text:
\section{Introduction}

The abundance of massive clusters of galaxies provides sensitive constraints
on the cosmological parameters that govern structure growth in the universe.
However, a prerequisite for this is reliable mass measurements for large samples
of clusters with well-understood selection criteria.
Cluster mass measurements used have traditionally come from
virial analysis of the velocity dispersion
measurements of cluster galaxies (e.g., Frenk et al.\ 1990; Carlberg et al.\ 1997;
Borgani et al.\ 1999), or X-ray temperature measurements of the hot intra-cluster gas
under the assumption that the gas is in hydrostatic equilibrium
\citep[for a review see ][]{rosati}.
Satellite observatories such as ROSAT, ASCA, XMM-Newton and {\it Chandra}
have made increasingly accurate X-ray temperature measurements of clusters,
and have produced well-defined cluster samples of sufficient size to
accurately measure the X-ray temperature and luminosity functions
\citep[e.g.][]{henry04,boehringer}. However, the relation between cluster mass
and X-ray temperature and luminosity, respectively, must be determined to convert
these into a reliable cluster mass function.

X-ray luminosities are available for large samples of clusters, but the
X-ray luminosity is highly sensitive to the complex physics of cluster cores,
making it challenging to relate to cluster mass.
Measuring X-ray temperatures is observationally much more demanding, but the
X-ray temperature is mainly determined by gravitational processes and is hence
more directly related to cluster mass than X-ray luminosity.
Both from simulations and observations the intrinsic scatter in mass around
the mass--temperature relation is thus found to be much smaller
\citep[$\Delta M/M \approx 0.15$, ][]{evrard96,borgani,sanderson,vik} than the
scatter in mass around the mass--luminosity relation
\citep[$\Delta M/M \approx 0.4$, ][]{reiprich}.

Two different routes have been followed for determining the mass--temperature
relation. Most studies have used a small sample (up to about a dozen) of
supposedly well understood clusters for which the assumptions underlying the
mass determination should be fulfilled to a high degree. The main concern
for this approach is that the selected clusters may not be representative of
the whole cluster population, and therefore the derived mass--temperature relation
may only apply to a subset of clusters. Alternatively, the mass--temperature
relation may be determined from a large sample of more objectively selected
clusters. This is more fruitful when comparing such a locally determined
mass--temperature relation to a sample of high-redshift clusters where the data
quality does not allow a similar selection of the ``most suitable'' clusters.
Also, mass--temperature relations derived from simulations are usually
based on a large range of simulated clusters with no pre-selection.
Hence it is most appropriate to compare observationally obtained
mass--temperature relations determined from all available clusters to
the relations from simulations.
On the other hand, for some of the clusters in such a sample the hydrostatic
assumption may be invalid, making X-ray based mass determinations unreliable
for a subset of the clusters. A larger scatter (which may not be symmetric) around
the mean mass--temperature relation may be expected, when such clusters are
included.

There are still poorly understood systematic uncertainties
associated with establishing the mass--temperature relation.
The normalization of the mass--temperature relation based on cluster masses
determined from X-ray data \citep[][]{fin,vik,arnaud05}, tend to differ significantly
between studies, and from the expectations based on numerical
simulations (e.g., Evrard et al.\ 1996; Eke et al.\ 1998; Pen 1998;
Borgani et al.\ 2004).
The determination of this normalization is currently the dominating
source of discrepancies between the reported values for the power spectrum
normalization on the scale of galaxy clusters,
$\sigma_8$, derived from the observed cluster temperature function
(Huterer \& White 2002; Seljak 2002; Pierpaoli et al.\ 2003; Henry 2004).
Observations using X-ray based mass determinations have traditionally favored
low normalizations (and hence low values of $\sigma_8$),
while simulations have favored somewhat higher normalizations.

Gravitational lensing provides an opportunity to measure cluster masses without
invoking the assumption of hydrostatic equilibrium in the hot intra-cluster gas
implicit in the X-ray based mass determinations. Also, in this case the measurement
of cluster mass is truly independent of the X-ray temperature measurement.
Hjorth, Oukbir \& van Kampen (1998) used weak gravitational mass measurements
for eight clusters drawn from the literature to find a relation between mass over
cluster-centric radius, and temperature. They determined a normalization of this relation
consistent with the value predicted by Evrard et al.\ (1996), but with a preference for
somewhat higher cluster masses (if the redshift scaling of equation~\ref{eq:theoryMT} is
assumed, see below).
However, Smith et al.\ (2005; hereafter S05) determined a mass--temperature relation with a
normalization significantly lower than indicated by the
Hjorth et al.\ (1998) study.
S05 based their results on a sample
of 10 clusters with weak lensing masses and temperatures determined from {\it Chandra} data.

Here, we present a new weak gravitational lensing-based measurement of the
normalization of the mass--temperature relation. The main improvements with
respect to the work of Hjorth et al.\ (1998) and S05 is that we
use a significantly larger cluster sample which represents a
significant fraction of all the clusters in an even larger sample with
well-defined objective selection criteria (Dahle et al.\ 2002;
H.\ Dahle 2006, in preparation). An additional improvement over the work of
Hjorth et al.\ (1998) is that the weak lensing analysis has been
performed in a consistent way for all clusters, using the same shear estimator and
making the same assumptions about e.g., the typical redshift of the lensed galaxy
population and the degree of contamination by cluster galaxies.
We note that the early data set of clusters with
published weak lensing masses used by Hjorth et al.\ (1998) is biased
at some level towards systems that were observed
because of ``extreme'' properties, such as being the hottest or most X-ray
luminous system known at the time, or having a large number of
strongly gravitationally lensed arcs.
Furthermore, we note that our gravitational lensing measurements are made at larger
radii than probed by S05, requiring smaller extrapolations to estimate the mass within
e.g., the virial radii of the clusters.

The data set used for the analysis is described in \S~\ref{sec:data},
our results for the mass--temperature relation and $\sigma_8$ are presented
in \S~\ref{sec:results}, and our results are compared to other work and the
implications discussed in \S~\ref{sec:discussion}.

Except when specifically noted otherwise (for easy comparison to previous results
using different cosmologies), we assume a spatially--flat cosmology
with a cosmological constant ($\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$), and
the Hubble parameter is given by $H_0 = 100 h\, {\rm km}\, {\rm s}^{-1} {\rm Mpc}^{-1}$.

\ \\ \

\section{Data Set}
\label{sec:data}

\subsection{Weak lensing data}
\label{sec:wldata}

Our weak lensing data set is a sample of 30 clusters (see Table~\ref{tab:dataset}),
of which 28 were included
in the weak lensing cluster sample of Dahle et al.\ (2002). Data for
two additional clusters come from a recent extension of this data set (H. Dahle 2006,
in preparation).
The clusters targeted for these weak lensing studies were generally selected to
lie above an X-ray
luminosity limit $L_{X, 0.1 - 2.4\,{\rm keV}} \geq 6 \times 10^{44}$ ergs s$^{-1}$
(this luminosity limit is for our chosen cosmology with $h = 0.7$) and within a
redshift range
$0.15 < z_{\rm cl} < 0.35$. The observed clusters were selected from the X-ray luminous
cluster samples
of Briel \& Henry (1993) and Ebeling et al.\ (1996;1998;2000). The cluster samples
of the first two of these papers
are based on correlating an optically selected cluster sample
(Abell 1958; Abell, Corwin, \& Olowin 1989) with X-ray sources from the
ROSAT All-Sky Survey (RASS; Tr{\"u}mper et al.\ 1993), while the two last papers
contain X-ray flux limited cluster catalogs, also based on RASS. Of the total sample
of 30 clusters, three (\objectname{A959}, \objectname{A1722}, and \objectname{A1995}) are drawn from the Briel \& Henry (1993)
sample and two (\objectname{A209} and \objectname{A2104}) are drawn from the XBAC sample of Ebeling et al.\ (1996).
Of the remaining 25 clusters, 22 are included in the X-ray brightest cluster sample
(BCS) of Ebeling et al.\ (1998), while three (\objectname{A611}, \objectname{A1576}, and \objectname{Zw3146}) come from its
low-flux extension (eBCS; Ebeling et al.\ 2000).
Of the BCS and eBCS clusters in our sample, 24 objects are included in a
volume-limited sample of 35 clusters selected from the BCS and eBCS samples (Dahle 2006).
Hence, while our sample is not strictly physically well-defined (in the sense that the availability of an
X-ray temperature measurement is one of the defining selection criteria), it still has significant
overlap with a well-defined cluster sample. In a recent paper, Stanek et al.\ (2006) discuss how a significant scatter
around the mean mass-luminosity relation may cause a significant Malmquist bias in X-ray flux-limited cluster samples,
causing high-mass, low flux clusters to drop out at high redshifts. This would result in a bias in the
mass-luminosity (or mass-temperature) relation derived based on such a sample. We note, however, that
although the RASS-based samples from which our cluster sample is drawn are flux-limited, the cluster sample discussed
here quite closely approximates a volume-limited sample, and we therefore expect any such bias to be
negligible.

The observations were made with the $8192^2$ UH8K mosaic CCD camera and the $2048^2$ Tek CCD
camera at the 2.24m University of Hawaii Telescope and
with the $2048^2$ ALFOSC CCD camera at the 2.56m Nordic Optical
Telescope. All clusters were imaged in both the $I$- and $V$-band,
with typical total exposure times of 3.5h in each passband for the UH8K data and
$\sim 1.5$h for the data obtained with the more sensitive $2048^2$ detectors.
The seeing was in the range $0\farcs6 \leq {\rm FWHM} \leq 1\farcs1$ for all the imaging data
used for the weak lensing analysis. The median seeing was 0\farcs82 in the $I$-band and
0\farcs9 in the $V$-band. This gave typically $\sim 25$ usable background galaxies per
square arcminute, or a ``figure of merit'' value of
$\sum Q^2/d{\Omega} \simeq 1.5 \times 10^5$deg$^{-2}$, as defined by Kaiser (2000).
As noted below, the background galaxies were selected based on signal to noise ratio rather
than magnitude, with limits corresponding to $21 \lesssim m_I \lesssim 24.5$ and
$22 \lesssim m_V \lesssim 25.5$ for point sources.
The observations and data reduction of the data set used for the weak lensing
mass measurements are described in detail by Dahle et al.\ (2002).

Major efforts are being made to improve the methods for the estimation of weak
gravitational lensing, particularly in connection with ongoing and future studies of
``cosmic shear'' based on wide-field optical surveys. The requirements for the precision of shear
estimates in these surveys are substantially more stringent than for weak lensing
observations of massive clusters, given the significantly weaker lensing effects measured
in random fields.

In this work, we have used the
shear estimator of Kaiser (2000), which was ``blind-tested'' (along with several
other shear estimators) by Heymans et al.\ (2005), using simulated lensing data.
The shear estimator of Kaiser (2000) is more mathematically rigorous than the currently
most widely used shear estimator (Kaiser, Squires, \& Broadhurst 1995),
but it displays a significant
non-linear response to shear, unlike most other shear estimators.
If we correct our shear values using a second order polynomial based on the test
results of Heymans et al.\ (2005), we find that most cluster masses stay within $+/-15$\%
of the mass
calculated based on uncorrected shear values. Furthermore, the change in
average cluster mass is $<2$\%, i.e., there is very little systematic shift in mass.
In the end, we chose not to apply this correction, since it would, in a few cases, require
extrapolations outside the range of shear values over which the shear estimator has
been tested.
For more details about the practical implementation of this shear estimator, see
Dahle et al.\ (2002).

To convert the measurements of weak gravitational shear into actual cluster masses,
the distances to the background galaxies need to be known.
The background galaxy redshifts were estimated from spectroscopic and photometric
redshifts in the Hubble Deep Field (for details, see Dahle et al.\ 2002).
For our data set and chosen cosmological model, the average value of the ratio
between the lens-source and observer-source angular diameter distances,
$\beta \equiv D_{ls}$/$D_s$, is well approximated by the relation
$\langle \beta \rangle = 1.37 z_{\rm cl}^2 - 2.00 z_{\rm cl} + 1.01$ within
the redshift range of our cluster sample. This then provides an effective
critical surface density for lensing
($\Sigma_{\rm crit} = (c^2/4\pi G)(D_l \langle \beta \rangle)^{-1}$;
where $D_l$ is the angular diameter distance to the cluster), which is used for
deriving cluster masses from the shear estimates. The quoted value of $\langle \beta \rangle$
corresponds to the value at large cluster radii; at smaller radii a correction term has to
be employed to account for contamination by cluster galaxies, as discussed below and illustrated
in Figure~\ref{fig:cluscont}.

The observable galaxy shape distortions caused by gravitational lensing provide a
measurement of the reduced tangential shear,
$g_T = \gamma_T/(1-\kappa)$, where $\gamma_T$ is the
tangential component of the shear and $\kappa$ is the convergence.
We fit an NFW-type mass density profile,

\begin{equation}
\rho (r) = \frac{\delta_c\, \rho_c (z)}{(r/r_s) (1+ r/r_s)^2}
\label{eq:NFW}
\end{equation}

\noindent
(Navarro, Frenk, \& White 1997),
to the observed reduced shear profile $g_T (r)$ of each cluster.
Here, $\rho_c (z)$ is the critical density of the universe at the redshift of
the cluster, and

\begin{equation}
\delta_c = \frac{200}{3} \frac{c_{200}^3}{\ln (1+c_{200}) - c_{200}/(1+c_{200})}.
\label{eq:deltacdef}
\end{equation}

\noindent
We assumed a concentration parameter $c_{200} = c_{\rm vir}/1.194 = 4.9 / (1+z)$,
corresponding to the median halo concentration predicted by Bullock et al.\ (2001) for a
$M_{\rm vir} \simeq 8\times 10^{14} M_{\sun}$ cluster from
simulations of dark matter halos in a $\Lambda$CDM universe.
Here, $c_{200} = r_{200c} / r_s$, and $c_{\rm vir} = r_{\rm vir} / r_s$,
where $r_{200c}$ is defined as the radius within which the average mass
density is 200 times the critical density $\rho_{c} (z)$, and $r_{\rm vir}$
is the virial radius of the cluster.

The lensing properties of the NFW model have been
calculated by Bartelmann (1996) and Wright \& Brainerd (2000).
From our fit, we calculated $M_{500c}$, the mass enclosed
by the radius $r_{500c}$.
The mass estimates are listed in Table~\ref{tab:dataset}.
The shear measurements used for the fit were made at clustercentric radii
$50\arcsec < r < 180\arcsec$ for the clusters that
were observed with $2048^2$ CCD cameras and $150\arcsec < r < 550\arcsec$
for the clusters that were observed with the UH8K camera.
By comparison, we find $r_{500c}$ values typically in the range
$300\arcsec < r_{500c} < 600\arcsec$ for
the clusters we study here. In many cases, we need to extrapolate the
NFW profile out to $r_{500c}$ (in Table~\ref{tab:dataset} we list the
ratio of the outermost radii of our shear measurements, $r_{\rm fit}$, to
$r_{500c}$, and note that $r_{500c} = 0.66 r_{200c}$ for our chosen NFW model).
In this extrapolation, we assume the median NFW concentration parameter given
above. Hence, any intrinsic scatter in $c_{\rm vir}$ will introduce an
extra uncertainty in the cluster mass estimates. If we assume a random scatter around
the mean value of $c_{\rm vir}$ at the level (a $1 \sigma$ $\Delta (\log c_{\rm vir}) \sim 0.18$)
predicted by Bullock et al.\ (2001), we find a corresponding scatter in the mass estimates
of 20\% for our data set. This additional scatter is not included in the uncertainties of the
listed mass measurements in Table~\ref{tab:dataset}, but is considered further in
Section~3.2.

The measured gravitational lensing signal is sensitive to the two-dimensional
surface mass distribution, including mass associated with the cluster
outside $r_{500c}$, and random structures seen in projection
along the line of sight (Metzler, White \& Loken 2001; Hoekstra 2001;
Clowe, De Lucia \& King 2004; de Putter \& White 2005).
This will introduce additional uncertainty (and potentially a net bias) to
any lensing-based estimates of the cluster mass contained within a 3D volume.
Studies based on simulated clusters (e.g., Clowe et al.\ 2004)
indicate that the net bias is no more
than a few percent when 3D cluster masses are estimated by fitting observations of
$g_T (r)$ to predictions from theoretical models of the mass
distribution, such as the NFW model.
However, the scatter in the mass estimates from projection effects
amount to a weak lensing mass dispersion of $\sim 15-25\%$ for massive
galaxy clusters, which should be added to the observational uncertainties of the
lensing mass estimates.
In this paper, we have assumed a lensing mass dispersion of 0.26 resulting from projection effects,
corresponding to the value estimated by Metzler, White \& Loken (2001) from their N-body simulations.
Although these authors considered a somewhat different mass estimator, more recent estimates
indicate a similar mass dispersion for the NFW profile fitting method that we have used.
This additional mass uncertainty has been added in quadrature to the uncertainties of $M_{500c}$
values listed in Table~\ref{tab:dataset}.

\begin{figure}
\resizebox{8cm}{!}{\includegraphics{f1.ps}}
\caption[Cluster galaxy contamination in the faint galaxy samples.]
{Cluster galaxy contamination in the faint galaxy catalogs as a function of distance from the cluster center. The solid line represents an average of 6 clusters at an average redshift $\langle z \rangle=0.31$, while the dashed line represents an average of 5 clusters at $\langle z \rangle =0.23$.}
\label{fig:cluscont}
\end{figure}

The absence of reliable information about the individual redshifts of the faint galaxies used
for the weak lensing measurement will inevitably result in some degree of confusion between
lensed background galaxies and unlensed cluster galaxies. The magnitude of this effect will
depend on the projected number density of cluster galaxies,
and should thus have a strong dependency on cluster radius. Hence, a radially dependent correction
factor was applied to the shear measurements to correct for
contamination from cluster galaxies in the faint galaxy catalogs that were used to
measure the gravitational shear (these catalogs included all galaxies in the cluster fields
that were detected at a signal-to-noise ratio $6 < S/N < 100$, with no additional selection
based on e.g., galaxy color).
The magnitude of this correction was estimated from the radial dependence of the average faint
galaxy density in two ``stacks'' of clusters observed with the UH8K camera,
one at $z\sim 0.30$ and the other at $z\sim 0.23$, assuming that the
contamination is negligible at the edge of the UH8K fields, $>1.5h^{-1}$ Mpc from the cluster center.
The estimated degree of contamination is shown in Figure~\ref{fig:cluscont}.

Given the difference in cluster redshift, the similarity of the two curves in
Figure~\ref{fig:cluscont} may be somewhat surprising, as one would naively expect the
more distant clusters to display a significantly lower surface density of cluster
galaxies.
However, there are several competing effects that affect the observed galaxy
density at a fixed angular radius: Firstly, if all cluster galaxies were detectable
regardless of cluster redshift, the change in apparent image scale with redshift should
increase the surface density by a factor given by the square of the ratio of the angular
diameter distances. On the other hand, a fixed angular radius would
correspond to a larger physical cluster-centric radius (and hence lower galaxy density in
physical units) at the larger redshift, the difference depending on the slope of the
radial galaxy density profile. At the radii probed in this study, both the radial
surface mass density profile and the number density profile of bright cluster galaxies
follow approximately the power law behavior of a singular isothermal sphere
($\sigma (r) \propto r^a$, with $a=-1$). Hence, the physical number density
(in galaxies/Mpc$^2$) at a fixed angular radius should decrease as the inverse of the
ratio of angular diameter distances. In addition, the faintest galaxies drop below
the detection limit at higher redshift, the effect depending on the slope of the cluster
luminosity function around $M_R \approx -15$. Assuming a Schechter (1976) luminosity function
with a faint-end slope $\alpha^{\star} = -1.25$ (typical of rich clusters) and
$M_R^{\star} (z=0.23) = -21.65$,
the luminosity function can be integrated down to the detection limit (corresponding
to $M_R \simeq -15.0$ and $M_R \simeq -15.7$ at $z=0.23$ and $z=0.30$, respectively),
to estimate the fraction of cluster galaxies that drop out at the higher
redshift ($\sim 30$\%).
Finally, a redshift-dependence given by $M_R^{\star} (z) = M_R^{\star} (0) + 5\log (1+z)$
was assumed to account for galaxy evolution in the clusters. The combination of all these
effects would predict a surface density of cluster galaxies which is 7\% less at
$z=0.3$, compared to $z=0.23$, for a fixed cluster richness.
Even this small difference would be erased by a slight decrease in
the assumed values of the slopes $\alpha^{\star}$ and $a$.
A faint-end slope of the luminosity
function of $\alpha^{\star} = -1.1$ would be sufficient to remove
the predicted difference in galaxy surface
density at the two different redshifts. Based on {\it Hubble Space Telescope} (HST) WFPC2
imaging of the galaxy cluster \objectname{A2218} (which is similar to the clusters studied here in
terms of optical richness, lensing mass and X-ray properties), Pracy et al.\ (2004)
find that the cluster core shows a relative depletion of dwarf
galaxies, leading to a radial profile of faint galaxies which is significantly shallower
than the SIS prediction. For the ``intermediate'' dwarf population
($-18 < M_{\rm F606W} < -15$, similar to the range in absolute magnitude of cluster
galaxies in our faint galaxy catalogs), these authors find a radial distribution with a
slope $a=-0.63\pm0.09$. Assuming a similar slope for the radial distribution of the
faint cluster galaxies in our catalogs
would also remove the predicted difference between the two curves in
Figure~\ref{fig:cluscont}. Based on this figure,
and the above discussion, we conclude that we are probably justified in ignoring the
redshift-dependence in our cluster galaxy contamination correction.

The level of cluster galaxy contamination for individual clusters will generally differ
from the mean level calculated above, as there will be significant cluster-to-cluster variations
in the abundances of cluster dwarf galaxies. Based on the sample of clusters observed with the
UH8K camera,
the scatter in dwarf galaxy richness was estimated to be $\sim 50\%$ (this estimate also includes
variations in the field galaxy density caused by uncorrelated large-scale structures along the line of
sight, and hence the true scatter in dwarf galaxy richness of the clusters is somewhat
overestimated). By employing the mean contamination correction calculated above rather than an
estimate appropriate for each cluster, we introduce an additional scatter of up to $20\%$ in our
mass estimates. This additional scatter is not included in the uncertainties of the
tabulated mass measurements in Table~\ref{tab:dataset},  but is considered further in
Section~3.2.

Eight of the clusters in our sample were also included in the combined strong and weak gravitational
lensing study of S05, based on observations of a sample of 10 X-ray luminous galaxy clusters at
$z\sim 0.2$ using HST WFPC2.
These authors estimated the projected cluster mass within a clustercentric radius of
$250 h^{-1}$ kpc, assuming an Einstein-de Sitter ($\Omega_m = 1$, $\Omega_{\Lambda} = 0$) cosmology.
Figure~\ref{fig:S05comp} shows a comparison of the mass values listed by S05 with our
 cluster mass estimates, using the best-fit NFW model to derive projected cluster masses, assuming
the same cosmology as S05. These authors assumed a spatially constant contamination of
20\% cluster galaxies in their background galaxy catalogs at radii $<2\arcmin$, while we find an
average contamination of 30\% for our data at these radii.
Hence, for the plot in Figure~\ref{fig:S05comp} we
have adjusted our radially dependent contamination correction such that the average contamination
at small radii is consistent with that assumed by S05. We find that our cluster mass estimates are
generally consistent with those of S05, although with a tendency for higher masses
(by about 30\%).

\begin{figure}
\resizebox{8cm}{!}{\includegraphics{f2.ps}}
\caption[Comparison with S05 mass estimates.]
{Comparison with estimates of the projected mass within $250 h^{-1}$ kpc published by
S05. The lensing masses in this plot are given for the
cosmological model assumed by S05, and our estimate of
the degree of galaxy cluster contamination was also adjusted to match the
contamination assumed by S05 (see text for details). }
\label{fig:S05comp}
\end{figure}

\subsection{X-ray data}

For clusters in the weak lensing data set, we compiled a list of
corresponding X-ray temperatures from the literature.
For many of these clusters, their global temperature,
or even a temperature map, has been determined using data
from {\it Chandra} and/or XMM-Newton.
However, these temperatures constitute a rather heterogeneous sample,
for which the systematics are not well established.
Consequently, X-ray temperatures
were primarily drawn from the samples of \cite{OM}, \cite{allen00} and \cite{white00},
each providing a homogeneous measure of the global cluster temperature
(i.e., temperature measured within a cluster-centric distance close to
$r_{500c}$) for a large fraction of the clusters in the weak lensing sample.
All these authors derived temperatures based on analysis of ASCA spectra.
For two clusters not in either of the samples mentioned above
we extracted published temperatures from other sources.

Specifically, from the works of \cite{OM} and \cite{allen00} we
extracted temperatures estimated by these authors by fitting an isothermal plasma model
with the Galactic absorbing column density as a free parameter.
The temperatures taken from \cite{white00} were derived by fitting an isothermal plasma
model with the nominal Galactic absorbing column density fixed, but since only
energies above 1~keV are used in the \cite{white00} spectral fitting the
fixed column density should not
introduce systematic effects relative to the temperatures from the
\cite{OM} and the \cite{allen00} samples.
For the remaining two clusters we
extracted published temperatures obtained in a similar way
(see Table~\ref{tab:dataset}).

For the clusters in two or more samples, their derived temperatures agree
within the uncertainties, and for any cluster the derived temperatures
differ by less than 20\% between samples. Also, the mean of temperature
differences between
any two of the samples by \cite{OM}, \cite{allen00}, and \cite{white00} is
less than 3\%, indicating the low level of systematic temperature variance between
different analyses.

Although the isothermal plasma model has proven too simplistic for nearby
clusters, the global cluster temperature is straightforward
to derive from observations as well as simulations, enabling a rather
direct comparison between observations and theory.
Furthermore, for the majority of distant ($z \gtrsim 0.5$) clusters only global
isothermal temperatures can be obtained in the foreseeable future.
Hence, we refrain from going into the detailed spatial and
spectral modeling of the intra-cluster gas.
The effects of cluster dynamics, ``cooling
cores'', non-sphericity etc. generally affects the global temperatures
only at the 10\%-20\% level \citep[e.g.,][]{evrard96,white00,smith}.

\begin{deluxetable*}{lcccccccc}
\tablecaption{Weak lensing masses and X-ray temperatures
	\label{tab:dataset}}
\tablehead{
\colhead{Cluster\hspace*{20mm}} &
\colhead{$z_{\rm cl}$\rlap{\tablenotemark{a}}} &
\colhead{$M_{500c}$} &
\colhead{$r_{\rm fit}/r_{500c}$} &
\colhead{$kT$ (Ota \& Mitsuda)} &
\colhead{$kT$ (Allen)} &
\colhead{$kT$ (White)} &
\colhead{$kT$ (other)\rlap{\tablenotemark{b}}} &
\\
 & & \colhead{($10^{14}\, h^{-1} M_{\sun}$)} & & \colhead{(keV)} & \colhead{(keV)} & \colhead{(keV)} & \colhead{(keV)}
}
\startdata
\objectname{A68} \dotfill  & 0.255 &   $21.37^{+6.79}_{-7.20}$ & 0.30 & $6.93^{+0.63}_{-0.59}$ & \nodata & \nodata & \nodata \\
\objectname{A115} \dotfill  & 0.197 &   $2.42^{+2.34}_{-1.84}$  & 0.50 &  $5.83^{+0.47}_{-0.30}$ & \nodata & \nodata & \nodata \\
\objectname{A209} \dotfill  & 0.206 &   $7.54^{+4.24}_{-3.87}$  & 1.62 & \nodata                & \nodata & \nodata & $7.10^{+0.40}_{-0.40}$ \\
\objectname{A267} \dotfill  & 0.230 &   $8.79^{+2.87}_{-3.53}$  & 1.32 & $5.51^{+0.44}_{-0.41}$ & \nodata & \nodata & \nodata \\
\objectname{A520} \dotfill  & 0.203 &   $8.67^{+3.36}_{-2.60}$  & 1.20 & \nodata                & $7.94^{+0.96}_{-0.90}$ & \nodata & \nodata \\
\objectname{A586} \dotfill  & 0.171 &   $25.27^{+7.01}_{-8.11}$ & 0.21 & $6.96^{+0.99}_{-0.83}$ & $7.02^{+0.94}_{-0.80}$ & $6.06^{+0.64}_{-0.52}$ & \nodata \\
\objectname{A611} \dotfill  & 0.288 &   $3.83^{+2.99}_{-2.79}$  & 0.59 & \nodata                & \nodata & $6.85^{+0.48}_{-0.46}$ & \nodata \\
\objectname{A665} \dotfill  & 0.182 &   $5.40^{+3.40}_{-3.07}$  & 0.36 & $6.96^{+0.28}_{-0.27}$ & $8.12^{+0.62}_{-0.54}$ & $7.73^{+0.41}_{-0.35}$ & \nodata \\
\objectname{A697} \dotfill  & 0.282 &   $12.18^{+4.97}_{-4.89}$ & 0.39 & $8.19^{+0.62}_{-0.60}$ & \nodata & $8.60^{+0.50}_{-0.49}$ & \nodata \\
\objectname{A773} \dotfill  & 0.217 &   $13.09^{+4.79}_{-6.15}$ & 0.30 & $8.07^{+0.70}_{-0.66}$ & $8.29^{+0.73}_{-0.64}$ & $8.63^{+0.68}_{-0.67}$ & \nodata \\
\objectname{A959} \dotfill  & 0.285 &   $9.33^{+3.50}_{-3.05}$  & 1.45 & $5.24^{+0.89}_{-0.73}$ & \nodata & \nodata & \nodata \\
\objectname{A963} \dotfill  & 0.206 & $4.42^{+4.27}_{-3.46}$  & 1.51 & $6.83^{+0.51}_{-0.51}$ & $6.13^{+0.45}_{-0.30}$ & $6.08^{+0.43}_{-0.33}$ & \nodata \\
\objectname{A1576} \dotfill & 0.299 & $8.62^{+3.40}_{-2.54}$  & 1.58 & \nodata                & \nodata & $6.57^{+0.56}_{-0.54}$ & \nodata \\
\objectname{A1682} \dotfill & 0.226 & $2.24^{+1.9}_{-1.33}$   & 0.55 & $6.42^{+0.63}_{-0.60}$ & \nodata & $7.24^{+0.68}_{-0.59}$ & \nodata \\
\objectname{A1722} \dotfill & 0.325 & $2.70^{+2.14}_{-1.58}$  & 2.58 & $5.81^{+0.59}_{-0.39}$ & \nodata & \nodata & \nodata \\
\objectname{A1758N} \dotfill & 0.280 & $20.37^{+6.37}_{-6.65}$ & 0.33 & $6.88^{+0.86}_{-0.75}$ & \nodata & \nodata & \nodata \\
\objectname{A1763} \dotfill & 0.228 & $4.90^{+2.42}_{-3.07}$  & 0.45 & $8.11^{+0.66}_{-0.63}$ & \nodata & $7.30^{+0.46}_{-0.38}$ & \nodata \\
\objectname{A1835} \dotfill & 0.253 & $8.42^{+4.41}_{-3.33}$  & 0.39 & $7.42^{+0.61}_{-0.43}$ & $7.33^{+0.35}_{-0.30}$ & $7.88^{+0.49}_{-0.46}$ & \nodata \\
\objectname{A1914} \dotfill & 0.171 & $2.62^{+2.03}_{-1.93}$  & 0.44 & \nodata                & \nodata & $10.53^{+0.51}_{-0.50}$ & \nodata \\
\objectname{A1995} \dotfill & 0.320 & $23.69^{+6.88}_{-6.13}$ & 1.23 & $9.06^{+1.77}_{-1.32}$ & \nodata & $7.57^{+1.07}_{-0.76}$ & \nodata \\
\objectname{A2104} \dotfill & 0.153 & $14.14^{+5.34}_{-5.55}$ & 0.23 & $7.66^{+0.49}_{-0.43}$ & \nodata & $9.12^{+0.48}_{-0.46}$ & \nodata \\
\objectname{A2111} \dotfill & 0.229 & $3.84^{+1.80}_{-2.14}$  & 0.47 & $6.94^{+0.76}_{-0.67}$ & \nodata & \nodata & \nodata \\
\objectname{A2204} \dotfill & 0.152 & $7.86^{+5.28}_{-4.57}$  & 0.27 & $6.68^{+0.28}_{-0.27}$ & $6.23^{+0.30}_{-0.28}$ & $6.99^{+0.24}_{-0.23}$ & \nodata \\
\objectname{A2219} \dotfill & 0.228 & $4.72^{+2.35}_{-2.94}$  & 0.45 & \nodata                & $9.46^{+0.63}_{-0.57}$ & $9.52^{+0.55}_{-0.40}$ & \nodata \\
\objectname{A2261} \dotfill & 0.224 & $11.52^{+5.40}_{-5.97}$ & 0.32 & $6.56^{+0.49}_{-0.48}$ & $6.64^{+0.51}_{-0.46}$ & $7.49^{+0.57}_{-0.43}$ & \nodata \\
\objectname{MS1455+22} \dotfill & 0.258 & $3.21^{+2.19}_{-1.78}$ & 0.58 & \nodata                & $4.33^{+0.27}_{-0.25}$ & $4.83^{+0.22}_{-0.21}$ & \nodata \\
\objectname{RX\,J1532.9+3021} \dotfill & 0.345 & $13.86^{+5.93}_{-5.64}$ & 0.44 & $4.91^{+0.29}_{-0.30}$ & \nodata & \nodata & \nodata \\
\objectname{RX\,J1720.1+2638} \dotfill & 0.164 & $3.28^{+2.65}_{-2.53}$ & 0.39 & \nodata                & \nodata & \nodata & $5.60^{+0.50}_{-0.50}$ \\
\objectname{RX\,J2129.6+0005} \dotfill & 0.235 & $8.35^{+4.62}_{-4.87}$ & 0.38 & $5.72^{+0.38}_{-0.30}$ & \nodata & \nodata & \nodata \\
\objectname{Zw3146} \dotfill & 0.291 & $7.57^{+4.13}_{-3.25}$ & 0.47 & \nodata                & $6.80^{+0.38}_{-0.36}$ & $5.89^{+0.30}_{-0.22}$ & \nodata \\
\enddata
\tablenotetext{a}{--- See Ebeling et al.\ (1996; 1998)
 for references to redshift measurements.}
\tablenotetext{b}{--- $kT$ value for \objectname{A209} from P.B.\ Marty
 (private communication); $kT$ value for \objectname{RXJ1720.1+2638} from \citet{mazzotta}.
}
\end{deluxetable*}

\section{Results}
\label{sec:results}
From the virial relation
\begin{equation}
M \propto \langle v^2 \rangle r \propto T r,
\end{equation}
between cluster mass, $M$, inside radius $r$, galaxy velocity, $v$, and gas temperature, $T$,
combined with the definition of mass within an over-density of 500 times the critical density
\begin{equation}
M_{500c} \propto r_{500c}^3 \rho_c(z) \propto r_{500c}^3 E^2(z) \rho_c(0) \propto r_{500c}^3 E^2(z),
\end{equation}
where the term $E^2(z)=\rho_c(z)/\rho_c(0)$ describes the evolution of the over-density for a given
cosmology, the mass--temperature relation is obtained as
\begin{equation}
E(z)M_{500c} \propto T^{3/2}.
\label{eq:theoryMT}
\end{equation}

In this study, we have measured $M_{500c}$, relating to $M_{\rm vir}$ through
$M_{\rm vir} = 1.65 M_{500c}$ for the average cluster redshift with
our chosen NFW model. We take into account that the slope may deviate from the simple theoretical
expectation $\alpha = 3/2$ and normalize the relation at 8~keV since our sample
is dominated by massive clusters. Hence, mass--temperature relations were obtained by fitting
the data in Table~\ref{tab:dataset} using the BCES($X_2|X_1$) estimator
of \cite{ab} to the following parameterization of the mass--temperature relation

\begin{equation}
E(z)M_{500c}= M_{\rm 500c, 8 keV} (T/8 {\rm keV})^{\alpha}.
\label{eq:fittedMTrelation}
\end{equation}

The redshift-dependent factor, $E(z)$, contained in
eq.\ref{eq:fittedMTrelation} must be calculated individually for
each cluster, as this would otherwise
produce an artificial 15\% variation in mass over the redshift
range spanned by our cluster sample. In effect, the normalization of the relation refers
to the present epoch ($z=0$).

The fitting procedure of \cite{ab} takes uncertainties in temperatures as well
as in weak lensing masses into account, and makes no assumptions about
the intrinsic scatter of both quantities. Results from fitting sub-samples
as well as the full sample are presented in Table~\ref{tab:Tstar} and
Figure~\ref{fig:MTrel}.

\begin{figure}
\resizebox{9cm}{!}{\includegraphics{f3.ps}}
\caption[Mass--temperature relation.]
{Weak lensing mass estimates and X-ray temperatures with BCES($X_2|X_1$)
regression lines for different subsamples. The full line is
the fit to the full sample, defined as described in the text; the dotted line
is the fit to the \cite{OM} sample; the dashed line is the fit to the \cite{allen00}
sample; and the dot--dashed line is the fit to the \cite{white00} sample.}
\label{fig:MTrel}
\end{figure}

For the full data set (for those clusters with temperature from more than one
sample the temperature was taken in prioritized order from \cite{OM}, \cite{allen00},
and \cite{white00}) we find the following normalization of the mass--temperature
relation at 8 keV
$M_{\rm 500c,8 keV}=(8.7 \pm 1.6)\times {10^{14} h^{-1} M_{\sun}}$ and a slope of $\alpha = 0.49 \pm 0.80$.
It is evident that the slope of the mass--temperature
relation is not well-determined since our data only span a modest
range at the high mass/high temperature end of the cluster distribution.
In fact, it is not obvious that there is a tight mass--temperature relation
at the high temperature end probed here.

\subsection{Normalization of the mass--temperature relation and $\sigma_8$}
The concentration of clusters around $6-8$~keV enables a robust
measurement of the normalization of the mass--temperature relation
at the high--mass end. Even though the slope of the mass--temperature
relation varies substantially between the three X-ray sub-samples
\citep{OM, allen00, white00} the best fit normalizations agree within their statistical uncertainty.
We note that for all fits, the four different regressions
of \cite{ab} all result in normalizations within 20\%.

The strongest constraints on the mass--temperature
relation normalization are obtained by taking advantage of previous
studies of massive clusters \citep{fin,allen01,arnaud05}, showing that the
mass--temperature relation slope is close to $\alpha=3/2$ as expected from simple
gravitational collapse models \citep{kaiser}.
Hence, in order to express the normalization of the mass--temperature relation in terms
of the characteristic temperature $T_{\star}= 8{\rm keV}\left(1.65 M_{\rm 500c,8 keV}\right)^{-1/\alpha}$
\citep{pier03} we assume $\alpha = 3/2$ \citep[with a representative uncertainty of 10\%, e.g.][]{fin}.
As is custom for quoting $T_{\star}$ values we adopt the redshift dependence factor
$F(z)=\left(\Delta_c E^2\right)^{-1/2} \left[ 1- 2\frac{\Omega_{\Lambda} (z)}{\Delta_c} \right]^{-3/2}$
\citep{pier03} where $\Delta_c$ is the mean overdensity inside the virial radius in units
of the critical density at the relevant redshift ($F(z)$ and $E(z)$ differs by 7\% at $z=0.23$).

We find $T_{\star} = 1.28\pm 0.20$ for our full sample and results from calculations of
$T_{\star}$ based on various subsamples are listed in Table~\ref{tab:Tstar2}.
From the $\sigma_8$ - $T_{\star}$ relation plotted by \cite{pier03}
in their Figure 2, we find $\sigma_8 = 0.88\pm 0.09$, based on our full sample.
We note that this relation is
valid only for an intrinsic scatter in temperature of $\lesssim 10\%$
around the mean mass--temperature relation. A larger intrinsic scatter will imply a lower
value of $\sigma_8$. We provide our constraints on the intrinsic scatter below.

\subsection{Scatter in the mass--temperature relation}
The squared scatter in lensing mass, $M_{500c}$, around the best fit,
$(\sigma_M^{tot})^2=\langle (\frac{M_{500c}^i-M_{500c}^{fit}}{M_{500c}^{i}})^2 \rangle$,
is the sum of the squared measurement error, the squared intrinsic scatter, and the
squared systematic errors
$(\sigma_M^{tot})^2=(\sigma_M^{err})^2+(\sigma_M^{i})^2+(\sigma_M^{sys})^2$.
The main systematic errors in the lensing mass (see Section~2.1) arise from extrapolating the
assumed NFW mass profile out to $r_{500c}$
(due to cluster-to-cluster variations in the assumed concentration parameter
$c_{vir}$) and from the separation of cluster/background galaxies (due to
cluster-to-cluster richness variations). Each of these introduces a scatter
of 20\%{} in the lensing mass, hence $\sigma_M^{sys}=0.28$. For the full sample
we find $\sigma_M^{tot}=0.94$ which is larger than expected from the mean lensing
mass error, $\sigma_M^{err}=0.52$ and the systematic errors, indicating either a sizable
intrinsic scatter in mass or that the measurement/systematic errors are severely under-estimated.

Accounting for errors in both mass and temperature, we find an
intrinsic scatter in $T_{\star}$ of $0.25^{+0.28}_{-0.25}$.
There is a 70\% probability that the scatter in temperature is larger than 10\%,
favoring somewhat lower values of $\sigma_8$ than quoted above.
However, most of the scatter is caused by the low mass clusters.

\subsection{Relaxed vs. non-relaxed clusters}
We looked into whether relaxed clusters and non-relaxed clusters have the
same normalization of the mass--temperature relation. Our ``relaxed''
cluster sample consists of A586, A963, A1835, A1995, A2204, A2261, RXJ1720,
and RXJ1532. These are clusters with ``spherical'' optical and X-ray
morphology, and no known cluster-scale dynamic disturbances.
For the relaxed clusters we find a normalization
of the mass--temperature relation of
$M_{\rm 500c, 8 keV, relax}=(17.3\pm 3.7)\times {10^{14} h^{-1} M_{\sun}}$
while the normalization for the non-relaxed clusters is
$M_{\rm 500c, 8 keV, nonrelax}=(7.6\pm 1.5)\times {10^{14} h^{-1} M_{\sun}}$
(see Figure~\ref{fig:relax}).
The higher normalization of relaxed clusters
is supported by the fact that the mean mass of relaxed clusters is a factor
$1.5$ larger than the mean mass of ``non-relaxed'' clusters, although
the relaxed and the non-relaxed clusters
span roughly the same temperature range.

The scatter in mass for the relaxed sample ($\sigma_M^{tot}=0.77$) is
similar to the scatter for the non-relaxed sample ($\sigma_M^{tot}=0.88$).
The mean error for both samples is $\sigma_M^{err}=0.57$. Either relaxed
clusters spread as much around their mass--temperature relation as
clusters in general, or we have used a poor definition of ``relaxed'' clusters.
However, the fact that the normalization of the mass--temperature relation for
relaxed clusters is higher than for non-relaxed clusters
indicates that there is a physical difference between the two sub-samples.
From the present study, it thus seems that relaxed clusters do not form a
tighter mass--temperature relation than clusters in general.

\begin{figure}
\resizebox{9cm}{!}{\includegraphics{f4.ps}}
\caption[Mass--temperature relation.]
{Weak lensing mass estimates and X-ray temperatures with BCES($X_2|X_1$)
regressions for ``relaxed'' clusters (filled symbols, full line)
and ``non-relaxed'' clusters (open symbols, dashed line).}
\label{fig:relax}
\end{figure}

For a given mass, non-relaxed clusters are found to be $\sim 75\pm 40$\% hotter than
relaxed clusters. Since we consider global, isothermal temperatures,
the presence of ``cooling cores''
in relaxed clusters will result in a lower global temperature than
the virial temperature. However, this effect is at the 10\%-20\% level
\citep[e.g.,][]{smith03, ohara} so this cannot alone explain the temperature
difference between
relaxed and non-relaxed clusters. Based on the mass--temperature relation from
10 clusters (3 of which are considered relaxed), S05
also find that non-relaxed clusters are hotter
than relaxed clusters. An objective classification of the degree of relaxation
for a sizeable cluster sample is required for further quantifying
the size of this effect.

\begin{deluxetable}{ccr}
\tablecaption{Best-fit mass-temperature relation (arbitrary slope)
	\label{tab:Tstar}}
\tablehead{
\colhead{$M_{\rm 500c, 8 keV}$} &
\colhead{$\alpha$} &
\colhead{Sample}\\
\colhead{$(10^{14} h^{-1} M_{\sun})$} &
\colhead{} &
\colhead{}\\
}
\startdata
$12.0\pm 2.4$   & $1.30\pm 0.97$ & Ota \& Mitsuda (2004) \\
$9.5\pm 1.9$   & $0.87\pm 0.78$ & Allen (2000) \\
$8.1\pm 1.5$   & $0.11\pm 0.98$ & White (2000) \\
$8.7\pm 1.6$   & $0.49\pm 0.80$ & All \\
$17.3\pm 3.7$   & $2.69\pm 1.30$ & ``Relaxed'' \\
$7.6\pm 1.5$   & $0.29\pm 0.76$ & ``Non-relaxed'' \\
\enddata
\end{deluxetable}

\begin{deluxetable}{ccr}
\tablecaption{Best-fit mass-temperature relation (fixed slope)
	\label{tab:Tstar2}}
\tablehead{
\colhead{$T_{\star}$} &
\colhead{$\alpha$} &
\colhead{Sample}
}
\startdata
$1.04\pm 0.18$ & $3/2$ & Ota \& Mitsuda (2004) \\
$1.22\pm 0.21$ & $3/2$ & Allen (2000) \\
$1.35\pm 0.21$ & $3/2$ & White (2000) \\
$1.28\pm 0.20$ & $3/2$ & All \\
$0.82\pm 0.14$ & $3/2$ & ``Relaxed'' \\
$1.42\pm 0.22$ & $3/2$ & ``Non-relaxed'' \\
\enddata
\tablecomments{The uncertainty in $T_{\star}$ from
$\alpha$ has been taken to be 10\%.}
\end{deluxetable}

\begin{deluxetable*}{lcccr}
\tablecaption{Normalizations of the mass-temperature relation
           \label{tab:Mnorm}}
\tablehead{
\colhead{Method} &
\colhead{$\langle z \rangle$} &
\colhead{$M_{\rm 500c,8 keV}$} &
\colhead{Slope} &
\colhead{Reference}
}
\startdata
X-rays        & 0.09 & $6.00\pm 0.35$   & Fitted & \citet{arnaud05} \\
                  & 0.09 & $6.07\pm 0.46$   & Fitted & \citet{vik} \\
     		    &  &  &  \\
Lensing       & 0.23 & $6.65\pm 0.52$   & Fixed & S05 \\
                  & 0.23 & $8.67\pm 1.57$   & Fitted & This study \\
                  &  &  &  \\
Simulations & 0.04 & $8.09\pm 0.48$   & Fixed  & \citet{evrard96} \\
                  & 0.00 & $6.82\pm 0.76$   &  Fitted & \citet{borgani} \\
\enddata
\tablecomments{Included here are some recent studies with a quoted
normalization of the $M_{500c}-T$--relation, scaled to $M_{\rm 500c,8 keV}$,
i.e., the mass contained within $r_{500c}$ of a cluster with $kT = {\rm 8 keV}$,
with errors propagated, and assuming $h=1$. The listed normalization has been scaled to a
common redshift of $z=0$.
The normalization of S05, which was
determined within a fixed physical radius of $250 h^{-1}$~kpc in an Einstein-de Sitter universe,
has been scaled to $M_{500c}$ for our adopted cosmology, making the same
assumptions about an NFW-type mass profile as we have made for our own data.
For each study, we indicate whether the slope of the relation
was calculated from a fit to the data, or whether the slope was
fixed at the theoretically expected value, $\alpha=3/2$.
}
\end{deluxetable*}

\section{Discussion}
\label{sec:discussion}
Based on the hitherto largest sample of X-ray luminous clusters with measured
lensing masses, we derive a normalization of the mass--temperature
relation at the high mass end, $M_{\rm 500c, 8 keV}=(8.7\pm 1.6)\,h^{-1}\,10^{14}M_{\sun}$.
This value is higher than the lensing based mass--temperature normalization of S05,
based on a smaller cluster sample, but is consistent with this
within $1\sigma$ errors; see Table~\ref{tab:Mnorm}.
Mass--temperature relations with masses determined from X-ray data tend to have
a lower normalization than lensing based relations, and they are only
marginally consistent with our normalization. This is also the case for
the two recent studies of \citet{vik} and \citet{arnaud05} based on smaller
samples of lower mass (and hence cooler) clusters.
\citet{vik} measured cluster masses inside $r_{500c}$ from X-ray observations
of a sample of 13 low redshift clusters with a median temperature of 5.0~keV while
\citet{arnaud05} determined the normalization
from X-ray derived masses of 10 nearby clusters with a mean temperature of 4.8~keV.
The two studies agree on the same normalization, higher than previous
X-ray mass based studies, but there still seems to be a $\sim 20\%$ discrepancy
between X-ray and lensing derived mass--temperature relations.

We note, however, that the lensing based and X-ray based normalizations are made at
different redshifts, and that this discrepancy would vanish if the redshift-dependence
predicted by the self-similar collapse model in equation~\ref{eq:theoryMT} were neglected.
Given the heterogeneous nature of these data sets, any claim of significant departures from
self-similarity would be premature, but this clearly provides an interesting avenue for
future research, involving even larger cluster samples spanning a wider interval in redshift.

We confirm the result of Smith et al.\ (2005) that non-relaxed clusters are
on average significantly hotter than relaxed clusters. This is qualitatively consistent with
N-body/hydrodynamical cluster simulations which show that major mergers can temporarily
boost the X-ray luminosities and temperatures well above their equilibrium values
\citep[e.g.][]{randall}.

In contrast to several previous (mainly X-ray mass based) published mass--temperature
relations, the normalization derived in this study is in good agreement with
the normalization derived from numerical simulations. However,
the accuracy of the normalization is not good enough to discriminate between
simulations including different physical processes.
Our results show that X-ray based measurements of the cluster abundances, after
reducing the major systematic uncertainties associated with the mass--temperature
normalization, give an amplitude of mass fluctuations on cluster scales that
is consistent with other methods.
This lends additional support to the ``concordance model'' cosmology, and lends
credence to the basic assumptions of Gaussian density fluctuations.
Our determination of $\sigma_8=0.88\pm 0.09$ is higher than most
$\sigma_8$ determinations from cluster data \citep[for a compilation of these,
see e.g.,][]{henry04}.
However, our finding is consistent with the value derived from weak
gravitational lensing in the combined Deep and Wide CFHT Legacy Survey
($\sigma_8 = 0.86\pm 0.05$; Semboloni et al.\ 2005) based on the
halo model of density fluctuations (Smith et al.\ 2003b). It is also
consistent with the CMB+2dFGRS+Ly$_{\alpha}$ forest
result ($\sigma_8 = 0.84\pm 0.04$) of Spergel et al.\ (2003), with
the joint CMB + weak lensing analysis of Contaldi, Hoekstra, \& Lewis (2003),
which gave $\sigma_8 = 0.89\pm 0.05$, and with CMB analyses \citep{bond}
yielding $\sigma_8 \approx 0.9$. However, the more recent 3-year WMAP
results (Spergel et al.\ 2006) give a significantly lower value of $\sigma_8$,
and also a preference for a value of $\Omega_m$ lower than 0.3.
Also, results from the recent 100 square degree weak lensing survey (Benjamin et al.\ 2007)
favor a lower value of $\sigma_8 = 0.74 \pm 0.06$ for $\Omega_m = 0.3$.
We note that our quoted value of $\sigma_8$ is based on the assumption
that the intrinsic scatter about the mass--temperature relation is $\lesssim 10\%$,
and that our $\sigma_8$ estimate will be biased high if the true scatter significantly
exceeds this value \citep{pier03}.

The limiting factor of our measurement of the normalization of the
mass--temperature relation is the magnitude of the measurement errors
(dominating the systematic errors, estimated to be $\sim 30\%$).
In order for the mass--temperature relation to be a competitive route
for constraining cosmological parameters and to discriminate
between simulations with different input physics, the normalization must be
measured to better than $\sim 10$\% accuracy.
However, there are good prospects for improving on these results in the near future.
Firstly, the superior spectro-imaging capabilities of {\it Chandra} and XMM-Newton
will allow the construction of large, homogeneous cluster temperature samples.
A comparison to tailored simulations
with realistic physics, analyzed in the same way as observations, will
advance our understanding of systematics and the link between the mass--temperature
relation and structure formation (C.B.\ Hededal et al.\ 2007, in preparation).
Secondly, more accurate weak lensing-based
mass measurements of a larger sample of clusters are feasible as large mosaic CCD
cameras that can probe intermediate-redshift clusters beyond their virial radii are
now common, and the cluster sample could easily be doubled from a similar survey
in the Southern celestial hemisphere.

Finally, we note that a more direct measurement of $\sigma_8$ from weak lensing by clusters is
possible, provided that weak lensing mass estimates are available for a large,
well-defined, volume-limited cluster sample. This makes it feasible to calculate the cluster mass
function directly from the lensing masses, rather than indirectly via the X-ray temperature function
(Dahle 2006). Since mass estimates based on baryonic tracers of the total cluster mass
 only enters indirectly as a selection criterion (e.g., clusters selected based on X-ray luminosity
above a certain threshold), the method is less susceptible to systematic and
random errors, as it does not require an accurate characterization of the
scatter around the mean mass--temperature relation.

\acknowledgments

We thank Per B. Lilje and Jens Hjorth for valuable comments on a draft version of
this paper. We also thank the anonymous referee for comments and suggestions
that improved the presentation of our results.
KP acknowledges support from the Danish National Research Council, the
Carlsberg foundation, and Instrument Center for Danish Astrophysics.
The Dark Cosmology Centre is funded by the Danish National Research Foundation.
HD acknowledges support from the Research Council of Norway and travel support
from NORDITA.

redpajama_set_name: RedPajamaArXiv


Charles Hartshorne, a philosopher, theologian and educator who wrote more than 20 books and 100 articles in a lifelong mission to prove that God was a participant in cosmic evolution rather than the supreme composer, died on Tuesday at his home in Austin, Tex. He was 103.
As such, God, like all else, changes constantly. God cannot see the future. What remains changeless is God's perfect responsiveness to all that is changing.
Randall Styers, a professor at Union Theological Seminary, said the theory led to a radical reformulation of the nature of God, one that continues to be debated.
The ''process'' concept, which Dr. Hartshorne developed from the ideas of one of his professors at Harvard, the philosopher Alfred North Whitehead, influenced progressive Protestant theologians and, more recently, Roman Catholics and Jews, said David Ray Griffin, a professor of the philosophy of religion at the Claremont School of Theology.
''He was clearly one of the major philosophers of the 20th century,'' Dr. Griffin said of Dr. Hartshorne.
Charles Hartshorne, born on June 5, 1897, in Kittanning, Pa., was descended from Quakers through his father, an Episcopal minister. He once recalled that no one in his family disbelieved in religion and no one rejected evolution. He brought both views to his work, the application of rationality to theological questions.
But his most important influence may have been four words spoken by his mother. ''Life is very big,'' she told her son.
''This remained for him the basic truth in everything he did,'' said Davidson Loehr, minister of the Unitarian Universalist Church in Austin.
The Hartshorne mission, Dr. Loehr said, was no less than ''saving face for the word God in the 20th century.'' Philosophers in the positivist and analytical schools, which have dominated the discussion, not to mention more recent postmodernists and deconstructionists, had little use for the deity.
Second, he developed his concept of a flexible, dynamic God. ''He really did an enormous amount of creative work on helping people rethink the nature of the divine and the relationship between the divine and known world,'' Dr. Styers said.
Charles Hartshorne entered Haverford College in 1915 but left to join the Army Medical Corps. He took a crate of philosophy books to the front lines in France in World War I. ''Every time I was not on duty I would read one,'' he said in an interview with The Pittsburgh Post-Gazette.
After leaving the Army, he graduated from Harvard. He then received a fellowship to study in Europe, where one of his teachers was the German philosopher Martin Heidegger. He returned to Harvard to study for a doctorate and, with the philosopher Paul Weiss, to edit the papers of Charles Sanders Pierce, the logician.
In 1928 he joined the philosophy department of the University of Chicago. He soon met Dorothy Cooper, who became his wife, editor and bibliographer. One of his favorite pastimes was listening to her sing Mozart.
Dr. Silber recalled a story that Mrs. Hartshorne told. At a reception, her husband pulled out an embarrassingly dirty handkerchief. She discreetly took it and put it in her purse. The same thing happened again, with a second handkerchief. And again.
A short time later, he muttered, ''I need a handkerchief, I thought I had one.'' She smiled, and handed him a tissue.
Dr. Hartshorne went on to teach at Emory University in Atlanta, and the University of Texas. His first book, ''The Philosophy and Psychology of Sensation,'' was influential because it brought philosophical insights to an empirical field, Dr. Silber said.
But the interests of the small, witty professor transcended his work. He was a vegetarian. He did not own an automobile, preferring to ride a bicycle. He wrote letters to newspapers supporting feminism, abortion rights and higher taxes.
In 1996, at 98, he wrote his last article in an academic journal, and two years later he delivered his last lecture. His wife died in 1995, and his brother, Richard, author of a prominent geography textbook, in 1992. He is survived by a daughter, Emily Schwartz of Austin, and two grandchildren.
The depth, breadth and utter playfulness of Dr. Hartshorne's mind is suggested by his 1973 book, ''Born to Sing.'' The book argued that some bird species had evolved the ability to appreciate melody and sing for the sheer pleasure of it, a notion that continues to intrigue zoological scientists.
''If he'd never been a philosopher, he would have been a very distinguished ornithologist,'' Dr. Silber said.


text:
AFA Targets Burger King For 'Promoting And Encouraging Abhorrent Behavior' With Proud Whopper
By Kyle Mantyla | July 15, 2014 10:23 am
On Friday, Bryan Fischer voiced his disgust that Burger King had sold an LGBT pride themed Whopper at a San Francisco location a few weeks back and announced that the American Family Association was going to be issuing an action alert in response, warning that "if this kind of nonsense" isn't stopped, it'll spread across the nation.
"When people sit down to eat a hamburger," Fischer said, "the last thing they want to be thinking about is two guys having sex":
Today, the AFA issued that action alert, asking activists to email Burger King and warn that "promoting and encouraging abhorrent behavior will drive families away":
Burger King recently promoted the "gay pride" message with a rainbow Whopper wrapper at one of its stores. Unless there is some pushback from consumers, there is a real possibility that they could expand this promotion.
During this year's annual gay pride event in San Francisco, the Burger King location along the parade route sold a "Proud Whopper" with fanfare promotion by the corporate office.
It was the same Whopper as always, but in a rainbow-colored wrapper.
Fernando Machado, Burger King's Senior Vice President of Global Brand Management defended the company's promotion, telling USA Today that the "Proud Whopper…showcases who we are as a brand," adding, "It shows how we, as a brand, believe in self-expression."
Unless Burger Kings sees a backlash for promoting cross-dressing and homosexual conduct as normal behavior, it will expand the promotion to other cities and additional stores next year.
We have prepared an email that you can send directly to Burger King executives.
In addition, a copy of your email will be sent to the Burger King Franchise Association, reinforcing your message that promoting and encouraging abhorrent behavior will drive families away.
The prewritten letter from AFA tells Burger King that the company's promotion of "abhorrent behavior" is an "insult to families,' which is why the letter-sender will now be boycotting the restaurant chain:
I am offended by Burger King's stunt in offering a so-called "Proud Whopper" in San Francisco. What were you thinking?
Your celebrated promotion of cross-dressers and homosexuality is an insult to families and I find your celebration of abhorrent behavior as a reason to dine elsewhere.
I hope you will learn from this publicity blunder and realize that while most stores did not participate in the corporate-approved program, the damage has been done and affects the image of all Burger King outlets.
Tags: Proud Whopper American Family Association
Steve King Threatens Government Shutdown, Impeachment Over Immigration Executive Action
Peter LaBarbera: Caitlyn Jenner 'Promoting Evil Worldwide'
Steve King Is A Walking Late Night Joke
Larry Klayman: 'Revolution' Needed After Clinton Email Announcement

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Vow of Worship of Lord Shiva for Sixteen Mondays ~~OM~~ This is the story of the worship to be performed on sixteen consecutive Mondays. One day. 13 Nov Proofs that SHIVA AND VISHNU ARE EQUAL and Isk'con Mis-interpretations REVEALED 1. SB ORIGINAL statement Lord Vishnu.
Thursday, October 10, iskCON is wrong 2.
He sivapuranam story in all gods and goddesses, but deliberately excluded Shiva. Now, He tried to convince Her that She shouldn't waste Her youth doing tapasbut should enjoy life getting married! The views of iskcon are written by their own people.
Though they went sivapuranam story in they initially were devotees. The process of search happened for ages and the outcome proved futile both of them not being able to succeed in their mission.
So bagIrata again started his penance and prayed the goddess ga. The Brahmin priest was immediately attacked by the disease, and he became very sad and was filled with great pain from the leprosy that developed.
In the form of male and female, matted hair with moon, axe, smeared in red aruNawearing snakes and the skin of sivapuranam story in, embracing the bull and with a bent leg, this the right half, and the left black in color, hand holding a lily flower close to the chest, with a silk like sivapuranam story in foot, wearing gold ornaments, salutations to the Half female God.
Meanwhile the dEvas, who were tortured by the sUrapadma and his sivapyranam tAraka, simhamukhaknew that those demons can be killed only storg the son of Lord Shiva and Shakthi. Disappointed that both Sivapuranam story in and Goddess were doing yoga instead of marrying, they asked the cupid to disturb the meditating Sivapuranam story in Shiva with his arrows in order to induce lust for pArvati.
Lord Shiva says that in order to attain salvation in Kaliyuga, one must go on pilgrimage to holy shrines and rivers. That pillar was not any ordinary column of fire, it was the Supreme Itself, the One that is beyond form, color and qualities! Ignoring his advice, dakshA continued his yAga. Can the Supreme sivapursnam induced with lust by anybody? But whatever the queen touched became ruined. As I have promised sivapuranam story in husband not to take any revenge, much less upon you, I merely denounce you before this assembly.
This is filthy and foolish as well.
This beautiful and shining angelic lady sivapuranam story in an Apsara, a celestial maiden who serves the Gods. It was some years later, that the King's daughter found out that her husband had been chosen for the marriage after he had performed the vow of Lord Shiva's worship for sixteen Mondays for that purpose.
When Shiva entered the Stoy hall, every one stood up to pay respect. Worshiping Ganapati Deva The area, where Shivlinga sivapuranam story in intended to be placed must be cleansed cow dung and gangajal, following by Bhoomi Pujan. Views Read Edit View history.
In this form the Lord is naked and quite enchanting. For this reason scriptures describe that shakti to shiva is a wife they are togethermother shakti becomes shiva – so shiva comes out of shakti and daughter shiva become shakti. At the same time one more poison came from the ocean hAla. The ministers advised him to leave the wife or he would face ruin.
Sivapuranam story in was eager to have a son, and decided to perform the vow of Lord Shiva's worship for sixteen Mondays in order to have a beautiful son who could become a king.
Saying that it is better to be killed by the God of sivapuranam story in than by the curses of dEvAshe went with his wife, ratito the abode of Shiva where He was in meditation. Shocked by the death of cupid all the dEvAs realized their plots would not sivapuranam story in out with God.
He further suggested that Sivapuranam story in could get married to Him, instead of desiring for Lord shiva Who dances in the cemeteries and wears skulls and bones! Many days passed and the priest suffered a great deal.
The unbelievable story of a woman who walked from Sivapuranam story in to Goa! Both Brahma and Vishnu set out to locate the start and end of that pillar.
When he became 16, he found his parents weeping. Shiva also created a huge army of demons to accompany Virabhadra.
The poison stayed there as a small black blue stain. The Lord forgave them and gave one of them the great work of sivapuranam story in Sivapuraam with chAmaramand the rest two as His security in His abode. Shiva is the best Vaishnava and the greatest devotee of Krishna.


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A couple of years ago my wife, writer Kate Sidley, had a humour column in a monthly health magazine. Each month she mined the great steaming petri-dish of gyms and other health obsessions and came away with all sorts of comedic nuggets to extract a couple of laughs from readers.
Around the same time we went to see a wonderful play written by our friend Craig Higginson entitled 'The Girl in the Yellow Dress'. The play was enjoying both popular and critical acclaim and was being (or was due to be) produced in multiple cities, including overseas.
We chatted to Craig, who described the economics of the successful playwright, and they were mouth-watering, with a juicy cut of each ticket sold ending up in the writer's pocket. A quick calculation showed this to be potentially much more lucrative than the pittance made by the average South African novelist and columnist.
Pfft. I said to Kate – let's write a play. How hard could it be? Pfft, she said – sounds like fun. when do we start?
So we sat down to fashion a play based on her column, and supported by our multiple degrees from Juilliard and the London Academy of Dramatic Arts and our stints at the Royal Shakespeare Company and Broadway.
Where things went quickly off the rails.
Firstly, Kate and I nearly got divorced within the first 2 pages of the stageplay. She would say – I don't think your characters' voices are clearly enough separated, and the hairs on my neck would rise and I would wonder whether I wouldn't have been better off with a Thai mail-order bride. I would say – I don't think your character's first joke was funny enough, and I would see her lips and eyes narrow as she contemplated an affair with someone younger and cuter than I.
Secondly, we have another friend, Rosalind Butler, who has wads of experience in bringing stories to stage and screen, and was in the process of looking for a producer for her own original stageplay. She described the landscape – producers had little money, sponsorships were rare, theatres were living hand-to-mouth, audiences sparce and uncommitted. In short, most playwrights climb a a daunting mountain, stageplay in hand, and no summit in sight. The real world seemed that it would be a tough place for unheralded playwrights like Sidley Inc. (Ros's play, the very funny 'An Unromantic Comedy' was produced and staged last October).
We threw in the towel almost immediately, and returned to the unforgiving world of novels and columns.
So, fast-forward a year or two. I was busy doing battle with my fourth novel (still am), and I was losing. Sloshing around in a pit of despond I accidentally opened the stillborn play that Kate and I had started. The first two pages were actually not bad. I told Kate that I wanted to poke at it, to which she gave her blessing.
I sprinted through the first 15 pages, and then paused. Not having invested great deal of effort at that point I figured that I may as well get some educated feedback, and if the verdict was the expected rolling of the eyes, I would simply abandon – little ventured, little lost.
So I sent it to a person-of-influence, in secret. .
Who said – this is wonderful. If you can finish this play at this level of quality I will produce it.
So we carefully separated the characters, the writing tasks, the schedules. We spitballed and lobbed ideas at dinner, before bed, during slush-mouthed morning toothbrushing, by cellphone during teenager pick-up duties. Kept egos to a minimum. Smiled a lot. Swallowed choking gobs of pride. And emerged with a competed stageplay some weeks later, perhaps in need of polish and tweak, but essentially complete.
I sent it to my person-of influence.
We received an SMS some weeks later which simply said – 'I love your play'.
And we are still happily married.