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

Mass and Light of A1703, A370 & RXJ1347-11
in the green sample. The total flux of the cluster in the n th radial bin is
therefore,
F cl (r n ) = ∑ i
F (G)
i − 〈D(B) 〉/〈D (G) 〉
〈g T (r n ) (B) 〉
∑
i
F (G)
i g (G)
T,i
(3.6)
and the flux is then translated to luminosity. First we calculate the absolute
magnitude,
M = m − 5 log d L − K(z) + 5, (3.7)
where the K-correction is evaluated for each radial bin according to its color.
The luminosity is simply,
L = 10 0.4(M ⊙−M) L ⊙ , (3.8)
where M ⊙ is the absolute magnitude of the Sun (AB system) in the relevant
band.
The results for all four clusters, including A1689, are shown in Fig. 3.8.
As explained in § 3.3, the green sample comprises mostly of cluster galaxies,
therefore the correction is not big for r < 10 ′ , and only present at large radii,
increasing the error. The cluster luminosity profiles mostly have a steady
linear decline with radius, and are well described by a power-law fit, but with
different slopes of d log(L)/d log(r) ∼ −0.95 ± 0.1, −1.4 ± 0.06, −0.9 ± 0.1 for
A1703, A370 and RXJ1347-11, respectively.
3.9 M/L profiles
We may now derive a radial profile of the differential mass-to-light ratio
(often referred to as δM(r)/δL(r)) by dividing the best-fit NFW projected
mass density profile by the newly derived luminosity density profile obtained
in § 3.8. The four M/L profiles are shown together in Fig. 3.9 to the limit of
our data, ∼ 3 h Mpc. The mass profiles for these clusters and their NFW fits
were derived in our earlier work, Broadhurst et al. (2005b) for A1689 and in
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