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

2.8 Cluster luminosity functions
10 15 θ [arcmin]
Luminosity density [L iο
h 2 Mpc −2 ]
10 14
10 13
10 12
Luminosity density [L i’ο
h 2 Mpc −2 ]
10 11
0.1 0.4 0.9 2 5 10 20
10 12 1 2 5 10 20
θ [arcmin]
Figure 2.12 – The “g-Weighted” luminosity
density vs. cluster radius. Each
galaxy’s flux F i (green sample) is weighted
by its tangential distortion g T,i with respect
to the background distortion signal
(red points). The filled circles represent the
ACS data, and the empty squares are for
the Subaru data. The blue points are derived
from integrating over the luminosity
functions of the same radial bins (see § 2.8),
and serve as a consistency check, showing
good agreement between these differing calculations.
The dashed line is the best fitting
linear relation for the blue points.
Figure 2.13 – The “g-Weighted” luminosity
density vs. cluster radius (red
squares), compared to the unweighted luminosity
density (green circles), showing
as expected the increasing size of the correction
with increasing radius, where the
sample becomes increasingly dominated by
background galaxies.
2.8 Cluster luminosity functions
The data allow the luminosity function to be usefully constructed in several
independent radial and magnitude bins, and hence we can examine the
form of the luminosity function of cluster members as a function of projected
distance from the cluster center. For this we combine the ACS and the Subaru
photometry. The ACS has the advantage of extending two magnitudes
fainter in the i ′ -band than the Subaru photometry for r < 2 ′ . As can be
seen in Figure 2.15, the ACS i ′ magnitudes agree with Subaru i ′ magnitudes
for galaxies found and matched in both catalogs. The background correction
to evaluate f cl , must be made in each magnitude bin independently, since
the relative proportion of background galaxies increases with apparent magnitude,
so that the lower luminosity bins of the green luminosity function
53