
0.7
0.68
0.66
0.9 2 5 10 20
θ [arcmin]
Figure 2.14 – Galaxy color profile after weighting the color of each object by its individual
distortion, g i , accounting for any difference between the color distribution of the cluster
and background populations comprising the green galaxy population. The color of the
cluster members becomes slowly bluer with increasing radius moving from E/S0 colors in
the center to mid-type galaxy colors at the limit of the data, r ∼ 2 h −1 Mpc. The green
points represent the uncorrected V − i ′ profile of the green sample.
are expected to contain a greater fraction of background galaxies and hence
should have a relatively higher value of g (G)
T
. This trend is apparent in Figure
2.16 (left panels), where we plot the recovered mean tangential distortion
(here the average is over a magnitude bin) for each of the four radial bins,
as a function of absolute magnitude. A clear trend is found at all radii towards
higher levels of g T at fainter luminosities. Note that the mean level
of the background distortion (black solid line) drops with increasing radius
so that the proportion g (G)
T
(M)/g(B) T
is generally an increasing function of
radius and a decreasing function of luminosity. To correct for this we simply
apply equation (2.18) to each magnitude bin:
Φ cl (M k ) = Φ(M k ) · [1 − 〈g (G)
T
(M k)〉/〈g (B)
T
(r)〉] (2.22)
(Note that the background signal is averaged over the whole range of magnitudes
at that radius.)
We then construct the luminosity function for four independent radial
bins, as shown in Figure 2.16 (middle panel) and fit a Schechter (1976) function
to each (dashed lines). It can be seen that there is no obvious tendency
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