From: Henk Hoekstra (hoekstra@uvic.ca)
Date: Sat Jan 21 2006 - 20:09:01 PST
Hi,
Below a rewrite of the lensing section. I wonder whether it is too
long. I thing the TJ is similar in size (and text), but the SJ is
probably a bit longer. But we should be able to tighten things up.
Cheers,
Henk
Science Justification:
{\bf Weak lensing estimates of cluster masses:} Weak gravitational
lensing of background galaxies is now a well-established technique to
measure the projected cluster mass {\it directly}. The mass estimate
does not depend on the geometry or dynamical state of the cluster,
which is important at any redshift, but crucial for clusters at the
redshifts studied here. Comparison of weak lensing masses to other
mass estimators (e.g., X-ray, SZ or optical properties) provides
unique constraints on cluster formation. Studying clusters at
$z=1-1.5$ is of particular interest as this corresponds to the era
where much of the cluster assembly takes place.
Another important application of the proposed observations is the most
accurate calibration of the masses of high redshift clusters for years
to come. These data will provide the necessary reference to ensure
that the next generation cluster surveys can reliably use clusters
beyond $z\sim 1$ in order to constrain $w$ to better than $5-10\%$.
Fortunately, recent work by Majumdar \& Mohr (2003;2004) on
``self-calibration'' has shown that only a moderate sample of
clusters, such as the one proposed, needs to be studied in detail to
reach those goals.
The sample studied here is larger by a factor of 4 from previous work,
and targets clusters at higher redshifts. The observations proposed
here provide a significant improvement over the data in hand. The
additional F775W and F850LP data will increase the ``effective number
density'' of sources by 65\%, thus reducing the uncertainty in the
mass of the individual clusters in our sample: these data will enable
us to estimate the mass of the ``average'' cluster in our sample
$(M=5\times 10^{14} M_\odot)$ to within 23\%. Given the small sample
of clusters available to us at these redshifts, the impact of the
improvement in accuracy should not be underestimated: with more
accurate masses for each cluster we can better constrain the scatter
in mass-observable relations. It also allows us to address the
important, but still outstanding question, whether different detection
techniques select different populations of clusters.
The proposed observations enable us to determine the zero-point in the
mass-observable relation to better than $10-15\%$ in each of four independent
redshift bins. These data will complement archival data and ground
based efforts at lower redshifts (e.g., the Canadian Cluster Comparison
Project, the CFHT Legacy Survey) that are undertaken by members of our
team. Consequently, we will be able to study the evolution in the properties
of clysters from the present day out to $z\sim 1.4$, thus paving the
way for cluster abundance studies in an era of precision cosmology.
Technical Justification:
To compute the accuracy with which we can determine the masses of
clusters we used data from the UDF (both F775W and F850LP) to
determine the ``effective'' number density of sources used in the
lensing analysis. These estimates include a proper weigthing for the
smaller sources which have sizes comparable to the PSF. We also
compared these numbers to the results obtained from the few clusters
already observed and find excellent agreement. We find that a strategy
with a balance of 25\% F775W and 75\% F850LP observations gives
similar source densities in both filters. The added depth of F850LP
observations and the new F775W observations increase the number
density of sources from $\sim 100$ to $\sim 165$ arcmin$^{-2}$ (we can
combine the measurements from the two filters). These is a significant
increase, which in combination with a realistic photometric redshift
distribution inferred from the UDF, indicates that we can measure the
mass of a cluster with $M=5\times 10^{14}M_\odot$ to within
$23\%$. These calculation also agree well with actual published
results (Jee et al. 2005; Lombardi et al. 2005; Jee et al. 2006).
Many other HST weak lensing cluster studies have used a mosaic to
measure the lensing signal out to large radii, in an effort to break
the mass-sheet degeneracy. Our detailed calculations show that the
gain from mosaicing is minimal for clusters beyond $z=1$ (where the
FOV of ACS is well matched to the angular extent of the cluster), and
that we obtain more accurate masses by obtaining deeper observations
instead. We determine masses by fiting parameterized mass models to
the data (e.g., NFW profile).
The accuracy with which we can determine the masses allows us to
extend measurements of the mass-observable (i.e., X-ray, SZ or
optical properties) out to $z=1.4$, thus probing the evolution
of clusters from the nearby universe out to the most active
period in their formation.
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