mn2eCSTEP.tex

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

\date{2013}

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

\maketitle

\label{firstpage}

\begin{abstract}
We present results from the Cluster Shear TEsting Program (CSTEP), an image
analysis challenge focused on weak gravitational shear in
the cluster regime. Shape measurement bias is an important source of systematic error in the 
measurement of cluster masses by weak gravitational lensing and,
consequently, cluster cosmology. In this work the accuracy of eight shape measurement pipelines is determined from image simulations
that have realistic distributions of galaxy properties and large gravitational shear. The best
performing methods exhibit a multiplicative bias of a few percent that
is stable as a function of redshift. Our results show that the
methods tested here do not have a strong quadratic bias. We find
that the shear bias due to selection effects varies widely
among the methods. We model the impact of the
biases found on a simulated stage III optical weak lensing cluster cosmology survey, such as the Dark Energy Survey (DES), and find it to
be below the statistical uncertainty in a realistic, binned cluster sample. Current shape measurement methods are therefore suitable for upcoming cluster lensing data sets, particularly when tested and calibrated by realistic image simulations.
\end{abstract}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sec 1
\section{Introduction}
The number density and distribution in mass and redshift of galaxy
clusters is a versatile cosmological probe \citep[cf.][for a recent review]{Allen}. There are a number
of different ways of detecting clusters, including the presence of red cluster member galaxies or the X-ray and SZ signal of hot intra-cluster gas.
All of these methods provide observables which, however, must be connected to cluster mass before they can be used for cosmology. One method of achieving this is 
weak lensing. Large optical surveys such as the Dark Energy Survey (DES, http://www.darkenergysurvey.org/) are able to detect and measure the
mass of large numbers of clusters and place strong constraints on the
halo mass function if sources of systematic error can be controlled.
Shape measurement pipelines have been developed to accurately measure the lensing signal, yet are known
to suffer from small systematic shape measurement errors (biases). As the mass estimated for 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.
 
Previous image simulation challenges were used to determine
the accuracy of shape measurement pipelines, e.g.~STEP1 \citep{STEP1},
STEP2 \citep{STEP2}, GREAT08 \citep{GREAT08}, GREAT10
\citep{GREAT10}, and GREAT3 \citep{great3}. These challenges used blinded image
simulations to characterize the shape measurement bias in
 lensing pipelines. All of these challenges have focused on
different aspects of shear estimation, and have led to
improvements in existing shear pipelines. The results have been
used to calibrate shape measurement pipelines \citep[e.g.][]{Apple},
and determine that lensing pipelines meet accuracy requirements for scientific
analyses \citep[e.g.][]{Berge}. Although previous challenges provided valuable information on many important
aspects of shear pipeline estimation, they were designed to test the regime of very weak cosmic shear with $|g| \leq 0.06$. 
It is important, however, to also test the accuracy of shape measurement
pipelines in the higher shear regime that occurs around the center of
massive galaxy clusters, where selection effects and non-linear biases
may play a more important role.


The Cluster Shear TEsting Program (CSTEP) is designed to extend image
simulation challenges to the high shear regime and study aspects of
shear estimation that would impact a weak lensing measurement of
cluster mass for a ground based large optical survey. For this, we
simulate ground-based images of galaxies with a realistic
distribution of signal-to-noise ratio (SNR), size and ellipticity. Lensing pipelines
were evaluated to determine their shape measurement bias as a
function of these properties. The shape measurement bias as 
determined for each lensing pipeline is then used to model the 
systematic error in the cluster mass for a stacked weak lensing measurement and its impact on cluster cosmology.


In Section 2 we describe the structure of the challenge and the image simulations used in this
project. We outline the characteristics of the shape
measurement pipelines used in this analysis in Section 3. We present
our findings on shape measurement bias including the impact of SNR, selection
effects, quadratic bias and redshift in Section 4. The
effect of shape measurement biases on stacked cluster weak lensing
analyses is discussed in Section 5.  Conclusions from this study are 
given in Section 6.  Finally there is an appendix which contains a more detailed
description of pipelines. 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sec 2
\section{Cluster STEP Challenge}
Gravitational lensing is the distortion of the images of
distant galaxies by the tidal gravitational field of massive structures near
their line of sight. This can
cause a change in the observed shape, size, and brightness of a
galaxy. \green{unclutter following sentence:} For massive galaxy clusters this leads to galaxies at a
higher redshift than the cluster often being
observed as arcs (strong lensing) near the cluster center , and to
appear aligned tangentialy with decreasing amount of distortion further from
the cluster center (weak lensing). Since physically unrelated galaxies 
have random orientations, a measurement of the average ellipticity of
an ensemble of galaxies unaffected by gravitational lensing would average
to zero. Measuring the mean tangential alignment of background galaxies therefore provides a way of
measuring the strength of the gravitational lensing signal, and thus the
mass of a galaxy cluster. 

For the larger shears of the cluster regime and analyses assuming radial symmetry, multiplicative ($m$) and
quadratic ($q$) shape bias (see eq.~\ref{Eqn:QMC})
affect the measurement to a greater extent than a
constant ($c$) shear bias, since the latter averages to zero when measuring
tangential shear over a full circle. It is therefore most
important to quantify the quadratic and multiplicative bias on images
with simulated shear comparable to the shear observed around large
galaxy clusters. 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 is being 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 + (1+m) \gamma_t + c,
\end {equation}
where $\gamma_t$ is the true shear and $\gamma_m$ is the measured
shear. A linear model that has been used to quantify systematic errors
for cosmic shear regimes was also used, defining the biases as \citep{STEP1}
\begin{equation}\label{Eqn:MC}
\gamma_m = (1+m) \gamma_t + c \; .
\end {equation}

An example fit to the im3shape data is shown in Figure~\ref{fig:eqfit}.

\begin{figure}
 \centering  % this centres figure in column
  \includegraphics[width=0.45\textwidth]{fig/fitplt.pdf} 
  \caption{An example of the two types of fit used to quantify shape
    measurement error for the shear as measured by the im3shape
    pipeline (I3) on galaxies with SNR greater than 50. \green{show an example with more significant difference between the two fits; use larger labels} }
\label{fig:eqfit}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%% Details on the sims (goes into Sec 2: CStep Challenge)
\input{sims}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sec 3
\section{Shape measurement pipelines}
\input{smp_sec}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sec 4
\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 the contribution of selection bias is included in Appendix \ref{App:shpipe}, along
with a description of the algorithms of the shape measurement pipelines. \\

The measure of signal-to-noise ratio (SNR) referred to in this section was measured on the CSTEP images
for each galaxy using \textsc{SExtractor}. It is defined as 
\begin{equation}\label{Eqn:SNR_ref}
\textrm{SNR} = \frac{\textrm{Flux}}{\textrm{Flux Error}} \; ,
\end{equation}
where the flux and flux error was determined using ... \green{say FLUX\_AUTO or FLUX\_ISO here and give details on detection threshold in case it's the latter; I don't think the figure adds much since the MJ and I3 definitions of SNR are less common than this one, so I've removed it}.

\green{can you comment here or elsewhere on how you get the error bars on q,m,c? you should probably also mention how you fit for q,m,c (subtracting the mean intrinsic ellipticity of all galaxies as far as I remember, rather than doing a ring-test type thing)}

\subsection{Mean shape measurement bias}
\input{avgres}

\subsection{Quadratic shear bias}
\input{quadratic_bias}

\subsection{Dependence on galaxy signal-to-noise ratio}\label{sec:SNR}
\input{snr_sec}

\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 an observable 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 ongoing and upcoming surveys such as DES  will provide deeper
imaging and better seeing over a wide area, the constraints on cosmology
from stacked cluster weak lensing will substantially improve if
sources of systematic error can be controlled.

There are a number of systematic effects that can bias the
stacked weak lensing mass measurement, including issues with background sample selection and redshift estimation like a contamination by cluster members, mis-centering of clusters, deviations of the fitted shear profile from the truth \citep[e.g.][]{mbecker}, orientation bias \citep{Joerg}, or a lack of full treatment of the intrinsic variation in cluster profiles \citep{ccv}. In this paper we focus
on the systematic bias in the stacked weak lensing cluster
mass measurement contributed by shape measurement. 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, we take the
average shear profile for each stacked cluster bin, apply a lensing
bias, and then determine what cluster mass would be measured. 
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}.

\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 realistic image simulations, comparable to the data collected by DES. 
We used these to analyzed the effectiveness and systematic errors of shear pipelines by several criteria,
and tested the impact shape measurement bias has on a stacked cluster weak lensing analysis. \\

The results of these analyses for the eight shape measurement pipelines tested are as follows:
\begin{itemize}
\item Multiplicative biases at the level of a few per-cent are common among the pipelines tested. These translate to relative systematic errors in cluster mass of the same order. For the most accurate pipelines participating in CSTEP, the statistical uncertainties of stacked weak lensing cluster masses in a realistic binning are larger than these systematic effects for a DES-like survey. The combined effect on the calibration of cluster mass-observable relation may, however, still be significant. We note that calibration of shape measurement biases from dedicated simulations (cf., e.g., \citealt{jarvis}, their Section~7.3.2) can reduce such biases considerably. Uncertainty in the multiplicative bias calibration should, however, still be included in analyses that use weak lensing constraints on cluster masses. 
\item We find that selection effects, i.e.~the dependence of the success rate of shape measurement on the true shape of galaxies, play a significant role for multiplicative biases. Depending on the methodology of calibration (e.g.~with ring tests), this effect has not always been accounted for in the past. The selection of galaxies should be made as independent of shear as possible (e.g. with \emph{roundified} measures of signal-to-noise ratio or size, cf.~\citealt{jarvis}).
\item On a similar note, we find a sometimes strong dependence of shear bias on signal-to-noise ratio. This suggests that a bias correction that takes signal-to-noise ratio into account, rather than a global calibration factor, is a promising calibration scheme. \green{got that from your previous summary, but can't really see it from what is in the paper:} The effect of other galaxy properties, such as morphology, is less drastic.
\item Quadratic biases, despite the larger distortions seen in the cluster regime, are subdominant in their effect on recovered shears and cluster masses, for most of the pipelines tested. We also do not find a strong dependence of mean biases on source redshift, which is particularly reassuring for the calibration of mass-observable relations.
\end{itemize}

This project has served as an early test of prospective shape measurement pipelines for applications in DES. The I3 and GM methods have, in updated form, been applied to DES Science Verification data \citep{jarvis} and have been shown to meet the requirements of several scientific weak lensing applications of this first DES data set \citep[cf.][]{vikram,chang,becker,troughs}. Despite recent advances in shape measurement techniques, larger future data sets will continue to require careful calibration and simulation-based testing of shear biases to make use of their full statistical potential.

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


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\appendix
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%\section{Shape Measurement Bias}
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\section{Shear Measurement Pipelines}\label{App:shpipe}
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\section{Stacked weak lensing error}\label{App:statsec_a}
\input{stata_sec}

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