From: Henk Hoekstra (hoekstra@uvic.ca)
Date: Wed Jan 18 2006 - 14:52:05 PST
Hi,
Let me provide a brief update on the lensing aspects. I spoke about this
with Saul in some detail, and I believe that we have to be careful
to put too much weight on the lensing aspects.
What is clear that the best approach from the lensing perspective
is to go as deep as possible in F814W. However, if the focus would
be to calibrate masses at high-z, a "pure lensing" proposal would
target clusters at somewhat lower z (say 0.9-1.0). The current
sample is challenging from a lensing perspective and we should keep
this in mind.
I believe that the real new angle should focus on the CMR of these
clusters. This can only be done with HST and we have a really unique
sample here! This is new science that wasn't in the previous proposal.
For the lensing aspects, there are some clear science goals, but the
improvements in mass might not be convincing for the TAC. In the
discussion with Saul yesterday, we abandoned (for the moment at least)
using F814W and go back for F775W.
Interestingly, the F775W integrations times need to be 1/3 of the
F850LP exposure times to reach the same effective number densities.
Hence F775W is 3 times faster. This is the reason why the best
strategy for lensing is to focus on the bluer filter. The changes in
redshift distribution appears not to be too much of a problem as
essentially all galaxies in detected in z' are also detected in i'
(for same integration time), but the converse is not true.
But this is not a good strategy for the SNe component. An interesting
balance is achieved if we ensure the F850LP total exposure time is
3x the F775W time. In that case the effective number densities are
remarkably similar, and one mostly sees the same galaxies.
With this approach we can improve the shape measurements of the
galaxies by combining measurements in the two filters. This increases
the effective number density somewhat. In addition about 20% of the
objects are found in only one of the two filters.
Here are the effective number densities for 4 strategies, based on
a total of 16 orbits (note that the last one is there only for
completeness):
# norbit norbit
# F775W F850LP n_eff
# [arcmin^{-2}
#
0 16 135
4 12 165 <----
8 8 180
16 0 215
For 8 orbits F814W and 8 orbits F850LP, we get n_eff ~ 220
currently we have something like
1.5 6.5 100
A strategy with a 3x longer total exposure in z vs i results
in a number density of ~165, which is 65% larger than what we
have now. As the error in the mass is proportional to 1/sqrt(N),
we reduce the error from 30% to about 23%
The difference with the "optimal" lensing approach (whihc is to
add 8 orbits of F814W) is fairly small, as this would reduce
the fiducial mass error to 20%.
Reducing the error from 30% to 23% may not seem much, but
effectively we increase the sample by 65%. This is very important,
because the current sample of clusters is very limited.
Based on these considerations I am happy to do the write up
based on a strategy of 25% F775W and 75% F850LP. This also works
better for the SNe.
An interesting question is whether this is (close to) the optimal
combination for CMR studies as well: we should have rather similar
S/N in both filters with this approach, so no single filter dominates
the error in the color. Is that correct?
Cheers,
Henk
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