text:
\section{Introduction}
X-ray emission traces the strength of a stellar magnetic dynamo and is tightly linked to stellar rotation and age. Rotational shear at the boundary between the radiative and convective zones is thought to power the solar dynamo \citep[e.g.,][]{parker93}. The generated magnetic fields heat the corona to temperatures sufficient to produce X rays \citep{parker79, cowling81}. Observations of solar-like main-sequence (MS) stars confirm this connection between rotation and X-ray emission, finding that the X-ray luminosity $L_{\mathrm{X}} \propto v_{\mathrm{rot}}$$^\beta$, where $v_{\mathrm{rot}}$ is the stellar surface rotational velocity and $\beta\approx2$ \citep{palla81, pizzo03}.

In addition, observations have shown that stars rotate more slowly as they age, with rotation decaying with time such that $v_{\mathrm{rot}} \propto t^{-\alpha}$, with $\alpha=0.5$ for solar-mass stars \citep[e.g.,][]{skumanich72,meibom2011}. Angular momentum lost through stellar winds is generally thought to be responsible for the Skumanich law, with the exact dependence of $v_{\mathrm{rot}}$ on age being a function of the assumed field geometry and degree of core-envelope coupling \citep{kawaler1988, krish1997}.

Combined, these two effects predict that for solar-type stars, $L_{\mathrm{X}}$ should decay such that $L_{\mathrm{X}} \propto t^{-\alpha\beta}$, with $\alpha\beta=1$. It is also known, however, that this picture of a uniformly decaying $L_{\mathrm{X}}$ does not apply to stars with ages $\lapprox$100 Myr. Surveys of solar-type stars in the Orion Nebula and the Pleiades ($\lapprox$10 and 100 Myr, respectively) found that $L_{\mathrm{X}}$ decays more slowly: $L_{\mathrm{X}} \propto t^{-0.75}$ \citep{queloz98, preibisch2005}. Because of the paucity of older, nearby clusters, constraints are more limited at $\gapprox$200 Myr and come mostly from field stars \citep[e.g.,][]{gudel2007}: observations of five solar analogs indicated that $L_{\mathrm{X}} \propto t^{-1.5}$ for $t$ > 1 Gyr \citep{gudel1997}, as did a survey of the 1--2 Gyr cluster NGC 752 \citep{giardino2008}. A change in the magnetic field topology or core-envelope decoupling are the commonly invoked explanations for this sharp drop-off in $L_{\mathrm{X}}$, but it remains poorly understood. Chromospheric activity, also thought to trace the strength of the stellar dynamo, may also suffer a similarly steep decline at ages $>$1 Gyr \citep{pace2004}.

The homogeneous, co-eval populations of open clusters provide an ideal environment for calibrating empirically the stellar age-rotation-activity relationship (ARAR). The Hyades's proximity ($\approx$50 pc) has facilitated observations of its members at many wavelengths and established it as the benchmark middle-aged (500-600 Myr) cluster \citep{perryman1998}. Empirical calibrations of the ARAR often interpolate directly between the observed properties of solar-type Hyads and that of the Sun. The Hyades therefore serves as the only anchor for our understanding of coronal emission between 500-600 Myr and 4.5 Gyr, a significant fraction of a solar-type star's MS lifetime.

However, the Hyades's proximity is a drawback for X-ray studies. The cluster spans  well over 10$^{\circ}$, and modern X-ray telescopes with small fields of view are poorly suited to large-scale studies of the cluster. Indeed, the most recent such study was conducted by \citet{stern1995}, who detected 185 Hyads with {\it ROSAT}.

Recently, \citet{Douglas14} probed the rotation-activity relation for stars in the Hyades and Praesepe, another $\approx$600-Myr-old cluster, using both coronal and chromospheric ($L_{\mathrm{H}\alpha}$) activity measurements. These authors found that coronal activity declines faster than chromospheric activity as a function of (unsaturated) Rossby number $R_o =\ P_{\rm rot}/\tau$, where $\tau$ is the convective turnover time. However, because of the paucity of stars in either cluster with measured rotation periods ($P_{\mathrm{rot}}$) and X-ray detection (24 in the Hyades and 15 in Praesepe), the exact relationship between coronal activity and rotation at this age remains elusive.

Other studies \citep[e.g.,][]{palla81, gudel1997, Randich2000b, mamajek2008, wright2011} have examined the stellar rotation-coronal activity relation, and generally suffer from similar issues: either there are too few stars at a given age to get significant statistics or the population is too heterogeneous to strongly constrain age-dependent properties.

M37 (NGC 2099), a Hyades analog at $\approx$1.5 kpc, has been extensively surveyed in the optical by \citet{messina08a} (hereafter ME08), \citet{hartman08a} (hereafter HA08), and \citet{hartman09} (hereafter HA09), resulting in hundreds of $P_{\mathrm{rot}}$\ measurements. As part of our Palomar Transient Factory Open Cluster Survey \citep[][]{agueros11}, we obtained a complementary deep (440.5 ksec) {\it Chandra} observation of the cluster. M37 is distant enough that a significant number of cluster stars fall within the footprint of {\it Chandra}'s ACIS-I chips. Our X-ray data, combined with M37's rich membership and the extensive set of available $P_{\mathrm{rot}}$\ data, make it an excellent laboratory for examining the dependence of coronal activity on rotation.

We begin in Section~\ref{observations} by describing our \textit{Chandra}\ data and data reduction, and the construction of our X-ray catalog. In Section~\ref{optical}, we consolidate the ME08 and HA09 $P_{\mathrm{rot}}$\ data for the cluster, and we re-visit the cluster membership using our own membership probability calculations (fully described in Appendix~\ref{membershipcalc}.) In Section~\ref{analysis}, we derive  stellar quantities using optical and X-ray data, and we match our X-ray sources to the consolidated list of optical objects. In Section~\ref{results}, we present our results and compare them to those in the literature. We conclude in Section~\ref{conclusion}. We present spectral and timing analysis of our highest-count X-ray \textit{Chandra}\ sources in Appendix~\ref{spectra}.

\section{{\it Chandra} Observations}\label{observations}
The central field of M37 was observed five separate times between 2011 Nov 14 20:58 and 2011 Nov 19 15:31 UTC for a total of 440.5 ksec with the Advanced CCD Imaging Spectrometer \citep[ACIS;][]{garmire03}. The four ACIS-I chips and the ACIS-S3 chip were used in Very Faint telemetry mode to improve the screening of background events and thus increase the sensitivity of ACIS to faint sources \citep{vikhlinin01}. The exposure-weighted average aimpoint of the 16$\farcm$9$\times$16$\farcm$9 ACIS-I field-of-view is $\alpha=05^{\mathrm{h}}52^{\mathrm{m}}17.^{\mathrm{s}}86$, $\delta=+32^{\circ}33'48\farcs23$ (J2000). The pitch angle for four observations was 103$^{\circ}$;  due to scheduling constraints, it was 253$^{\circ}$ for the fifth. Table \ref{tbl:obslog} provides the basic information for our five \textit{Chandra}\ observations and Figure \ref{fig:optical} shows their footprints superimposed on a 40$\arcmin$$\times$40$\arcmin$ $i'$ image centered on M37 obtained by HA08 with the Megacam on the MMT telescope.

\begin{figure}
\includegraphics{Figure1.pdf}
\caption{Thick blue squares (with chip numbers) indicate the footprint of the \textit{Chandra}\ ACIS chips for four of our observations; the thin orange squares indicate that of our fifth observation. A 40$\arcmin$$\times$40$\arcmin$ $i'$ Megacam image of M37 from \citet{hartman08a} serves as the background.}
\label{fig:optical}
\end{figure}

\input{Table1}

The data reduction was done using the \textit{Chandra}\ Interactive Analysis of Observations \citep[CIAO;][we used CIAO 4.6 and CALDB 4.6.1.1]{fruscione2006} tools. We began by using \texttt{chandra\_repro}, which executes all recommended data processing steps on the level 1 data, including subpixel randomization using the EDSER algorithm. This tool creates a new bad pixel file by identifying known bad pixels and pixels with bad bias values, searching for afterglows and hot pixels, and marking pixels adjacent to afterglows and hot pixels. \texttt{chandra\_repro} also creates a new level 2 event file that includes only events with grades 0, 2, 3, 4, 6, and a status of 0. To avoid excluding potentially good events in modestly bright point sources, we did not use the very-faint correction in \texttt{chandra\_repro}.

\subsection{X-ray Source Extraction}\label{extraction}
Our source extraction procedure was divided into two steps. First, we merged our observations using CIAO and ran \texttt{wavdetect} \citep{freeman02} with a liberal significance threshold to obtain a raw candidate source list. Second, we used the ACIS Extract (AE) point-source analysis software \citep[][we used AE Version 2014feb17]{broos10}\footnote{Available from \url{http://www2.astro.psu.edu/xray/docs/TARA/ae_users_guide.html}} to prune spurious detections from our candidate list and extract photometry. AE's algorithms are tailored to calculate source properties accurately when multiple observations are merged and analyzed.

\subsubsection{Merging the Observations}\label{merging}
To construct the merged event file, we first ran \texttt{wavdetect} on the observations using a false-positive probability threshold of 10$^{-6}$. We then used \texttt{reproject\_aspect} to register the observations to the astrometric frame of the longest exposure (ObsId 13656), using only source regions with \texttt{SRC\_SIGNIFICANCE} > 7, a 3$\arcsec$ matching radius, and a residual rejection limit (a parameter used to remove source pairs based on pair positional offsets) of 0$\farcs$6. The values of these parameters were chosen to have \texttt{reproject\_aspect} work with a more stringent source list \citep[see e.g.,][]{xue11}. The linear translations ranged from $-0\farcs38$ to $0\farcs63$, rotations ranged from $-0^{\circ}.006$ to $0^{\circ}.018$, and scale changes ranged from $0.9997$ to $1.0002$.

We used the CIAO tool \texttt{merge\_obs} to produce a merged event file, a combined exposure map, and exposure-corrected flux images. We constructed flux images and exposure maps for three bands: 0.5--7 keV (full), 0.5--2 keV (soft), and 2--7 keV (hard).

Figure~\ref{fig:expmap} shows the full band effective-exposure map for the merged 440.5 ksec event. Since one of our five observations is rotated 150$^{\circ}$ relative to the others, the merged exposure map is inhomogeneous, with the longest exposure near and around the average aimpoint. We used \texttt{ds9} to produce a representative color composite image by combining, overbinning, and smoothing (using a Gaussian of kernel radius 5) the 0.5--1.5 keV (red), 1.5--2.5 keV (green), and 2.5--7 keV (blue) exposure-corrected flux images, and the result is shown in Figure~\ref{fig:colorcomposite}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.195]{Figure2.pdf}
\caption{Effective exposure map for the full (0.5--7 keV) band of our merged \textit{Chandra}\ event displayed in logarithmic gray scale (in units of ksec). The average aimpoint is indicated by the plus sign.}
\label{fig:expmap}
\end{center}
\end{figure}

\begin{figure*}
\begin{center}
\includegraphics[scale=0.4]{Figure3.pdf}
\caption{\textit{Chandra}\ smoothed RGB composite image of the central region of M37. We combined, overbinned, and smoothed (using a Gaussian of kernel radius 5) the 0.5--1.5 keV (red), 1.5--2.5 keV (green), and 2.5--7 keV (blue) exposure-corrected flux images from our merged \textit{Chandra}\ event file. The plus sign indicates the average aimpoint.}
\label{fig:colorcomposite}
\end{center}
\end{figure*}

\subsubsection{Source Detection and Pruning}\label{detection}
To obtain an initial list of candidate X-ray sources, we first created point-spread function (PSF) maps for the individual observations using \texttt{mkpsfmap} with an encircled counts fraction (the fraction of the PSF to enclose) of 0.9. We then selected the minimum PSF map size out of the five observations at each pixel using \texttt{dmimgfilt}, which allowed us to detect point sources that are smaller than the mean size, but still larger than the local PSF in the individual maps.

To obtain an initial candidate source list, we ran \texttt{wavdetect} using this minimum PSF map and the merged event file and exposure map. We used a scale sequence ranging from 1 to 8$\sqrt{2}$\ for the ACIS-I chips and from 8 to 32$\sqrt{2}$\ for ACIS-S3;\footnote{Larger scales are needed for  ACIS-S3 because of the large PSFs far from the aimpoint.} in both cases the scales had factor increments of $\sqrt{2}$. \citet{alexander01} pointed out that real sources can be inadvertently lost using a too stringent false-positive probability threshold. We therefore reset our threshold to $10^{-5}$ in \texttt{wavdetect} to allow for a non-negligible number of spurious sources to be included in the initial candidate list.

Separate candidate source lists were prepared for the full, soft, and hard energy bands. To consolidate the three lists, we matched these lists against each other using a 2$\arcsec$ matching radius for sources with angular separation $\theta$ < 5$\arcmin$ from the average aimpoint, and 4$\arcsec$ for sources with $\theta$ > 5$\arcmin$. No multiple matches occurred using this approach. Once matched, the central location of each point source was adopted, in order of priority, from the full, soft, or hard energy band list. The resulting list consists of 794 candidate X-ray sources: 694 detected in the soft band (53 only in the soft band), 173 in the hard band (10 only in the hard band), and 608 in the full band (50 only in the full band).

To prune spurious sources from this list, we used AE's binomial probability \textit{P} \citep[][Appendix~A2]{weisskopf2007}.\footnote{\texttt{prob\_no\_source}, see section~5.10.3 of the AE manual, \url{http://www2.astro.psu.edu/xray/docs/TARA/ae_users_guide.pdf}.} \textit{P} is the probability that, based on the source and local background measurements, a candidate source is a background fluctuation. This approach to producing a final source catalog is preferable to implementing \texttt{wavdetect} with a more stringent false-positive probability threshold \citep[e.g.,][]{lehmer09, xue11, wright2014}. Not only is the pruning based on a transparent mathematical criterion, \textit{P}, but AE also uses a more complex approach to treat source regions in multiple images by replacing \texttt{wavdetect}'s ellipses with polygons that more closely simulate the PSF, and by calculating more accurate source positions, which maximizes the signal-to-noise ratio. We followed AE's suggestion and rejected candidate sources with \textit{P}~$\geq0.01$ as spurious.

To refine the source positions, we improved those calculated by \texttt{wavdetect} using AE's source positions estimates. For source regions with $\theta\le5\arcmin$ we used the ``mean data'' position estimate, which is simply the mean position of events. For source regions with $\theta$ > 5$\arcmin$, we used the ``correlation'' position estimate, which determines the source center by correlating the neighborhood around the source (not just the extracted counts) with the PSF of the source. This is a more accurate source center position when the PSF is asymmetric, which is the case for source regions far off-axis.\footnote{See section~5.3 of the AE manual, \url{http://www2.astro.psu.edu/xray/docs/TARA/ae_users_guide.pdf}, for a discussion of source center estimates.}

The absolute astrometry of the individual observations was then corrected by using \texttt{reproject\_aspect} again to register them to the astrometric frame of the 2MASS Point Source Catalog \citep{cutri03}. This time, the procedure used the refined source positions of our X-ray sources and a 2MASS list of point sources of photometric quality A\footnote{Source confusion was not an issue for the 2MASS sources in the list we used.} in the {\it JHK}$_{\mathrm{s}}$ bands within a square of side 20$\arcmin$ centered on the ACIS-I average aimpoint ($\approx$1900 objects). We used a 2$\farcs$5 matching radius and a residual rejection limit of 0$\farcs$6. When multiple matches occurred, the closest one was selected as the true match. The linear translations ranged from $-0\farcs28$ to $-0\farcs16$, and a rotation angle of $-0^{\circ}.01$ and scale factor of $1.0003$ was applied to all five observations.

We iterated over the process of source and local background extraction, \textit{P} calculation, candidate source list purging of $P\geq0.01$ sources, source position refinement, and absolute astrometric correction, until no more sources were discarded. This was necessary because source and local background extraction in surviving sources may be affected by the disappearance of nearby purged sources. Our final \textit{Chandra}\ catalog contains 774 sources. Of these, 321 were detected in the three energy bands, four were detected in the full band only, and twelve in the soft band only. Almost half of the discarded sources were originally detected only in the full band.

The regions used to extract these sources are shown in Figure~\ref{fig:sourceregions} drawn on the merged full-band flux image, smoothed using a Gaussian function of kernel radius 4. Figure~\ref{fig:PBs} shows the distribution of the binomial probability for all the sources in our catalog. This histogram clearly shows that most sources have negligible probabilities of being false detections. The final merged event file has an absolute astrometry accuracy of $<$0$\farcs$63, based on 210 matches to 2MASS. We investigate the positional uncertainty of the individual X-ray sources in more detail in Section~\ref{uncertainty}.

\begin{figure*}
\begin{center}
\includegraphics[scale=0.4]{Figure4.pdf}
\caption{Merged full-band (0.5--7 keV) flux image smoothed using a Gaussian function of kernel radius 4, with the polygons used for extracting source events, photometry, and spectra drawn in blue. The average aimpoint is indicated by the plus sign. Red stars indicate the four bright sources for which we perform spectral and timing analysis in Appendix \ref{spectra}. We identified 774 X-ray sources. The varying sizes of the source regions illustrate the degrading of the PSF far from the aimpoint.}
\label{fig:sourceregions}
\end{center}
\end{figure*}

\begin{figure}
\includegraphics{Figure5.pdf}
\caption{AE's binomial probability $P$ that a source is just a background fluctuation for all sources that have $P$ < 0.01 in at least one of the three energy bands. We considered sources with $P\geq$ 0.01 to be spurious detections. For clarity, $P$ values lower than $10^{-30}$ are set to $10^{-30}$.}
\label{fig:PBs}
\end{figure}

\subsubsection{Extracting X-ray Photometry}\label{xphotometry}
We followed AE's recipe for photometry extraction\footnote{See \url{http://www2.astro.psu.edu/xray/docs/TARA/ae_users_guide/procedures/photometry_procedure.txt}} using the three energy bands (full, soft, and hard) described in Section~\ref{merging}.
AE first defines each extraction region with a polygon that approximates the $\approx$90\% encircled-energy fraction contour of the local PSF measured at 1.497 keV. It then calculates exposure times, source counts, and background counts for each region and energy band.\footnote{For background counts, we used AE's \texttt{BETTER\_BACKGROUNDS} algorithm, which models several background components simultaneously. See section~7.6.1 of the AE manual, \url{http://www2.astro.psu.edu/xray/docs/TARA/ae_users_guide.pdf}.}

AE executes these steps on each \textit{Chandra}\ observation independently and then merges the extraction data from each source by optimizing the source's signal-to-noise ratio. AE then computes photon fluxes using net (i.e., background-subtracted) source counts, exposure times, and ancillary response files generated by the CIAO tool \texttt{mkarf}.

Figures~\ref{fig:counts_hist} and \ref{fig:fluxes_hist} show the net counts and absorbed X-ray flux distributions in the three energy bands for all the sources in our catalog. We calculated the latter by multiplying the band photon flux by its median photon energy. The median number of net counts for the full, soft, and hard band is $\approx$19, 14, and 3, respectively. There are 78 sources with more than 100 net counts in the full band. In general, hard band detections are less common than full band detections, and most hard band detections have fewer than ten net counts. The median absorbed X-ray flux for the full, soft, and hard band is $4.8\times 10^{-16}$, $2.4\times 10^{-16}$, and $3.0\times 10^{-16}$ $\mathrm{erg}$~$\mathrm{cm}^{-2}$~$\mathrm{s}^{-1}$, respectively.

\begin{figure}
\includegraphics{Figure6.pdf}
\caption{Cumulative distribution of sources in our catalog based on their net counts in the full (0.5--7 keV), soft (0.5--2 keV), and hard (2--7 keV) bands.}
\label{fig:counts_hist}
\end{figure}

\begin{figure}
\includegraphics{Figure7.pdf}
\caption{Cumulative distribution of sources in our catalog based on their absorbed X-ray fluxes in the full (0.5--7 keV), soft (0.5--2 keV), and hard (2--7 keV) bands.}
\label{fig:fluxes_hist}
\end{figure}

\subsection{Estimating the Source Positional Uncertainties}\label{uncertainty}
To parametrize the dependence of the X-ray positional uncertainty on $\theta$ and source counts, we applied the approach of \citet{kim07}, who described the positional uncertainty $\Delta_x$ as
\begin{equation}\label{posunc}
    \textrm{log}\Delta_x = a_0 + a_1\theta + a_2\textrm{log}\ C,
\end{equation}
where $\Delta_x$ is in arcseconds, $\theta$ is the off-axis angle in arcminutes, $C$ is the net full-band counts, and $a_0$, $a_1$, and $a_2$ are constants. This parametrization takes into account the fact that the statistical uncertainty of the calculated PSF center of a \textit{Chandra}\ source increases with lower source counts, and that the size of the PSF increases with larger $\theta$. We performed our own parametrization of the relation above because the one by \citet{kim07} was based on \texttt{wavdetect}-derived positions and photometry.

We started by doing a preliminary match of our X-ray sources to objects in the optical survey of HA08, which is registered to the 2MASS astrometric frame, using 2$\farcs$5 and 4$\farcs$0 matching radii for X-ray sources with $\theta < 5\arcmin$ and > 5$\arcmin$, respectively. We selected these separations by inspecting a histogram of the number of matches as a function of angular separation, and selecting the values that resulted in a mismatch probability $<$1\%.  We excluded likely false matches based on full-band counts, $\theta$, and matching radius (e.g., a source with $>$100 net counts, $\theta<5$, and matching offset $>$1$\ifmmode^{\prime\prime}\else$^{\prime\prime}$\fi$). When multiple matches occurred, the closest one was selected as the true one. Using these criteria, we identified 452 X-ray sources as having optical counterparts. In Section~\ref{matching} we use a more rigorous matching technique that considers the derived positional uncertainty of each X-ray source from this section to create our final list of X-ray-to-optical matches.

Next, we performed a multivariate $\chi^2$ minimization of Equation~\ref{posunc} using the offsets between our X-ray sources and HA08 optical objects as proxy for positional uncertainties. Once we obtained values for $a_0$, $a_1$, and $a_2$, we adjusted the value of $a_0$ until $\gtrsim$80 \% of our X-ray sources with optical counterparts had $\Delta_x$ values larger than the match offsets. The final values are $a_0 = -0.2928$, $a_1=0.1200$, and $a_2=0.3401$.

We then used these values in Equation~\ref{posunc} to calculate the $\approx$80\% confidence positional uncertainties for all our sources, and we report these values in Table~\ref{tbl:X_sources}. Figure~\ref{fig:theta_v_offset} shows the positional offset as a function of $\theta$ for the X-ray-to-optical matches just described. We overplot three curves generated from Equation~\ref{posunc} using $C$ = 10, 30, and 100 counts.

\begin{figure}
\includegraphics{Figure8.pdf}
\caption{Positional offset for our X-ray sources with optical counterparts in the HA08 survey, shown as a function of distance $\theta$ from the \textit{Chandra}\ aimpoint. Black stars are X-ray sources with >100 net counts in the full band; green squares, between 30 and 100, orange circles, between 10 and 30; and small gray circles, <10. We indicate $\approx$80\% positional uncertainty curves for sources with 10, 30, and 100 net counts following Equation~\ref{posunc}.}
\vspace{0.05 in}
\label{fig:theta_v_offset}
\end{figure}

To estimate the expected number of false matches in our catalog, we shifted the X-ray source positions by 30$\arcsec$ out to 6$\arcmin$ in all directions, and then re-matched them to the optical positions using a 2$\farcs$5 matching radius. The 2$\farcs$5 value was selected by inspecting a histogram of the number of matches as a function of matching radius (from 0$\farcs$2 to 4$\farcs$0) at all shifted locations. We found that the median number of false matches is 96 ($\approx$12.5\% of our matched catalog) with a median offset of 1$\farcs$7.

Table~\ref{tbl:X_sources_cols} describes the 31 columns in our \textit{Chandra}\ source catalog. Table~\ref{tbl:X_sources} is a sample of the full catalog. This table is available online in its entirety.

\input{Table2}

\input{Table3_stub}

\section{Optical Observations}\label{optical}
\subsection{Description of the Optical Surveys}\label{optsurveys}
ME08 selected images from the survey taken with the 1.0-m telescope at the Mt.~Lemmon Optical Astronomy Observatory, AZ, of a 22$\farcs$2$\times$22$\farcs$2 area centered on M37, and used both the Scargle-Press and CLEAN periodogram techniques to measure variability for stars with 13 < $V$ < 20 mag. ME08 found 135 variables and reported $P_{\mathrm{rot}}$\ for 120 of them, and the adopted $P_{\mathrm{rot}}$\ for each star is the one from the two periodogram calculations with the least-scattered phased light curve. The typical $P_{\mathrm{rot}}$\ uncertainty is $<$2\%. Based on ($B-V$) colors, these authors identified 28 of the objects as K stars, 60 as G stars, and 32 as F stars. For the latter, ME08 noted that their periods indicate pulsation instead of rotation, as F stars are not expected to display magnetic activity and, thus, no star spots.

HA08 used $g'r'i'$ filters on Megacam and the 6.5-m MMT telescope at the MMT Observatory, AZ, to survey a 24$\arcmin$$\times$24$\arcmin$ area around the center of M37. They obtained photometry for $>$38,000 objects in at least one band. HA08 converted the photometry of objects that had measurements in all three bands ($\approx$16,500) to $gri$ magnitudes. The typical one-sigma error is 0.01 mag for the $gri$ HA08 photometry, which covers the range $15\ \lapprox\ r\ \lapprox\ 23$ mag.

\citet{hartman08b} identified 1445 variable stars in the HA08 survey. These authors used the Lomb-Scargle, box-fitting least-squares, and phase-binning Analysis of Variance (AoV) algorithms to measure periodicity. The most likely period for each star was selected from these three measurements by eye.

Finally, HA09 identified periodic variability due to rotation for 575 \citet{hartman08b} variable stars. For these stars, HA09 determined $P_{\mathrm{rot}}$\ using the multiharmonic AoV algorithm of \citet{schwarzenberg96}, which fits the harmonic series
\begin{equation*}
\tilde{r}(t)=a_0 + \sum\limits_{i=1}^N a_i \mathrm{cos}(2\pi it /P_{\mathrm{rot}} + \phi_i),
\end{equation*}
to light curves, where $a_i$ are the amplitudes and $\phi_i$ are the phases. HA09 calculated three $P_{\mathrm{rot}}$\ using $N=1$, 2, and 3. For the 372 stars with $<$10\% differences between the three $P_{\mathrm{rot}}$\ values, the $N$=2 $P_{\mathrm{rot}}$\ was adopted; these are referred to as clean periods. For the other stars, the (non-clean) period quoted in \citet{hartman08b} was kept. Here the typical $P_{\mathrm{rot}}$\ uncertainty is $<$1\%.

\subsection{Consolidating the Optical Surveys}\label{consolidation}
We consolidated photometry and $P_{\mathrm{rot}}$\ from the surveys described above. We matched the ME08 and HA08 positions using a 10$\arcsec$ matching radius and inspected by eye multiple-match cases to determine the most likely match using available $gri$ and $BV$ photometry as guidance. The liberal matching and individual inspection was necessary because, as noted by HA09, the absolute astrometry of ME08 objects displays a widespread non-linear distortion. Of the 153 stars in the full ME08 catalog, 16 have no HA08 counterpart. We found 37 matched stars to have  ME08 and HA09 $P_{\mathrm{rot}}$\ measurements.\footnote{HA09 listed 22 matches to ME08 with clean $P_{\mathrm{rot}}$, but we find that their match between HA09 ID 424 and ME08 ID 3208 appears to be a mis-identification based on their available photometry.} For consistency, we adopted the HA09 period for all 37.

We used $gri$ photometry for our analysis. For ME08 stars, we adopted the $gri$ magnitudes of their HA08 counterparts. Of the 16 ME08 stars with no HA08 counterpart, we found three with available SDSS photometry. For the remaining 13 ME08 stars, we derived $gri$ photometry from the $V$ and $(B-V)$ reported by ME08 using the transformations derived by \citet{jester2005} and Lupton (2005).\footnote{See \url{http://www.sdss.org/dr12/algorithms/sdssUBVRITransform}}

Our consolidated optical catalog includes 16,584 objects in the M37 field with $gri$ photometry. Of these, 657 stars have a $P_{\mathrm{rot}}$\ measurement. Table~\ref{tbl:opt_sources_cols} summarizes the 25 columns in our catalog of optical objects, a preview of which is presented in Table~\ref{tbl:opt_sources}. This table, which includes all objects from our optical catalog with either a $P_{\mathrm{rot}}$, a non-zero probability of being a cluster member (see discussion below), or an X-ray counterpart (see Section~\ref{matching}), is available online in its entirety.

\input{Table4}
\vspace{0.3 in}

\input{Table5_stub}

\subsection{Membership Determination}\label{membership}
ME08 and HA08 relied solely on distance from a fiducial isochrone in a color-magnitude diagram (CMD) to determine M37's membership. Other studies have used radial velocity or proper motion measurements to determine membership \citep[e.g.,][]{dias2002, nilakshi2002, mermilliod2008, frinchaboy2008}, but these surveys have very few measurements and typically only cover the blue end of the MS or the cluster's red giants. We therefore used the $gi$ photometry of HA08 for $\approx$16,800 objects with $-0.5$ < $(g-i)$ < 4 and combined it with the stars' distances from M37's center to determine  membership probabilities ($P_{\mathrm{mem}}$).

The full description of our $P_{\mathrm{mem}}$\ calculations is in Appendix~\ref{membershipcalc}. Stars with $0.2<(g-i)<3.6$ were assigned a probability of being a single star ($P_{\mathrm{s}}$), a binary star ($P_{\mathrm{b}}$), or a field (non-member) star ($P_{\mathrm{f}}$), so that $P_{\mathrm{s}} + P_{\mathrm{b}} + P_{\mathrm{f}} = 1$ for every star. We considered stars with $P_{\mathrm{mem}}$\ $\equiv P_{\mathrm{s}}$ + $P_{\mathrm{b}}\ge0.2$ to be candidate cluster members. Members with $P_{\mathrm{b}}$ > $P_{\mathrm{s}}$ were labeled as likely binaries.  The low $P_{\mathrm{mem}}$\ threshold we used allows for a non-negligible number of contaminants into our cluster sample. However, since we expect most field stars to be much older and, thus, inactive or significantly fainter in X rays, the contamination in our rotation-activity analysis of cluster stars will be minimal. In Figure~\ref{fig:CMD}, we show the ($i$,~$g-i$) CMD and we highlight single members, likely binary members,  and field stars.

We inspected objects with $0.1\leq P_{\rm mem} <0.2$ that also have an X-ray counterpart with a hardness ratio $<$$-0.3$ (see Sections~\ref{matching} and \ref{HR},) as these could potentially be stars that are younger than the average contaminating field star, and hence potential cluster members. We found 12 objects that met these criteria, and we assigned them a $P_{\mathrm{mem}}$\ value of  $999$. We use this $P_{\mathrm{mem}}$\ value as a flag to highlight those stars that we consider to be cluster members based on additional criteria.

For stars bluer than $(g-i) = 0.2$, we defined a separate CMD locus and calculated $P_{\mathrm{mem}}$\ for those based only on distance from the cluster center and without distinguishing between $P_{\mathrm{s}}$ and $P_{\mathrm{b}}$. This is because the MS is almost vertical in $(g-i)$ for these stars, so that our standard approach cannot be applied. Objects considered cluster members based on these criteria are labeled as blue members. We show these as blue triangles in Figure~\ref{fig:CMD}.

We did not apply our $P_{\mathrm{mem}}$\ calculation to stars without HA08 $gri$ photometry, namely, the 16 ME08 stars without an HA08 counterpart. Instead, we determined their membership by visually inspecting their location on the ($i$,~$g-i$) CMD using their $BV$ photometry transformed into $gri$ (see Section~\ref{consolidation}.) We also considered whether they matched to a soft (hardness ratio <$-0.3$) \textit{Chandra}\ source. Six of these stars lie near or inside the locus of MS stars on the CMD and/or match a soft \textit{Chandra}\ source. We assigned to these six either $P_{\mathrm{s}}=999$ or $P_{\mathrm{b}}=999$, based on their binary flag in ME08, and we indicate them with orange-filled squares in Figure~\ref{fig:CMD}.

We examined the literature for cluster membership information for stars beyond the MS turn-off. \citet{dias2002} identified 40 cluster members near the turn-off point based on proper motion measurements, but \citet{frinchaboy2008} used radial velocity measurements to show that only three are M37 members. We found an HA08 match for one of these stars in our optical catalog. For the other two, we converted the available $BV$ photometry to $gri$ using the transformations described in Section~\ref{consolidation}, assigned them $P_{\mathrm{mem}}$\ $=999$, and added them to our optical catalog.

We searched for surveys identifying white dwarfs and red giants in the field of M37. Using a 5$''$ tolerance radius, four cluster white dwarfs in \citet{kalirai2005} and 31 cluster red giants in \citet{mermilliod2008} matched objects in our optical catalog; we assigned all these matched objects either $P_{\mathrm{s}}=999$ or $P_{\mathrm{b}}=999$, based on their binary flag in the literature.

Lastly, we matched the cluster red giants in \citet{mermilliod2008} and massive cluster stars in \citet{nilakshi2002} to our \textit{Chandra}\ catalog. We found that one red giant and two massive stars matched X-ray sources that had no HA08 or ME08 counterpart (see Section~\ref{matching}). For these three cluster stars, we converted their $BV$ photometry to $gri$ using the transformations described in Section~\ref{consolidation}, assigned them either $P_{\mathrm{s}}=999$ or $P_{\mathrm{b}}=999$, based on their binary flag in the literature, and added them to our optical catalog.

Our final membership catalog contains 1699 candidate M37 members, of which 265 are likely binaries. Twenty likely binary and 406 single members have $P_{\mathrm{rot}}$\ measurements. Table~\ref{tbl:opt_sources} includes all optical objects to which we assigned a non-zero $P_{\mathrm{mem}}$\ value.

We note that there is a segregation of binary candidates toward the blue and red ends of the MS. That most stars at the red end of the MS are likely binaries may be a sign of mass segregation and tidal evaporation of the low-mass single stars, or it could be a sign of increased photometric uncertainty. Such mass segregation and preferential loss of low-mass single members has been observed in many other clusters, including Praesepe \citep{pinfield2003} and the Pleiades \citep{lodieu2007}, where the binary fraction increases in the lowest-mass bins in a way not seen for cool field stars \citep[e.g.,][]{duchene2013}. Furthermore, the lack of binaries at 1.4 < ($g-i$) < 3.2 suggests that the binary sequence is not sufficiently well detected to be fit as a distinct component by our algorithm; the small number of over-luminous binary systems is likely being incorporated into the fit for the field population, indicating one possible source of incompleteness.

\begin{figure}
\includegraphics{Figure9.pdf}
\caption{CMD for all optical objects in the M37 field. Objects with $P_{\mathrm{mem}}$\ $\geq0.2$ are likely cluster members (blue, black, red, and orange symbols); objects with $P_{\mathrm{mem}}$\ $<0.2$ are likely field stars (gray points). Members with $P_{\mathrm{b}}$ > $P_{\mathrm{s}}$ are flagged as likely binary members (red crosses). Blue members (i.e., those beyond the MS turn-off) have no single/binary flag (blue triangles). Orange-filled squares indicate ME08 stars without HA08 counterpart classified as members. The faint blue members are white dwarfs \citep{kalirai2005}. The black arrow indicates the extinction vector.}
\label{fig:CMD}
\end{figure}

\section{Analysis}\label{analysis}
\subsection{Stellar Properties Derived from Optical Photometry}\label{quantities-opt}

\subsubsection{Stellar Masses and the 500-Myr Mass-Period Distribution}\label{masses}
To estimate masses for all the stars in our optical catalog, we used the mass-absolute $r$ magnitude ($M_r$) relation of \citet{adam2007}. These authors compiled a set of empirical observations from the literature to generate a complete list of derived masses and spectral energy distributions (SEDs) for B8-L0 stars, calibrating spectral types with stars in the 600-Myr-old Praesepe cluster \citep{adam2007}.

To obtain $M_r$ we estimated the total absorption in $r$ ($A_r$) using the extinction tables by \citet{schlafly2011} assuming $R_V=3.1$ and adopting a reddening of $E$($B-V$) = 0.227$\pm$0.038 (HA08). We then adopted HA08's distance to M37 of 1490$\pm$120 pc. Finally, we linearly interpolated between the \citet{adam2007} $M_r$ values to obtain masses.

Our optical catalog includes stars ranging from 0.16 to 3.8 $\ifmmode {M_{\odot}}\else${M_{\odot}}$\fi$. The top histogram in Figure \ref{fig:masshist} shows the derived masses for cluster members, and the bottom histogram includes only those members with X-ray counterparts in our \textit{Chandra}\ catalog. We find X-ray emitting cluster members covering the entire surveyed mass range. We derived mass uncertainties from photometric and distance uncertainties; we indicate typical uncertainty values with gray diamonds and error bars in the bottom panel of Figure~\ref{fig:mass_per}, the mass-period distribution for cluster stars. We distinguish between members with HA09 clean or ME08 $P_{\mathrm{rot}}$\ and those with HA09 non-clean $P_{\mathrm{rot}}$\ in the upper panel (see Section~\ref{optsurveys}), and between single and binary members with HA09 clean or ME08 $P_{\mathrm{rot}}$\ in the lower panel.

There is a well-defined sequence of slow rotators in Figure~\ref{fig:mass_per} that runs from $M \approx 1.2\ M_{\odot}$, $P_{\mathrm{rot}}$\ $\approx$ 3 d, to $M \approx 0.4\ M_{\odot}$, $P_{\mathrm{rot}}$\ $\approx$ 20 d. Below this sequence is another distinguishable sequence composed mainly of rotators with non-clean $P_{\mathrm{rot}}$\ that are roughly half the $P_{\mathrm{rot}}$\ of the slow rotators. This suggests that the second sequence is composed of stars whose reported $P_{\mathrm{rot}}$\ are a harmonic of their true $P_{\mathrm{rot}}$.

Although more than half of the cluster members with non-clean $P_{\mathrm{rot}}$\ lie in or near the main mass-period sequence and therefore display the same behavior as stars with clean $P_{\mathrm{rot}}$, we conclude that non-clean $P_{\mathrm{rot}}$\ add unnecessary ambiguity to our results. We therefore included non-clean rotators in our analysis only if they also had a ME08 $P_{\mathrm{rot}}$\ and the two $P_{\mathrm{rot}}$\ measurements did not differ by more than 20\%, which is the typical vertical width of the main mass-period sequence.

The mass-period distribution for M37 indicates that the more massive cluster members have spun down to the slow-rotating sequence, where $P_{\mathrm{rot}}$\ has a weak dependence on stellar mass. This breaks down around $\approx$0.7 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi; lower-mass stars span a range of 1 $\lapprox$ $P_{\mathrm{rot}}$\ $\lapprox$ 20 d. This is consistent with expectations based on M37's slightly younger age than the Hyades and Praesepe. In the 625-Myr-old Hyades \citep{perryman1998} and 600-Myr-old Praesepe clusters, this transition occurs at $\approx$0.6 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi\ \citep{agueros11, Douglas14}.

Cluster members with X-ray counterparts (filled symbols in the lower panel of Figure~\ref{fig:mass_per}) cover the entire mass-period plane, suggesting that X-ray detection is not just limited to the fast rotators ($P_{\mathrm{rot}}\lesssim1$ d) and, hence, to the more active stars. Nine of the 18 fast rotators in our cluster sample have no X-ray counterpart. Eight of those nine rotators are at an off-axis angle $\theta >5\arcmin$ in the \textit{Chandra}\ field-of-view, beyond which the \textit{Chandra}\ PSF quickly degrades. Furthermore, based on their derived masses, four of them are likely to be early F stars, and the measured periods are probably due to pulsations and not to rotation.

\begin{figure}
\includegraphics{Figure10.pdf}
\caption{\textit{Top}: Stacked histogram of stellar masses for M37 members. Likely binary members are indicated in red and blue members (which have no single/binary flag), in hashed blue. \textit{Bottom}: Histogram of stellar masses for M37 members with an X-ray counterpart in our \textit{Chandra}\ catalog. We do not derive the masses of the red giants and white dwarfs in our optical catalog and these are excluded from these histograms.}
\vspace{0.05 in}
\label{fig:masshist}
\end{figure}

\begin{figure}
\includegraphics{Figure11.pdf}
\caption{\textit{Top}: $P_{\mathrm{rot}}$\ versus mass for M37 members. Our consolidated optical catalog has 426 cluster members with $P_{\mathrm{rot}}$: 296 have either HA09 clean $P_{\mathrm{rot}}$\ or ME08 $P_{\mathrm{rot}}$\ (blue stars), and 130 have HA09 non-clean $P_{\mathrm{rot}}$\ (gray crosses). A well-defined, slow-rotating sequence runs from $M \approx 1.2$ \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi, $P_{\mathrm{rot}}$\ $\approx$ 3 d, to $M \approx 0.4$ \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi, $P_{\mathrm{rot}}$\ $\approx$ 20 d. This sequence breaks down around a mass of $\approx$0.7 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi; lower-mass stars include both fast and slow rotators. \textit{Bottom}: Same as the top panel, but for the 296 members with HA09 clean $P_{\mathrm{rot}}$\ or ME08 $P_{\mathrm{rot}}$. Single members (283) are indicated with black circles, and likely binary members (13) with red triangles. Stars with X-ray counterparts are shown as filled symbols (69 single members and seven likely binaries). Typical mass uncertainties, derived from photometric and distance uncertainties, are indicated along the top with error bars around gray diamonds.}
\label{fig:mass_per}
\end{figure}

\subsubsection{Bolometric Luminosities}\label{bolometric}
To obtain $L_{\mathrm{bol}}$ for the stars in our catalog, we once again adopted HA08's distance to M37 of 1490$\pm$120 pc. We used the SED table of \citet{adam2007} to convert the $M_r$ values obtained in Section~\ref{masses} into corresponding effective temperatures $T_{\mathrm{eff}}$. We then used $T_{\mathrm{eff}}$ to find bolometric corrections $BC_r$ using the tables collected by \citet{Girardi04}, which are tailored to the SDSS filter system. Using $M_r$ and $BC_r$, we then calculated bolometric magnitudes and luminosities.

\subsubsection{Rossby Numbers}\label{rossby}
Stellar activity increases with increasing rotation rates only up to a saturation velocity, beyond which activity remains constant. This saturation point has been observed to have a dependence on stellar mass \citep[see e.g.,][]{pizzo03}. \citet{Noyes1984} found that the Rossby number $R_o$ = $P_{\mathrm{rot}}/\tau$, where $\tau$ is the convective turnover time, removes this mass dependence, thus revealing the general relationship between stellar rotation and activity. $R_o$ serves as an indicator of the strength of a rotationally driven dynamo, which can be compared more evenly between stars of different masses.

To estimate $\tau$ for M37 members, we used the empirical stellar mass-$\tau$ relation of \citet[][hereafter W11]{wright2011}, who collected over 800 stars spanning a mass range of 0.09--1.36 $M_{\odot}$ with both $P_{\mathrm{rot}}$\ and $L_{\rm X}$ measurements. These authors fitted the $L_{\mathrm{X}}/L_{\mathrm{bol}}$-$P_{\mathrm{rot}}$\ relation following a formulation equivalent to Equation~\ref{eq:rossby} and adopting the canonical slope $\beta=-2.0$. W11 reported $\tau$ values for ten mass bins, and we used these to fit a second-order polynomial in the mass-$\tau$ plane. The resulting mass-$\tau$ relation is
\begin{equation*}
\mathrm{log} \tau = 1.24 - 1.63\ \mathrm{log} (M/\ifmmode {M_{\odot}}\else${M_{\odot}}$\fi) - 0.56\ \mathrm{log}^2 (M/\ifmmode {M_{\odot}}\else${M_{\odot}}$\fi),
\end{equation*}
with a correlation coefficient $r$ = 0.989, and we used this relation to calculate $\tau$ for cluster members within the 0.09--1.36 $M_{\odot}$ mass range. 72\% of cluster members and 99\% of the cluster rotators fall within this mass range.

W11 also reported $\tau$ values for the same mass bins adopting $\beta=-2.7$, which is the slope they found in their analysis of a subset of 36 solar-type stars. We used the second-order polynomial that W11 fit to these $\tau$ values in the mass-$\tau$ plane to calculate $\tau$ for our cluster stars, and found that these $\tau$ values were 30$\pm$5\% smaller than those based on $\beta=-2.0$.

Using both sets of $\tau$ values, we calculated $R_o$ and examined the $L_{\mathrm{X}}/L_{\mathrm{bol}}$-$R_o$ plane for our cluster sample, performing the parametrization analysis described in Section~\ref{results} twice. We found that the two $\beta$ values we derived for our sample differed $<$3\% and were well within one standard deviation ($\sigma$) of each other. The two saturation points $R_{o,\mathrm{sat}}$ differed by 20\%, but were still within 1$\sigma$ of each other. We therefore opted to use $\tau$ values based on $\beta=-2.0$ for the rest of our analysis.

\subsection{Stellar Properties Derived from X rays}\label{quantities-xray}
The stellar magnetic field manifests itself above the photosphere and heats the plasma in the stellar corona above $10^6$ K \citep{Vaiana81}. X rays from MS stars originate in this high-temperature plasma. In such stars, the ratio of X-ray luminosity to bolometric luminosity $L_{\mathrm{X}}/L_{\mathrm{bol}}$\ appears to decrease by several orders of magnitude between zero-age MS stars and solar-age stars \citep[e.g.,][]{Feigelson2004, wright2010}. The $L_{\mathrm{X}}/L_{\mathrm{bol}}$\ ratio thus allows us to compare the contribution of X rays in a mass-independent way.

To estimate the unabsorbed fluxes of our \textit{Chandra}\ sources, we converted our soft-band fluxes using WebPIMMS\footnote{\url{http://cxc.harvard.edu/toolkit/pimms.jsp}} and an APEC model with solar abundance and $kT$ = 0.768 (log $T$ = 6.95). Given that 95\% of the X-ray sources with M37 counterparts have similar, soft X-ray spectra (with hardness ratios between $-0.4$ and $-1.0$; see Section~\ref{HR}), assuming the same plasma temperature for all is a reasonable approximation. We set the Galactic atomic neutral hydrogen column density to 1.26$\times 10^{21}$ cm$^{-2}$, derived using $E$($B-V$) = 0.227 from HA08, and obtained the fluxes for the $\it ROSAT$ band (0.1--2.4 keV) in order to compare our results to those of previous studies. We then calculated $L_{\mathrm{X}}$ using a distance of 1490$\pm$120 pc (HA08).

\subsection{Matching the Optical and X-ray Catalogs}\label{matching}
We used the $\approx$80\% confidence X-ray positional uncertainties calculated in Section~\ref{uncertainty} to match our \textit{Chandra}\ sources to optical objects from HA08 by using a tolerance radius 1.6 times the positional uncertainty of each X-ray source. We found that this factor provided a large number of matches without introducing too many potentially false matches. We found 540 X-ray sources with HA08 optical counterparts. Multiple matches occurred $<$15\% of the time, and we selected the closest match as the true one in such cases. Fourteen more near-matches were inspected individually and considered to be true matches.

To match our X-ray sources to ME08 objects, we used the same method as described in Section~\ref{consolidation}, where we described how a distortion in the absolute astrometry of ME08 objects led us to apply a liberal 10$\arcsec$ tolerance radius and then to inspect by eye the most likely true match using available $gri$ and $BV$ photometry as guidance. We found 37 X-ray sources with ME08 optical counterparts.

For the remaining unmatched X-ray sources, we found one red giant match in \citet{mermilliod2008} and two massive star matches in \citet{nilakshi2002} (see Section~\ref{membership}) also using a tolerance radius 1.6 times the positional uncertainty of each X-ray source. Neither of these three optical objects has a HA08 or ME08 counterpart (two of them have $V$ photometry outside the $V$ range studied by ME08).

Combining all X-ray-to-optical matches, we have 561 X-ray sources with optical counterparts, 278 of which have $P_{\mathrm{mem}}$\ $\geq$ 0.2: 195 single stars (69 with $P_{\mathrm{rot}}$) and 83 binaries (7 with $P_{\mathrm{rot}}$). Figure \ref{fig:Xfraction} shows the fraction of optical objects with X-ray counterparts as a function of $P_{\mathrm{mem}}$. It is close to zero for field stars and then increases linearly to some intrinsic fraction of M37 stars.

\begin{figure}
\includegraphics{Figure12.pdf}
\caption{Fraction of optical objects with X-ray counterparts per 10\%-$P_{\mathrm{mem}}$\ bin.}
\label{fig:Xfraction}
\end{figure}

Two hundred and thirteen X-ray sources have no optical counterparts. The log of the median spurious detection probabilities $P$ for matched and unmatched X-ray sources are $-$9.5 and $-$10.6, respectively. The median net counts in the full band for matched and unmatched X-ray sources are 17.2 and 25.9, respectively. Lastly, the median photon energy for matched and unmatched X-ray sources are 1.2 and 1.95 keV, respectively.

\subsection{X-ray Hardness Ratios and Spectral Information}\label{HR}
We obtained spectral information for our X-ray sources by computing a hardness ratio ($HR$). The $HR$ is (hard counts$-$soft counts)/(hard counts$+$soft counts); we followed the definitions of the hard and soft bands described in Section~\ref{merging} and used net counts. Soft spectra are characterized by $HR < 0$, and hard spectra, by $HR > 0$.

An \textit{a posteriori} analysis of the matching done in Section~\ref{matching} revealed that 96\% of the 278 X-ray sources matched to optical cluster members have $HR \lesssim -0.3$, a strong indication of their stellar nature. Only two such sources have $HR$ > 0, and both are flagged as likely binaries. By contrast, 72\% of the 283 X-ray sources matched to optical non-members (i.e., field stars) have $HR \lesssim -0.3$, and 12\% have $HR > 0$. Furthermore, only 32\% of the 213 X-ray sources without any optical counterpart have $HR\lesssim -0.3$, and 45\% have $HR>0$. Figure~\ref{fig:HR} shows a histogram of $HR$ values for X-ray sources matched to M37 members, X-ray sources matched to non-members, and X-ray sources with no optical counterpart.

\begin{figure}
\includegraphics{Figure13.pdf}
\caption{Normalized stacked histogram of hardness ratios for X-ray sources matched to M37 members (white), X-ray sources matched to non-member objects (red), and X-ray sources with no optical counterpart (hashed blue).}
\label{fig:HR}
\vspace{0.05 in}
\end{figure}

Only three X-ray sources matched to an optical cluster member have $>$150 net counts in the full band; the highest has 260. Thus, there are no cluster X-ray sources with enough counts for a meaningful analysis of their X-ray spectra or light curves. Four X-ray sources in our \textit{Chandra}\ catalog have  $>$1000 net counts. Two of these are matched to an optical non-member; the other two lack optical counterparts. We discuss these four sources in Appendix~\ref{spectra}.

\section{Results and Discussion}\label{results}
Our analysis of $L_{\mathrm{X}}/L_{\mathrm{bol}}$\ versus $R_o$ only included M37 members ($P_{\mathrm{mem}}$\ $\geq$ 0.2) that had either HA09 clean $P_{\mathrm{rot}}$\ or that had both HA09 non-clean $P_{\mathrm{rot}}$\ and ME08 $P_{\mathrm{rot}}$\ and the two $P_{\mathrm{rot}}$\ measurements differed by less than 20\%. Figure \ref{fig:rossby} shows the resulting 51 single members (blue stars) and 4 likely binary members (red circles) that are included in the following fit.

The conventional way to parametrize the $L_{\mathrm{X}}/L_{\mathrm{bol}}$--$R_o$ relationship is with a flat region connected to a power-law \citep[e.g.,][]{Randich2000b, wright2011, Douglas14}:
\begin{equation}\label{eq:rossby}
  \frac{L_{\mathrm{X}}}{L_{\mathrm{bol}}} = \left\{
  \begin{array}{l l}
    \left(\frac{L_{\mathrm{X}}}{L_{\mathrm{bol}}}\right)_{\mathrm{sat}} & \quad \textrm{if $R_o\le R_{o\mathrm{,sat}}$}\\
    C R_o^\beta & \quad \textrm{if $R_o$ > $R_{o\mathrm{,sat}}$}
  \end{array} \right.
\end{equation}
where $\left(L_{\mathrm{X}}/L_{\mathrm{bol}}\right)_{\mathrm{sat}}$ is the activity saturation level, $R_{o\mathrm{,sat}}$ is the turnover point, $\beta$ is the power-law index characterizing the unsaturated regime, and $C$ is a constant. We fit this model to the 55 members described above.

We followed a similar fitting procedure to that described in \citet{Douglas14}. We converted the model in Equation \ref{eq:rossby} into log-space for the fit, and assumed flat priors over all three parameters. We used the open-source Markov-chain Monte Carlo (MCMC) package \texttt{emcee}\footnote{\url{http://dan.iel.fm/emcee/current/}} \citep{Foreman13} to carry out the fit. It builds posterior probability distributions for each parameter (shown in Figure~\ref{fig:corr}) by performing a random walk in parameter space.

Two hundred models drawn at random from the posterior probability distributions are shown in gray in Figure~\ref{fig:rossby}. The most probable model, i.e., the maximum $a\ posteriori$ model, is indicated by a solid black line. The resulting best-fit parameters are log($L_{\mathrm{X}}/L_{\mathrm{bol}}$)$_{\mathrm{sat}} = -3.06\pm0.04$, $R_{o\mathrm{,sat}}=0.09\pm0.01$, and $\beta=-2.03_{-0.14}^{+0.17}$. The parameter values correspond to the 50$^{\rm th}$ quantile, and the uncertainties correspond to the 16$^{\rm th}$ and the 84$^{\rm th}$ quantiles (for consistency with $1\sigma$ Gaussian uncertainties).

\subsection{The Saturated Regime}\label{saturated}
Several hypotheses aim to explain the decoupling of rotation and activity seen in the saturated regime. These include dynamo saturation \citep{Gilman83, Vilhu87}, saturation of the filling factor of active regions on the stellar surface \citep{Vilhu84}, and centrifugal stripping of the corona \citep{Jardine1999}. However, a satisfactory explanation remains elusive (see e.g., W11).

We detect this saturation phenomenon for stars with $R_o < 0.09\pm0.01$. This turnover point is similar to $R_{o\mathrm{,sat}}= 0.13\pm0.02$ found by W11 for their $Einstein/\it ROSAT/XMM$ heterogeneous sample of 824 field and cluster stars collected from the literature, and it is slightly smaller than $R_{o\mathrm{,sat}}\approx0.16$ found by \citet{Randich2000b} for her heterogeneous $\it ROSAT$ sample of field and cluster stars. Our saturation level log$\left(L_{\mathrm{X}}/L_{\mathrm{bol}}\right)_{\mathrm{sat}}=-3.06\pm0.04$ agrees with log$\left(L_{\mathrm{X}}/L_{\mathrm{bol}}\right)_{\mathrm{sat}}=-3.13\pm0.22$ found by W11. It is slightly lower than log$\left(L_{\mathrm{X}}/L_{\mathrm{bol}}\right)_{\mathrm{sat}}\approx-3$ found by \citet{Randich2000b}.

\begin{figure}
\includegraphics{Figure14.pdf}
\caption{X-ray to bolometric luminosity ratio as a function of Rossby number $R_o$ for cluster members. Likely binary members are indicated with red circles. The solid black line is the maximum $a\ posteriori$ fit from the MCMC algorithm and the gray lines are 200 random samples from the posterior probability distributions. The dashed line indicates the fit found by \citet{palla81}, and the dotted line indicates the fit found by \citet{wright2011}.}
\label{fig:rossby}
\end{figure}

\begin{figure}
\includegraphics{Figure15.pdf}
\caption{Marginalized posterior probability distributions from the MCMC analysis using \texttt{emcee}. The parameter values of the \textit{a\ posteriori} model are the peaks of the one-dimensional distributions; the vertical dashed lines approximate the median and 68-percentiles. The two-dimensional distributions illustrate covariances between parameters; the contour lines approximate the 68- and 95-percentile of the distributions.}
\label{fig:corr}
\end{figure}

\subsection{The Unsaturated Regime}\label{unsaturated}
The increase in stellar activity with increasing rotation (smaller $R_o$) is believed to indicate the heating of the corona by the stellar dynamo \citep{palla81, pizzo03}. One of the challenges of the past few decades has been to characterize empirically this relationship. \citet{palla81} first discovered this behavior in an $Einstein$ sample of 17 late-type stars of luminosity classes II to V, and found a power-law index $\beta=-1.9\pm0.5$. More recently, \citet{gudel1997} found $\beta = -2.64\pm0.12$ for a $\it ROSAT/ASCA$ sample of 12 solar-type stars of ages 0.07 to 9 Gyr, and \citet{Randich2000b} found $\beta = -2.10\pm0.09$ for her $\it ROSAT$ sample. Finally, W11 found $\beta = -2.18\pm0.16$ for their heterogeneous sample of cluster and field stars. W11 also analyzed a subset of 36 solar-type stars detected only with $\it ROSAT$ to eliminate X-ray luminosity biases. They found $\beta = -2.70\pm0.13$ for this sample. We include the power-law relation for the unsaturated regime of both the latter sample and of the \citet{palla81} sample in Figure~\ref{fig:rossby}.

For our sample of unsaturated, co-eval M37 stars, which cover a mass range of 0.55--1.28 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi, the index $\beta=-2.03_{-0.14}^{+0.17}$ agrees with that by \citet{palla81} $\beta=-1.9\pm0.5$. It differs from the W11 result for the unbiased sample of solar-type stars by 3$\sigma$. That $\beta$ found for our sample of $\approx$500 Myr stars does not agree with some of the $\beta$ values in the literature suggests that previous studies that include stars with a range of ages may be missing interesting age-dependent effects in the behavior of stellar activity. It may also be evidence that the unsaturated regime is better described by a broken power law instead of a single power law \citep[e.g.,][]{petit2008,donati2009,saar1999}. Unfortunately, our sample of M37 does not extend to large enough $R_o$ values to fully test this idea.

Did our \textit{Chandra}\ observation or the $P_{\mathrm{rot}}$\ surveys of ME08 and HA09 bias our sample toward those stars with higher $L_{\rm X}$ and/or faster $P_{\mathrm{rot}}$? We may not have identified the faintest X-ray sources in the cluster because of their very low counts and/or large $\theta$, making their detection much harder. Likewise, ME08 and HA09 may not have measured $P_{\mathrm{rot}}$\ for the faintest cluster members, thus excluding members with possibly the longest $P_{\mathrm{rot}}$.

Our X-ray catalog contains 18 sources, 15 of which are cluster members, with log($L_{\mathrm{X}}/L_{\mathrm{bol}}$) $\leq-6.0$, while our optical catalog contains only six objects, three of which are members, with $R_o\geq 1.0$. Indeed, the light curves used by both ME08 and HA09 span only 30 days, suggesting that lack of slow rotators may be the limiting factor in determining the behavior of unsaturated stars at the high-$R_o$ end.

Still, our sample of $\approx$500 Myr M37 members with both $P_{\mathrm{rot}}$\ and X-ray measurements spans a wide set of stellar properties, as it covers masses ranging from 0.4 to 1.3 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi, $P_{\mathrm{rot}}$\ ranging from 0.4 to 12.8 d, and $L_{\rm X}$ ranging from 10$^{28.4}$ to $10^{30.5}$ $\mathrm{erg}$~$\mathrm{s}^{-1}$. Our results make M37 a new benchmark open cluster for calibrating the rotation--activity relation at ages of $\approx$500 Myr.

\subsection{The Dependence of X-ray Activity on Age}\label{LX_age}
We compared $L_{\mathrm{X}}$ for 64 M37 solar analogs (masses 0.8--1.2 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi) with X-ray detections of 62 stars in Alpha Persei \citep[$\alpha$-Per,][]{randich1996, Prosser1996, Prosser1998, Prosser1998b, pillitteri2013}, 62 Pleiads \citep{micela1990, stauffer1994, micela1996, micela1999, briggs2003}, 28 Hyads \citep{stern1994, stern1995}, and five stars in NGC 752 \citep{giardino2008} within the same mass range. The adopted ages are 85$\pm$10 Myr for $\alpha$-Per \citep{lodieu2012}, 130$\pm$20 Myr for the Pleiades \citep{barrado2004}, 485$\pm$28 Myr for M37 (HA08), 625$\pm$50 Myr for the Hyades \citep{perryman1998}, and 1.6$\pm$0.2 Gyr for NGC 752 (Ag\"ueros et al.~in prep.). Figure~\ref{fig:LX_t} shows the data for these five clusters, where the boxes extend from the lower to the upper quartile, the whiskers extend to cover the entire range, the red line inside the boxes indicates the median, and the blue stars indicate the mean. The maximum and minimum $L_{\mathrm{X}}$ of the Sun \citep{peres2000} is indicated by black whiskers at 4.5 Gyr.

We performed a linear regression analysis in log space using the median $L_{\mathrm{X}}$ values of the five clusters to determine the dependence of $L_{\mathrm{X}}$ on age. We found that $L_{\mathrm{X}}\propto t^{-1.23\pm0.16}$, with a correlation coefficient $r=-0.98$. This result, which corresponds to the black dashed line in Figure~\ref{fig:LX_t}, is close to the expected power-law exponent value of $-1$ for stars with ages $\gapprox$100 Myr. It is within 1$\sigma$ of the power-law exponent $-1.5^{+0.3}_{-0.2}$ found by \citet{maggio1987} using a set of Pleiades, Hyades, and Orion Ic solar-like stars and their observations of nearby solar analogs. Similarly, \citet{gudel1997} and \citet{giardino2008} found an exponent of $-1.5$. Plugging our $\beta=-2.03_{-0.14}^{+0.17}$ into the relation $L_{\mathrm{X}}\propto t^{-\alpha\beta}$, we find that $\alpha$ must lie in the range 0.49--0.75, with $\alpha=0.60$ as the most likely value. This agrees very well with the relation $v_{\mathrm{rot}} \propto t^{-0.5}$ for solar-like stars found by \citet{skumanich72} and \citet{meibom2011}.

\begin{figure}
\includegraphics{Figure16.pdf}
\caption{X-ray luminosity of solar-like members (mass range of 0.8--1.2 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi) of five open clusters as a function of age. The adopted ages are 85$\pm$10 Myr for $\alpha$-Per, 130$\pm$20 Myr for the Pleiades, 485$\pm$28 Myr for M37, 625$\pm$50 Myr for the Hyades, and 1.6$\pm$0.2 Gyr for NGC 752. The data includes 62 $\alpha$-Per stars, 62 Pleiades stars, 64 M37 stars, 28 Hyades stars, and 5 NGC 752 stars. For each cluster, the box extends from the lower to the upper quartile, and the whiskers cover the entire $L_{\rm X}$ range. The median $L_{\rm X}$ for each cluster is indicated by a red line inside the box, and the mean by a blue star. We indicate the minimum and maximum of the Sun \citep{peres2000} with black whiskers at 4.5 Gyr. A linear regression analysis in log space (excluding the Sun) suggests a relationship between X-ray luminosity and age of $L_{\mathrm{X}}\propto t^{-1.23\pm0.16}$, and we indicate it with a dashed line.}
\label{fig:LX_t}
\vspace{0.05 in}
\end{figure}

\section{Summary}\label{conclusion}
We have assembled an extensive sample of stars with X-ray and $P_{\mathrm{rot}}$\ measurements in the M37 open cluster to study the stellar rotation-activity relation at $\approx$500 Myr. We observed the center of the cluster with \textit{Chandra}\ and detected $\approx$770 high-confidence X-ray sources. We also consolidated two optical surveys of M37 with $P_{\mathrm{rot}}$\ measurements \citep{messina08a, hartman09}, obtaining a merged sample of $\approx$650 rotators. We calculated new membership probabilities for optically detected objects in the M37 field, and complemented the resulting catalog of cluster members with massive stars, red giants, and white dwarfs identified as members in the literature. By matching our X-ray and optical catalogs, we generated a sample of 76 solar- and late-type members of M37 with X-ray and $P_{\mathrm{rot}}$\ measurements.

We used soft-band X-ray fluxes extracted from our \textit{Chandra}\ observations and the cluster distance of $\approx$1.5 kpc to derive $L_{\mathrm{X}}$ for all X-ray sources. We then used $gri$ photometry and reddening values from \citet{hartman08a} to derive stellar masses and $L_{\mathrm{bol}}$ for all cluster members. Finally, we calculated $\tau$ values using the \cite{wright2011} empirical model as a function of mass, thereby obtaining $R_o$ for our stars.

We then examined the $\approx$500 Myr mass-rotation and rotation-activity relations. M37's mass-period distribution indicates that the cluster's more massive stars have spun down to a single-valued relation. There is a well-defined sequence of slow rotators that runs from $M \approx 1.2\ M_{\odot}$, $P_{\mathrm{rot}}$\ $\approx$ 3 d, to $M \approx 0.4\ M_{\odot}$, $P_{\mathrm{rot}}$\ $\approx$ 20 d. This single-valued relation breaks down around a mass of 0.7 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi; lower-mass stars span a range from fast ($P_{\mathrm{rot}}$\ $\approx 1$ d) to slow ($\approx$20 d) rotators. This is consistent with expectations based on M37's slightly younger age than the Hyades and Praesepe. In these $\approx$600-Myr-old clusters, this transition occurs at $\approx$0.6 \ifmmode {M_{\odot}}\else${M_{\odot}}$\fi\ \citep{agueros11, Douglas14}.

In examining the dependence of $L_{\mathrm{X}}/L_{\mathrm{bol}}$\ on $R_o$, we identified a saturated and an unsaturated regime. All rotators with $R_o<0.09\pm0.01$ (a turnover point consistent with that found in the literature for other rotation-activity samples) are saturated, and converge to an activity level of log($L_{\mathrm{X}}/L_{\mathrm{bol}}$)$=-3.06\pm0.04$, close to the canonical value of $-3$ and similar to recent values found for heterogeneous samples of field and cluster stars.

In the unsaturated regime, faster rotators (smaller $R_o$) have increasing levels of coronal activity (larger $L_{\mathrm{X}}/L_{\mathrm{bol}}$) following a power law of index $\beta=-2.03^{+0.17}_{-0.14}$, in agreement with the $\beta=-1.9\pm0.5$ found by \citet{palla81}. Interestingly, however, this $\beta$ differs from the \citet{wright2011} result for their unbiased sample of solar-type stars by 3$\sigma$. This suggests that previous studies that include stars with a range of ages may be missing interesting age-dependent effects in the behavior of stellar activity, or that a broken power law may describe better the unsaturated dependence of activity on rotation.

A comparison of solar-type X-ray emitters in M37 and similar stars in the $\alpha$-Per, Pleiades, Hyades, and NGC 752 open clusters, covering an age range of 0.85--1.6 Gyr, shows that $L_{\mathrm{X}}\propto t^{-1.23\pm0.16}$, suggesting that the surface rotational velocity in solar-type stars declines as $v_{\mathrm{rot}} \propto t^{-0.60}$, in agreement with previous studies \citet[e.g.,][]{skumanich72, meibom2011}.

By probing the stellar rotation-activity relation with our homogeneous, co-eval sample of M37 members, we are helping to calibrate empirically the ARAR at $\approx$500 Myr. More importantly, the wide coverage in stellar masses, rotation periods, and X-ray luminosities of our sample of cluster members puts M37 in a position to become a new benchmark middle-aged open cluster.

\acknowledgments We thank the referee for a careful reading of the paper. We thank Patrick Broos for his help with the AE package and Maureen van den Berg for her help with obtaining unabsorbed X-ray fluxes. Support for this work was provided by NASA through \textit{Chandra}\ Award Number G02-13025A issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. M.A.A.\ acknowledges support provided by the NSF through grant AST-1255419.

\setlength{\baselineskip}{0.6\baselineskip}

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Rose and butterfly cutting dies! The Roses cutting die set from Paper Artist™ features a large grouping of intricate roses and a smaller accent butterfly! Use these cutting dies to create stunning flower die-cuts that can be backed with papers and layered for a gorgeous, bold floral look ideal for greeting cards, scrapbook accents, mini albums and even gift tag embellishments! Use with suede papers for a luxurious effect! This set features 2 cutting dies measuring from 1 1/4" to 5 1/2" wide, and are designed to work with most leading die cutting machines including the BigShot Die Cutting Machine (link). Use these dies along with inks, stamps or on their own! Be sure to check out these other cutting dies from Paper Artist™ including , Wreath (link), Hello Ferns (link), 10 Tiny Things + Shadows (link) and Wildflowers (link).


text:
« Bürger and Cubasch
Rutherford, Mann et al [2005] »
The A&W Little Whopper
For your reading pleasure, here is our Reply to Ammann and Wahl (GRL). as submitted on Jan. 29, 2006. You don't have access to the A&W Comment itself; [update: now here ] but if you re-read the Huybers article, it has the same points without all the mischaracterizations and misrepresentations of A&W.
A&W also have a longer article that has been submitted to Climatic Change, which they say has been"provisionally accepted". The list of misrepresentations in the GRL article is pretty amazing, but it's even worse in the longer Climatic Change article. We will henceforth refer to the two articles as the Big Whopper and the Little Whopper .Too bad there's no root beer and fries on the side.
Yeah, yeah, I know that it's Burger King that makes the Big Whopper, but somehow the A&W Teen Burger didn't have quite the same ring.
This entry was written by Stephen McIntyre, posted on Jan 26, 2006 at 11:19 PM, filed under MBH98, Wahl and Ammann and tagged ammann, wahl. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Both comments and trackbacks are currently closed.
I like the phrase (in point 8 of your response) "backdoor insertion of bristlecones". Sounds painful!
There should be a line:
"We are grateful that Ammann & Wahl could at least spell Ross' surname correctly, unlike [Regalado A., WSJ 2005]"
I, for one, would be happy to see AGU/GRL trash their own response policies (as they started to do in the Ritson reply matter) and, having dug this response from Ammann & Wahl out of the trash, now let it be published along with the M&M reply. Any other votes?
Our Reply is temporarily offline and will be posted up on Monday.
John Hekman
Oops. Here's the link
http://www.tcsdaily.com/article.aspx?id=012706B
This was submitted today and is online again.
IanCastles
Re #2. Regalado in the WSJ only got Ross's surname wrong, but an article on the Australian Greenhouse Office website, published under the Australian Coat of Arms under the authority of the Australian Government, gets both surnames wrong and also misspells a word in the title of the paper. See the list of references to Hot Topics in Climate Change No. 3 on the AGO website at http://www.greenhouse.gov.au/science/hottopics/ , which includes the following:
"McKitrick, S (sic) and McIntyre, R (sic) (2005). Hockey sticks, principle (sic) components and spurious significance. Geophysical Research Letters, 32, L03710.
The article was prepared by Australia's major scientific research organisation, CSIRO, and there's an "Important notice" at the bottom that says that "This document is produced for general information only and does not represent a statement of the policy of the Australian Government." The paragraph in which the citation to the GRL article appears reads, in full, as follows:
"Some of these results have been questioned. A study by Soon and Baliunas (2003) challenged the unusual nature of the 20th century warming, but this study was found to be scientifically flawed (Mann et al, 2003a; Mann and Jones, 2003). Another study by McIntyre and McKitrick (2003) claimed that temperatures estimated by Mann et al (1998) from 1400 to 1980 contained errors, and that corrections to the data showed that the early 15th century was warmer than any period in the 20th century (sic). However, these claims were countered by Mann et al. (2003b) who found that McIntyre and McKitrick (2003) made errors in their analysis and omitted or truncated key proxy indicators from 1400-1600. Mann et al (2004) acknowledge that their 1998 paper contained several errors that, when appropriately corrected, had no effect on previously published results. McIntyre and McKitrick (2005) claimed that the method of Mann et al. (1998) is biased towards producing a "hockey stick' shaped curve and underestimates uncertainty in the 15th century."
The article prepared by CSIRO makes no reference to Burger & Cubasch (2005), Huybers (2005) or to the papers referenced in the reply to A&W as M&M (2005b) and M&M (2005c). However, the article does cite, and provide an email link to the MB&H note of 3 November 2003: "Mann, M, Bradley R and Hughes M (2003b) Note on paper by McIntyre and McKitrick in "Energy and Environment" at http://www.cru.uea.ac.uk/%7Etimo/paleo/EandEPaperProblem_03nov03.pdf
CSIRO Publishing, an autonomous unit within the research organisation, has published online some "Supplementary Notes and References' by A. Barrie Pittock, the author of "Climate Change: Turning up the Heat", a book that was recently published with a laudatory foreword by Dr Rajendra Pachauri and is being promoted by Earthscan (London) as "a major new textbook". Dr. Pittock's reference to the temperature reconstructions and the criticisms thereof reads as follows:
"There is a further attack on the temperature reconstructions in Figure 1 by McIntyre and McKitrick in the journal Energy and Environment 14, 751-771 (2003). The argument centres on the different selection and correction of data. Mann and co-authors are the recognised experts in this field, and thus best qualified to make the expert judgments on data quality and representativeness needed. Mann and Jones, in Geophysical Research Letters, 30 (15), 1820-1823 (2003) have extended their temperature reconstructions back to 2000 years. See other discussions on http://www.greenhouse.gov.au/science/hottopics/."
Dr. Pittock does not mention any of the relevant papers published in 2005, although his Notes are sufficiently up-to-date to include the following: "[Hurricane Katrina] is an ongoing story, with a further paper arguing that there has been a systematic increase in hurricane intensity, due to higher sea surface temperatures, appearing in Science, 16 September 2005, pp. 1844-46 by Peter Webster and colleagues. Discussion can be followed at http://www.realclimate.org." This is one of many references to Hurricane Katrina, and one of many citations to the realclimate site (which is also cited in the book to which Dr. Pachauri has contributed a Foreword). However there are no references, either in Dr. Pittock's book or his Notes, to climateaudit.
This is an illustration of the capacity that IPCC and its member governments have to control the flow of information, including to students.
Ian Castles
Louis Hissink
Are you interested having this view published in AIG NEWS?
Armand MacMurray
Very nice! I would enjoy seeing both AW and your Reply published, if only just to clarify both sides' thinking for the scientific community. Though I've not read AW, I get the distinct impression that A&W might be better off if it didn't see the light of day.
"a&w whopper" – guess what's on top of google?
ET SidViscous
Pickles?
It's a trademark you're using Steve. I'd suggest you remove the picture.
A variant on Armand's comment: I suspect that after reading your reply, A&W will want their comment sent back to the trash can.
Russ Steele
Re:13 Steve:
You can go to Google Images and search for "hamburger fries" and you will find multiple images you can use to replace the trademarked image. Even burgers that look more like the A&W style.

redpajama_set_name: RedPajamaCommonCrawl


In my house we go through quite a bit of napkins. There is always something or someone to wipe. After looking around for a bit and finding that really I have more than enough fabric to make a napkin for everyone in the world…not really, but maybe!
Anyways- fabric napkins might be the best thing to do for us. Today I thought I'd share how to make a few quick and simple fabric napkins using one piece of fabric.
This simple trick with the corners is a great way to quickly finished the hemmed outside. You can make multiple napkins at a time and whip right through a pile before you know it.
These napkins can be made with any kind of fabric….they would be super cute to make in custom fabric depending on who is going to use them.
Make a bunch and give them in a little house warming present or an addition to any shower gift you need.
Just make sure that you make enough so there is one for everyone, and there is enough to go in between wash times.
Do you use fabric napkins?
Love Love Love this tutorial! I'm going to try when I get my machine back from repair! I need a hundred or a few more. This looks so much easier than how I have been making them. Thank YOU!
Thanks so much for the tutorial. One of my friends likes cloth napkins, so I make them for her. I have been making double sided napkins, because I could never get the hems on single sided napkins to turn out right. Maybe this will help me be able to make them.
You are so welcome Judy! Thanks for stopping by. Hems are not as hard as we think they are! Good luck!
Very nice, Becky. Thanks for sharing.


Give your sanctuary an instant facelift without breaking your budget with some custom-fit pew cushions. These beautiful, durable pew cushions are an easy way to make older pews look like new, while bringing your congregation some added comfort. Choose from our selection of reversible pew cushions, pew back padding, and flat base cushions for the perfect look and level of comfort to freshen up your worship space.
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We often think that making ourselves holy is all about praying and dedicating ourselves to the Lord. We can also become pure and holy by performing some good deeds towards our faith. Investing in for the development of worship places such as churches and chapels is something that you can do towards your religion and also attain the blessings of the Lord.
To make this spiritual investment in terms of the worldly considerations, get the best church furniture that is not only comfortable as well as stylish. So, when you are looking for such church furniture, it is always better that you go with the pews. This is because pews are much more comfortable and appealing than the simple chairs for a church. Pews are long chairs that were initially considered ideal for their use in grave yards or cemeteries. But with the realizations of their efficiency, pews are being designed for their use in the churches or chapels also. Today, there are even pews that come along with cushions and flexible seats.
They are much more comfortable than the single seats in the church.
They are large, thus give a lot of space. The pews cushions increase the beauty of the furniture.
There are various kinds of pews cushions that come in different textures, giving the furniture a unique appeal.
As the saying goes, 'everything that shines is not gold', the same thing is applicable to the pews cushion chairs too. Not all the pews cushions are beneficial. There are certain things you need to look into while buying the pews cushions. Scroll down to know about them.
While buying pews cushions, there are certain things that do matter a lot to make your choice stand wise.
The Purpose of Buying Them: This may seem a very complex aspect to you. You may wonder that the purpose of buying furniture for church is making a good deed or playing a role in the development of the church, and then what does this factor say about? It is true that you will be great hand in the development of the church and also will collect some blessings by making an investment into church furniture, but don't you want to count in the blessings from the people. The blessings that the people give and the appreciation they show by looking at the comfortable furniture is the whole purpose of buying good chairs. Look for pews cushions that are not only pleasing but also colorful and comfortable.
The Feature of Lumbar Support: Another factor that you need to consider while buying pews cushions is the lumbar support. When we sit on chairs, our lower part of the back reclines to form a curve. This lower part of the skin is called the lumbar region. When buying church furniture, it is very important that you count in the factor of the lumbar support. The pews cushions that have a lumbar support give an additional comfort factor.
They Should be Water Proof or Water Resistant: When you are looking for pews cushions, look for seats that are water proof. It is much possible that you get leather cover pews cushions only of this type. So look for something that is even stylish and water resistant.
They Should have a Foam Density: When you look for pews cushions of foam density, make sure that you pick up something that is very soft, considering all the factors. The pews cushions should be durable and the foam should not destroy on regular use of the pews cushions.
The Price of the Pews Cushions: Another factor that must be considered while buying the pews cushions is the price of the pews cushions. This is very important that you take something that counts in all the aspects above, and also should be reasonable.
When you are looking for church furniture, there are two sources that you can go for; the online church furniture stores or the store that deals in the church furniture sale in the market. Ordering the church furniture online is a much better option as you will not have any efforts of running all around to buy the best church pews cushions.


KB Home goes on using Mickey Mouse and friends to boost sales of new homes.
The builder, one of several hurt by the ongoing housing slump, inked a licensing deal with The Walt Disney Co. to offer home design features based on many of the entertainment company's most popular characters.
Financial terms of the deal with the Disney Consumer Products unit were not disclosed.
KB Home will begin offering the Disney Home features early next year. Customers can choose from flooring, lighting, wall coverings and other products featuring Disney characters.
"It's a very unique proposition that will help us sell homes, will raise our brand and will generate revenue for both companies," said Jeffrey Mezger, KB Home's president and chief executive.
Homebuilders across the country have been grappling with declining sales by slashing prices to lure in buyers.
In June, KB Home reported a loss for the second quarter ending May 31 of $148.7 million (105.26 million EUR), or $1.93 per share. That compared with net income of $205.4 million (145.4 million EUR), or $2.45 per share, in the same quarter in 2006.
Mezger declined to discuss specifics of how the company has been faring more recently, noting it was scheduled to report financial results for the third-quarter on Thursday.
Wall Street analysts were expecting the company to report a loss of 67 cents per share on revenue of $1.52 billion (1.08 billion EUR), according to Thomson Financial.
"There's no question it's tough times for the housing industry," Mezger said, adding that KB Home has survived down cycles before in its 50-year history. "Branding initiatives like this, where you differentiate yourself, we feel are a very strong element to our success."
KB Home shares fell $1, or 4 percent, to $24.09 Wednesday. Shares of Disney rose 45 cents, or 1.3 percent, to $34.52.
Disney stands to benefit from the deal because anyone who would choose to festoon their new home with Disney elements could look to complete the decor with Disney furniture and other products.
Two years ago, KB Home decided to offer homes featuring design elements from Martha Stewart. The move generated "very high" traffic levels and sales, Mezger said.