text:
\section{Introduction}

Gravitational lensing allows for a measurement of the Hubble
constant $H_0$ that is independent of the ``distance ladder''
and is not susceptible to the peculiar velocities of the local universe
\citep{refsdal64}.
This unique opportunity is available for special lenses strong enough to
generate multiple images from a single source, and when this source has
intrinsic variability, such that a differential time delay can be
observed between the multiple images.

The doubly-imaged quasar Q0957+561 is the first confirmed example of
strong gravitational lensing [SL] \citep{Walsh79}.  The quasar is variable;
with the time delay accurately determined to $<1\%$
between the two images \citep{kundic97, colley03, shalyapin08},
the lack of precision in obtaining $H_0$ from this system in past measurements
($\pm35\%$, 2$\sigma$) lies in determining the mass distribution of the lens
\citep{BF99, keeton00}.

One well-known problem in uniquely determining the mass distribution
(and hence $H_0$) is the ``mass-sheet degeneracy''
\citep{falco85, gorenstein88}.
The lens mass is modeled given the multiple images as constraints;
the lensed light is traced back from the multiple image according to
a given lens model, and checked for a consistent, single source.
Unfortunately, the true angular position of the source is
not observable and hence not constrained; the mass-sheet degeneracy
occurs because the angular position of the source object is
degenerate with the constant surface mass density, or the
``mass sheet'' \citep{BF99}.  Thus, the
mass sheet manifests itself as a uniform magnification of the
(unobservable) source plane.

This degeneracy in the SL model can be lifted if the average
mass overdensity in the SL model region is known.
This is done by using the aperture-mass weak gravitational lensing [WL]
technique \citep{KS93}.
WL generates a subtle but coherent distortion of the background galaxies,
which can be used to infer the mass distribution.
In particular, the integrated tangential shear around a circular aperture
non-parametrically determines the two-dimensional average mass overdensity
within the aperture.

The WL measurement suffers from its own mass-sheet degeneracy, because
the WL signal must formally be integrated over the
surrounding region out to infinity to obtain the mass distribution.
While this is not practical, a realistic scheme to
estimate the average mass sheet in a SL region is to
integrate the WL distortions over an annular region surrounding the SL model.
WL then measures the differential mass sheet $\Delta\bar\kappa$ of the
disk region defined by the inner and outer circle of the annulus, where
the average convergence within the large circle is small, and
can be estimated from an assumed mass profile.
The mass sheet for Q0957+561 has previously been measured in
this way \citep{FischerProFit}.

There are other sources of degeneracy in obtaining $H_0$ from SL.
The Q0957+561 lens is a galaxy which sits within a modest cluster, so
the lens mass model must include both sharply and smoothly varying terms,
corresponding to that of the galaxy and cluster, respectively.
The cluster potential can be expanded in Taylor series; the second-order
terms (the lowest order contributing to gravitational lensing) corresponds
to the mass sheet and constant shear within the SL region.
Past studies of the lens model have shown that the uncertainty in
$H_0$ measured from
Q0957+561 is dominated by the degeneracy between the galaxy
ellipticity and cluster shear \citep[and references therein]{keeton00}.
For many models, the parametric fits tend to converge to
a large cluster shear ($\gamma_c\sim$0.1--0.3),
while the quasar host galaxy lensed images seem to imply
a small shear ($\gamma_c\leq0.1$)
\citep{keeton00}.
Additionally, \citet{kochanek91} and subsequent papers have shown that
the third-order terms cannot be neglected for the Q0957+561 cluster.

The goal of this paper is to constrain the smoothly varying components
of the lens, i.e., the mass-sheet and a few of the lowest-order
cluster terms, using WL analysis.  The convergence and shear pattern
multipoles relative to an aperture are related to each other
in a simple manner \citep{SB97, BN08}, and this relation has been
applied to the newly acquired images from Hubble Space Telescope (HST)
Advanced Camera for Surveys (ACS).
The combined lens model from strong lensing analysis
of the system is discussed in an accompanying paper \citep{fadely09},
as well as its implication for $H_0$.

\section{Theoretical Background}

\subsection{Time Delay and Hubble Constant}

When the gravitational field of a lens object is strong enough,
the light path can be sufficiently perturbed such that it
generates multiple images of a single light source.
The bending of two or more separate light paths arriving at the observer
is determined from the lens configuration; i.e.,
the distances between observer, lens and source, as well as
the mass distribution of the lens.
The SL observations consist of (dimensionless) angular separations, redshifts,
and relative magnitudes of the multiple images,
and have no distance or mass scales directly associated to them.
A measurement of the time delays between
the multiple images provide an absolute time/distance scale to
the lensing system \citep{refsdal64}.

Two light paths originating from the same object
undergo different time delays due to differences in
(a) their overall path lengths, and
(b) the depth of gravitational potential as they cross the lens.
The time delay (with respect to a straight path from {\boldmath$\beta$},
the true, unobserved angular position of the source, with no intervening lens)
for a single light path traveling through {\boldmath$\theta$} in the lens plane is
\begin{equation}
  t(\mbox{\boldmath$\theta$})
  = \frac{(1+z_{\rm lens})}{c}\,\frac{D_{OL}D_{OS}}{D_{LS}}\,
  \left[\frac{1}{2}(\mbox{\boldmath$\theta$}-\mbox{\boldmath$\beta$})^2-\psi(\mbox{\boldmath$\theta$})\right]
\end{equation}
where the delay due to the path difference is proportional to
$(\mbox{\boldmath$\theta$}-\mbox{\boldmath$\beta$})^2/2$, and
the other term represents the Shapiro time delay, where $\psi$ is
the dimensionless, projected and scaled gravitational potential of the lens:
\begin{equation}
  \psi(\mbox{\boldmath$\theta$}) \equiv
  \frac{D_{LS}}{D_{OL}D_{OS}}\frac{2}{c^2}
  \int\Phi(D_{OL}\mbox{\boldmath$\theta$},\ell)d\ell.
\end{equation}
Here, $\Phi$ is the ordinary 3D Newtonian potential,
$\ell$ is the distance along the line-of-sight, and
$D$ indicates angular diameter distances between observer ($O$),
lens ($L$) and source ($S$).
The absolute delay $t(\mbox{\boldmath$\theta$})$ is not observable, but the
difference $\Delta t = t(\mbox{\boldmath$\theta$}_1) - t(\mbox{\boldmath$\theta$}_2)$ is,
where $c\Delta t$ is proportional to $H_0^{-1}$ from the definition of
angular diameter distances.
Hence, we see that
the Hubble constant $H_0$ can be obtained from the geometry of the
lens system if $\Delta t$ is measured and the lensing potential
$\psi(\mbox{\boldmath$\theta$})$ is known.
In general, $\psi$ is obtained from fits to parameterized lens
models \citep[\protect{\it e.g.,}][]{BF99,keeton00},
where the best fit to the strongly lensed images is chosen.

\subsection{Mass Sheet Degeneracy}
\label{sec:msdegeneracy}

A fit to a parameterized lens model $\psi$ does not provide
us with a unique solution, however.
A uniform mass sheet cannot be constrained by (and hence not included in)
the SL models.
Specifically, for a lens potential $\psi(\mbox{\boldmath$\theta$})$ and
source position $\mbox{\boldmath$\beta$}$ that satisfies the SL constraints,
\begin{eqnarray}
  \psi'(\mbox{\boldmath$\theta$})
  &=& \frac{1}{2}\kappa_0|\mbox{\boldmath$\theta$}|^2 + (1-\kappa_0)\psi(\mbox{\boldmath$\theta$}) \\
  \mbox{\boldmath$\beta$}'
  &=& (1-\kappa_0)\mbox{\boldmath$\beta$}
\end{eqnarray}
also satisfies the constraints, where $\kappa_0$ is
the constant convergence (see Eq.(\ref{eq:convergence})) from
the additional uniform mass sheet.
Under this degenerate transformation, the time delay is
\begin{equation}
  (\Delta t)' = (1-\kappa_0) \Delta t,
\end{equation}
requiring the Hubble parameter to rescale by $H_0' = (1-\kappa_0)H_0$.

The lensing convergence $\kappa(\mbox{\boldmath$\theta$})$ is a normalized
surface density, and is defined as
\begin{equation}
  \nabla^2\psi(\mbox{\boldmath$\theta$})
  = 2\kappa(\mbox{\boldmath$\theta$})=2\frac{\Sigma(\mbox{\boldmath$\theta$})}{\Sigma_{\rm crit}}
\label{eq:convergence}
\end{equation}
where $\Sigma(\mbox{\boldmath$\theta$})$ is the surface mass density, and
the critical surface density is determined from the lens and source redshifts,
and the assumed cosmology:
\begin{equation}
  \Sigma_{\rm crit}
  = \frac{c^2}{4\pi G} \frac{D_{OS}}{D_{OL}D_{LS}}.
\end{equation}
A SL region which can generate multiple images has
$\Sigma\apgt\Sigma_{\rm crit}$, or $\kappa\apgt 1$, while WL
techniques are generally valid only in a region where $\kappa \ll 1$.

To remove the $(1-\kappa_0)$ degeneracy in $H_0$, one must obtain
the uniform mass sheet $\kappa_0$ not included in the SL model.
The overall average mass sheet ($\bar\kappa$) can be constrained via WL,
which constrains the sum of $\bar\kappa_{\rm SL}$ and $\kappa_0$,
where $\bar\kappa_{\rm SL}$ is the average convergence of the SL model
lens mass distribution.  The WL information is obtained
over a field wider than the area where $\psi(\mbox{\boldmath$\theta$})$ is modeled,
and its procedure is described in \S\ref{sec:multipoles}.

\subsection{Cluster Model}
\label{sec:clustermodel}

The Q0957+561 lens system consists of the primary lens galaxy G1 at redshift
$z_{\rm lens}=0.355$, the relatively weak cluster which contains G1, and
the quasar itself which lies at $z_{\rm src} = 1.41$.
The lens model in the SL analysis consists of a mass concentration
with near elliptical symmetry representing the galaxy, with
additional cluster potential components that are Taylor expanded
in position to the third order
\citep{BN08, fadely09}.
The expansion is defined within $r\leq R_{SL}$ centered at the
central peak of G1, and
is fully general to order $(r/R_{SL})^3$, where
$R_{SL}$ is the radius of the circular boundary where the SL modeling
takes place:
\begin{eqnarray}
\lefteqn{ \psi({\bf r}) = (1-\kappa_c) \times }\nonumber \\
&& \left[\psi_g({\bf r}) +{\rm Re}\left(
\frac{\gamma_c}{2}r^2 e^{-2i\phi} +
\frac{\sigma_c}{4}r^3 e^{-i\phi} +
\frac{\delta_c}{6}r^3 e^{-3i\phi} \right)\right] \nonumber\\
&& \ \ \ \ \ \ \ \ \ + \frac{\kappa_c}{2}r^2
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (r\leq R_{SL})
\label{eq:galcluster}
\end{eqnarray}
where ${\bf r}\equiv(x,y)\equiv(r,\phi)$ is the transverse distance in the
lens plane
(and is equivalent to $\mbox{\boldmath$\theta$}$ in the previous sections),
$\psi_g({\bf r})$ is the galaxy potential,
and $\kappa_c$, $\gamma_c$, $\sigma_c$ and $\delta_c$
are the (complex) constants corresponding to the cluster mass sheet,
constant shear, internal mass dipole moment, and $m=3$ shear moment,
respectively.
The complex notation corresponds to the two-dimensional
description of the gravitational potential such that, {\it e.g.},
the derivative is
$$
\partial \equiv \frac{\partial}{\partial x}
             + i\frac{\partial}{\partial y}
= e^{i\phi}\left(\frac{\partial}{\partial r}
  + \frac{i}{r}\frac{\partial}{\partial \phi}\right).
$$
The potential and the mass sheet $\kappa_c$ are always real.
The first four terms in the square bracket are those modeled in SL,
and are multiplied by $(1-\kappa_c)$
due to the mass sheet degeneracy associated with the analysis;
$\kappa_c$ is the mass sheet that is not part of the SL model, and
cannot be constrained from SL model within $r<R_{SL}$ alone, due to
degeneracy (\S\ref{sec:msdegeneracy}).
The four quantities $\kappa_c$, $\gamma_c$, $\sigma_c$ and $\delta_c$
are constrained by WL measurements from data in
$R_{SL}<r<R_{\rm max}$ and the multipole formalism (\S\ref{sec:multipoles}).
The inner and outer annular radii
were chosen to be $R_{SL}=30''$ and $R_{\rm max}=186''$ for our analysis,
such that we consider a region sufficiently removed from the SL region,
but with reasonable WL signal from the cluster.

\section{Observations and Data}

\subsection{HST/ACS Imaging}

The images for the cluster around the double quasar
Q0957+561 were taken as a $2\times 2$ mosaic of HST ACS
pointings of the Wide Field Channel (WFC) detector on October 10--13, 2005
(Fig.~\ref{fig:q0957field}).
Each ACS WFC pointing has $202''\times202''$ field of view (FOV),
resulting in a $6'\times6'$ mosaic image.
Each pointing has 4 orbits (4 $\times$ 1920s) in the F606W
(Broad V) filter and 2 orbits (2 $\times$ 1880s) in the F814W
(Broad I) filter;
the mosaic has the central $30''$ region overlapped
such that the region around the quasar images have
four times the depth (30ks and 15ks for F606W and F814W, respectively)
for studies of SL features \citep{fadely09}.

The HST WFC is a mosaic of two $4096\times2048$ pixel charge-coupled devices
(CCDs) of approximately $0.05''$/pixel.
Each orbit is split into four dithered exposures to sample the
diffraction-limited point-spread function (PSF) and to remove
defective pixels and cosmic rays in the combined image.

\begin{figure}
\plotone{bigALL05.txt.eps}
\caption[The $6'\times6'$ combined image of the 0957+561 field in ACS F606W.]
{The $6'\times6'$ combined image of the 0957+561 field in ACS F606W.
Each quadrant is a single pointing (with pixel scale dithering) which
has been imaged to a depth of 7.5ks, while all four quadrants overlap
in the central $30''$ region to yield a depth of 30ks.
The chip gap is apparent in each of the quadrants.
The orientation and the image scale are as labeled.
The apparent shear in the FOV is from correcting for the image distortion
due to the ACS focal plane located off-center from the telescope axis.
\label{fig:q0957field}}
\end{figure}

\subsection{Object Catalog}

We created an initial stacked mosaic image using {\tt MultiDrizzle}
\citep{multidrizzle}, where we refine relative shifts between
individual exposures by cross-correlating the positions of compact sources
in overlapping regions.  Objects were detected in this image using
{\tt SExtractor} \citep{Bertin}.
We took the initial {\tt SExtractor} detection parameters and
refined the centroid, size and shape of each object using a native {\tt GLFit}
\citep[\S\ref{sec:eglmethod};][]{NB07}.
The refined parameters determined here are still those which are
convolved with the PSF, therefore the size-magnitude
diagram allows us to determine the stellar locus
(Figure~\ref{fig:size-mag}).
The stellar objects have an average full-width half maximum (FWHM) of
$0.13\arcsec$ in F606W, or a corresponding $\sigma=0.054\arcsec$,
where $\sigma$ is the characteristic width of the best-fit gaussian.

\begin{figure}
\plotone{size_mag.epsi}
\caption[Size-magnitude diagram of all detected objects from
native {\tt GLFit}.]
{Size-magnitude diagram of all detected objects from
native {\tt GLFit}.
The boxed region shows a portion of the stellar locus with
no saturation and no galaxy contamination.
The stellar size  $\sigma$ is approximately the size of the
ACS WFC pixel, $0.054''$, where $\sigma$ is the characteristic
width scale for the best-fit gaussian (for objects with elongated shapes,
$\sigma$ is the geometric mean of the two characteristic widths).
The crosses are all detected objects, while the
circles indicate objects which satisfy the size, magnitude, flags, and
signal to noise (S/N)$>25$ cut for use in WL analysis.
The size and magnitude cuts are
indicated by a dotted horizontal and vertical line, respectively.
\label{fig:size-mag}}
\end{figure}

Once the stars and galaxies were separated,
the true (pre-PSF) galaxy shapes were obtained by performing
a deconvolution {\tt GLFit}, based on an interpolated PSF
(\S\ref{sec:psfinterp}).
Both the native and deconvolution {\tt GLFit} are done as a
``multifit''---an individual object is fitted simultaneously
over pixel data from each exposure rather than from the combined
image---hence the measured shapes are not affected by distortion or
aliasing induced by the image-combining process (\S\ref{sec:multifit}).

\section{Weak Lensing Analysis}

\subsection{EGL Method}
\label{sec:eglmethod}

For our WL analysis, we employ the Elliptical Gauss Laguerre (EGL)
method of shape measurement and shear estimation \citep{BJ02, NB07},
implemented as {\tt GLFit}; we provide here a brief description.
In characterizing their shapes, star and galaxy images are decomposed into
2d Gauss-Laguerre (GL) basis functions \citep{BJ02}.  In the EGL method,
the GL basis functions are described upon a ``basis ellipse,'' i.e.,
a sheared and stretched coordinate system such that a unit circle
appears as an ellipse of chosen size, shape or orientation; and
so that the lowest order GL function is an elliptical 2d Gaussian.
The combination of the basis ellipse and coefficients to the GL functions
then fully describes the image.

The choice of basis ellipse varies depending on its purpose.
In describing the PSF, we choose a common basis ellipse: a circle
with radius of the average PSF size.
The PSF variation across the FOV can then be traced through the variation
in the GL coefficients, and allows for a simple description of the necessary
interpolation.

In contrast, when measuring galaxy shapes, the basis ellipse is chosen
such that (in the simplified case of no PSF smearing) the lowest order
GL function is the best-matched 2d gaussian ellipse to the galaxy image.
This basis ellipse then describes the shape (ellipticity) of the galaxy.
In the observed image, the true galaxy shape has been convolved with the PSF.
So our fitting does a simple deconvolution by modeling the true galaxy shape
with a GL expansion, and adjusting the coefficients so that convolution
of this model with the PSF best matches the data \citep{NB07}.

\subsection{PSF Interpolation}
\label{sec:psfinterp}

In order to obtain the true galaxy shapes,
the PSF must be known at the position of the galaxy image.
This is done by selecting the stars in the image and
interpolating the shape at the galaxy position.
There are two problems  that make this difficult for our images.
First, the PSF spatial variation is not stable over time:
HST is known to ``breathe'' going in and out of the earth's shadow,
causing its focus to vary on time scales of a single orbit ($\sim1.5$ hour).
Hence it is unlikely that a single PSF spatial variation model
would be valid for all exposures \citep[and references therein]{Schrabback07}.
Second, there are not enough stars ($\sim$20/chip) in our cluster
image to create a reliable model of the PSF variation across every exposure.

To circumvent the aforementioned difficulties, we use
publicly available ACS WFC stellar field images to create the models of
the PSF variation for every exposure.
A given PSF spatial pattern is highly reproducible, since the spatial
variation of PSF patterns in different exposures is caused by the
thermal breathing of the HST focus.
If the few PSF available on a given exposure can constrain a portion
of the pattern, the rest of the PSF pattern can be predicted
\citep{rhodes05, jee07}.

The noise in the interpolation is minimized by utilizing
principal component analysis (PCA).  Our procedure is as follows:
\begin{enumerate}
\item Obtain the stellar field (SF) images available from the HST archive.
There were 184 archival F606W exposures of dense stellar fields;
the criteria for selection are described in \citet{Schrabback07}.
\item The PSF anisotropy is measured from each star
in terms of the anisotropy kernel $q$ \citep{Schrabback07},
and its variation across the field-of-view is characterized by a
third-order polynomial fit.
\item We then choose, for each of our Q0957 exposure, the SF image that
best matches the anisotropy pattern of the stars.
The ``best-fit'' stellar field is identified by that which yields the minimal
$$
\chi^2_{\rm SF}
= \sum_{i=1}^{N_{\rm stars}} [q_i - q_{\rm model}^{\rm SF}(x_i,y_i)]^2
$$
for a given exposure, where
$q_i$ is the kernel for the $i$th star in our exposure (which have
very few stars), and $q^{\rm SF}_{\rm model}(x_i,y_i)$
is the interpolated kernel at the position of the $i$th star
for the matching stellar field.
\item For the PSF interpolation, obtain the PSF GL coefficients by
(a) dividing each stellar field exposure into a $8\times8$ grid, and then
(b) fitting all stars within the grid to a constant PSF model for that cell,
resulting in 64 PSFs per exposure (32 PSFs per chip).
We choose to average the PSF in this way because the ACS WFC
undersamples the PSF; by using multiple PSF images within the grid,
the PSF is effectively ``dithered'' to obtain better sampling for the fit.
We then have, for a given stellar field $f$ and within every grid cell $g$,
a GL coefficient vector ${\bf b}^{fg} = \{b^{fg}_i\}$ describing the PSF,
where $i$ runs over the GL indices.  All PSF coefficients from $\{f,g\}$
are described over a common basis ellipse, which we take to be a circle
with radius equal to the average size of the PSF.
\item Extract the principal components ${\bf b}^\alpha = \{b^\alpha_i\}$
of the collection of PSF GL coefficients $\{{\bf b}^{fg}\}$ \citep{JarvisPCA}.
Express the PSF in terms of the PCA vectors,
${\bf b}^{fg} = \sum_\alpha \beta^{fg}_\alpha{\bf b}^\alpha$,
where $\alpha$ runs over the PCA vectors.
The PSF is now described in terms of
PCA coefficients $\mbox{\boldmath$\beta$} = \{\beta_\alpha\}$
instead of the GL coefficients ${\bf b} = \{b_i\}$.
\item Truncate the PCA coefficients by using only the
major principal components which corresponds to the PSF (spatial and
temporal) variation, but not to the noise.
These components are identified by ranking the variance of each, and
identifying a gap in the variance (see Fig.~\ref{fig:principalcomponents}).
Most of the variation in PSF is described
in the first several terms in $\alpha$.
\item Obtain a third-order, two-dimensional polynomial fit
across the image for the relevant PCA components $\alpha$
for each field $f$, such that the interpolated PCA coefficients
are described as
$$
\tilde\beta^{fg}_\alpha
= \sum_{0\leq(n+m)\leq 3} c_{\alpha,nm}^{f} x_g^n y_g^m
$$
where
$\chi^2=\sum_g(\beta^{fg}_\alpha - \tilde\beta^{fg}_\alpha)^2$ is minimized,
$c_{\alpha,nm}^f$ is the polynomial coefficient for $\alpha$ in field $f$,
and $(x_g,y_g)$ are the grid center coordinates.
Each PCA description of the PSF on every grid
($\mbox{\boldmath$\beta$}^{fg}$) was visually inspected;
obvious failures in the PSF descriptions (due to lack of sufficient
stars within the grid) were eliminated before being used in this fit.
\item The PSF at any location $(x,y)$ over any field $f$ can then be
modeled using the known principal components and
its 2-dimensional polynomial fit coefficients across the given exposure.
\end{enumerate}

Figure~\ref{fig:principalcomponents} shows the variance of
each of the PSF principal components, for each WFC ACS CCD.
The zeroth component is the average PSF shape over all grid cells and
exposures.  We find that the first seven components constitute the
primary variance and are sufficient to describe the PSF variation;
from visual inspection, the residual is consistent with $\sim1\%$ noise
with respect to the peak.
These seven components are used to model the PSF across the exposure.

\begin{figure*}
\plottwo{plot_rank.epsi}{KLchip1.eps}
\caption[(a) The variance of each of the principal components
from each of the CCD chips.
(b) The first ten principal components of PSF in chip 1.]{
(a) The variance of each of the principal components from each of the
CCD chips.  The dotted line indicates the last major gap in the principal
component variance.
There are seven principal components to the left of this line.
(b) From top left to bottom right:
the first ten principal components of PSF in chip 1.
\label{fig:principalcomponents}}
\end{figure*}

\subsection{Galaxy Multifit}
\label{sec:multifit}

Once the PSF is known at a given galaxy location, we perform the
deconvolution {\tt GLFit} to obtain the true galaxy shape.
We utilize the multiple exposures taken of each galaxy without combining them.
The ``multifit'' technique performs simultaneous fitting over
individual exposures, each with distinct PSFs, assuming a single
``true'' galaxy model, and the fitting done with the convolved GL
basis functions of each exposure to their respective PSFs.
The simultaneous fitting is iterated over the basis ellipses
to obtain the best-fitting true galaxy shape.

The pixel image is distorted with respect to the true image, so
distortion correction is necessary within the multifit procedure.
The galaxy model, described in sky coordinates, is fitted to
the pixel flux information via a pixel-to-sky coordinate map, which
corrects for optical distortions in the pixel image.
The pixel map is based on a known, stable solution of 4th order polynomial
in combination with a supplementary look-up table
\citep{anderson02, anderson06}, to which a linear correction (rotation,
translation, shear and uniform scale) is applied to fit to the
USNO-B catalog \citep{usnob} for alignment and absolute astrometry.
Bad pixels, such as those affected by cosmic rays or saturation, are not
used in the fitting procedure.  The bad pixel masks for each exposure were
generated using the {\tt multidrizzle} package \citep{multidrizzle}.

\subsection{Galaxy Selection for Weak Lensing}

Once the object catalog has been generated, we select the galaxies
for WL analysis by imposing the following cuts:
\begin{itemize}
\item Size.  The stellar contamination is removed by choosing objects
which have characteristic size $\sigma$ which are $\geq1.5$ times that
of the PSF.
Our cut is conservative  to ensure PSF deconvolution
to be in the range where it performs well \citep{NB07}.
\item Significance (S/N).  From our performance analysis of {\tt GLFit}
\citep{NB07}, we know that the deconvolution starts to produce
biases below S/N of 20 to 40, depending on the galaxy size with respect
to the PSF.  Here we choose the cut to be S/N $>25$.
\item Magnitude.  Since we only want the background galaxies to the
cluster for the lensing analysis, foreground cluster member contamination
must be minimal.  Lacking redshift information, and
unable to utilize color information for this purpose for reasons
listed below, we cut the brightest objects
($m_{\rm F606W}<24$) as foreground.  By plotting the galaxy number
density as a function of the radius from the central brightest galaxy
of the cluster (Figure~\ref{fig:rgalcounts}), we estimate that there is
at most 10\% cluster member contamination for $r<75''$ from
the cluster center for the $m_{\rm F606W}>24$ objects.
\item Flags.  Any object whose {\tt GLFit} flags indicate that the shape
has not been measured (an unsuccessful fit to the basis ellipse) is
rejected from the catalog.
\end{itemize}
After these cuts, 1866 galaxies remain for our WL analysis, or
galaxy number density of $50$ arcmin$^{-2}$ (Fig.~\ref{fig:rgalcounts}).

We have not included a color cut (for a rough exclusion of cluster members)
for the following reason:  Although several of the red-sequence
cluster members of known redshifts have the predicted
${\rm F606W} - {\rm F814W}$ color of 1.0 \citep{bc93} in our color-magnitude
plot, no peak was found in the galaxy count at this color.
This is because (1) majority of the cluster members are blue,
and (2) the expected member galaxy count in this halo is small.
The first point is verified from $>50\%$ of cluster members of known redshifts
which are bluer than red-sequence, with ${\rm F606W} - {\rm F814W}$
colors in the range 0.3--0.8.  Many of these galaxies were found
to have spiral morphology \citep{angonin94}.
The Q0957 cluster mass (and hence the number of its luminous members)
is expected to be low based on the cluster richness \citep{johnston07}.
The richness $N_{200}$ is defined by the number of member galaxies which are
consistent with the red-sequence color, is within a certain radius of
the brightest cluster galaxy, and have luminosity above $0.4L_*$
\citep[see][for details]{koester07}.
Although their definition for $N_{200}$ is given only to $z=0.3$,
we extend their red-sequence color cut to $z=0.35$ based on Table~1 of
\citet{eisenstein01}, and determine the equivalent richness to be
$N_{200} = 2$ from their SDSS magnitudes \citep{sdssdr6}.
This is lower than the lowest richness bin available in \citet{johnston07},
an indication that the Q0957 cluster is more of a group than a cluster,
and hence that the member count is low.

\begin{figure}
\plotone{gal_counts.epsi}
\caption[Weighted galaxy number density as a function of radial distance
from the central galaxy of the cluster.]
{Weighted galaxy number density as a function of radial distance
from the central galaxy of the cluster.
The weighted number density for use in shear estimating \citep{BJ02}
were essentially identical to the straight-forward number density.
The error bars are based on Poisson statistics.
The dimmer $m_{\rm F606W}>24$ objects are used for weak lensing analysis
(see text), where
both set of objects have the size, significance and flag cuts applied.
The dotted lines are the average weighted galaxy density for
the region $75''<r<186''$, where the density averages to
11.1 and 49.2 arcmin$^{-2}$ for the bright and dim galaxies, respectively.
The brighter objects ($m_{\rm F606W}<24$) have an excess of $\sim(30\pm15)\%$
in galaxy density for $r<75''$ from the cluster brightest galaxy G1;
the fainter objects (used for WL) appear to have an excess of
$\sim(10\pm10)\%$.
\label{fig:rgalcounts}}
\end{figure}

\subsection{CTE Correction}

The galaxy shape is affected by the degradation of the
charge transfer efficiency (CTE) in the ACS WFC CCD.
When a charge is read out from a CCD pixel, some of the
charge is trapped and released at a later time, causing
the galaxy image to elongate along the charge read-out direction,
adding an excess shear $\gamma^{\rm cte}_+<0$ along the pixel axis,
where $\gamma_+$ of $>0$ or $<0$ indicates elongation in the horizontal
or vertical direction, respectively (see \S\ref{sec:multipolemoments}
for definition of the orthogonal shears $\gamma_+$ and $\gamma_\times$).
The effect of charge-trailing on the object shape is worse for
objects that are smaller, have low flux, require larger number of
transfers to the readout register
(i.e., objects located close to the chip gap in the ACS WFC), and
exposures that have been taken at a later date.

We correct for CTE effects using a parametric model given
the flux, size, location on CCD and observation date to estimate the
spurious elongation, and correct for it by removing this shear from
each object in the shape catalog.
The model was derived from galaxies in the HST/COSMOS Survey
similarly to the one used by \citet{rhodes07},
but additionally takes sky background variations into account
\citep[see][for further details]{schrabback09}.

The mean correction averaged over all galaxies in our sample is
$\langle \gamma_+^\mathrm{cte}\rangle = -0.008\pm 0.010$,
with the worst case correction for small, dim objects near the
chip gap being up to $\gamma_+^\mathrm{cte}=-0.04$.
Given the $2\times2$ mosaic configuration, we expect the
CTE effect on the measured shear multipole moments
to vanish to first order for the even multipoles.  Overall,
we find the correction to the mass distribution to be negligible,
of the order $<3\%$ (well within the error bar, see \S\ref{sec:results})
for the mass sheet, and within $<10\%$ of
1$\sigma$ error bar for the multipole moments.

\subsection{Mass Sheet and Multipole Moments}
\label{sec:multipoles}

The two-dimensional multipole mass distribution within an aperture
can be obtained in a non-parametric fashion from the WL shear information
surrounding the aperture.  The overall mass sheet (i.e., the combined
average mass sheet from the SL model and the unconstrained cluster term
$\kappa_c$) corresponds to the monopole.
Here we summarize the results from \citet{BN08}.

\subsubsection{Mass Sheet}

For any mass distribution,
the expected azimuthally averaged tangential shear at radius $r$
from the mass center is \citep{escude91}
\begin{equation}
  \bar\gamma_t (r)
= \frac{\bar{\Sigma}(<r)-\bar{\Sigma}(r)}{\Sigma_{\rm crit}}
\equiv \frac{\Delta\Sigma(r)}{\Sigma_{\rm crit}}
= \bar{\kappa}(<r) - \bar{\kappa}(r)
\label{eq:tangentshear}
\end{equation}
where $r$ is the angular distance from the cluster center,
$\bar\gamma_t(r)$ is the tangential shear averaged at $r$,
$\bar{\Sigma}(<r)$ is the mean surface density within an aperture
of radius $r$, $\bar{\Sigma}(r)$ is the azimuthally averaged
surface density at radius $r$, and $\Sigma_{\rm crit}$ is the critical
surface density, and $\Delta\Sigma(r)\equiv\Sigma_{\rm crit}\bar\gamma_t$
is the value often quoted in WL literature.
The ratio of the surface density to $\Sigma_{\rm crit}$ is the convergence
$\kappa$.
We can directly estimate the mass sheet within an aperture
using the aperture mass method \citep{fahlman94}:
the average convergence within a circular aperture of radius $R$ is
\begin{equation}
 \bar{\kappa}(<R) \equiv \frac{1}{\pi R^2}\int_{r<R} d^2r\,\kappa({\bf r})
=\frac{1}{\pi} \int_{r>R} d^2r\,\frac{\gamma_t({\bf r})}{r^2}
\label{eq:masssheet}
\end{equation}
where the tangential shear is integrated over $R<r<\infty$ \citep{KS93}.
The average convergence gives the average surface density
if the critical surface density $\Sigma_{\rm crit}$ is known.
We discuss $\Sigma_{\rm crit}$ estimation in \S\ref{sec:zestimation}.

The practical estimator for Eq.~(\ref{eq:masssheet}) is a summation
over galaxy shapes
\begin{equation}
  \bar{\kappa}(<R)
= \frac{1}{\bar{n}\pi{\mathcal R}} \sum_{i \in (r>R)}
\frac{\gamma_{t,i}}{r^2}
\label{eq:mssummation}
\end{equation}
where $\bar{n}$ is the surface number density of source galaxies and
$\gamma_{t,i}$ is the tangential component of the $i$th galaxy shape.
Here we have assumed that the locally averaged galaxy shape (tangential
component) is an estimator of the shear,
$\gamma_t \approx \langle\gamma_{t,i}\rangle/{\mathcal R}$,
where ${\mathcal R}$ is the responsivity, the multiplicative
correction factor for the estimation of shear from galaxy shapes \citep{BJ02}.

In practice, the summation over all galaxies at $r>R$ is truncated
at a maximum radius $R_{\rm max}$.
Equation~(\ref{eq:mssummation}) then becomes
\begin{equation}
  \bar{\kappa}(<R) - \bar{\kappa}(<R_{\rm max})
= \frac{1}{\bar{n}\pi{\mathcal R}} \sum_{i \in (R<r<R_{\rm max})}
\frac{\gamma_{t,i}}{r^2}
\label{eq:msannulus}
\end{equation}
The truncation at $R_{\rm max}$ is a source of uncertainty;
that is, only the difference in the mass sheet at different aperture radii
can now be determined (this is the WL mass sheet degeneracy).
We then assume an appropriate model to derive the mass distribution
within $R_{\rm max}$, and hence $\bar{\kappa}(<R_{\rm max})$.
We feel safe in doing so, since this correction is reasonably smaller
than $\bar{\kappa}(<R)$.

If the WL measurement yields an average convergence of $\bar\kappa$
within $r=R$ (normalized to the quasar redshift)
and the SL modeling (assuming $\kappa_c=0$ in Eq.~(\ref{eq:galcluster}))
yields an average convergence of $\bar\kappa_{SL}$,
then the relation of the degenerate mass sheet $\kappa_c$ to the measured
mass sheet $\bar\kappa$ is
$\bar\kappa = \kappa_c + (1-\kappa_c)\bar\kappa_{SL}$, or
\begin{equation}
  1-\kappa_c = \frac{1-\bar\kappa}{1-\bar\kappa_{SL}}.
\label{eq:kappa}
\end{equation}

\subsubsection{Multipole Moments}
\label{sec:multipolemoments}

The method of aperture mass \citep{fahlman94, schneider96, SB97}, which
integrates tangential shear to obtain the mass sheet within an aperture,
can be generalized to obtain the ``interior'' and ``exterior'' multipoles
defined relative to a circle of radius $R$ \citep{BN08}.
The ``interior monopole'' corresponds to the mass sheet, and is constrained
from the shear information exterior to $r=R$.  The other multipoles are
constrained in a similar manner, where the shear information exterior to
$r=R$ constrains the mass multipole moments interior to $r=R$, and vice versa.

In order to utilize the shear information to extract mass multipoles,
first we define the complex shear relative to the tangent to the circle
\citep[see Eq.~(11) of ][]{BN08}
\begin{equation}
  \Gamma({\bf r}) \equiv \gamma_t({\bf r}) + i\gamma_s ({\bf r})
   = -\gamma({\bf r}) e^{-2i\phi}
\label{eq:Gamma}
\end{equation}
where the coordinate origin of ${\bf r}\equiv(r,\phi)$ is
at the center of the circle, and $\gamma_t$ and $\gamma_s$ are the (real)
tangential and ``skew''\footnote{The conventional name for this term is
``radial'' shear ($\gamma_r$).
However, a shear which elongates in the radial direction is simply a
negative tangential shear, and is not orthogonal to $\gamma_t$.
The shears orthogonal to the tangential/radial
directions are aligned $\pm$45 degrees from tangential/radial; hence
we flout past conventions and rename this the ``skew'' shear, $\gamma_s$. }
shear components with respect to the polar coordinates, respectively.
$\gamma({\bf r})\equiv \gamma_+({\bf r}) + i\gamma_\times({\bf r})$
is the complex shear defined in the $(x,y)$ coordinates, where
$\gamma_+$ is the shear along the $x$- or $y$-axis, and
$\gamma_\times$ is the shear along the diagonal halfway between the axes.

The interior and exterior mass multipole moments relative
to a circle of radius $R$ are defined as
\begin{eqnarray}
Q^{(m)}_{\rm in}(R) & \equiv & \int_{r<R} d^2r\, r^m e^{-im\phi} \kappa({\bf r}) \\
Q^{(m)}_{\rm out}(R) & \equiv & \int_{r>R} d^2r\, r^{-m} e^{im\phi}
\kappa({\bf r})
\end{eqnarray}
where these definitions are normalized to agree with
Eqns~(B5) of \citet{SB97}, but with an alteration in the phase convention.
If the {\em cluster} potential at $r<R$ is described
as Eq.~(\ref{eq:galcluster}), then, assuming
no contribution from the galaxy potential $\psi_g$,
the interior and exterior multipoles $Q^{(m)}$ are related to
the cluster constants as
\begin{eqnarray}
Q^{(0)}_{\rm in} (R) & = & \pi R^2 \kappa_c \\
Q^{(1)}_{\rm in} (R) & = & \frac{\pi}{4} R^4 \sigma^*_c\;(1-\kappa_c) \\
Q^{(2)}_{\rm out} (R) & = & - \pi  \gamma_c\; (1-\kappa_c) \\
Q^{(3)}_{\rm out} (R) & = & - \frac{\pi}{2} \delta_c \;(1-\kappa_c)
\end{eqnarray}
independent of the cluster mass distribution at $r>R$, where
$\kappa$ and $\sigma$ are the monopole and dipole mass
and $\gamma$ and $\delta$ are the constant
and $m=3$ shear terms within $r=R$, respectively, and
$\sigma^*$ indicates complex conjugation.
The terms $Q^{(2)}_{\rm in}$ and $Q^{(3)}_{\rm in}$ vanish (i.e.,
there are no mass distribution within $R$ of these multipoles), since
$\kappa\equiv\frac{1}{2}\nabla^2\psi=0$ if $\psi\propto r^me^{\pm im\phi}$,
and the $Q^{(1)}_{\rm out}$ term produces no shear internal to $r<R$.
These terms have no effect upon the
lens model or the time delay, and therefore can be ignored.
The $m=-2$ and $m=-3$ shear patterns {\it within} $R$ (corresponding to
$\gamma_c$ and $\delta_c$ terms in Eq.~(\ref{eq:galcluster}))
are generated by a quadrupole and sextupole mass distribution, respectively,
external to $R$ \citep[see Fig.~1 of][]{BN08}, hence these terms correspond
to the external mass distributions $Q^{(m)}_{\rm out}$.
If $\psi_g\neq0$, then the appropriate multipole terms
$Q^{(m)}_{g,\rm in}$ or $Q^{(m)}_{g,\rm out}$
for the galaxy potential enter each of the multipole terms,
and the WL measurement constrains the sum of the SL galaxy model
and cluster terms.

The multipoles of the convergence $\kappa$ are related to the
integrals over the complex shear $\Gamma$, Eq.~(\ref{eq:Gamma}), as
\begin{eqnarray}
\label{eq:annulus1}
\int_{r>R}d^2r \, \Gamma({\bf r})
r^{-m-2}e^{-im\phi} & = &
R^{-2m-2} Q^{(m)}_{\rm in}(R) \\
&&\qquad (m\ge 0) \nonumber\\
\label{eq:annulus2}
\int_{r<R}d^2r \, \Gamma({\bf r})
r^{m-2}e^{im\phi} & = &
 R^{2(m-1)} Q^{(m)}_{\rm out}(R) \\
&& \qquad (m\ge 1) \nonumber
\end{eqnarray}
where the integral can be converted to a summation over
source galaxy shapes as an estimator to the integral.
The practical estimators avoids summation over $R\rightarrow\infty$
or in the $r<R$ region (where the weak lensing shear estimator breaks down)
by integrating over an annular region $R_1<r<R_2$:
\begin{eqnarray}
\lefteqn{\frac{1}{\bar{n}{\mathcal R}}\sum_{R_1<r_j<R_2} r_j^{-2}\gamma_{t,j} =}
 \nonumber \\
&& \qquad \qquad R^{-2}_1 {Q}^{(0)}_{\rm in}(R_1)
     - R^{-2}_2 {Q}^{(0)}_{\rm in}(R_2)
\label{eq:Q1} \\
\lefteqn{\frac{1}{\bar{n}{\mathcal R}}\sum_{R_1<r_j<R_2} r_j^{-3}(\gamma_{t,j} + i\gamma_{s,j}) e^{-i\phi_j}=} \nonumber \\
&& \qquad \qquad R^{-4}_1 {Q}^{(1)}_{\rm in}(R_1)
     - R^{-4}_2 {Q}^{(1)}_{\rm in}(R_2)
\label{eq:Q2} \\
\lefteqn{\frac{1}{\bar{n}{\mathcal R}}\sum_{R_1<r_j<R_2} (\gamma_{t,j} + i\gamma_{s,j}) \, e^{+2i\phi_j}=} \nonumber \\
&& \qquad \qquad R^2_2 {Q}^{(2)}_{\rm out}(R_2) - R^2_1 {Q}^{(2)}_{\rm out}(R_1)
\label{eq:Q3} \\
\lefteqn{\frac{1}{\bar{n}{\mathcal R}}\sum_{R_1<r_j<R_2} r_j (\gamma_{t,j} + i\gamma_{s,j}) \,e^{+3i\phi_j} = } \nonumber \\
&& \qquad \qquad R^4_2 {Q}^{(3)}_{\rm out}(R_2) - R^4_1 {Q}^{(3)}_{\rm out}(R_1)
\label{eq:Q4}
\end{eqnarray}
where the summation is over the $j$th galaxies at radial distance $r_j$
and azimuth angles $\phi_j$.
In Eq.~(\ref{eq:Q1}), the summation over $\gamma_t$ is referred to
as the E-mode aperture mass, which corresponds to the physical quantity
which is the surface mass density, while a summation over $\gamma_s$
is the B-mode aperture mass which is expected to vanish, and hence
provides some measure of systematics present in the monopole
\citep[similar measures are not available for the higher-order
multipole terms, as discussed in][]{BN08}.
The multipoles on the right hand sides are that of the combination of
the cluster and galaxy potential; hence the summation constrains
the {\em combination} of the cluster and galaxy multipoles.

\subsection{Redshift Estimation}
\label{sec:zestimation}

Our mass estimators from tangential shear yields estimates of
the convergence, but not the mass sheet density $\Sigma$ itself.
It is important to know the critical surface mass density $\Sigma_{\rm crit}$,
which normalizes the convergence $\kappa \equiv \Sigma/\Sigma_{\rm crit}$
and is redshift dependent, since the convergence obtained from WL
(at a given source redshift distribution) must be converted to an
appropriate value for SL modeling, where the source is at
$z_{\rm src}=z_{\rm quasar}=1.41$.

In order to obtain the critical surface density $\Sigma_{\rm crit}$
for WL, the source galaxy redshift distribution must be estimated.
We adopt the magnitude dependent parameterization \citep{BF93}
\begin{equation}
\left\{
\begin{array}{l}
\frac{dN}{dz}(z,m) \propto z^2\exp[-(\frac{z}{z_0(m)})^{3/2}]\\
z_0(m) = \frac{z_{\rm med}(m)}{1.412}
\end{array}
\right.
\label{eq:zdist}
\end{equation}
where $\frac{dN}{dz}(z,m)$ is the magnitude dependent redshift distribution,
and $z_{\rm med}(m)$ is the median redshift as a function of magnitude $m$.
From the COSMOS\footnote{Cosmic Evolution Survey
({\tt http://cosmos.astro.caltech.edu/}).
COSMOS is an ACS survey over 1.67 deg$^2$, where a single orbit
($\sim2000$ seconds) exposure is tiled over this relatively wide field
in F814W.  It has 50\% completion for sources $0.5''$ in diameter
at F814W $I_{\rm AB} =26.0$ \citep{scoville07}.}
ACS data, \citet{Leauthaud07} obtain the
median redshift as a function of F814W magnitude as
\begin{equation}
  z_{\rm med} = (0.18\pm 0.01) \times m_{\rm F814W} - (3.3 \pm 0.2)
\label{eq:medianz}
\end{equation}
This relation is valid over the magnitude range $20 < m_{\rm F814W} < 24$;
however, their data suggest that
the relation can be extended out to $m_{\rm F814W} < 26$,
based on the
UDF\footnote{Hubble Ultra Deep Field ({\tt http://www.stsci.edu/hst/udf/}).
The UDF data is a multi-color, deep image over a single ACS
field-of-view (11.97 arcmin$^2$) and has a 10-$\sigma$ limiting magnitude
(for a $0.5''$ diameter aperture) of $28.4$ in the
F850LP filter, with 144 orbit exposures.
The F850LP filter is narrower and less efficient than the F814W filter.}
data \citep{Coe06}, which show agreement in the
$20<m_{\rm F814W}<24$ region with COSMOS data.
Hence we use Equation~(\ref{eq:medianz}) to estimate our median redshift,
since our objects are within this magnitude range (Figure~\ref{fig:maghist}).

\begin{figure}
\plotone{mag_hist.epsi}
\caption[Distribution of F606W and F814W AB magnitudes of galaxies used in
the WL analysis.]
{Distribution of F606W (solid line) and F814W (dotted line)
AB magnitudes of galaxies used in the WL analysis.
The objects were detected in the F606W/F814W combined image, and
the magnitudes in each were determined using the {\tt SExtractor}
double-image mode \citep{Bertin}.
The majority (92\%) of our objects have F814W magnitude less than 26.
\label{fig:maghist}}
\end{figure}

The final redshift distribution was estimated in the following manner:
\begin{enumerate}
\item Divide the galaxies into $\Delta m_{\rm F814W}=0.25$ bins,
\item determine the redshift distribution for each bin
using Eq.~(\ref{eq:zdist}) and $z_{\rm med}$ from Eq.~(\ref{eq:medianz}), and
\item sum over each distribution with each bin properly weighted.
\end{enumerate}
The weight of each bin is determined from the weight each galaxy shape
gets in estimating the shear \citep{BJ02}.
From the estimated source redshift distribution, we calculate the mean
lensing strength, which is proportional to $\Sigma_{\rm crit}^{-1}$,
and hence to
\begin{equation}
\left\langle\frac{D_{LS}}{D_{OS}}\right\rangle
 = \frac{\int dm \int dz \, \frac{dN}{dz}(z,m) \, w(m) \frac{D_{LS}}{D_{OS}}}
        {\int dm\,w(m)}
\end{equation}
where $\frac{dN}{dz}(z,m)$ is normalized to unit integral,
and $w(m)$ is the weight per magnitude bin.
We find $\left\langle\frac{D_{LS}}{D_{OS}}\right\rangle = 0.572$, or
the mean weak lensing critical density to be
\begin{equation}
  \Sigma_{\rm crit} = \frac{c^2}{4\pi G}
    \frac{1}{D_{OL}}
    \left[\left\langle\frac{D_{LS}}{D_{OS}}\right\rangle\right]^{-1}
   = 3800 h \, M_\sun\,{\rm pc}^{-2}
\end{equation}
for a flat $\Lambda\mathrm{CDM}$ cosmology with $\Omega_\mathrm{m} = 0.24$,
 and where $z_{\rm lens} = 0.355$.

Since the geometry dependence of the gravitational lens system is
contained in $\Sigma_{\rm crit}$, its value differs for the same lens
if the source object is at different redshift.
We compare the critical density $\Sigma_{\rm crit}$ obtained above to
$\Sigma_{\rm crit}^Q = 3350 h \, M_\sun\,{\rm pc}^{-2}$ for the lensed quasar source at
$z=1.41$, and find that the lensing signal, which is proportional to
$\Sigma_{\rm crit}^{-1}$, is enhanced by 13\% relative to the WL galaxy population.
In other words,
\begin{equation}
\kappa^Q({\bf r})
= \frac{\Sigma_{\rm crit}}{\Sigma_{\rm crit}^Q} \, \kappa({\bf r})
\label{eq:WLtoSL}
\end{equation}
where $\kappa^Q({\bf r})$ is the convergence at quasar redshift,
$\Sigma_{\rm crit}$ and $\Sigma_{\rm crit}^Q$ are the critical density for sources at
the WL galaxy population and quasar, respectively, and
$\kappa({\bf r})$ is the convergence with respect to the WL galaxy population.

\section{Results}
\label{sec:results}

\subsection{Mass Sheet}

The average tangential shears at different radii
are plotted in Figure~\ref{fig:tangentshear}.
The data points, although noisy, are independent of each other,
so it is appropriate to fit a model to these data.
We assume a core-softened isothermal sphere (CIS) mass distribution
\begin{equation}
\kappa({\bf r}) = \frac{\Sigma_0}{\Sigma_{\rm crit}}\;[1+(r/r_c)^2]^{-1/2}
\end{equation}
and use Eq.~(\ref{eq:tangentshear}) to compute the corresponding
tangential shear.  Fixing the core radius at $r_c=5''$, we find
$\Sigma_0/\Sigma_{\rm crit} = 0.47\pm0.17$, or
$\Sigma_0 = (1800 \pm 600)h\,M_\sun\,{\rm pc}^{-2}$
(1 $\sigma$ error estimates), with reduced $\chi^2$ of $0.93$.
This corresponds to a cluster velocity dispersion of
$\sigma_v = 420\pm70$ km s$^{-1}$ ($h=0.7$).
A fit to a NFW model \citep{NFW} was attempted, but did not
provide any useful constraint on the concentration.

\begin{figure*}
\plotone{tangent_shear.epsi}
\caption[Plot of azimuthally averaged tangential shear,
$\langle \gamma_t \rangle$.]
{{\it Left}: Plot of azimuthally averaged tangential shear,
$\langle \gamma_t \rangle$, centered
on G1, as a function of radius $r$ (solid squares).
The dashed line is the best fit isothermal sphere with $5''$ core, with
the short-dashed lines indicating the one-sigma deviation of the fit.
The B-mode (``skew'') shear $\langle \gamma_s \rangle$
(open squares) is consistent with
zero, as expected from shears generated from a centrally distributed mass.
{\it Right}: Radial bins used in obtaining the mean tangential shear.
Each dot indicates a galaxy in the $6'\times 6'$ ACS mosaic which are
suitable for use in the weak lensing analysis,
while the annuli delineated by the dotted line indicate the radial bins.
The radius of the outermost circle is $R_{\rm max}=186''$.
The coordinates are centered around the lensing galaxy G1.
\label{fig:tangentshear}}
\end{figure*}

\begin{figure*}
\plotone{radial_profile.epsi}
\caption[The aperture mass statistic of the Q0957+561 cluster.]
{{\it Left}: The aperture mass statistic, which plots the
differential convergence calculated from integrating over the
tangential shear in Eq.~(\ref{eq:msannulus}).
The solid squares are the tangential shear integrals, the dashed line
is the fit to an core-softened isothermal sphere with $5''$ core with
the dotted lines indicating
one-sigma deviations of the fit, and the open squares
are the imaginary components (B-mode aperture masses, or
azimuthally averaged skew shears)
whose signal should be consistent with zero.
The points in this figure are correlated,
since each point is an integral over the annulus from $R_{\rm max}$
to the inner radius $R$.
{\it Right}: The same plot in log scale.
\label{fig:map}}
\end{figure*}

Figure~\ref{fig:map} shows the aperture mass statistic as defined in
Eq.~(\ref{eq:msannulus}), with respect to a varying inner annulus.
The points in this figure are correlated, since each point is
an integral over galaxies in the annulus from $R_{\rm max}=186''$
to the inner radii $R$.  The points show the azimuthally averaged
radial profile of the mass concentration around Q0957.  Because of the
WL mass sheet degeneracy, it is not the true radial profile, but
a relative value with respect to a mass sheet averaged within a
circular aperture of $r<R_{\rm max}$.

From the aperture mass, we find the average convergence overdensity to be
$$
\Delta\bar\kappa=\bar\kappa\,(<30\arcsec) - \bar\kappa\,(<186\arcsec)
 = 0.122\pm0.048
$$
where the radii $R=30\arcsec$ and $R_{\rm max}=186\arcsec$ are
with respect to G1.
The average convergence within $R_{\rm max}=186\arcsec$ can be estimated
from the CIS model, whose fit value yields
$\bar\kappa\,(<186\arcsec) = 0.024\pm0.012$.  The error here is
conservative (i.e., not based on the error in the fit) to account for
various possible mass distributions.
The two results can then be combined to yield
$$
  \bar\kappa\,(<30\arcsec) = 0.146\pm0.049
$$
From the redshift distribution of the WL source galaxies,
this convergence corresponds to a mean mass sheet density of
$$
  \bar\Sigma\,(<30\arcsec) = (550\pm190)h \,M_\sun{\rm pc}^{-2}
$$
For sources at the quasar redshift $z=1.41$,
this mass sheet then corresponds to a convergence of
$$
\bar\kappa(<30\arcsec) =
0.166\pm0.056
$$
for the strong lensing analysis (see Eq~(\ref{eq:WLtoSL})).
As explicitly stated above, this ``mean mass sheet'' includes
the G1 mass averaged over the $r<30''$ disk;
hence to obtain the cluster mass sheet $\kappa_c$, the galaxy mass
(modeled from SL) must be properly removed from the above quantity
\citep[Eq.~(\ref{eq:kappa});][]{fadely09}.

\subsubsection{Comparison with Fischer {\it et al.}}

Our result is consistent with the WL results based on
Canada France Hawaii Telescope (CFHT) images from \citet{FischerProFit}.
They obtain $\bar\kappa(<30\arcsec)=0.16\pm 0.05$ (from their Figure~6)
compared to our $\bar\kappa(<30\arcsec)=0.146\pm 0.049$, where we have
compared the shears as obtained from the galaxy shapes, without normalizing
to the quasar redshift.
While the two results and error magnitudes are nearly identical,
they are obtained in a completely different fashion.
We obtain the shear calibration factor (our responsivity ${\mathcal R}$)
and propagate the shape noise and shape measurement errors from individual
galaxies into the estimated shear in a deterministic manner based on
the formalisms of \citet{BJ02}, while Fischer {\it et al.}\ calibrate
the shear and obtain the error based on Monte-Carlo simulations.

The similarity in the error magnitude could possibly be
attributed to the similar number of galaxies we use (1651 and 1866 galaxies
for Fischer {\it et al.}\ and this study, respectively), since shear estimate error
is typically dominated by the statistical shape noise.  Both studies
use source galaxies in a similar area and magnitude range.
However, the resolution of the images used in the two studies are
vastly different:
the CFHT images have $0.6\arcsec$ FWHM seeing with 0.207\arcsec/pixel,
compared to our $0.13\arcsec$ FWHM with with 0.05\arcsec/pixel.
Since the images with the smaller seeing and pixel scale should reveal
the galaxy shapes better, the similarity in the results indicates that
the error is indeed dominated by the statistical error.
Therefore, in order to improve upon the mass sheet precision, we would need to
increase the number count of the source galaxies, which would be possible
if source galaxies of lower S/N in the HST images can be utilized.
Currently, the accuracy in our galaxy shape measurement and shear
estimation method is limited to high S/N objects ($>25$).
Hence a shape measurement method which can be shown to be
accurate at low S/N would improve precision in the mass sheet measurement,
given the same HST images.

Although the two observed convergence are consistent with each other,
\citet{BF99} report a convergence of $\bar\kappa(<30\arcsec)=0.26\pm 0.08$
based on the results of \citet{FischerProFit},
when normalized to the quasar redshift.
This discrepancy comes from the difference in the assumed
$\Sigma_{\rm crit}$ values: although the redshift of the quasar
has not changed, both the assumed WL source galaxy distribution
and the cosmology are different between the two analyses.
While we use a magnitude-based empirical redshift distribution
(\S\ref{sec:zestimation}) with a flat $\Lambda$CDM with $\Omega_m=0.24$,
\citet{FischerProFit} estimate the redshift distribution based on
Monte-Carlo simulation of an assumed redshift evolution of galaxy size,
along with an open CDM cosmology with $\Omega_m=0.1$.

\subsubsection{Comparison with Other Cluster Mass Estimates}

\citet{chartas02} use $2'\times2'$ Chandra observation to
determine the mass distribution of the cluster.
From the spatial distribution of the X-ray luminosity and the
X-ray temperature, they find the cluster mass to be
$5.0^{+1.3}_{-2.0}\times10^{13} M_\sun$ within a radius of
0.5 $h_{75}^{-1}$ Mpc ($\sim2'$) of the cluster center.
Our corresponding WL mass estimate within the same radius is
$(3.3\pm1.1)\times10^{13} M_\sun$ (for $h=0.7$),
an agreement within $\sim1\sigma$.  We note that since
the mass here is an integral over a radial density profile,
the cluster mass estimate agreement between WL and X-ray, which
assumes a different radial profile (CIS and $\beta$-model,
respectively), will differ depending on the outermost radius chosen.

On the other hand, \citet{garrett92} and \citet{angonin94} obtain
a cluster member velocity dispersion of $\sigma_v=715\pm130$ km s$^{-1}$
from redshifts for 21 probable cluster members, compared to our
$\sigma_v$ equivalent of $420\pm70$km s$^{-1}$ ($h=0.7$).
The dispersion data correspond to cluster mass of
$(17.8\pm6.5)\times10^{13}M_\sun$ ($h=0.7$) within a
$0.5 h_{75}^{-1}$ Mpc radius.
The $2\sigma$ discrepancy between the WL and velocity-dispersion mass
estimates suggests that the velocity dispersion is possibly highly
anisotropic, with an enhanced peculiar velocity along the
line of sight.
\citet{angonin94} suggest that cluster member selection could also be
the cause for the large dispersion, where they find removing a single galaxy at
the edge of the velocity distribution reduces the velocity dispersion to
660 km/s.

\subsection{Multipole Moments}

The rest of the (differential) multipole moments as obtained from
Eqns.~(\ref{eq:Q2}--\ref{eq:Q4})
are listed in Table~\ref{tab:multipole}, where the
differential is between the values at $R=30''$ and $R_{\rm max}=186''$.
Figure~\ref{fig:multipole} plots the multipoles
with respect to the value at $R_{\rm max}$ for various inner radii $R$,
which highlights the problem with constraining the $Q^{(m)}_{\rm out}$ terms.
Due to the powers of $R$ involved in the summation,
the shear signal, as well as the shape noise, are weighed by $R^{-2m-2}$
for $Q^{(m)}_{\rm in}$,  and by $R^{2m-2}$ for $Q^{(m)}_{\rm out}$.
For $Q^{(m)}_{\rm in}$, the outer region (dominated by shape noise) are
weighted less, and the signal at smaller radii can be seen
(Fig.~\ref{fig:multipole} left).
At $Q^{(m)}_{\rm out}$, $m>1$, (Fig.~\ref{fig:multipole} center and right),
whatever signal
existing at the inner radii is overwhelmed by the shape noise in the outer
radii, and hence the differential signal as $R$ decreases to $30''$ is
merely noise which dominates at larger radii.  This effect is more severe for
$Q^{(3)}_{\rm out}$ (Fig.~\ref{fig:multipole} right),
where higher powers of $R$ are involved,
that the shear from $R<100''$ hardly contributes to the integrated shear.

If we are to constrain the multipoles at $R=30''$,
it is also necessary to have a handle on their values at $R_{\rm max}$.
This value is estimated to be up to $20\%$ of the values at $R=30''$
for the $Q^{(2)}_{\rm out}$ and $Q^{(3)}_{\rm out}$  terms, and
around $1\%$ for the $Q^{(1)}_{\rm in}$ term, for a CIS cluster
whose center is displaced from the G1 center by $5''$ to $30''$.
Since our multipole signals are already significantly smaller
than the measurement errors, we deduce that the correction from the
$R_{\rm max}$ term is significantly smaller than the errors
if it arises from a cluster that resembles a CIS profile beyond $R_{\rm max}$.

\begin{table*}
\center
\begin{tabular}{rcll}
\hline\hline
$R^{-4}_1 Q^{(1)}_{\rm in}(R_1) - R^{-4}_2 Q^{(1)}_{\rm in}(R_2)$
& = & $[(-1.2\pm2.9) + i(+2.1\pm3.6)]\times 10^{-3}$ & arcsec$^{-1}$\\
$R^2_2 Q^{(2)}_{\rm out}(R_2) - R^2_1 Q^{(2)}_{\rm out}(R_1)$
& = & $[(+0.1\pm8.5) + i (-2.3\pm8.2)]\times 10^{2}$ & arcsec$^{2}$ (*)\\
$R^4_2 Q^{(3)}_{\rm out}(R_2) - R^4_1 Q^{(3)}_{\rm out}(R_1)$
& = & $[(-1.3\pm1.1) + i (-0.5\pm1.1)]\times 10^{5}$ & arcsec$^{3}$\\
\hline\hline
\end{tabular}
\caption[Table of multipole values in cluster Q0957+561.]
{Table of multipole values, where $R_2 = R_{\rm max} = 186''$, and
$R_1 = 30''$.
These values correspond to the innermost points
plotted in Figure~\ref{fig:multipole}, and hence are normalized to the
WL source redshifts.
(*) There is an alternative means of obtaining the
$\gamma_c$ [$R^2Q^{(2)}_{\rm out}$] term, via straightforward averaging of
the weak shear values within the annulus around $R=R_1$ (see text).
\label{tab:multipole}}
\end{table*}

\begin{figure*}
\plotone{multipole_moments.epsi}
\caption[Differential multipole moments of Q0957+561 cluster, centered at
G1.]
{{\it Left}: Differential $R^{-4} {Q}^{(1)}_{\rm in}(R)$ with respect to
the value at $R_{\rm max}$.
{\it Center}: Differential $R^2 {Q}^{(2)}_{\rm out}(R)$.
{\it Right}: Differential $R^4 {Q}^{(3)}_{\rm out}(R)$.
In all three figures, the solid squares indicate the real components,
while the open squares indicate the imaginary components.
The complex numbers encode the multipole orientation, where the
axes are aligned with West (``$x$'') and North (``$y$'').
The internal mass dipole term has a directionality that points
approximately to the Northeast with respect to G1, consistent with previous
studies \citep{FischerProFit,chartas02}.
\label{fig:multipole}}
\end{figure*}

Ignoring the $R_{\rm max}$ terms from the cluster and
assuming the lensing potential as stated in Eq.~(\ref{eq:galcluster}),
the cluster expansion coefficients (normalized to the quasar redshift)
are constrained to
\begin{eqnarray*}
\lefteqn{(1-\kappa_c)\,\sigma_c
 +  \frac{4}{\pi} (1-\kappa_c)
\left[R^{-4}_1 Q^{(1)}_{{\rm in},g}(R_1)
 - R^{-4}_2 Q^{(1)}_{{\rm in},g}(R_2)\right]}
\nonumber \\
&& \ \ = (-0.0018\pm0.0042) + i (-0.0031\pm0.0052) \ \ \ {\rm arcsec}^{-1}
\\% \label{eq:q1result} \\
\lefteqn{(1-\kappa_c)\,\gamma_c
 +  \frac{1}{\pi} (1-\kappa_c)
\left[ Q^{(2)}_{{\rm out},g}(R_1)
 - \left(\frac{R_2}{R_1}\right)^2 Q^{(2)}_{{\rm out},g}(R_2)\right] }
\nonumber\\
&& \ \  = (0.00\pm0.34) + i (+0.09\pm0.33) \\
\lefteqn{(1-\kappa_c)\,\delta_c
 +  \frac{2}{\pi} (1-\kappa_c)
\left[Q^{(3)}_{{\rm out},g}(R_1)
 - \left(\frac{R_2}{R_1}\right)^4 Q^{(3)}_{{\rm out},g}(R_2)\right] }
\nonumber\\
&& \ \ =  (+0.115\pm0.098) + i (-0.047\pm0.097) \ \ \ {\rm arcsec}^{-1}
\end{eqnarray*}
As explicitly stated above,
the galaxy model contribution $Q_{\rm g}^{(m)}$
to each moment must be subtracted from the results
to obtain the cluster moments $\gamma_c, \sigma_c$, and $\delta_c$;
the measurements constrain only the sum of the galaxy and cluster
contributions.

As seen in Figure~\ref{fig:multipole}, the error in the $\gamma_c$ and
$\delta_c$ terms do not converge to any sufficient degree.
However, we attempt to constrain $\gamma_c$ by the following means:
Since this term is simply the constant shear across $r<30''$,
we measure the average of the (WL) shear within this region.
However, since the central portion of this region is strongly lensed,
we average the shear signal over an annular region of $20''<r<40''$
to estimate the constant shear within $r<30''$.
We find the average shear, normalized to the quasar redshift, to be
\begin{eqnarray*}
(1-\kappa_c)\,\gamma_c
& + & \frac{1}{\pi} (1-\kappa_c)
\left[ Q^{(2)}_{{\rm out},g}(R_1)
 - \left(\frac{R_2}{R_1}\right)^2 Q^{(2)}_{{\rm out},g}(R_2)\right] \\
& = & (-0.009 \pm 0.045) + i(+0.092 \pm 0.045).
\end{eqnarray*}
This allows us to shrink the error bar considerably, and by doing so
we have assumed that $\gamma_c$ is generated exclusively by mass
exterior to $40''$.  The directionality of the constant shear term
is consistent with an exterior mass quadrupole distribution with
positive weight along the Northeast/Southwest direction with respect to G1.

\section{Conclusion}

The Q0957+561 gravitational lens system allows for a
determination of the Hubble constant $H_0$, based on
its firm time delay between the double images of the quasar;
the remaining uncertainty originates from our knowledge of the
lens mass distribution.
The lens consists of the galaxy G1 and the 0957+561 cluster to
which the galaxy belongs.
WL offers complementary constraints to the lens mass
provided by the SL modeling analysis, by providing the mass sheet and
multipole moments of the underlying cluster.
We have developed and utilized the formalism for an exact solution for
aperture mass multipoles from WL shear data in the thin-lens approximation.

The mean convergence in the SL region $r<30''$ is estimated to be
$\bar\kappa=0.166\pm0.056$ (1 $\sigma$) normalized to the quasar redshift,
based on shear data from the annular region $30''<r<186''$,
where the radii are centered on the lens galaxy G1.
Although our shear measurements are consistent with \citet{FischerProFit},
the new quasar-normalized $\bar\kappa$ is more reliable since they are
based on better data, a more accurate galaxy redshift distribution, and
a standard cosmology.
Our results give a $7\%$ precision in the mass sheet degeneracy term
$(1-\overline{\kappa})$.

The uncertainty in the external multipole terms $\gamma_c$ and $\delta_c$
are too large to provide useful constraints to
the lens potential $\psi$ within $r<30''$.
However, the constant shear term $(1-\bar\kappa)\gamma_c$ within $r<30''$
can be estimated by straightforward averaging of the shear in the WL region
at $20''<r<40''$.
The internal dipole $(1-\bar\kappa)|\sigma_c|$
(whose galaxy contribution is expected to be negligible)
has a value of $0.006\pm0.006$, compared to
the Monte Carlo parametric fit values $\sim0.011\pm0.007$
obtained by \citet{keeton00}.
The implications for $H_0$ with the full SL lens modeling
are discussed in an accompanying paper \citep{fadely09}.

\acknowledgements {
This work has been supported by grant HST-GO-10569 from the Space Telescope
Science Institute, which is operated by the Association of Universities
for Research in Astronomy, Inc., under NASA contract NAS5-26555.
RN and GMB acknowledge additional support from NASA grant BEFS-04-0014-0018.
TS acknowledges financial support from the Netherlands Organization for
Scientific Research (NWO) and the German Ministry for Education and Research
(BMBF) through TR33.
}

redpajama_set_name: RedPajamaArXiv


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text:
What Your Airline Won't Tell You About Those Creepy Airport Face Scanners
Hudson Hongo
Filed to:airlines
Last week, a Twitter conversation between an airline passenger and JetBlue went viral after she asked about the company's creepy facial recognition cameras. Mostly, the passenger seemed shocked to learn airlines were scanning customers' faces at all.
"Instead of scanning my boarding pass or handing over my passport, I looked into a camera," wrote writer MacKenzie Fegan. "Did facial recognition replace boarding passes, unbeknownst to me? Did I consent to this?"
Fegan had a lot of questions about the program, and JetBlue's official Twitter account didn't offer many answers. As alarming as airport face scanners may be, however, their rollout across the U.S. has hardly been secret. And there's a lot we can tell you about them that airlines' customer service agents never will.
Facial scanners are already at more than a dozen U.S. airports
The use of facial recognition in American airports has been spearheaded by U.S. Customs and Border Protection (CBP)—part of the Department of Homeland Security—which has been testing these systems as part of its "Biometric Exit" program since 2015. The initiative scans the faces of passengers taking international flights out of the U.S. and matches them to identity photos the CBP has on file.
Earlier this month, Homeland Security said it plans to scan the faces of "over 97 percent" of departing international passengers by 2023. According to Buzzfeed, 17 U.S. airports are currently part of the program.
"Since its inception, over two million passengers on over 15,000 flights have used the technology on exit," the agency boasted earlier this month. By the end of 2021, CBP has been given the goal of scanning the faces of passengers on 16,300 flights per week.
Some major airlines are enthusiastic partners
Both airports and airlines have been all too happy to participate in the scheme. JetBlue, Delta, Lufthansa, British Airways and, most recently, American Airlines have all tested CBP face scanners on their customers. These airlines emphasize that passengers can choose to opt out, but as Fegan's case illustrates, this option isn't always clear to customers. (Delta has said less than two percent of fliers at one terminal opted out of face recognition.)
Photo: Delta
JetBlue and Delta have even gone one step further, giving passengers more opportunities to have their faces scanned. In November, Delta debuted what it called America's "first biometric terminal" in Atlanta, celebrating an (optional!) "end-to-end Delta Biometrics experience" that would use facial recognition for check-in, bag check, TSA identification, and boarding. And in December, JetBlue told Travel Weekly it planned to install two "self bag drop" machines in New York that would scan passengers' faces and check them against CBP data.
We don't know how facial data collected by airlines is protected
While CBP has said it will only keep facial exit scans for a maximum of 14 days, the rules for partner airlines are vaguer. Speaking to the New York Times last summer, a CBP official said that while he doubted airlines would want to keep fliers' biometric data, it "would really be up to them."
More recently, CBP claimed in December that it has "developed business requirements which do not allow approved partners to retain the photos they collect." If so, these requirements do not appear to have been made public, and it's unclear when they were instituted.
In a statement to Gizmodo, a CBP spokesperson said "only CBP has access to this biometric data" and "no personally identifiable information associated with biometrics" is ever shared with partner companies. For their part, JetBlue, Delta, and American Airlines have said that they don't retain facial scans and say they are sent directly to CBP for matching.
In a 2017 report, Georgetown Law's Center on Privacy and Technology noted that by partnering with private companies, Homeland Security makes it easier for these companies to track travelers for their own business interests.
"[D]espite the risk that airlines will use biometric exit data and technology for their own tracking purposes, [the agency] has not published any guidelines for or agreements with its private partners," wrote the authors.
It's not clear why Homeland Security even needs to scan faces
As its name suggests, the Biometric Exit program scans people leaving the country. How this makes us any safer is difficult to explain. The government seems to believe that knowing—100 percent, for sure—when people legally admitted to the U.S. have left is important enough to scan everyone's face.
In a recent report, Homeland Security bragged that the program has biometrically confirmed "over 7,000" cases of people leaving the country after their visas expired—again, leaving. Out of 2 million passengers, that's a hit rate of about 0.0035 percent.
Asked what the Biometric Exit program does that traditional verification can't, a CBP spokesperson told Gizmodo that facial scans help the agency secure the border, identify persons of interest, and improve statistical reporting. Additionally, the spokesperson said it was convenient for travelers.
Facial recognition tech has repeatedly shown racial and gender bias
Over and over again, facial recognition systems have been found to be less accurate when identifying women and people with dark complexions. Just last year, the ACLU found that Amazon's face-scanning system matched 39 percent of non-white U.S. representatives to mugshot photos.
When it comes to CBP's face-scanning program, we don't even know how biased it may or may not be. Asked if the CBP's facial scans had a disparate impact on any demographic groups, a CBP spokesperson told Gizmodo the agency was "still looking further into this question." (A CBP official gave a similar answer in 2017.)
Facial recognition isn't just coming to airports
While airports might be the place where this creepy tech is being introduced the most rapidly, all kinds of industries are excited about the possibilities of facial recognition. Companies in the U.S. have tested out face-scanning kiosks designed to do everything from track fast food customers to secretly identify Taylor Swift stalkers.
Just last month, Twitter users were disturbed by a facial recognition kiosk in a Chinese airport that appeared to be passively scanning passersby. The New York Times recently reported that police in that country are now specifically requesting systems that can identify faces belonging to members of the Uighur ethnic minority. If we don't demand tighter rules on face scanning, this type of surveillance won't be surprising anymore: It will just be normal.
Update 4/23/2019 3:15 p.m. ET: This story has been updated throughout with comments from U.S. Customs and Border Protection.
The Dystopian Surveillance State Will Be Extremely Convenient
Cops Are Trying to Stop San Francisco From Banning Face Recognition Surveillance
Creepy Airport Face Scans Like China's Aren't Just Coming to America—They're Already Here
Man Hiding Face From Police Facial Recognition Test Fined for Telling Cops to 'Piss Off'

redpajama_set_name: RedPajamaCommonCrawl


Andrew and Karen Parker are sailing Highland Fling, their 10.5m Kirie Feeling yacht all the way north from Port Phillip Bay, Victoria along the east coast of Australia departing early January 2011. Along the way they expect to catch and eat (or buy and eat!) great Australian seafood! We also intend to swim, snorkel and dive many of the offshore highlights of the East Coast upon which we grew up.
This site was inspired by and set up by Bryan Drummond who used a similar site during his and Sue's trip north on Folie A Deux last year. Bryan spent hours assisting us at Refuge Cove and has offered loads of help since. Without his help you would be merely receiving the odd postcard!
Simply click on any of the pages listed across the top under the header picture.
To scoll rapidly back to the top, just click the button on the right hand side at the bottom of each page, just outside the margin of the text screen.
Go directly to the comments page link just under the picture at the top. Follow the instructions and make our day by letting us know you're interested! You will be asked to leave an email adddress which will not be published, your email address is needed so we can verify who you are and it goes no further than us. Comments come directly to us for filtering before we authorise them to be published, so if you don't want your comment to appear on the page just let us know in your comment.
You can also click on the facebook 'like' button at the end of each comment to let us know you're around.
The Where's Fling page has a Google Earth map which we update as we move further north. We will endeavour to put in as much Marina/anchorage and other cruising info in as we can so that if you are planning a passage, our information may assist you. Please remember that the prices we list are as of 2011.
This is the page where we will record our cruising recipes and new food experiences.
Enjoy the site, and keep in touch!


3) Describe problem: I am new and not really a coder but like this functionality. I understood most (well nearly all needed) to set up the tabs. Only question I have is how do I use the downloadtabs.zip files. Do I upload them somewhere to use for my blog? Thanks.
ThinkI sort of understand the codes a bit more more.Can someone please help.
1) am I supposed to upload these codes (dropdowntabs.js)to somewhere? I uploaded to a googlepages account but could not get a url link to it at all.
After many trials, I still could not get this working. I would appreciate assistance from anyone to push this forward.
I am testing the codes in my testing blog which is structured the same as my running one- I just want to make sure I know all the pitfalls before putting them to my "live" one.


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Deliberative Citizenship Initiative
Building Democracy One Conversation at a Time
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Debate and Deliberation: Commonalities and Contrasts Through the Lens of the First Presidential Debate of 2020
October 1, 2020 by Clare Magee Leave a Comment
By Cadie McNaboe, DCI Fellow
On September 29th, countless Americans tuned in to watch the first presidential debate between President Donald Trump and Former Vice President Joe Biden. For those who persevered through the antagonistic comments and arguments with the moderator, Fox News anchor Chris Wallace, it was clear that it was impossible to call the back and forth exchange a deliberation, and unlikely to term it a debate. NBC anchor Lester Holt, right after the debate had closed said, "If hearing that this debate is over was music to your ears, you may not be alone … I'm at a bit of a loss for words here to describe what we've just witnessed." I stand in agreement with him.
While this is only my third round of presidential debates (that I remember-it's distinctly possible my parents set me in front of the TV to watch the debates as a child), my years of competing in debate taught me about the rigidity and rules of debating, none of which were present in this debate. The DCI defines debate as structured discourse that is oriented towards highlighting differences and exposing weaknesses; with previous presidential debates, it also has been utilized to signify an alignment towards policy and an opportunity for a "winner" to emerge through their use of political prose and powerful rhetoric. This debate, with its insults, interruptions, and cross-talk intended only to derail the moderator's questioning, should be considered more of a reality-TV scene than anything else.
Deliberation, on the other hand, has something else to offer the American public. Based on cooperation rather than competition, deliberation seeks to build collective and individual understanding, and works to bridge the divides across the political spectrum so frequently apparent at the national level. Going beyond the constraints of debate's binary pro-con style, deliberation calls for good-faith arguments, ones that seeks to understand our commonalities rather than our differences.
Through deliberation, with its use of an active facilitator, connections can be woven, and viewpoints can be shared through the strategic use of stories, statistics, productive cross-talk and thoughtful consideration of new perspectives beyond our own. This non-adversarial approach builds on the unique perspectives each deliberator holds, and their inherent power to share their perspective with others.
Deliberation also stands to provide an opportunity to enable action after its closing. In a debate, participants would shake hands (pre-COVID), get the judge's feedback and "scoresheets" and then proceed to move to the next topic of concern. Instead of positing a temporary topic of concern, deliberation allows and encourages voluntary action as a relevant part of the deliberative process. Communication around these contentious issues is essential but does little without action tied to it.
This is why after each D-Team meeting or deliberative forum, the DCI sends out Beyond the Deliberation, a compilation of tangible action pathways for participants to consider if they feel inspired to pursue any of them. These pathways, with ways to get informed, get connected, and get involved, contribute to the autonomy of each deliberator, who can individually and collectively continue the work our democracy requires. After watching the first presidential debate, it's easy to feel unsure about the state of our country, but if instead of a reason to forfeit anything related to politics, we must use that debate as a call for cooperation as a collective response. If we do that, then we are empowered and also well positioned to begin the lifelong work of deliberation and action – for the benefit of ourselves and our democracy.
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In a mixing bowl, combine mustard, vinegar, lemon juice, onion, dill, olive oil, salt and pepper; whisk well.
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Supreme Court Grants Chippewas of the Thames First Nation Challenge to Line 9
News: Supreme Court Redefines Indigenous Consultation in Inconsistent Rulings
Fundraiser: Support COTTFN, 10 Carden in Guelph, and Laos based Gender Development Association with one donation (external link)
A message from the Chippewas of the Thames First Nation's Leslee White-Eye - Ogimaa Kwe (Chief)
Chippewas of the Thames then Chief Joe Miskokomon, and councillor Myeengun Henry at the Line 9 NEB hearings with a Two-Row wampum belt
Supreme Court Grants Chippewas of the Thames First Nation Challenge to Line 9 Supreme Court Grants Chippewas of the Thames First Nation Challenge to Line 9: Community Hopeful of Meaningful Consultation with the Crown https://chippewassolidarity.org/en/news/supreme-court-grants-chippewas-of-the-thames-first-nation-challenge-to-line-9 https://chippewassolidarity.org/en/news/supreme-court-grants-chippewas-of-the-thames-first-nation-challenge-to-line-9/@@download/image/COTTFNatNEB.jpg
Supreme Court Grants Chippewas of the Thames First Nation Challenge to Line 9: Community Hopeful of Meaningful Consultation with the Crown
MUNCEY, March 10, 2016 – the Supreme Court of Canada has granted the Chippewas of the Thames leave to appeal a decision of the Federal Court of Appeal relating to an Application before the National Energy Board to repurpose the Line 9 Pipeline.
At issue is whether the Crown exercised its duty to meaningfully consult and accommodate the Chippewas on a project that may potentially impact their Aboriginal and Treaty rights. The Chippewas are challenging the Crown's paternalistic policies based on denial and extinguishment of rights. Relying on s. 35 of the Constitution and previous Supreme Court rulings, the First Nation continues to urge negotiation and reconciliation.
Chief of the Chippewas of the Thames, Leslee White-Eye welcomed the decision, saying, "Our community is pleased by this forward step but the path before us is still long as we continue to seek protection of our Aboriginal and Treaty rights. We need to bring home that we are not acting alone in the action, nor that it is for our sole benefit but an attempt to seek protection of our water – these energy developments are one of many across the nation impacting our rights".
According to Chief White-Eye, "Our members were very distressed by the Federal Court of Appeal's dismissal of the appeal when they failed to acknowledge our Aboriginal and Treaty rights. The Court did not consider previous decisions, which establish the Crown's duty to meaningfully consult with and accommodate us on projects that may potentially impact those rights, such as Line 9."
The Crown's failure to consult has stalled negotiations, prevented Chippewas of the Thames from benefiting from their collective rights and has impeded economic development for all stakeholders. It has also undermined the Nation's development as a government. Still, Chief White-Eye remains optimistic by stating that "a positive final decision from the Supreme Court will hopefully pave the way for reconciliation with the Crown."
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Supreme Court Redefines Indigenous Consultation in Inconsistent Rulings Jul 26, 2017
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Indigenous legal challenges at Supreme Court put approvals of major energy projects on the line Dec 10, 2016
A message from the Chippewas of the Thames First Nation Nov 12, 2016
Press Release: November 5th Earthstock: Protecting the Water. A Benefit Concert for the Chippewas of the Thames First Nation Nov 03, 2016
This website and campaign have been undertaken in collaboration with Chippewas of the Thames First Nation. However, Chippewas Solidarity is a distinct group, and as such, does not represent COTTFN. Chippewas Solidarity's goal is to raise awareness and funds for the legal case. Website content is created by multiple parties and should not be taken as the legal opinion of COTTFN.
Please direct any questions to support@chippewassolidarity.org
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Video: Jurgen Klopp pre-match press conference – Liverpool vs. Crystal Palace
Watch as Jurgen Klopp speaks to the media ahead of Sunday's Premier League match against Crystal Palace at Anfield.
The Reds entertain Sam Allardyce's mid-table hopefuls in the first of their final five games of the season, looking to continue their fine unbeaten run.
Klopp spoke to reporters at Melwood on Thursday—strangely holding his pre-match press conference over three days before the game.
This saw him address a series of questions on Palace's Liverpool loanee Mamadou Sakho, of which he naturally fended off, ignoring speculation of a possible summer return.
The German provided an injury update on his squad, suggesting Jordan Henderson's foot injury could keep him out for the rest of the season.
Joel Matip, Ragnar Klavan and Lucas Leiva were all revealed to be struggling with minor problems, while Adam Lallana's return to training will not see him feature on Sunday.
Klopp was more positive on the fitness of Roberto Firmino, however, while he served up an optimistic view on Danny Ings' recovery.
"Danny Ings, after a long time in the gym, is running," he said. "He enjoys it a lot, but of course not even close to coming back."
There was plenty of praise for Divock Origi, with Klopp urging him to "get consistency."
Finally, the 49-year-old ruled out a summer move for Man City goalkeeper Joe Hart, but admitted targeting a new centre-back "would make sense."
Tags Jurgen Klopp, Press Conference


Your feelings have changed... now what?
You know how you're thinking of one of your friends on a constant basis? Looking for any reason to hang out with them? Or text them? You can hang out all day long and you never tire of them. They make you laugh and you always feel good when you're around them.
You both like the same Netflix shows, same music, same books.Then one day, you notice their eyes. Their arms and their legs; their entire bodies. And those lips! How soft are they?
Wait, hang on. This is one of your close friends! You've known them for years! What are you thinking?!
So, it looks like you're falling for your friend. We can't really blame you there. Friendships form strong bonds and allow for you to get to know someone on a deep level. Some of the longest-lasting and closest love relationships are between people who are truly good friends.
But when it comes to seeing if you can be more, taking that step from friends to romantic lovers can feel like a big and treacherous move to make.
Before we get to that, you need to figure out if you want to act on your feelings or not. There is a chance that a wonderful and fulfilling love relationship could bloom from the friendship and that it could just happen naturally.
However, there is also a chance that the attraction could be there — for both people — but neither one has the courage to admit it. This scenario leaves two friends hungering for more and afraid to do anything about it.
1. Don't go screaming you're madly in love with them just yet.
If you value your friendship with this person, we don't advise you to run in screaming your declaration of your love for them. Acknowledge the risks first.
It can be excruciating to pretend that you don't have romantic feelings for your friend and we don't recommend bottling those feelings. But, we do think it's wise to really come to grips with what you are about to do before you do it.
It's impossible to know how your friend will react to the news of you having romantic or sexual feelings for them. It's possible that your friend will be surprised and maybe a bit shocked by your admission.
It's also possible (depending on the circumstances) that knowing how you feel will change the dynamics of your friendship. There is a chance that it will feel "too weird" for them to continue to be as close to you as before if the feelings aren't shared or if for some reason you two cannot be together as a couple.
Yet another possibility is that your friend may have not yet realized how they feel about you. In other words, your friend's initial reaction might not be what you expected or wanted... and it might not reflect what's possible. Or maybe it might. Just keep this all in mind, as cruddy as it is.
2. Be true with how you feel.
Choose your words carefully when you tell your friend how you feel about them. You know your friend pretty well if you're close. If it seems like saying, "I am madly in love with you" would be a bit much (and it might be), be honest but pull it back a bit.
For example, you might say something like, "I've realized that my feelings for you have changed. I want to be more than friends with you. How does that make you feel?"
Phrases like these may be pretty toned down in comparison to what you feel inside, but they are still honest and they open the door for you two to talk about what's possible in the future without causing your friend to run for the hills.
3. Open your heart and your ears.
As we said above, your friend might be a bit freaked out to hear that you have romantic or sexual feelings for them. Even if the feelings are actually mutual, just making that transition from friends to romantic partners or lovers is huge. Take a deep breath and really open your heart and your ears. Listen closely to what your friend says in response.
If they emphatically let you know that the feelings are not mutual and that being more than friends is not going to happen, respect that.
Take your time in determining if you want to continue the friendship or if you need some space to regroup. Being pushy or trying to convince your friend to be in a love relationship with you is probably not going bring either of you happiness or satisfaction.
If your friend talks about feeling surprised or confused, honor that too. Let your friend know that you will be available if they wants to talk more about this... or not talk more and possibly act on those new romantic feelings!
Susie and Otto Collins are authors and relationship coaches who help people attract and sustain more love in their lives. Click here to receive their free ebook: Passionate Heart ~ Lasting Love.


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Divided reactions over court order allowing Mumbai nurse to terminate foetus with Down syndrome
Get-hooked June 26, 2020
The Supreme Court recently allowed a woman from Mumbai to selectively terminate one of her twin foetuses which is said to have Down syndrome. This has been allowed even though the nurse has passed the legal time limit for abortions. The report has evoked strong reactions from many people, who say this underlines the need for greater awareness and support for people with disabilities and their caregivers.
'Shameful'. 'A quest for flawless babies.' These are some of the reactions on social media to a newspaper report on a recent Supreme Court order allowing a Mumbai nurse to terminate one of her twin foetuses which is said to have Down syndrome. The court has allowed this even though she has passed the legal time limit for abortions under the Medical Termination of Pregnancy (MTP) Act.
A genetic disorder, Down syndrome is caused due to extra genetic material from chromosome 21. The disorder causes a distinct facial appearance and certain developmental delays. Speaking to The Times of India, the nurse and her husband said they made the decision given the difficulties faced in raising a child with disability.
Indicates larger mindset about Down syndrome
Days after the order was passed, the report continues to evoke strong reactions, much of it targeting the couple. However, as Dr Rekha Ramachandran, Co-founder, Down Syndrome Federation of India (DSFI), points out, there is no right and wrong in the issue.
The fact is that everyone is worried about having a child with any type of disability", said Dr Rekha, who is a parent to an adult with Down syndrome. "Even a cleft palate gets people into a panic! We have to look at it as an individual".
Instead, she says, one needs to look at the perceptions about Down syndrome that are still prevalent.
No one who has seen a person with Down syndrome from up close will take such a step. What this shows is the picture that has been painted to this couple. And the fact is that in India, we are always petrified about 'who after me'. In any other part of the world, the government takes responsibility and offers support. It's easy to say life is precious but it is finally an individual decision. – Dr Rekha Ramachandran, Co-founder, Down Syndrome Federation of India
Dr Rekha came up against the perception battle as well when she contracted German Measles during her pregnancy. "The doctor told me I should abort given the consequences, but my family stood by me. I finally believe that it's all about karma because you will have a child with special needs if he/she chooses us. We are all chosen because we had the capacity to handle it".
Parents come together to spread awareness
A large part of the problem stems from lack of awareness. Something that Tejal Shah, co-founder of Bangalore Humsafar, a support group for parents with children with Down syndrome, is trying to address. Tejal says it is important to empathise with the Mumbai nurse and not judge.
"The decision comes from poor awareness and stigma about Down syndrome", says Tejal, who is also a parent to a child with the condition. "I had a similar mindset when my child was born. If people are aware and know how to handle the situation, then the decisions taken would be different. I understand her worries. There are also many people choosing to adopt a child with Down syndrome and that comes from a place of greater awareness. As parents, we have to spread the awareness as we are experiencing it".
Thanks to Bangalore Humsafar, support is a phone call away for Down syndrome families
Film with a cast of over 80 people with disabilities to release worldwide in November
"Focus on your abilities, not disability" - My Take by Ira Singhal, IAS Officer
Kerala parent support group TogetherWeCan's series 'Speak Up' addresses mental health
Understanding Fine Motor Skills


These models were available unpainted, or painted and lettered with any of these NKP road numbers: 740, 748, 759, 765, 769. Manufactured by Boo Rim Precision in Seoul, Korea. The video tab shows testing, installing, and running the model with a sound decoder (notice how little current the model requires!).


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Antitumor Activity of Cytotoxic Cyclooxygenase-2 Inhibitors.
Uddin MJ, Crews BC, Xu S, Ghebreselasie K, Daniel CK, Kingsley PJ, Banerjee S, Marnett LJ
ACS Chem Biol. 2016 11 (11): 3052-3060
PMID: 27588346 · PMCID: PMC5289892 · DOI:10.1021/acschembio.6b00560
Targeted delivery of chemotherapeutic agents to tumors has been explored as a means to increase the selectivity and potency of cytotoxicity. Most efforts in this area have exploited the molecular recognition of proteins highly expressed on the surface of cancer cells followed by internalization. A related approach that has received less attention is the targeting of intracellular proteins by ligands conjugated to anticancer drugs. An attractive target for this approach is the enzyme cyclooxygenase-2 (COX-2), which is highly expressed in a range of malignant tumors. Herein, we describe the synthesis and evaluation of a series of chemotherapeutic agents targeted to COX-2 by conjugation to indomethacin. Detailed characterization of compound 12, a conjugate of indomethacin with podophyllotoxin, revealed highly potent and selective COX-2 inhibition in vitro and in intact cells. Kinetics and X-ray crystallographic studies demonstrated that compound 12 is a slow, tight-binding inhibitor that likely binds to COX-2's allosteric site with its indomethacin moiety in a conformation similar to that of indomethacin. Compound 12 exhibited cytotoxicity in cell culture similar to that of podophyllotoxin with no evidence of COX-2-dependent selectivity. However, in vivo, compound 12 accumulated selectively in and more effectively inhibited the growth of a COX-2-expressing xenograft compared to a xenograft that did not express COX-2. Compound 12, which we have named chemocoxib A, provides proof-of-concept for the in vivo targeting of chemotherapeutic agents to COX-2 but suggests that COX-2-dependent selectivity may not be evident in cell culture-based assays.
MeSH Terms (9)
Animals Antineoplastic Agents Cell Line, Tumor Crystallography, X-Ray Cyclooxygenase 2 Inhibitors Humans Kinetics Mice Mice, Nude
Shu Xu (Member)


This article will show you how to use the features available for NBN™ Fibre Phone (Enhanced Fibre Phone) services. Although similar to Netphone (VoIP), NBN™ Fibre Phone is available exclusively for NBN™ Fibre to the Premises (FTTP) broadband.
Everything you need to know to get your NBN™ Fibre Phone service plugged in and running.