---
abstract: |
    We validate the performance and accuracy of the current SEGUE (Sloan Extension for Galactic Understanding and Exploration) Stellar Parameter Pipeline (SSPP), which determines stellar atmospheric parameters (effective temperature, surface gravity, and metallicity) by comparing derived overall metallicities and radial velocities from selected likely members of three globular clusters (M 13, M 15, and M 2) and two open clusters (NGC 2420 and M 67) to the literature values. Spectroscopic and photometric data obtained during the course of the original Sloan Digital Sky Survey (SDSS-I) and its first extension (SDSS-II/SEGUE) are used to determine stellar radial velocities and atmospheric parameter estimates for stars in these clusters. Based on the scatter in the metallicities derived for the members of each cluster, we quantify the typical uncertainty of the SSPP values, $\sigma (\rm [Fe/H])$ = 0.13 dex for stars in the range of 4500 K $\le T_{\rm eff} \le 7500$ K and $2.0
    \le \log g \le 5.0$, at least over the metallicity interval spanned by the clusters studied ($-2.3 \le {\rm [Fe/H]} < 0 $). The surface gravities and effective temperatures derived by the SSPP are also compared with those estimated from the comparison of the color-magnitude diagrams with stellar evolution models; we find satisfactory agreement. At present, the SSPP underestimates \[Fe/H\] for near-solar-metallicity stars, represented by members of M 67 in this study, by $\sim$ 0.3 dex.
author:
- 'Young Sun Lee, Timothy C. Beers, Thirupathi Sivarani'
- 'Jennifer A. Johnson, Deokkeun An'
- Ronald Wilhelm
- 'Carlos Allende Prieto, Lars Koesterke'
- Paola Re Fiorentin
- 'Coryn A.L. Bailer-Jones'
- 'John E. Norris'
- Brian Yanny
- Constance Rockosi
- 'Heidi J. Newberg'
- 'Kyle M. Cudworth'
- Kaike Pan
- 
title: 'The SEGUE Stellar Parameter Pipeline. II. Validation with Galactic Globular and Open Clusters'
---

Introduction
============

The Sloan Extension for Galactic Understanding and Exploration (SEGUE) is one of three key projects (LEGACY, SUPERNOVA SURVEY, and SEGUE) in the current extension of the Sloan Digital Sky Survey, known collectively as SDSS-II. The SEGUE program is in the process of obtaining $ugriz$ imaging of some 3500 square degrees of sky outside of the SDSS-I footprint (Fukugita et al. 1996; Gunn et al. 1998, 2006; York et al. 2000; Stoughton et al. 2002; Abazajian et al. 2003, 2004, 2005; Pier et al. 2003), with special attention being given to scans of lower Galactic latitudes ($|b|$ $<$ 35$^{\circ}$) in order to better probe the disk/halo interface of the Milky Way. SEGUE is also obtaining $R$ $\simeq$ 2000 spectroscopy over the wavelength range 3800 $-$ 9200[Å]{} for some 250,000 stars in 200 selected areas over the sky available from Apache Point, New Mexico.

The SEGUE Stellar Parameter Pipeline (hereafter, SSPP) processes the wavelength- and flux-calibrated spectra generated by the standard SDSS spectroscopic reduction pipeline (Stoughton et al. 2002), obtains equivalent widths and/or line indices for 77 atomic or molecular absorption lines, and estimates $T_{\rm
eff}$, log $g$, and \[Fe/H\] through the application of a number of approaches. The current techniques employed by the SSPP include a minimum distance method (Allende Prieto et al. 2006), neural network analysis (Bailer-Jones 2000; Willemsen et al. 2005; Re Fiorentin et al. 2007), auto-correlation analysis (Beers et al. 1999), and a variety of line index calculations based on previous calibrations with respect to known standard stars (Beers et al. 1999; Cenarro et al. 2001a,b; Morrison et al. 2003). The SSPP employs five different methods for estimation of $T_{\rm eff}$, eight for estimation of log $g$, and nine for estimation of \[Fe/H\]. Details of the methods used are discussed in detail by Lee et al. (2007a, hereafter Paper I). The use of multiple methods allows for empirical determinations of the internal errors for each parameter, based on the range of reported values – typical internal errors for stars in the temperature range $4500$ K $\le$ $T_{\rm eff}$ $\le$ 7500 K are $\sim$ 73 K, $\sim$ 0.19 dex, and $\sim$ 0.10 dex, in $T_{\rm eff}$, log $g$, and \[Fe/H\], respectively. Allende Prieto et al. (2007, hereafter Paper III) point out that the internal uncertainties provided by the SSPP underestimate the typical random errors at high signal-to-noise ($S/N$) ratios because most methods in the SSPP make use of similar parameter indicators (e.g., hydrogen lines for effective temperature) and similar atmospheric models. Paper III empirically determines empirically external uncertainties of $\sim$ 130 K, $\sim$ 0.21 dex, and $\sim$ 0.11 dex, for $T_{\rm
eff}$, log $g$, and \[Fe/H\], respectively, by comparison with high-resolution spectroscopy ($7000 < R < 45,000$) of brighter SDSS-I/SEGUE that have been obtained with 8m$-$10m class telescopes. Somewhat larger errors apply to stars with temperatures near the extremes of the range above. The present study of Galactic globular and open cluster stars tests the SSPP’s ability to derive accurate results for stars with a wide range of temperatures and gravities appropriate for metal-poor and near-solar-metallicity stellar populations in the Galaxy, and demonstrates that the derived metallicity scale is identical for dwarfs and giants.

Although the SSPP will continue to evolve in the near future, it has been frozen for now at the version used for obtaining results for stars with suitable data from SDSS Data Release 6 (DR-6; Adelman-McCarthy et al. 2007b). Previous versions of the SSPP have already been used for the analysis of SDSS-I observations. For example, Allende Prieto et al. (2006) report on the application of one of the methods included in the SSPP to some 20,000 F- and G-type stars from SDSS-I DR-3 (Abazajian et al. 2005). Beers et al. (2006) have compiled a list of over 6000 stars with \[Fe/H\] $< -2.0$ (including several hundred with \[Fe/H\] $< -3.0$), based on application of the present SSPP to some 200,000 stars from SDSS-I DR-5 (Adelman-McCarthy et al. 2007a). Carollo et al. (2007) reports on an analysis of the kinematics of relatively bright stars from SDSS-I that have been used as calibration objects during the main survey.

In this paper, the second in the SSPP series, we show that estimates of the atmospheric parameters and radial velocities obtained by the SSPP for stars with a reasonable likelihood of membership in previously studied Galactic globular and open clusters are sufficiently accurate to justify the use of the present SSPP parameters for carrying out detailed studies of the halo and thick-disk populations of the Milky Way. In deriving the overall iron abundance for each cluster, we assume it comprises a chemically homogenous population. In §2, the photometric and spectroscopic data obtained for M 13, M 15, M 2, NGC 2402, and M 67 are described. Section 3 presents the methods used to separate likely cluster members from field stars in the directions toward these clusters. Best estimates of the overall \[Fe/H\] and radial velocity of each cluster are derived in §4. In §5 we compare the SSPP determinations of $T_{\rm eff}$ and log $g$ for selected member stars in each cluster with their expected positions on color-magnitude diagrams. A summary and brief conclusions are provided in §6.

Photometric and Spectroscopic Data
==================================

Galactic globular and open clusters are nearly ideal testbeds for validation of the stellar atmospheric parameters estimated by the SSPP. In most clusters, it is expected that their member stars were born simultaneously out of well-mixed, uniform-abundance gas at the same location in the Galaxy. Therefore, with the exception of effects due to post main-sequence evolution, primordial variations in carbon and nitrogen, or contamination from binary companions that have transferred material, the member stars should exhibit very similar elemental abundance patterns. Three of the clusters in our study, M 13, M 15, and M 2, have well-known CN variations that extend to the main-sequence turnoffs (Smith & Briley 2006 for M13; Cohen, Briley, & Stetson 2005 for M15; Smith & Mateo 1990 for M2). However, these abundance variations can be ignored when deriving metallicities from regions of the spectra that do not include CH, CN, or NH features, as is the case with most of our techniques (those that may be affected by the presence of such features are automatically de-selected in the determination of the adopted \[Fe/H\]).

True cluster members should exhibit small radial velocity differences with respect to their parent clusters. Furthermore, it is possible to examine theoretical predictions of temperatures and surface gravities for member stars that lie along the cluster main sequence (MS), red giant branch (RGB), or horizontal branch (HB) in color-magnitude diagrams (CMDs). As part of tests of the SEGUE star-selection algorithm (Adelman-McCarthy et al. 2007b) and the SSPP, and during normal SEGUE operation, we have obtained $ugriz$ photometry and medium-resolution (2.3 [Å]{}; $R$ = 2000) spectroscopy for large numbers of stars along lines of sight toward the globular clusters M 13, M 15, and M 2 and the open clusters NGC 2420 and M 67. Below we discuss these photometric and spectroscopic data in more detail.

Photometric Data
----------------

The SDSS obtains scans of the sky using the ARC 2.5m telescope on Apache Point, New Mexico. These data are collected in five broad bands ($u, g, r, i, z$) with central wavelengths 3551, 4686, 6166, 7480, and 8932[Å]{} (Fukugita et al. 1996), respectively, using an imaging array of 30 ($6 \times 5$) 2048 $\times$ 2048 Tektronix CCDs (Gunn et al. 1998). The pixel size is 24 $\mu$m, corresponding to $0.396{''}$ on the sky. A series of software procedures, collectively known as the SDSS PHOTO pipeline (Lupton et al. 2001), processes and reduces the scanned images shortly after data are obtained. As part of these procedures, the instrumental fluxes and astrometric positions (Pier et al. 2003), as well as a determination of whether an object is likely to be stellar (i.e., a *point source*), or not (an *extended* source) are obtained. Afterwards, the photometric data are further calibrated by matching to brighter known standards observed with a smaller calibration telescope on Apache Point (Hogg et al. 2001; Smith et al. 2002; Tucker et al. 2006). The processed photometric data have been shown to exhibit 2% relative and absolute errors (0.02 magnitudes) in $g$, $r$, and $i$, and $3 \%-5 \%$ errors in $u$ and $z$ for all stellar objects brighter than $g = 20$ (Stoughton et al. 2002; Abazajian et al. 2004, 2005; Ivezic et al. 2004). The first-pass photometric data for each of the clusters used in the present study were secured by querying the DR-3 (Abazanjian et al. 2005), DR-5 (Adelman-McCarthy et al. 2007a), and DR-6 (Adelman-McCarthy et al. 2007b) releases from the SDSS Catalog Archive Server (CAS).

Figure 1 illustrates one of the primary challenges in working with data for clusters obtained with SDSS – the automated PHOTO pipeline (Lupton et al. 2001) was not designed to adequately deal with crowded fields such as the central regions of globular clusters. As a result, essentially all of the stars in this region (which are by definition the most likely ones to be cluster members) do not have reported apparent magnitudes in the SDSS CAS. To circumvent this limitation as much as possible, we have instead performed crowded field photometry for the center of the clusters, using the DAOPHOT/ALLFRAME suite of programs (Stetson 1987; Stetson 1994) in IRAF[^1]. A full description of the methods used and the photometric measures obtained is provided by Johnson et al. (2007). Briefly, DAOPHOT was run on each image, and the five images of each field (one for each filter) were then simultaneously run through ALLFRAME. DAOGROW (Stetson 1990) was used to derive aperture corrections to the point-spread-function photometry for the SDSS aperture radius of 7.4 arcsecs. Finally, the zeropoint term from the [*tsField*]{} files was applied to calibrate the data. This procedure also permits a check on the techniques used by the SDSS PHOTO pipeline in regions outside the cluster where the areal density of sources on the sky is sufficiently low that it may be used.

After completing the above procedures, we finally combine the results from the PHOTO pipeline with those from the crowded-field photometry to obtain an almost complete catalog of $ugriz$ photometry for stars in the region of each of our program clusters. All photometric data are corrected for extinction and reddening by application of the Schlegel, Finkbeiner, $\&$ Davis (1998) maps. The average reddening ($E(B-V)$) for stars in the direction of these clusters is 0.017, 0.110, 0.045, 0.041, 0.032 for M 13, M 15, M 2, NGC 2420, and M 67, respectively. Comparing with the literature values listed in Table 1, most of the average reddenings of the clusters agree within about 0.02 mags.

Spectroscopic Data
------------------

The spectroscopy discussed in the present paper was obtained during the course of SEGUE tests and normal SEGUE observations. In normal SEGUE operation mode, a pair of plug-plates (referred to as the “bright” and “faint” plates) are obtained over the $3^{\circ}$ field of the ARC 2.5m. A total of 640 optical fibers are employed to obtain $R=2000$ spectra for on the order of 600 program stars for each plate (the remaining fibers are used for spectrophotometric and reddening calibration objects and observations of the night sky). The exposure time depends on observation conditions. For a bright plate, exposures are set to achieve a total $(S/N)^{2} >$ 15/1 from the two blue-side CCDs on the SDSS spectrographs; the exposure for a faint plate is set such that a total $(S/N)
^{2} >$ 50/1 for all four (red and blue CCDs) on the SDSS spectrographs is achieved. In order to identify and remove cosmic ray hits, each plate must have at least three exposures; the integration time for any single exposure is not longer than 30 minutes. For the purposes of targeting objects on these plates, the boundary between the bright and faint plates is set at $r \sim$ 18.0. The data thus obtained are processed through the SDSS spectroscopic pipeline software (SPECTRO2D and SPECTRO1D), which produces wavelength and flux-calibrated spectra, and also obtains estimates of radial velocities and line indices (Stoughton et al. 2002). Tests of the quality of stellar radial velocities from the SSPP (which uses initial estimates from the SDSS processing pipelines) indicate precisions better than 5 km s$^{-1}$ are achieved for brighter stars, with zero-point offsets of no more than a few km s$^{-1}$, respectively (Paper III). These errors degrade for fainter stars, as expected.

An initial set of candidate member stars of the globular and open clusters studied in the present paper were selected on the basis of photometric and astrometric data (proper motions) from the literature. The central cores of the clusters were not targeted because the PHOTO pipeline does not resolve the very crowded fields into single star detections, and also due to limitations on the separations of the fibers during the spectroscopic follow-up stage. The primary method for selecting member candidates was performed by plotting a photometric CMD for a given cluster, and choosing stars from regions of this diagram that correspond to location on the MS turnoff or RGB of the cluster. An additional list of bright stars for M 15 and M 2 with previously available proper motions consistent with membership in the clusters was provided by Cudworth (1976 and private communication) and Cudworth $\&$ Rauscher (1987). Other stars in the fields of these clusters were used to fill spectroscopic fibers using the default SEGUE target selection algorithm (Adelman-McCarthy et al. 2007b). While many of these additional targets turned out to be stars from the general field populations, a significant fraction turned out serendipitously to be members of the clusters.

For M 13, three specially designed plates were obtained. Two of the three plates followed the standard SEGUE target selection procedure (Adelman-McCarthy et al. 2007b) of sampling stars with a variety of spectral types based on the SDSS imaging and PHOTO processing. An additional set of likely M 13 members, including several stars that were saturated in the SDSS image ($r < 14.5$) and with coordinates from Cudworth $\&$ Monet (1979) and Cudworth (private communication), were added to the target list with high priority (bumping ordinary SEGUE targets), in order to obtain spectra of several likely giant-branch and horizontal-branch members.

In the case of NGC 2420, the stars chosen for spectroscopy were primarily targeted from the SDSS photometry obtained by the PHOTO pipeline, using the normal SEGUE target selection algorithm. Additional stars with apparent magnitudes in the range 14.5 $< g <$ 20.5 that fell within 0.5 degrees from the center of NGC 2420 were also targeted for spectroscopy. However, due to crowding, if two objects were within 55${''}$ of one another, then only one received a fiber. Thus, not every star in the central region of NGC 2420 was targeted. There were about 480 objects selected in this way, including a number of non-cluster members that are located in the NGC 2420 field.

For M 67, the initial targets came from the SDSS imaging data processed by the PHOTO pipeline. However, for this cluster, many candidate members with positions, magnitudes, and colors from the WEBDA (http: //www.univie.ac.at/webda/) catalogs were added to the target lists. The bright targets (with $r < 14$) saturate the SDSS imaging camera, so these were added from the literature (Sanders 1989; Fan et al. 1996). Such bright stars normally saturate a regular SDSS spectroscopic exposure, so there were exposed for shorter than normal. About 200 very bright stars between about 12 $<$ $g$ $<$ 14 were targeted.

In total, we obtained SDSS spectroscopy for 1920, 1280, 640, 1280, and 640 targets, including sky spectra and calibration object spectra, in the fields of M 13, M 15, M 2, NGC 2420, and M 67 respectively. The reduced spectra were then processed through the SSPP in order to estimate $T_{\rm eff}$, log $g$, and \[Fe/H\], among other quantities. Table 1 summarizes the global properties of the clusters under consideration in this paper, taken from the compilation of Harris (1996) for the globular clusters and from WEDBA or Gratton (2000) for the open clusters.

Radial Velocities
-----------------

There are two estimated radial velocities provided from the SDSS spectroscopic pipeline. One is an absorption redshift obtained by cross-correlating the spectra with templates that were obtained from SDSS commissioning spectra (Stoughton et al. 2002). Another comes from matching the spectra with ELODIE template spectra (Prugniel $\&$ Soubiran 2001). In most cases the velocity based on the ELODIE template matches appears to be the best available estimate, as spectra of “quality assurance” stars with multiple measurements show the most repeatable values for this estimator. However, this is not always the case. We proceed to select the best available velocity in the following manner. If the velocity determined by comparison with the ELODIE templates has a reported error of 20 km s$^{-1}$ or less then this velocity is adopted. If the error from the ELODIE template comparison is larger than 20 km s$^{-1}$, and the relative offset between the two radial velocities is less than 40 km s$^{-1}$, we take an average of the two. If none of the criteria above are satisfied, which happens only rarely, and mainly for quite low $S/N$ spectra, or for hot/cool stars without adequate templates, we obtain the calculated radial velocity from a custom routine that examines the wavelengths of a number of prominent absorption features. If none of these methods yield a reasonable estimate of radial velocity, or it appears spurious (i.e., falls outside of the range $\pm 1000$ km s$^{-1}$), we simply ignore the star in subsequent analyses. A more detailed description of the procedures used for determination of the best available radial velocity, and of zero-point offsets of the radial velocities, can be found in Paper I.

Membership Selection from the Spectroscopic Samples
===================================================

Owing to an insufficient number of stars with available spectroscopy for each cluster, it is not possible to obtain a well-defined Color Magnitude Diagram (CMD) based solely on spectroscopically confirmed member stars. Thus, we make use of photometric data in the field of each cluster, and describe below how we obtain a relatively clean CMD for individual clusters, and select likely member stars from the spectroscopic data.

Likely Member Star Selection for Globular Clusters
--------------------------------------------------

One of the primary issues that one needs to address when creating a CMD, or selecting likely member stars, for a star cluster is removal of contamination from field stars. In order to approximately isolate the likely cluster members from the field stars we have made use of the CMD mask algorithm described by Grillmair et al. (1995). We illustrate the basic idea by application of this algorithm to the M 13 field shown in Figure 1. We first select all stars inside the estimated tidal radius (25.2$^{'}$; Harris 1996), shown as the innermost green circle in Figure 1. This is regarded as the cluster region. The red dots represent stars with available photometry from the SDSS PHOTO pipeline (Lupton et al. 2001); the black dots are stars with photometry obtained from DAOPHOT. The blue open circles indicate stars with available spectroscopy. We then choose an annulus outside the cluster region, indicated on the Figure as the region between the two black circles, as the field or background region.

We next obtain CMDs of each region, spanning $-1.0 \le (g-r)_0 \le 1.5$ and $12
\le g_0 \le 22$, and then subdivide these diagrams such that the size of each sub-grid is 0.2 mag wide in $g_0$ and 0.05 mag wide in $(g-r)_0$ color. The total number of sub-grids for the CMDs in each region is thus 2500 (50$\times$50). Figure 2 shows the resulting CMDs of the cluster (left panel) and field (right panel) regions, overplotted with squares representing the selected sub-grids, obtained as described below.

We first calculate the signal-to-noise ($s/n$) in each preliminary sub-grid by application of Eqn. (1) over the entire CMD region shown in Figure 2. Here we assume that the field stars outside the tidal radius are uniformly distributed throughout the annulus area.

$$s/n(i,j) = \frac{n_{c}(i,j) - gn_{f}(i,j)}{\sqrt{n_{c}(i,j) + g^{2}n_{f}(i,j)}}.
\label{eq1}$$

In the above, $n_{c}$ and $n_{f}$ refer to the number of stars in each sub-grid with color index $i$ and magnitude index $j$, counted within the cluster region and field region, respectively. The parameter $g$ represents the ratio of the cluster area to the field area.

The following procedures are followed in order to find the optimal range of colors and magnitudes that correspond to the likely members of each cluster. First, we sort the elements of $s/n(i,j)$ in descending order, so that we obtain a one-dimensional array of $s/n(i,j)$ with index $l$; the array element with the highest $s/n(i,j)$ corresponds to $l=1$. The next step is to obtain star counts in gradually larger regions of the CMDs. The accumulated area is represented as $a_{k} = ka_{l}$, where $a_{l} = 0.01$ mag$^{2}$, which is the same for all sub-grids, and is the area of a single sub-grid in the CMD array, and the $k$ is the number of sub-grids to combine. Finally, the cumulative signal-to-noise ratio, $S/N(a_{k}) $, as a function of $a_{k}$, is calculated from:

$$S/N(a_{k}) = \frac{N_{c}(a_{k}) - gN_{f}
(a_{k})}{\sqrt{N_{c} (a_{k})  + g^{2} N_{f} (a_{k})}}
\label{eq3}$$

where,

$$N_{c}(a_{k}) = \sum_{l=1}^{k} n_{c}(l), ~~~N_{f}(a_{k}) = \sum_{l=1}^{k} n_{f}(l) \label{eq4}$$

The parameter $n_{c}(l)$ denotes the number of stars within the cluster region having ordered color-magnitude index $l$; $n_{f}(l)$ represents the same quantity for the field region. Based on the maximum value of $S/N(a_{k})$, a threshold value of $s/n$ is picked in order to select high- contrast surface-density areas (i.e, high $s/n$) between the cluster and field regions. These are considered to be the sub-grids that contain likely cluster members. After removing single-star events in areas of the CMDs where the field-star density is low, all stars in sub-grids with $s/n(i,j)$ greater than the threshold value of $s/n$ are selected. These stars are considered as the photometrically likely member stars for a given cluster.

The red squares shown in the left panel of Figure 2 are the sub-grids with $s/n$ greater than the threshold value; the corresponding sub-grids in the field region are shown as green squares in the right panel of this Figure. Figure 3 depicts the CMD of the selected likely members of M 13 from the photometric data, shown as black dots. The same procedures are performed to differentiate the likely member stars of M 15 and M 2 from the photometric sample.

We now proceed to select the stars that are likely members of the globular clusters from the available spectroscopic sample. This step begins by selection of the stars within the cluster tidal radii that pass the photometric criterion for membership, based on their location on the cluster CMDs according to the algorithm described above.

Figure 3 displays the cleaned CMD of M 13, overplotted with the likely members from the spectroscopic sample (shown as red circles). The same procedures are carried out to identify likely member stars of M 15 and M 2 from their spectroscopic data. Based on these cuts, at this stage of the analysis there are 296 (338) likely members for M 13, 124 (160) for M 15, and 21 (22) for M 2 identified. In the above, the first listed numbers indicate the stars with available estimates of \[Fe/H\] from the SSPP, while the quantities in parentheses represent the number of stars with available radial velocities (RVs). Additional cuts, based on the derived metallicity estimates and RVs, are described in §4.

Likely Member Star Selection for Open Clusters
----------------------------------------------

Since the fields of nearby open clusters are not as crowded as those of globular clusters, the signal-to-noise ratio between the cluster region and the background region is not sufficiently high to select likely cluster members by means of the CMD mask algorithm. As an alternative, we first obtain a fiducial line for an open cluster (including its main sequence and sub-giant branch, if it exists) by use of an robust polynomial fitting procedure. As an example, Figure 4 shows the CMD of the NGC 2420 field inside a radius of 0.3 degrees from the center of the cluster. According to the open cluster catalog of Dias et al. (2002), the apparent diameter of this cluster is only 5$^{'}$ on the sky, but we prefer to adopt a 20$^{'}$ radius, in order to include as many member stars as possible. The red line is the fiducial line derived from the robust polynomial fit. The blue lines are the upper and lower limits (fiducial $\pm$ 0.06 dex in $(g-r)_{0}$), determined by eye. Stars from the spectroscopic sample that fall within the 20$^{'}$ radius and inside the blue limit lines in Figure 4 are identified.

A similar procedure is applied to M 67, except that a 30$^{'}$ (apparent diameter of 25$^{'}$; Dias et al. 2002) radius and fiducial $\pm$ 0.10 mag in $(g-r)_{0}$ is used. Based on this selection method, there are 195 (234) and 61 (64) for NGC 2420 and M 67, respectively. The first listed numbers indicate the stars with available estimates of \[Fe/H\] from the SSPP, while the quantities in parentheses represent the number of stars with available radial velocities (RVs) . Additional cuts, based on the derived metallicity estimates and RVs, are described below.

Determination of Overall Metallicities and Radial Velocities of the Clusters
============================================================================

In order to investigate the accuracy of our derived metallicities and RVs, we now consider the global distribution of these parameters obtained from the current version of the SSPP for the likely cluster members. In this section, we describe a method to best isolate “true member stars” from the spectroscopic samples described above. We then use these subsamples to determine our best estimates of the overall metallicities and RVs of the clusters considered in this study.

Selection of True Members
-------------------------

We establish the criteria for carrying out metallicity and RV cuts as follows. The left panel of Figure 5 illustrates the \[Fe/H\] distribution for three different subsamples of stars. The first, shown as the black dot-dashed line, represents the distribution of derived metallicities for the 1547 stars with available estimates of \[Fe/H\] along the line of sight to M 13. Note that this distribution includes numerous stars that cannot be considered members of the cluster, as they cover a much wider range of \[Fe/H\] than might be expected if they were drawn exclusively from the cluster member population. The dot-dashed line in the right panel of Figure 5 shows the RV distribution of these same stars.

The red dashed line in the left panel of Figure 5 is the distribution of \[Fe/H\] for the 296 likely members selected from the spectroscopic sample as described above. We obtain a Gaussian fit to the [*highest peak*]{} of the distribution of these stars (solid blue line in Figure 5), and obtain an estimate of the mean ($<$\[Fe/H\]$>$) and standard deviation ($\sigma$) for this distribution. Similar fits are obtained for the distribution of RVs for the likely members shown in the right panel of Figure 5. On the basis of these fits, we now trim likely outliers by application of a 2-$\sigma$ clipping procedure, for example:

$$\rm <[Fe/H]> - 2\sigma_{\rm [Fe/H]} \leq \rm [Fe/H]_{\star} \leq
\rm<[Fe/H]> + 2\sigma_{\rm [Fe/H]} \label{eq6}$$

$$\rm <RV> - 2\sigma_{\rm RV} \leq \rm RV_{\star} \leq \rm<RV> +
2\sigma_{\rm RV} \label{eq7}$$

In the above, \[Fe/H\]$_{\star}$ and RV$_{\star}$ correspond to the values of these parameters for each star under consideration. The stars surviving both of these clips are considered true cluster members for the purpose of this study. Note that at no point have we considered the external “known” values of \[Fe/H\] and RV for the clusters as a whole.

Based on the application of these membership cuts, we now have a total of 169 stars identified as true members of M 13, 63 stars as true members of M 15, 9 stars as true members of M 2, 195 stars as true members of NGC 2420, and 51 stars as true members of M 67. The distribution of \[Fe/H\] and RV for the surviving members of M 13 are shown as green histograms in the left and right panels of Figure 5, respectively. Similar plots for M 15, M 2, NGC 2420, and M 67 are shown in Figures 6, 7, 8, and 9, respectively. The distribution of \[Fe/H\] for the selected true member stars of each cluster, as a function of $T_{\rm eff}$, is shown in Figure 10.

Table 2 summarizes the results of the above exercise. Column (1) lists the cluster name. Columns (2) and (3) are the lower and upper limits for the 2-$\sigma$ cuts on \[Fe/H\], respectively. Columns (4) and (5) are the corresponding adopted limits on RV used for these cuts.

Tables 4$-$8 list the observed and derived quantities for all of the individual stars considered as true member stars in the analysis of each cluster. The columns are as defined in the table notes for Table 4.

Determination of Overall Estimates of Mean Cluster Metallicity and Radial Velocity
----------------------------------------------------------------------------------

We now obtain final estimates of the cluster metallicities and RVs based on Gaussian fits to the surviving true member stars for each cluster, as shown by the blue curves in Figures 5$-$9. Table 2 summarizes these determinations. The mean metallicity and 1-$\sigma$ spread of the metallicities of the true member stars are listed in columns (6) and (7), respectively. Similar quantities for the RVs are listed in columns (8) and (9). Column (10) lists the total number of true member stars associated with each cluster, based on our analysis. External estimates of the metallicities and RVs for these clusters, adopted from the Harris (1996) compilation for M 13, M 15, and M 2 and from WEBDA (and references therein) for NGC 2420 and M 67, are listed in columns (11) and (12). Column (13) lists metallicity estimates for these clusters obtained from high-resolution spectroscopy of a limited number of brighter stars by Kraft & Ivans (2003) for M 15 and M 13, Ivans (private communication) for M 2, and Gratton (2000) for NGC 2420 and M 67.

For M 13, our estimate of the mean abundance, $<$\[Fe/H\]$>$ = $-1.56$, is very close to the Harris (1996) estimate (\[Fe/H\]$_{\rm H}$ = $-$1.54). However, the recent study of Kraft & Ivans (2003) reported a revised cluster abundance for M 13, derived from high-resolution spectroscopy of 28 giants. Their value indicates a metallicity for M 13 that is a bit lower than that given by Harris, \[Fe/H\]$_{\rm HR}$ = $-$1.63, and is lower by 0.07 dex than our estimate. Cohen & Mel$\acute{\rm e}$ndez (2005) reported \[Fe/H\] = $-1.50$ from a high-resolution ($R$ = 35,000) analysis of a sample of 25 stars, consisting of stars from the giant branch to near the main-sequence turnoff. Our derived spread in the metallicities of the M 13 true member stars (0.16 dex) is also satisfyingly low, especially considering the wide range of temperatures for true members that are considered here. Our estimate of the mean radial velocity, $<$RV$>$ = $-$245.1 km s$^{-1}$, with a standard deviation of 8.7 km s$^{-1}$, is in good agreement with that given by Harris ($-$245.6 km s$^{-1}$). It is important to note that, as mentioned in Paper I, we have already added $+$7.3 km s$^{-1}$ to all DR-6 (Adelman-McCarthy et al. 2007b) stellar radial velocities. Before the adjustment of this offset, an average offset of $-$8.6 km s$^{-1}$ for M 13 and $-$6.8 km s$^{-1}$ for M 15 is obtained. Thus, together with an offset of $-$6.6 km s$^{-1}$ that was obtained from a preliminary result of a high-resolution spectroscopic analysis of SDSS-I/SEGUE stars (Paper III) before DR-6 (Adelman-McCarthy et al. 2007b), we derived an average offset of $-$7.3 km s$^{-1}$. However, a recent high-resolution spectroscopic analysis of SDSS-I/SEGUE stars indicates an offset of about $-$6.9 km s$^{-1}$, resulting in an average of $-$7.4 km s$^{-1}$, Hence, in future data releases (e.g, DR-7), this very minor difference might be reflected. For the analysis of our clusters, all radial velocities have been corrected by $+$7.3 km s$^{-1}$, in order to be consistent with DR-6.

Our estimate of the mean abundance of M 15, $<$\[Fe/H\]$>$ = $-2.12$, is close to the value listed by Harris (\[Fe/H\]$_{\rm H}$ = $-$2.26). While Kraft $\&$ Ivans (2003) obtained \[Fe/H\]$_{\rm HR}$ = $-$2.42, based on high-resolution spectroscopy for nine giants in this cluster, Otsuki et al. (2006) reported \[Fe/H\] = $-$2.29 from an analysis of high-resolution spectra for six giants belonging to this cluster. Our derived spread in the metallicities of true member stars in M 15 is quite low (0.14 dex). Our estimate of the mean radial velocity, $<$RV$>$ = $-$107.4 km s$^{-1}$, with a standard deviation of 10.5 km s$^{-1}$, agrees very well with that of the Harris (1996) value ($-$107.0 km s$^{-1}$).

There are only a very small number of true member stars (9) for M 2. Their average metallicity, $<$\[Fe/H\]$>$ = $-$1.58, is similar to the Harris (1996) value (\[Fe/H\]$_{\rm H}$ = $-$1.62), and is in very good agreement with the value obtained by Ivans (private communication) (\[Fe/H\]$_{\rm HR}$ = $-$1.56). The estimated spread in our derived metallicities, 0.08 dex, is quite small. Our estimate of the mean radial velocity, $<$RV$>$ = $+$0.4 km s$^{-1}$, with a standard deviation of 7.7 km s$^{-1}$, is higher (by about 6 km s$^{-1}$) than that provided by Harris ($-$5.3 km s$^{-1}$). Clearly, for the purposes of validation of the SSPP, it would be highly desirable to obtain a larger number of member stars in M 2; a new plate (640 spectra) will be obtained in the near future. Note that M 2 presents a special challenge, since its mean metallicity is quite close to that expected for members of the field halo population, while its radial velocity is buried in the peak of foreground disk stars. Our stringent criterion for true cluster members should remain effective, however, since few non-cluster members will fulfill both the RV and metallicity criteria.

There are 130 true member stars selected for the open cluster NGC 2420. The mean iron abundance of the selected true member stars is $<$\[Fe/H\]$>$ = $-$0.46, which is in excellent agreement with the value (\[Fe/H\] = $-$0.44) determined by Gratton (2000) from high-resolution spectroscopy of one member star. Friel $\&$ Janes (1993) reported \[Fe/H\] = $-$0.42 for nine member stars, based on medium- and low-resolution spectroscopic data. Friel et al. (2002) determined \[Fe/H\] = $-$0.38 $\pm$ 0.07, based on medium-resolution spectra of 20 member stars. Most of these literature values are within the spread of our derived value. The derived spread in the metallicities of true member stars (0.12 dex) is very low. The radial velocity for NGC 2420 listed in Table 2, ($+74.0$ km s$^{-1}$), is an average of the values $+84.0$ km s$^{-1}$, $+71.1$ km s$^{-1}$, and $+67.0$ km s$^{-1}$ from Friel (1989), Scott et al. (1995), and Rastorguev et al. (1999), respectively. This value agrees very well with our derived estimate of $+74.8$ km s$^{-1}$, with a standard deviation of $6.2$ km s$^{-1}$.

For M 67, 51 stars are identified as true member stars. A mean metallicity of $<$\[Fe/H\]$> = -$0.35 is derived, with a small spread of 0.15 dex. This derived $<$\[Fe/H\]$>$ differs by 0.37 dex from that of Gratton (2000), \[Fe/H\] = $+$0.02, who derived this value from a high-resolution study of one member star. Randich et al. (2007) analyzed 10 member stars of this cluster, based on high-resolution ($R \sim 45,000$) spectroscopy, and derived \[Fe/H\] = $+0.03 \pm 0.01$. \[Fe/H\] = $+0.02 \pm 0.03$ was determined by Yong et al. (2005) from a high-resolution spectroscopic analysis of three member stars. However, based on medium-resolution spectra of 25 members, Friel et al. (2002) reported \[Fe/H\] = $-0.15 \pm 0.05$. Other catalogs of open clusters (e.g., Twarog et al. 1997; Chen et al. 2003) also report a solar metallicity for this cluster. The literature values based on high-resolution spectroscopic analyses clearly suggest that the present SSPP tends to under-estimate \[Fe/H\] by about 0.3 dex for near-solar-metallicity stars. This is perhaps related to the difficulties arising from the strong atomic and molecular lines (and possibly unreliable synthetic spectra) for metal-rich stars. As mentioned by Gratton (2000), it might be desirable to re-calibrate the metallicity scale used for the analysis of medium-resolution spectra for stars with the solar iron abundance to better match the results obtained from high-resolution analyses. The radial velocity of $+32.9$ km s$^{-1}$ for M 67 from the literature listed in Table 2 (the average of the Scott et al. 1995; Friel $\&$ Janes 1993; Rastorguev et al. 1999 values) agrees with our derived mean radial velocity of $+34.9$ km s$^{-1}$ within the standard deviation of our measurements, 5.6 km s$^{-1}$.

Thus, taking into account only the scatter in the metallicities and radial velocities calculated from the members of each cluster, we are able to derive estimates of typical external uncertainties for the SSPP values, $\sigma (\rm [Fe/H])$ = 0.13 dex, and $\sigma (\rm RV)$ = 7.7 km s$^{-1}$ (after 5$\sigma$ clipping is applied).

A Comparison of Derived $T_{\rm eff}$ and log $g$ for True Cluster Members with Color-Magnitude Diagrams
========================================================================================================

In the previous section, we have considered the accuracy with which the SSPP obtains estimates of metallicity and radial velocity. We now consider the accuracy with which the SSPP obtains estimates of effective temperatures, $T_{\rm eff}$, and surface gravities, log $g$. One excellent “global” test of these estimates is to examine the locations of the true member stars on the observed CMD (based on the totality of likely photometric member data) for each cluster. One can also compare with corresponding theoretical CMDs.

Figures 11$-$15 show plots of the SSPP-estimated temperatures and gravities for true member stars superposed on the photometrically cleaned CMDs for each of our clusters. Note that in order to obtain the theoretical temperature scales (shown along the top of the left-hand panels in each Figure), we make use of a linear relation between $(g-r)_0$ color and $T_{\rm eff}$ by performing a least square fit in this plane to the theoretical models of Girardi et al. (2004). We choose the isochrones from this study that have the closest \[Fe/H\] to the derived metallicity of each cluster, and adopt an age of 13.5 Gyr for the globular clusters, 2.2 Gyr for NGC 2420, and 4.3 Gyr for M 67 (adopting the ages from WEBDA for the open clusters). A similar procedure is applied for transforming the $g_0$ magnitude to a theoretical log $g$ scale (shown along the far right axis in the right-hand panels of each Figure). Distance moduli from the Harris (1996) compilation for the globular clusters and WEBDA for the open clusters (also listed in Table 1 of this study) are used in order to compute apparent magnitudes.

In these Figures, we plot the SSPP-estimated parameters for true member stars in different colors, corresponding to different ranges of temperature and surface gravity (as shown in the legend for each plot). Each color represents a range of 500 K in $T_{\rm eff}$ and 0.5 dex in log $g$. The effective temperature estimated by the SSPP appears in excellent agreement for most of the true member stars, with only a few exceptions. Such stars could either be outright errors in SSPP predictions, or could just be foreground/background stars that survived the various membership cuts we have applied. Inspection of the Figures also reveals the presence of a few stars close to the main-sequence TO in M 13 and M 15 that appear to have slightly lower SSPP-estimated log $g$ than expected from the theoretical scale. The surface gravities of stars along the RGB appear to be very well estimated. Such behavior is perhaps to be expected, since the stars close to the TO region are at the low end of the $S/N$ range that we accept for analysis, and thus are subject to greater errors in the determination of their atmospheric parameters. The RGB stars are among the brightest, and hence are likely to have the best-determined estimates.

Inspection of Figure 14 for NGC 2420 indicates that gravity estimates for most of the main-sequence stars are well-estimated from the SSPP, with the exception of the faintest stars. These stars have only low $S/N$ spectra available, resulting in higher uncertainties in determinations of their surface gravities. It should also be recalled that surface gravity is a difficult parameter to estimate, especially from spectra of the resolving power obtained by the SDSS. Overall, we are pleased to see as good a behavior in the estimates of this parameter as is demonstrated in Figures 11$-$15.

In addition, using the derived relations between $(g-r)_0$ and $T_{\rm eff}$, and $g_0$ and log $g$ from the isochrones, we predicted $T_{\rm eff}$ and log $g$ from the observed $(g-r)_0$ and $g_0$, respectively. Table 3 lists the averages and standard deviations of the residuals of the effective temperatures and surface gravities between the SSPP estimates and the calculated values. Even though we have employed a simple relationship between $(g-r)_0$ with $T_{\rm
eff}$, we see good agreement between the SSPP estimates and the theoretical values in $T_{\rm eff}$. Although, as expected, we notice a rather large offset and scatter in the gravity, indicating a more complex function is needed, the scatters are still within each bin size (0.5 dex) in Figures 11$-$15. M 2 exhibits a larger scatter in both $T_{\rm eff}$ and log $g$ than the other clusters, owing to the small number of member stars selected.

Summary and Conclusions
=======================

Based on photometric and spectroscopic data reported in SDSS-I and SDSS-II/SEGUE, we have examined estimates of stellar atmospheric parameters and heliocentric radial velocities obtained by the SEGUE Stellar Parameter Pipeline (SSPP) for likely members of three Galactic globular clusters, M 13, M 15, and M 2, and two open clusters, NGC 2420 and M 67, and compared them with those obtained by external estimates for each cluster as a whole.

From the derived scatters in the metallicities and radial velocities obtained for the likely members of each cluster, we quantify the typical external uncertainties of the SSPP-determined values, $\sigma (\rm [Fe/H])$ = 0.13 dex, and $\sigma (\rm RV)$ = 7.7 km s$^{-1}$, respectively. These uncertainties apply for stars in the range of 4500 K $\le T_{\rm eff} \le 7500$ K and $2.0 \le \log
g \le 5.0$, at least over the metallicity interval spanned by the clusters studied ($-2.3 \le {\rm [Fe/H]} < -0.4$). Therefore, the metallicities and radial velocities obtained by the SSPP appear sufficiently accurate to be used for studies of the kinematics and chemistry of the metal-poor and moderately metal-rich stellar populations in the Galaxy. We have also confirmed that $T_{\rm eff}$ and log $g$ are sufficiently well-determined by the SSPP to distinguish between different luminosity classes through a comparison with theoretical predictions.

A comparison of the analysis of the available high-resolution spectroscopy of SDSS-I/SEGUE stars (Paper III) with the SSPP predictions indicates that the uncertainty in radial velocities adopted by the SSPP is no more than 5 km s$^{-1}$ (after adjusting for an empirical offset of +7.3 km s$^{-1}$). The empirically determined precisions in estimated atmospheric parameters are $\sim$ 130 K for effective temperature, $\sim$ 0.21 dex for surface gravity, and $\sim$ 0.11 dex for \[Fe/H\]. These errors apply to the brightest stars obtained by SDSS-I/SEGUE observations, on the order of $14.0 \le g \le 15.5$, and are expected to degrade somewhat for fainter stars. We also found that the SSPP tends to underestimate \[Fe/H\] for near-solar-metallicity stars (represented by members of M 67 in this study), by $\sim$ 0.3 dex.

In future papers we will compare the predictions of the SSPP with intermediate-metallicity clusters (\[Fe/H\] $\sim$ $-$0.7) and with additional near-solar-metallicity populations, as sampled by metal-rich globular clusters and nearby open clusters. Additionall metal-poor clusters will also be examined. Further refinements in the SSPP, which hopefully will be better able to recover accurate abundances for near-solar-metallicity stars, are anticipated.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

Y.S.L., T.C.B., and T.S. acknowledge partial funding of this work from grant PHY 02-16783: Physics Frontiers Center / Joint Institute for Nuclear Astrophysics (JINA), awarded by the U.S. National Science Foundation. NASA grants (NAG5-13057, NAG5-13147) to C.A.P. are thankfully acknowledged. J.E.N acknowledges support from Australian Research Council Grant DP0663562. C.B.J and P.R.F acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) grant BA2163.

Abazajian, K., et al. 2003, , 126, 2081

Abazajian, K., et al. 2004, , 128, 502

Abazajian, K., et al. 2005, , 129, 1755

Adelman-McCarthy, J. K., et al. 2007a, , in press

Adelman-McCarthy, J. K., et al. 2007b, , accepted

Allende Prieto, C., et al. 2007, , submitted (Paper III)

Allende Prieto, C., Beers, T. C., Wilhelm, R., et al. 2006, , 636, 804

Bailer-Jones, C. A. L. 2000, , 357, 197

Beers, T. C., et al. 2006, BAAS, 38, 168.08

Beers, T. C., Rossi, S., Norris, J. E., Ryan, S. G., $\&$ Shefler, T. 1999, , 506, 892

Carollo, D., et al. 2007, Nature, submitted (astro-ph/0706.3005)

Cenarro A.J., Cardiel N., Gorgas J., Peletier R.F., Vazdekis A., $\&$ Prada F. 2001a, , 326, 959

Cenarro A. J., Gorgas J., Cardiel N., Pedraz S., Peletier R.F., $\&$ Vazdekis, A. 2001b, , 326, 981

Chen, L., Hou, J.L., $\&$ Wang, J.J. 2003, , 125, 1397,

Cohen, J. G., Briley, M. M., $\&$ Stetson, P. B. 2005, , 130, 1177

Cudworth, K. M. 1976, , 81, 519

Cudworth, K. M. $\&$ Monet, D. G. 1979, , 84, 774

Cudworth, K. M. $\&$ Rauscher, B. 1987, , 93, 856

Dias, W. S., Alessi, B. S., Moitinho, A., $\&$ Lepine, J. R. D. 2002, , 389, 871

Fan, X., et al. 1996, , 112, 628

Friel, E. D.1989, , 101, 244

Friel, E. D. $\&$ Janes, K. A. 1993, , 267, 75

Friel, E. D., Janes, K. A., Tavarez, M., Scott, J., et al. 2002, , 124, 2693

Fukugita, M., Ichikawa, T., Gunn, J.E., Doi, M., Shimasaku, K., $\&$ Schneider, D.P. 1996, , 111, 1748

Girardi, L., Grebel, E. K., Odenkirchen, M., $\&$ Chiosi, C. 2004, , 422, 205

Gratton, R. 2000, in Stellar Clusters and Associations: Convection, Rotation, and Dynamos, ASP Conference Series (eds. R. Pallavicini, G. Micela, & S. Sciortino), 198, p. 225

Grillmair, C. J., Freeman, K. C., Irwin, M., $\&$ Quinn, P. J. 1995, , 109, 2553

Gunn, J. E., et al. 1998, , 116, 3040

Gunn, J. E., et al. 2006, , 131, 2332

Harris, W. E. 1996, , 112, 1487

Hogg, D.W., Finkbeiner, D.P., Schlegel, D.J., $\&$ Gunn, J.E. 2001, , 122, 2129

Ivezic, Z., et al. 2004, Astron. Nach., 325, 583

Johnson, J. A. et al. 2007, in preparation

Kraft, R. P. $\&$ Ivans, I. I. 2003, , 115, 143

Lee, Y. S., et al. 2007a, , submitted (Paper I)

Lupton, R., et al. 2001, in ASP Conf. Ser. 238, Astronomical Data Analysis Software and Systems X, ed. F. R. Harnden, Jr., F. A. Primini, and H. E. Payne (San Francisco: Astr. Soc. Pac.), p. 269

Morrison, H. L., Norris, J., Mateo, M., et al. 2003, , 125, 2502

Moultaka, J., Ilovaisky, S. A., Prugniel, P., $\&$ Soubiran, C. 2004, , 116, 693

Otsuki, K., Honda, S., Aoki, W., Kajino, T., $\&$ Mathews, G. 2006, , 641L, 117

Pier, J.R., Munn, J.A., Hindsley, R.B., Hennessy, G.S., Kent, S.M., Lupton, R.H., $\&$ Ivezic, Z. 2003, , 125, 1559

Prugniel, Ph. $\&$ Soubiran, C., 2001, , 369,1048

Randich, S., Sestito, P., Primas, F., Pallavicini, R., $\&$ Pasquini, L., 2006, , 450, 557

Rastorguev, A.S., Glushkova, E.V., Dambis, A.K., $\&$ Zabolotskikh M.V. 1999, Astron. Letters, 25, 689

Re Fiorentin, P., Bailer-Jones, C. A. L., Lee, Y. S. et al. 2007, , 467, 1373

Sanders, W. L. 1989, Rev., Mex. Astron. Astro. 17, 31

Schlegel, D. J., Finkbeiner, D. P., $\&$ Davis, M., 1998, , 500, 525

Scott, J. E., Friel, E. D., $\&$ Janes, K. A. 1995, , 109, 1706

Smith, G. H $\&$ Briley, M. M. 2006, , 118, 740

Smith, G. H. $\&$ Mateo, M. 1990, , 353, 533

Smith, J.A., et al 2002, , 123, 2121

Stetson, P. B. 1987, , 99, 191

Stetson, P. B. 1990, , 102, 932

Stetson, P. B. 1994, , 106, 250

Stoughton, C., et al. 2002, , 123, 485

Twarog, B.A., Ashman, K.M., $\&$ Anthony-Twarog, B.J. 1997, , 114, 2556

Tucker, D., et al. 2006, AN, 327, 821

Willemsen, P.G., Hilker, M., Kayser, A., $\&$ Bailer-Jones, C. A. L. 2005, , 436, 379

Yong, D., Carney, B. W., $\&$ Teixera de Almeida, M. L. 2005, , 130, 597

York, D. G., et al. 2000, , 120, 1579

![Color-Magnitude Diagrams of the M 13 stars inside the tidal radius (left panel), and inside the field region (right panel), shown as black dots. The selected sub-grids from the $S/N$ cut are shown as red squares in the left panel and green squares in the right panel. These selected sub-grids are used in the analysis.](f2.eps)

![\[Fe/H\] and radial velocity distributions for stars in the direction of M 13. Gaussian fits (blue solid curves) to the distribution of the selected true members, shown in the green histograms, are over-plotted. ](f5.eps)

![Same as Fig. 5 but for M 15.](f6.eps)

![Same as Fig. 5 but for M 2.](f7.eps)

![Same as Fig. 5 but for NGC 2420.](f8.eps)

![Same as Fig. 5 but for M 67.](f9.eps)

![Distribution of \[Fe/H\] as a function of effective temperature for selected true member stars of M 13, M 15, M 2, NGC 2420, and M 67. The mean \[Fe/H\] determined for each cluster based on these estimates is shown with the blue dashed line; the red solid line represents the adopted literature value in each panel.](f10.eps)

![Temperature and gravity distributions of the selected true member stars for M 13. Each color represents a temperature range of width 500 K, and a surface gravity range of 0.5 dex, respectively. The temperature scales on the top of the left hand panel come from a linear relation between $(g-r)_0$ color and $T_{\rm eff}$ by performing a least squares fit to the theoretical models of Girardi et al. (2004). A similar procedure is applied for transforming the $g_0$ magnitude to a theoretical log $g$ scale on the ordinate in the right-hand panel.](f11.eps)

![Same as Fig. 11 but for M 15.](f12.eps)

![Same as Fig. 11 but for M 2.](f13.eps)

![Same as Fig. 11 but for NGC 2420.](f14.eps)

![Same as Fig. 11 but for M 67.](f15.eps)

[^1]: IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.
