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\title[Cluster Shear TEsting Program]{Cluster STEP}
\author[J. Young and Other]{J. Young$^{1}$\thanks{E-mail:
email@address (AVR); otheremail@otheraddress (ANO)} and 
Other.\\
$^{1}$OSU/USM \\
}
\begin{document}

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\date{2013}

\pagerange{\pageref{firstpage}--\pageref{lastpage}} \pubyear{2002}

\maketitle

\label{firstpage}

\begin{abstract}
Shape measurement bias is an important source of systematic error in the 
measurement of galaxy cluster masses by weak gravitational lensing. The
cluster mass function as measured by weak lensing for the Dark Energy Survey (DES)
will be used to constrain cosmology, so it is important that shape measurement
bias is small. Comparing the current level of systematic bias of different 
weak lensing pipelines measured on simulated images allows us to model the expected error
in the cluster mass measurement for the stacked weak lensing
result. The accuracy of the shape measurement pipelines is determined from image simulations
that have the expected distribution of galaxy properties that will be observed by DES. Eight 
different shape measurement pipelines, including several which have not competed in previous
image simulation challenges, are included. The best performing weak
lensing pipelines exhibit a multiplicative bias of several percent 
that is stable as a function of redshift. This level of shape measurement bias does not have a statistically
significant impact on DES cluster cosmology, and can be further reduced by simulation based calibration.
\end{abstract}

\begin{keywords}
gravitational lensing: weak, techniques:image processing
\end{keywords}

\section{Introduction}
The abundances and masses of galaxy clusters provide an important constraint on 
cosmology \citep{obscos}. Weak lensing is one of the most direct way to measure cluster
masses for large optical surveys such as the Dark Energy Survey (DES)
(http://www.darkenergysurvey.org/), which due to its depth and
survey area will very accurately measure the halo mass function.
Measuring the correlated distortion in the shapes of galaxies caused by lensing is complicated
by the distortion of observed images caused by the atmosphere and telescope optics, called the 
Point Spread Function or PSF. Shape measurement pipelines have been developed to remove the 
effect of the PSF and accurately measure the lensing signal. As the
mass measured from a galaxy cluster depends on the strength of the
shear measured on galaxies behind the cluster, a biased weak lensing
pipeline will lead to a biased determination of the cluster mass.
 
\indent Previous image simulation challenges were used to determine the accuracy of shape measurement pipelines. 
Previously published publicly available weak lensing challenges\footnote{STEP1 \citep{STEP1},
STEP2 \citep{STEP2}, GREAT08 \citep{GREAT08}, GREAT10
\citep{GREAT10}} used blinded image
simulations to characterize the shape measurement bias created by
different lensing pipelines. Results from these challenges have been
used to calibrate shape measurement pipelines \citep[e.g.][]{Apple}, determine
that lensing pipelines meet accuracy requirements for scientific
analysis \citep[e.g.][]{Berge}, and provide insight for further pipeline
development. These previous challenges focused on calibrating shear
measurement pipelines in the cosmic shear regime ( $| \gamma | < 0.06$
) and on the importance of shape measurement bias for the shear power
spectrum of large scale structure. Simulations
were created to study how specific galaxy and PSF properties affect the accuracy of 
shape measurements, rather than on the total shape measurement bias expected for any specific 
optical survey. \\
\indent To determine the error on the cluster mass measurement in a
specific survey due to shape measurement bias it is important to use
image simulations that have properties similar to the data. 
The size, shape, morphology, and signal-to-noise ratio of sources all impact the accuracy of the 
lensing pipelines, as does the strength of the lensing signal. For the
larger shears of the cluster regime both the quadratic (q) and
multiplicative (m) shape measurement bias (c.f. Eqn.~\ref{Eqn:QMC})
affect the bias in lensing signal to a greater extent than any
constant (c) shear bias which is an order of magnitude smaller. It is
important to quantify the quadratic and multiplicative bias on images
with simulated shear comparable to the shear observed around large
galaxy clusters. For an accurate characterization of the level of shear measurement bias, it is important to test the current implementation of lensing algorithms. Several new implementations
of lensing pipelines that are candidates for implementation
in DES are included in this project. Among those there are several
pipelines which have not been previously tested, a crucial step 
before using them in a scientific analysis. \\
\indent The Cluster Shear TEsting Program (CSTEP) tested eight weak lensing pipelines on images of constant shear
($|\gamma| = [0.03, 0.06, 0.09, 0.15]$ ) with galaxy and PSF properties that simulate the properties
of data that will be observed with DES. Systematic shape measurement bias was quantified by the Q, M and C
determined by a fit of the quadratic equation.
\begin{equation}\label{Eqn:QMC}
\gamma_m = q \gamma_t^2 + m \gamma_t + c,
\end {equation}
where $\gamma_t$ is the true shear and $\gamma_m$ is the measured
shear. In this paper we use $m \gamma_t$ instead of  $(m-1.0)
\gamma_t$ as used in STEP2 to quantify the multiplicative bias. Lensing pipelines
were evaluated to determine if their shape measurement bias was
constant as a function of simulated redshift, which is particularly
important to the accuracy of the halo mass function. The shape measurement bias as a
function of redshift determined for each lensing pipelines was used to
model the expected systematic error in the cluster mass for a stacked weak lensing measurement.

This paper contains six sections. Section 1 is the
Introduction. Section 2 describes the image simulations used in this
project. Section 3 describes the characteristics of the shape
measurement pipelines used in this analysis. Section 4 presents
findings on the impact of Signal to  Noise, selection effects and
Redshift on measurement bias and efficiency. Section 5 discusses how
shape measurement biases on data used for stacked cluster weak lensing analysis would affect
the mass of halos measured . Section 6 summarizes our conclusions. 


\section{Simulations}
\input{sims}

\section{Shape measurement pipelines}
\input{smp_sec}


\section{Evaluation of pipelines}
In this section we evaluate the performance of shape measurement 
pipelines based on a set of criteria important for large cluster weak
lensing studies. The success of a shape measurement pipeline depends
on its ability to accurately measure shear on small faint galaxies, be unbiased
when all galaxies present in an image are used to measure the shear, and
have a shear bias that does not change as a function of the redshift
of the galaxies included in the lensing measurement. A good shape
measurement method would also be able to successfully measure shear on
a high percentage of the galaxy images which it attempts to analyze. 
The relative importance of the above criteria in determining
the best shear measurement pipeline to use, may depend both on the 
data being evaluated and the lensing application. A more detailed examination
of the performance of each individual lensing pipeline 
as a function of PSF ellipticity, PSF size, galaxy size, 
and selection bias is included in Appendix \ref{App:shpipe}, along
with a description of the algorithms of the shape measurement pipelines. \\

\subsection{Galaxy signal to noise ratio}\label{sec:SNR}
\input{snr_sec}

\subsection{Average results on galaxies SNR $>$ 20}
\input{avgres}


\subsection{Selection effects and pipeline efficiency }
\input{seleff}

\subsection{Shape measurement bias as a function of Redshift}
\input{smb_sec}


\section{Stacked cluster weak lensing}
An accurate measurement of the abundance of galaxy clusters within a
given survey volume provides powerful constraints on cosmological
parameters.  While weak lensing can provide individual mass
measurements of high mass clusters, lower mass clusters can only be
measured on average by stacked weak lensing. Stacked weak lensing
measures the mean tangential shear of  background galaxies behind
galaxy clusters which are binned by observable parameters such as
richness. Stacked weak lensing
of clusters in the MaxBCG catalog \citep{Koester, Eshel} on data from the 
Sloan Digital Sky Survey \citep{York} has been used to derive
cosmological constraints on $\Omega_m$ and $\sigma_8$ in
\citep{Ying, ERozo}. Since upcoming surveys such as DES  will include deeper
imaging and better seeing, the constraints on cosmology
from stacked cluster weak lensing will substantially improve if
sources of systematic error can be controlled. \\
\indent There are a number of systematic effects that can bias the
stacked weak lensing mass measurement, and in this paper we focus
on studying the systematic bias in the stacked weak lensing cluster
mass measurement contributed by shape measurement errors. If lensing
pipelines provide a biased measurement of the shear profile of galaxy
clusters this will bias the observed average cluster mass, and bias
the derived cluster abundance function. To model the possible
impact on a DES like survey by shape measurement errors, we take an
average NFW profile for each stacked cluster bin, apply a lensing
bias, and then determine what cluster mass would be measured by
an NFW fitting program. By comparing the true and the measured cluster
mass this provides an estimate of the effect of shape measurement bias
for each lensing pipeline. In this paper we compare the expected statistical errors
expected in a DES like survey stacked weak lensing cluster mass measurement
described in section \ref{sec:p1} to the modeled bias on the mass
from shape measurement errors described in section \ref{sec:p2}. \\
\indent There are several other significant sources of systematic bias for
stacked weak lensing not included in this study. As shown by
\citep{Joerg} if optically detected clusters are binned by richness
they have orientation bias and are not spherically symmetric, which
leads to bias in the measured cluster abundance. Currently
orientation bias will dominate over the statistical error for DES but
it can perhaps be calibrated using simulations, or corrected using
other methods. There are additional sources of possible systematic
error such as photometric errors and cluster miscentering which are 
areas of ongoing research and not discussed in this project.

\subsection{Stacked cluster weak lensing: statistical errors}\label{sec:p1}
\input{stat_sec_n}

\subsection{Stacked cluster weak lensing: modeled systematic errors}\label{sec:p2}
\input{mse_sec_n}

\section{Summary}
The CSTEP project tested shape measurement pipelines in the cluster
shear regime on simulated data of the Dark Energy Survey. This project
analyzed the effectiveness of the shear pipelines by several criteria,
and tested the impact shape measurement bias would have on a stacked
cluster weak lensing analysis. \\
\indent In this paper we measured Quadratic, Multiplicative and
Additive bias of galaxy shape estimates for eight shape measurement
pipelines. The shape measurement bias found in several of the pipelines was within the
desired limits of a stacked cluster weak lensing measurement for
DES. In particular the I3 pipeline has consistently good bias properties
across a wide range of simulation input parameters.\\
\indent The results on the simulations showed that the strongest
determination of high bias was a low Signal to Noise Ratio (SNR). A
low signal to noise ratio occurs when the differentiation between
galaxy boundaries and their background is poor. In contrast, galaxies 
simulated at different redshifts had the same level of bias. An
important finding is based on an analysis of bias as a function of galaxy model
type. For many of the pipelines, and I3 in particular, galaxy
model type has little impact on measures of pipeline bias. \\
\indent The results showed that in general the Quadratic bias was not
significant for most pipelines and that it did not contribute
significantly to the error in the mass measured on stacked cluster
weak lensing profiles. \\
\indent This project has helped determine the properties of pipelines
to be used in the Dark Energy Survey. The use of the I3 pipeline
finds support by the consistently high quality of the shape
estimates. In addition, the characteristics of bias have been further
clarified, leaving in general bias as a multiplicative function
dominated by Signal to Noise ratio - leading to support of future
multiplicative corrections for Signal to Noise ratio in future
analysis. \\

 

 


\section*{Acknowledgments}
I thank......


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\appendix
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%\section{Shape Measurement Bias}
%\input{smb}

\section{Shear Measurement Pipelines}\label{App:shpipe}
\input{pipe_sec}

\section{Stacked weak lensing error}\label{App:statsec_a}
\input{stata_sec}

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