\omega Centauri Abundances

Chemical Abundances for 855 Giants in the Globular Cluster Omega Centauri (NGC 5139)

Christian I. Johnson11affiliation: Department of Astronomy, Indiana University, Swain West 319, 727 East Third Street, Bloomington, IN 47405–7105, USA; cijohnson@astro.ucla.edu; catyp@astro.indiana.edu 22affiliation: Department of Physics and Astronomy, University of California, Los Angeles, 430 Portola Plaza, Box 951547, Los Angeles, CA 90095–1547, USA 33affiliation: Visiting astronomer, Cerro Tololo Inter–American Observatory, National Optical Astronomy Observatory, which are operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation. and Catherine A. Pilachowski11affiliation: Department of Astronomy, Indiana University, Swain West 319, 727 East Third Street, Bloomington, IN 47405–7105, USA; cijohnson@astro.ucla.edu; catyp@astro.indiana.edu 33affiliation: Visiting astronomer, Cerro Tololo Inter–American Observatory, National Optical Astronomy Observatory, which are operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.
Abstract

We present elemental abundances for 855 red giant branch (RGB) stars in the globular cluster Omega Centauri (\omega Cen) from spectra obtained with the Blanco 4m telescope and Hydra multifiber spectrograph. The sample includes nearly all RGB stars brighter than V=13.5, and span’s \omega Cen’s full metallicity range. The heavy \alpha elements (Si, Ca, and Ti) are generally enhanced by \sim+0.3 dex, and exhibit a metallicity dependent morphology that may be attributed to mass and metallicity dependent Type II supernova (SN) yields. The heavy \alpha and Fe–peak abundances suggest minimal contributions from Type Ia SNe. The light elements (O, Na, and Al) exhibit >0.5 dex abundance dispersions at all metallicities, and a majority of stars with [Fe/H]>–1.6 have [O/Fe], [Na/Fe], and [Al/Fe] abundances similar to those in monometallic globular clusters, as well as O–Na, O–Al anticorrelations and the Na–Al correlation in all but the most metal–rich stars. A combination of pollution from intermediate mass asymptotic giant branch (AGB) stars and in situ mixing may explain the light element abundance patterns. A large fraction (27\%) of \omega Cen stars are O–poor ([O/Fe]<0) and are preferentially located within 5–10\arcmin of the cluster center. The O–poor giants are spatially similar, located in the same metallicity range, and are present in nearly equal proportions to blue main sequence stars. This suggests the O–poor giants and blue main sequence stars may share a common origin. [La/Fe] increases sharply at [Fe/H]\gtrsim–1.6, and the [La/Eu] ratios indicate the increase is due to almost pure s–process production.

stars: abundances, globular clusters: general, globular clusters: individual (\omega Centauri, NGC 5139), stars: Population II

1 INTRODUCTION

For many years, globular clusters were regarded as prototypical simple stellar populations. However, recent observations have revealed that several of the most massive known globular clusters contain multiple main sequence, subgiant, and/or red giant branch (RGB) populations (Piotto et al. 2007; Marino et al. 2008; Milone et al. 2008; Anderson et al. 2009; Moretti et al. 2009; Piotto 2009; Milone et al. 2010). These data, combined with the well–known and pervasive light element abundance correlations and anticorrelations that appear to be unique to the globular cluster environment, suggest that many, if not all, globular clusters undergo at least some degree of self–enrichment (e.g., Carretta et al. 2009a). While nearly all of these clusters exhibit small (\lesssim0.1 dex) star–to–star metallicity variations (e.g., see review by Gratton et al. 2004), Omega Centauri (\omega Cen) has long been known to exhibit both a complex color–magnitude diagram and a metallicity spread of more than a factor of ten.

Early color–magnitude diagrams of \omega Cen indicated that it hosts an unusually broad RGB (e.g., Woolley 1966; Cannon & Stobie 1973). Subsequent photometric surveys have discovered that this trend continues into both the main sequence and subgiant branch regions as well (Anderson et al. 1997; Lee et al. 1999; Hilker & Richtler 2000; Hughes & Wallerstein et al. 2000; Pancino et al. 2000; van Leeuwen et al. 2000; Bedin et al. 2004; Ferraro et al. 2004; Rey et al. 2004; Sollima et al. 2005; Castellani et al. 2007; Sollima et al. 2007; Villanova et al. 2007; Bellini et al. 2009a; Calamida et al. 2009). Additionally, detailed photometric and spectroscopic analyses have shown that at least 4–5 discrete populations are present in the cluster (Norris et al. 1996; Lee et al. 1999; Hilker & Richtler 2000; Pancino et al. 2000; Bedin et al. 2004; Rey et al. 2004; Sollima et al. 2005; Castellani et al. 2007; Villanova et al. 2007; Johnson et al. 2008; Bellini et al. 2009a,b; Calamida et al. 2009; Johnson et al. 2009; Marino et al. 2010). These individual populations span a metallicity range from [Fe/H]111We make use of the standard spectroscopic notations where [A/B]\equivlog(N{}_{\rm A}/N{}_{\rm B}){}_{\rm star}– log(N{}_{\rm A}/N{}_{\rm B}){}_{\sun} and log \epsilon(A)\equivlog(N{}_{\rm A}/N{}_{\rm H})+12.0 for elements A and B.\approx–2.2 to –0.5. However, few stars are found with [Fe/H]<–2, and more than half of \omega Cen’s stars reside in a population peaked near [Fe/H]\approx–1.7 (Norris & Da Costa 1995; Suntzeff & Kraft 1996; Hilker & Richtler 2000; Smith et al. 2000; Cunha et al. 2002; Sollima et al. 2005; Kayser et al. 2006; Stanford et al. 2006; Villanova et al. 2007; Johnson et al. 2008; Calamida et al. 2009; Johnson et al. 2009; Marino et al. 2010). The rest of the stars reside in the intermediate metallicity populations, and a minority (\lesssim5\%) of stars are found to lie along the “anomalous”, metal–rich sequence (Lee et al. 1999; Pancino et al. 2000; Ferraro et al. 2004; Sollima et al. 2005; Villanova et al. 2007).

The large metallicity spread in \omega Cen is commonly believed to be due to significant self–enrichment induced by multiple star formation episodes (e.g., Ikuta & Arimoto 2000; Tsujimoto & Shigeyama 2003; Marcolini et al. 2007; Romano et al. 2007, 2010). Despite being the most massive known cluster in the Galaxy, with an estimated mass of \sim2–7\times10{}^{\rm 6} M{}_{\sun} (Mandushev et al. 1991; Richer et al. 1991; Meylan et al. 1995; van de Ven et al. 2006), Gnedin et al. (2002) showed that \omega Cen does not currently possess an abnormally deep gravitational potential well. Additionally, the cluster’s Galactic orbit indicates that it should pass through the disk at least every 1–2\times10{}^{\rm 8} years (Dinescu et al. 1999). This makes it hard to believe that \omega Cen could have experienced the 2–4 Gyr period of star formation that seems required to fit observations of the main sequence turnoff (e.g., Stanford et al. 2006). However, the cluster’s retrograde motion through the Galaxy (Dinescu et al. 1999) suggests that it may be a captured system and therefore could have been more massive in the past. In fact, the most popular scenario is that \omega Cen, and perhaps several other globular clusters containing multiple populations, are the remnant cores of tidally disrupted dwarf galaxies (e.g., Dinescu et al. 1999; Majewski et al. 2000; Smith et al. 2000; Gnedin et al. 2002; McWilliam & Smecker–Hane 2005; Bekki & Norris 2006). This is now favored over an accretion or merger scenario because the individual stellar populations within \omega Cen all exhibit the same proper motion, rotation, and average radial velocity (e.g., Pancino et al. 2007; Bellini et al. 2009a).

Although the observed evolutionary sequences have now been mostly matched to the different populations derived from spectroscopy, one of the remaining puzzles is how these populations relate to \omega Cen’s bifurcated main sequence. The discovery that \omega Cen’s main sequence splits into a red and blue sequence over a span of at least two magnitudes (e.g., Anderson 1997; Bedin et al. 2004) is difficult to explain because the blue main sequence is more metal–rich than the red main sequence (Piotto et al. 2005). A possible explanation for this is that the blue main sequence stars are selectively enhanced in helium at Y\sim0.38 (e.g., Norris 2004; Piotto et al. 2005). While the source of the proposed helium enrichment is not clear, the leading candidate appears to be intermediate mass (\sim3–8 M{}_{\sun}) asymptotic giant branch (AGB) stars with perhaps some contribution from massive, rapidly rotating main sequence stars (e.g., Renzini 2008; Romano et al. 2010). Interestingly, the blue main sequence stars appear to be preferentially located near the cluster core (Sollima et al. 2007; Bellini et al. 2009b), which is an indication that He–rich material may have collected there at some point in the cluster’s evolution. A similar radial segregation near the core has been found for stars with [Fe/H]\gtrsim–1.2, but the more metal–poor stars appear to be rather uniformly distributed across the cluster (Suntzeff & Kraft 1996; Norris et al. 1997; Hilker & Richtler 2000; Pancino 2000; Rey 2004; Johnson et al. 2008; Bellini et al. 2009b; Johnson et al. 2009). It is worth noting that helium enrichment may also play a role in determining the chemical composition of stars in monometallic globular clusters (e.g., Bragaglia et al. 2010).

\omega Cen shows clear signs of extended star formation and chemical self–enrichment, and the large abundance dispersion is not limited to just the Fe–peak elements. Instead, the [X/H] ratios for all elements analyzed so far are found to vary by at least a factor of ten as well (e.g., Cohen 1981; Paltoglou & Norris 1989; Norris & Da Costa 1995; Smith et al. 2000; Cunha et al. 2002; Johnson et al. 2009; Villanova et al. 2009; Cunha et al. 2010; Stanford et al. 2010). Despite the current interpretation that \omega Cen may be the surviving core of a disrupted dwarf galaxy, the [X/Fe] abundance ratios for the light elements (O, Na, Mg, and Al) and heavy \alpha elements (Si, Ca, and Ti) more closely resemble the patterns found in individual globular clusters. These patterns include the O–Na, O–Al, and Mg–Al anticorrelations concurrent with the Na–Al correlation and consistently supersolar [\alpha/Fe] ratios (e.g., Norris & Da Costa 1995; Smith et al. 2000; Johnson et al. 2009). This suggests that both Type II supernovae (SNe) and the products of proton–capture nucleosynthesis have played a significant role in shaping \omega Cen’s chemical enrichment. However, the abundance patterns of neutron–capture elements in \omega Cen stars with [Fe/H]\gtrsim–1.5 indicate that the slow neutron–capture process (s–process) was also a dominant production mechanism. This strongly contradicts the trends found in other globular clusters, and is instead more similar to observations of dwarf galaxies (e.g., see reviews by Venn et al. 2004; Geisler et al. 2007). While dwarf galaxies also contain many s–process enhanced stars, the low [X/Fe] ratios for the light and especially \alpha elements suggests a significant contribution from Type Ia SNe. In contrast, the enhanced [\alpha/Fe] ratios, high [Na/Fe] and [Al/Fe] abundances, and low [Cu/Fe] ratios seem to indicate that Type Ia SNe have played only a minimal role in \omega Cen. However, Type Ia SNe may have contributed in the most metal–rich stars, as is evidenced by a potential downturn in [\alpha/Fe] and rise in [Cu/Fe] at [Fe/H]>–1 (Pancino et al. 2002; Origlia et al. 2003; but see also Cunha et al. 2002).

In this paper we have obtained a nearly complete sample that includes 855 RGB stars and covers \omega Cen’s full metallicity range down to V=13.5. We present new chemical abundance measurements of several light odd–Z, \alpha, Fe–peak, and neutron–capture elements, and compare these results with abundance trends found in the Galactic disk, halo, bulge, globular cluster, and nearby dwarf galaxy populations. We also compare the abundance patterns found for the different \omega Cen populations in an effort to understand the cluster’s formation and chemical enrichment history.

2 OBSERVATIONS AND REDUCTIONS

The observations for this project were taken at the Cerro Tololo Inter–American Observatory (CTIO) using the Blanco 4m telescope equipped with the Hydra multifiber positioner and bench spectrograph. We obtained all of the spectra in two separate runs spanning 24–28 March 2008 and 6–8 March 2009. We employed two different wavelength setups encompassing \sim6135–6365 and \sim6500–6800 Å with wavelength centers near 6250 and 6670 Å, respectively. This required the use of two separate order blocking filters for each echelle spectrograph setup. The red setup centered near 6670 Å used the echelle filter #6 (E6757); however, neither the echelle filter #7 nor #8 provides sufficient transmissivity over the bluer region spanning 6135–6365 Å. Since a primary goal of this project is to obtain both oxygen and sodium abundances from the 6300 Å [O I] line and 6154/6160 Å Na I lines, we purchased a new, single–piece echelle filter (E6257222This filter is on long–term loan at CTIO and available for public use.) that provides >75\% transmissivity from \sim6135–6365 Å and allowed for the simultaneous observation of both the oxygen and sodium lines. For both setups, the “large” 300\micron (2\arcsec) fibers combined with the 400 mm Bench Schmidt Camera and 316 line mm{}^{\rm-1} echelle grating to yield a resolving power of R(\lambda/\Delta\lambda)\approx18,000 (0.35 Å FWHM). A summary of the Hydra observations is provided in Table 1.

Photometry, coordinates, and membership probabilities for all stars were taken from the proper motion study by van Leeuwen et al. (2000). We targeted stars with V\leq13.5 and 0.70\leqB–V\leq1.85 while excluding those with membership probabilities below 70\%. Field stars located along \omega Cen’s line–of–sight are easily removed due to the cluster’s comparatively large radial velocity and small velocity dispersion (\langleV{}_{\rm R}\rangle\sim232 km s{}^{\rm-1}; \sigma\sim10 km s{}^{\rm-1}; e.g., Reijns et al. 2006; Sollima et al. 2009). The magnitude and color restrictions provide a balance between maximizing the signal–to–noise ratio (S/N) of observations and limiting the number of required Hydra configurations. At V=13.5, one can obtain a S/N\approx100 after three hours of integration. This luminosity cutoff also allows for the observation of all giant branches in \omega Cen, and is at least 1 mag. below the RGB tip of the most metal–rich stellar population (see Figure 1).

In order to limit the number of repeat observations, stars were given a low priority in the Hydra assignment code following their inclusion into a Hydra configuration, and stars were completely removed from the fiber assignment process if incorporated into two Hydra configurations. The total number of fibers assigned to objects ranged from 50–110, and the co–added S/N ratio for almost all stars extended from about 100 to more than 350. The full sample obtained for this project is shown in Figure 1 along with the non–repeat stars from our previous papers on the cluster.

The complexity of \omega Cen’s color–magnitude diagram requires a large sample of stars to fully interpret its chemical history. Therefore, we have obtained a nearly 100\% complete sample of RGB members with V\leq13.0 and achieved more than 75\% completion for V\leq13.5. Since \omega Cen exhibits a moderate radial metallicity gradient (Norris et al. 1996; Suntzeff & Kraft 1996; Norris et al. 1997; Hilker & Richtler 2000; Pancino et al. 2000; Rey et al. 2004; Johnson et al. 2008; Bellini et al. 2009b; Johnson et al. 2009), we targeted stars spanning a wide range of cluster radii. Figure 2 shows the observed completion fraction in terms of V magnitude, B–V color, and distance from the cluster center, and Figure 3 illustrates the spatial location of our sample relative to the cluster center. For V\leq13.0, B–V>1.1, and 10\arcmin<D<24\arcmin, the completion fraction exceeds 0.90. However, the completion fraction for the inner 10\arcmin of the cluster ranges from 0.52–0.90. The decrease is due to both stellar crowding near the cluster core and physical limitations on fiber placement. Despite the large sample size, a modest evolutionary selection effect is present because the most metal–rich stars have both lower V magnitudes and tend to be located closer to the cluster center. Therefore, we have only observed stars along the most metal–rich giant branch that are within \sim1 mag. of the RGB tip.

Data reduction was handled using the necessary tasks provided in standard IRAF333IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. packages. We used ccdproc to trim the overscan region and apply the bias level correction. However, the majority of the data reduction process was carried out with the dohydra package, which was used to trace the fiber locations on the detector, remove scattered light, apply the flat–field correction, identify lines in the ThAr comparison spectrum, apply the wavelength calibration, remove cosmic rays, subtract the background sky spectra, and extract the one–dimensional spectra. The reduction processes were identical for both the 6250 and 6750 Å data with the exception of the wavelength calibration. A problem with the calibration lamp during the 6750 Å observations meant that we had to use a high S/N, daylight solar spectrum for wavelength calibration instead of the ThAr comparison source.

Following completion of the dohydra task, the data were continuum fit and normalized before being corrected for telluric contamination. We obtained high S/N spectra of multiple bright, rapidly rotating B–stars spanning air masses ranging from 1.05 to 1.75. These spectra were used as the templates for removing the telluric features in the 6270–6350 Å window. Fortunately, the cluster’s radial velocity corresponds to a wavelength shift of roughly +4.8 Å. This moves the 6300 Å [O I] stellar absorption line away from the telluric emission feature at 6300 Å, and places it cleanly between the 6302 and 6306 Å telluric absorption doublets. After applying the telluric correction, the spectra were then co–added to remove any remaining cosmic rays and increase the S/N.

3 Analysis

3.1 Model Stellar Atmospheres

Effective temperatures (T{}_{\rm eff}) were determined via the empirical V–K color–temperature relation from Alonso et al. (1999, 2001; their equations 8 & 9), which is based on the infrared flux method (Blackwell & Shallis 1977). The V magnitudes were taken from van Leeuwen et al. (2000) and the K magnitudes were taken from the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) database444The 2MASS catalog can be accessed online at: http://irsa.ipac.caltech.edu/applications/Gator/.. All photometry was corrected for interstellar reddening and extinction using the recommended values of E(B–V)=0.12 (Harris 1996) and E(V–K)/E(B–V)=2.70 (McCall 2004). While there is some evidence for minor differential reddening near the cluster’s core (Cannon & Strobie 1973; Calamida et al. 2005; van Loon et al. 2007; McDonald et al. 2009), the well–defined evolutionary sequences observed in the photometry by Villanova et al. (2007) seem to suggest that differential reddening is not a major issue. Therefore, we have applied a uniform reddening correction that is independent of a star’s location in the cluster. Although our data set did not contain enough Fe I lines of varying excitation potential to strongly constrain T{}_{\rm eff} via excitation equilibrium, we did not find any strong, systematic trends in plots of Fe I abundance versus excitation potential. It is likely that our photometric temperatures are accurate to within the roughly 25–50 K uncertainty range given by the Alonso et al. (1999) empirical fits.

Surface gravity (log g) estimates were obtained using the photometric temperatures and absolute bolometric magnitudes (M{}_{\rm bol}). The bolometric corrections were taken from Alonso et al. (1999; their equations 17 and 18) and applied to the absolute visual magnitudes (M{}_{\rm V}), which assumed a distance modulus of (m–M){}_{\rm V}=13.7 (van de Ven et al. 2006). Final surface gravity values were calculated with the standard relation,

log(g_{*})=0.40(M_{bol.}-M_{bol.\sun})+log(g_{\sun})+4[log(T/T_{\sun})]+log(M/% M_{\sun}), (1)

and assumed stellar mass of 0.80 M{}_{\rm\sun}. However, the likely age spread of \sim2–4 Gyr (e.g., Stanford et al. 2006) among the stars in different populations means that a mass spread among RGB stars undoubtedly exists as well. This is further complicated by the inferred existence of a helium–rich population (Bedin et al. 2004; Norris 2004; Piotto et al. 2005) in which stars will evolve more rapidly. When one also includes “contamination” of first ascent RGB stars with AGB stars, which could account for as much as 20–40\% of the RGB above the horizontal branch (e.g., Norris et al. 1996), it is not unreasonable to assume \omega Cen giants will have a mass range spanning \sim0.60–0.80 M{}_{\rm\sun}. Fortunately, the surface gravity estimates scale with log(M) and are thus relatively insensitive to small changes in the assumed stellar mass. We estimate that the uncertainty introduced into our surface gravity values due to the inherent mass range on \omega Cen’s RGB does not exceed \Deltalog g=0.15. Comparison between the abundances of elements in different ionization states seems to substantiate this with \langle[FeI/H]-[FeII/H]\rangle=–0.09 (\sigma=0.10) and \langle[ScI/Fe]-[ScII/Fe]\rangle=–0.18 (\sigma=0.21). We provide a more detailed analysis regarding how surface gravity uncertainties affect abundance ratio determinations in \lx@sectionsign3.3.

In addition to effective temperature and surface gravity, metallicity and microturbulence (v{}_{\rm t}) information are required to generate a suitable 1–D model atmosphere. For an initial metallicity estimate, we used the empirical [Ca/H] calibration provided by van Leeuwen et al. (2000; their equation 15) with the assumptions that stars with [Fe/H]<–1 have [Ca/Fe]=+0.30 and those with [Fe/H]>–1 decline to [Ca/Fe]=0 at solar metallicity. This assumption is verified in our new [Ca/Fe] data (see \lx@sectionsign4.6). An initial microturbulence value was determined from the empirical v{}_{\rm t}–T{}_{\rm eff} relation given in Johnson et al. (2008; their equation 2). The initial T{}_{\rm eff}, log g, [Fe/H], and v{}_{\rm t} values were used to generate the necessary model atmospheres via interpolation within the available ATLAS9555The model atmosphere grids can be downloaded from http://cfaku5.cfa.harvard.edu/grids.html. grid. The final determination of all microturbulence values followed the prescription outlined by Magain (1984) in which the microturbulence was adjusted until trends of Fe I abundance versus line strength were removed. The overall model atmosphere metallicity was then adjusted to match the derived [Fe/H] abundance for each star. This value was also used to further refine the calculated effective temperature, which has a slight metallicity dependence. A full listing of star identifiers, photometry, model atmosphere parameters, and S/N ratios is provided in Table 2.

3.2 Derivation of Abundances

3.2.1 Equivalent Width Analysis

Chemical abundances for Na, Si, Ca, Sc, Ti, Fe, and Ni were determined through standard equivalent width (EW) analyses using the abfind driver in the LTE line analysis code MOOG666The MOOG code can be downloaded at: http://www.as.utexas.edu/ chris/moog.html. (Sneden 1973). Individual EWs were measured by fitting single or multiple Gaussian profiles to isolated and blended stellar absorption lines using the interactive EW fitting code developed for Johnson et al. (2008). The high resolution, high S/N solar and Arcturus atlases777These are available online from the NOAO Data Archives at: http://www.noao.edu/archives.html. (Hinkle et al. 2000) were used to aid in line identification and continuum placement. The Arcturus atlas was also used as a reference for selecting suitable spectral lines. However, the atomic log gf values were determined by an inverse solar analysis in which the EWs measured in the Sun were forced to match the photospheric abundances given in Anders & Grevesse (1989)888The solar log \epsilon(Fe) abundance was assumed to be 7.52 (Sneden et al. 1991a).. When comparing our derived log gf values to those given in the NIST999The NIST Atomic Line Database can be accessed at: http://www.nist.gov/physlab/data/asd.cfm. (Ralchenko et al. 2008), Thevenin (1990), and VALD101010The VALD linelist can be accessed at: http://www.astro.uu.se/ vald/php/vald.php. (Kupka et al. 2000) compilations, we find very good agreement such that \langlelog gf{}_{\rm ours}–log gf{}_{\rm lit.}\rangle=–0.02 (\sigma=0.08).

While most abundances were determined through a straight–forward EW analysis, the odd–Z Fe–peak and neutron–capture elements have line profiles that may be affected by hyperfine structure. For the purposes of this study, this includes the elements Sc, La, and Eu. Prochaska & McWilliam (2000) give hyperfine log gf values for the 6245 Å Sc II line, but unfortunately their work does not include the 6309 Å Sc II nor the 6210 and 6305 Sc I lines used here. Similarly, the Zhang et al. (2008) analysis of solar Sc abundances only includes the 6245 Å line as well. However, the error introduced by ignoring hyperfine structure increases as a function of EW, and the small Sc EWs in our sample (\langleEW\rangle=42 mÅ, \sigma=26 mÅ) lead us to believe a standard EW abundance analysis is a reasonable approach for this element.

For abundance determinations of the neutron–capture elements La and Eu, we have employed the hyperfine structure linelists available in Lawler et al. (2001a) for the 6262 Å La II line and Lawler et al. (2001b) for the 6645 Å Eu II line. However, the La abundances were determined by spectrum synthesis and are described in \lx@sectionsign3.2.2. Eu abundance determinations are more complicated than those for most elements because the line profiles are both affected by hyperfine splitting and Eu has two stable, naturally occurring isotopes ({}^{\rm 151}Eu and {}^{\rm 153}Eu) with solar system isotopic fractions of 47.8\% and 52.2\%, respectively (Lawler et al. 2001b). The Eu EWs were measured using the same interactive fitting code mentioned previously, and the EWs were combined with the Eu linelist and isotope fractions as inputs into the MOOG blends driver to obtain the final abundances.

All EWs measured for this project and the atomic linelists are provided in Tables 3a–3b for Fe and Tables 4a–4b for all other elements. Similarly, the chemical abundance ratios for all elements are given in Table 5, and the number of lines measured for each element per star along with the \sigma/\surd(N) values are available in Tables 6a–6b. The log gf values listed for La and Eu in Table 4b represent the total gf values instead of an individual hyperfine component. The interested reader can find the full linelists for these elements in the references given above.

3.2.2 Spectrum Synthesis Analysis

The abundances of O, Al, and La were determined by spectrum synthesis rather than the EW fitting method described in \lx@sectionsign3.2.1. The primary motivation for using synthesis instead of an EW analysis for these elements is that the available lines suffer from varying degrees of contamination with either nearby metal lines or molecular CN. The 6300.31 Å [O I] line is blended with the nearby 6300.70 Sc II feature, and is also moderately sensitive to the C+N abundance. Similarly, the 6696/6698 Å Al I lines are both moderately blended with nearby Fe I and CN features, and the 6262 Å La II line is lightly blended with both CN and a Co I line at 6262.81 Å.

Spectrum synthesis modeling was carried out using the synth driver in MOOG. The atomic linelist was generated primarily from the Kurucz online database111111The online database can be found at: http://kurucz.harvard.edu/LINELISTS/GF100/ with updated log gf values provided by C. Sneden (2008, private communication). The atomic linelist was merged with a molecular CN linelist that was created through a combination of the Kurucz molecular linelist121212The molecular linelist can be found at: http://kurucz.harvard.edu/LINELISTS/LINESMOL/ and one provided by B. Plez (2007, private communication; see also Hill et al. 2002). Individual log gf values for lines of interest were verified through spectrum synthesis of both the solar and Arcturus atlases. As was mentioned in \lx@sectionsign3.2.1, the La II hyperfine structure linelist was taken from Lawler et al. (2001a).

Since most stars in our sample do not have published [C/Fe], [N/Fe], and/or {}^{\rm 12}C/{}^{\rm 13}C ratios, we set [C/Fe]=–0.5, {}^{\rm 12}C/{}^{\rm 13}C=4, and treated the N abundance as a free parameter to fit the available CN features. Previous work on evolved RGB stars in \omega Cen (e.g., Norris & Da Costa 1995; Smith et al. 2002; Origlia et al. 2003; Stanford et al. 2010) has shown that our set values for [C/Fe] and {}^{\rm 12}C/{}^{\rm 13}C are a reasonable approximation given that all of the stars in our sample will have already undergone first dredge–up and are above the RGB luminosity bump. With these assumptions, values of +0.80\lesssim[N/Fe]\lesssim+1.50 tended to provide the best fits to the CN lines.

Figure 4 shows sample spectra of four moderately metal–poor ([Fe/H]\approx–1.45) program stars along with synthetic spectrum fits to the O, La, and Al regions. The bottom panels of Figure 4 indicate the uncertainty introduced when the abundances of CN and other nearby, blended metals are altered by \pm0.50 dex. In warmer stars and those that are moderately metal–poor, the CN contamination does not provide a significant change in the derived abundance. However, cooler and more metal–rich stars have O, La, and Al abundances that can deviate by at least 0.10–0.20 dex compared to an analysis that does not properly account for molecular blends. For the Al lines, the nearby Fe lines are generally not much of an issue in cool giants because the Fe transitions have excitation potentials \gtrsim5 eV. The O and La lines are also not significantly affected by blends from neighboring Fe–peak element features unless the [Fe–peak/Fe] abundance exceeds roughly +0.3 dex. However, the O and Sc lines are blended strongly enough at this resolution to warrant spectrum synthesis regardless of the [Sc/Fe] abundance.

3.2.3 Comparison to Other Studies

As described in \lx@sectionsign1, the chemical composition of \omega Cen has been extensively studied using a variety of abundance indicators. However, there are only four high resolution spectroscopic studies for which we have more than five stars in common: Norris & Da Costa (1995; 35 stars), Smith et al. (2000; 7 stars), Johnson et al. (2008; 171 stars), and Johnson et al. (2009; 59 stars). Figure 5 illustrates the differences between our adopted model atmosphere parameters and those found in the literature. The average differences in T{}_{\rm eff}, log g, [Fe/H], and v{}_{\rm t}, in the sense present minus literature values, are 0 K (\sigma=61 K), –0.02 cgs (\sigma=0.09), –0.03 dex (\sigma=0.17 dex), and 0.02 km s{}^{\rm-1} (\sigma=0.24 km s{}^{\rm-1}), respectively. We conclude from these results that there are no strong systematic offsets among the studies with regard to the adopted model atmosphere parameters. This conclusion is in agreement with the [X/Fe] abundances comparisons shown in Figure 6. The average differences in the chemical abundances between this study and those in the literature tend to be <0.10 dex (\sigma\lesssim0.20 dex).

The paucity of Al and Eu comparisons shown in Figure 6 is due to two effects: (1) we only obtained about \sim40\% as many spectra in the spectral region that contains the Al and Eu lines and (2) we purposely chose to observe stars in the Al/Eu region for which Al and/or Eu abundances were not already available in the literature. Further examination of Figure 6 indicates that La is the only element showing a systematic abundance offset. We tend to find systematically lower [La/Fe] ratios, especially at [Fe/H]\gtrsim–1.7, because of our inclusion of hyperfine structure for the 6262 Å La II line. Norris & Da Costa (1995), Smith et al. (2000), and Johnson et al. (2009) base all or part of their La abundances on the 6774 Å La II line, which suffers from hyperfine broadening. However, there are no hyperfine linelists available in the literature for this transition. Since our present data, combined with that from Johnson et al. (2009), include both the 6262 and 6774 Å lines, we have derived an empirical hyperfine structure correction factor for the 6774 Å line that is described in Appendix A.

In addition to the studies mentioned above, we also have five stars in common (ROA 211, 300, 371, WFI 618854, and WFI 222068) with the Pancino et al. (2002) work that measured [Fe/H], [Si/Fe], [Ca/Fe], and [Cu/Fe] in six relatively metal–rich ([Fe/H]\geq–1.2) \omega Cen giants. However, despite sharing small differences in our derived T{}_{\rm eff}, log g, [Fe/H], and v{}_{\rm t} values, we find noticeably different [\alpha/Fe] abundances for two of the most metal–rich stars (ROA 300 and WFI 222068). This is important because the Pancino et al. (2002) result is one of the primary studies suggesting that Type Ia SNe may have significantly affected \omega Cen’s chemical enrichment. Origlia et al. (2003) also find a decrease in [\alpha/Fe] at [Fe/H]>–1, and we note similar discrepancies in our derived abundances for the most metal–rich stars. However, their abundances are based on low resolution, infrared spectra and may be subject to systematic offsets with our data.

For a direct comparison with the Pancino et al. (2002) data, in star ROA 300 we find Si and Ca offsets of \Delta[Si/Fe]=+1.14 and \Delta[Ca/Fe]=+0.17. Similarly, WFI 222068 exhibits differences of \Delta[Si/Fe]=+0.60 and \Delta[Ca/Fe]=+0.42. To investigate this discrepancy, we ran spectrum syntheses for the 6155 Å Si I line and 6156, 6161, and 6162 Å Ca I lines (see Figure 7). The results shown in Figure 7 indicate that the Pancino et al. (2002) [Si/Fe] and [Ca/Fe] abundances are too low to match the observed spectra using our linelist and model atmospheres. Instead, we find better agreement by using the upper limits on the error bars given by Pancino et al. (2002; their table 3), which results in increasing their [Si/Fe] and [Ca/Fe] abundances by \sim+0.2 dex.

Further inspection of Figure 7 shows that our EW–based [Si/Fe] abundances may have overestimated the true [Si/Fe] abundances for these two stars by \sim+0.3 dex. We did not find any clear reason for this discrepancy because the EW–based abundances for calcium and all other elements were in agreement with the spectrum synthesis fits, but it is possible that an unaccounted for (probably CN) blend is present near the silicon line in these very cool (T{}_{\rm eff}<4000 K), relatively metal–rich ([Fe/H]\sim–0.7) giants. It is worth noting that the [Si/Fe] and [Ca/Fe] abundance values are in much better agreement for two of the warmer, more metal–poor stars where the differences between EW– and synthesis–based abundances are negligible. In the remaining star (ROA 371), the difference between our derived [Ca/Fe] abundance and that from Pancino et al. (2002) is mostly negligible, but the [Si/Fe] abundance offset is noticeably larger at \Delta[Si/Fe]=+0.48. However, this star was also analyzed by both Paltoglou & Norris (1989) and Norris & Da Costa (1995), and we find in agreement with those two studies that ROA 371 is Si–rich with [Si/Fe]\gtrsim+0.5. It seems likely that most, if not all, of the discrepancy between our derived abundance values and Pancino et al. (2002) are the result of differences in adopted log gf values, model atmospheres, and line choice.

3.3 Abundance Sensitivity to Model Atmosphere Parameters

Table 7 shows the sensitivity of our derived log \epsilon(X) abundances to changes in the adopted model atmosphere parameters. The tests were conducted at T{}_{\rm eff}=4200 K and T{}_{\rm eff}=4600 K, values typical of stars in our sample, and metallicities ranging from [Fe/H]=–2.0 to –0.50. The analyses for each test star were run by adjusting T{}_{\rm eff}\pm100 K, log g\pm0.30 cgs, [Fe/H]\pm0.30 dex, and v{}_{\rm t}\pm0.30 km s{}^{\rm-1} individually while holding the other parameters constant.

We find that the chemical abundances derived from subordinate ionization state transitions (e.g., most neutral metals) are most sensitive to changes in T{}_{\rm eff}. However, abundances derived from dominant ionization state transitions (e.g., neutral oxygen; singly ionized transition metals and heavy elements) are more sensitive to uncertainties in surface gravity and metallicity because of their stronger dependence on electron pressure and H{}^{\rm-} opacity. For stars with [Fe/H]<–1, microturbulence was found to have a negligible effect on abundances derived from all transitions except Fe I and Ca I. Abundances derived from Fe I and Ca I lines were more sensitive to microturbulence uncertainties because of their typically larger EWs than other lines at a given metallicity. In stars with [Fe/H]>–1, most abundances were affected at the 0.05–0.10 dex level due to the increased line strengths. Similarly, the abundances of most elements in warmer stars were less sensitive to changes in microturbulence because of the generally weaker line strengths. It seems likely that our derived log \epsilon(X) abundance uncertainties do not exceed \sim0.20 dex based on our choices of model atmosphere parameters. Additionally, the [X/Fe] abundance ratios for most elements are expected to exhibit an even weaker dependence on model atmosphere parameter uncertainties because of their similar behavior to Fe I.

In addition to the parameters shown in Table 7, we also tested the abundance uncertainties based on changes to CN and He. Since CN lines are strongest in the O–poor stars, it is possible that standard EW and spectrum synthesis analyses may not give the same abundances for lines significantly blended with CN. However, we find that none of the lines chosen for this study that were analyzed via a standard EW approach were significantly affected by continuum suppression or blending from CN. The robust agreement between the synthesis and EW–based analyses for elements other than O, Al, and La is demonstrated in Figure 4, where the abundances of all other elements studied here were preset to those values obtained from a standard EW analysis.

Since the current interpretation of \omega Cen’s blue main sequence is that stars belonging to that population are He–rich (Y\sim0.38), we investigated the effects helium enrichment might have on our analyses. To test this, we ran both EW and spectrum synthesis analyses using He–normal (Y=0.27) and He–rich (Y=0.35) ATLAS9 models131313The He–rich models can be downloaded at http://wwwuser.oat.ts.astro.it/castelli/grids.html.. We find that the He–rich model does not result in a significantly different abundance (\Deltalog \epsilon(X)<0.1 dex), and the effects on our derived [X/Fe]141414Also note that the decrease in N(H) for He–rich stars will not affect abundances reported as [X/Fe] ratios because [X/H] and [Fe/H] both increase by the same amount. ratios are further mitigated for the low ionization potential metals. These results are in agreement with helium enrichment predictions by Boehm–Vitense (1979), and are consistent with similar tests on \omega Cen stars in Piotto et al. (2005), Johnson et al. (2009), and Cunha et al. (2010). Furthermore, Girardi et al. (2007) conclude that increasing the He abundance to the extreme values predicted in some \omega Cen stars should not significantly alter either the bolometric correction or V–K color–temperature relation. We therefore believe that our adopted atmospheric parameters are reliable even for He–rich giants.

4 RESULTS

4.1 Iron and the Metallicity Distribution Function

As discussed in \lx@sectionsign1, \omega Cen’s large metallicity spread has been previously verified in many photometric and spectroscopic analyses. However, the results presented here are based on direct measurements from high resolution, high S/N spectra in a nearly complete sample of \omega Cen giants with V\leq13.5. These new data cover the cluster’s full metallicity regime, and are also nearly complete out to \sim50\% of the tidal radius. The data presented here, along with that from Johnson et al. (2008; 2009), yield spectroscopic [Fe/H] measurements for 867 giants.

In Figure 8, we plot our derived metallicity distribution function and compare with the results of two other large spectroscopic surveys that spanned the upper RGB and SGB (Norris et al. 1996; Suntzeff & Kraft 1996). The general trend among all studies is that a dominant, metal–poor stellar population exists at [Fe/H]\approx–1.7 along with a higher metallicity tail terminating around [Fe/H]\approx–0.5. Our data confirm this result, and also support previous observations that found multiple peaks in the metallicity distribution function but a paucity of stars with [Fe/H]<–2. The full range of iron abundances in our sample extends from [Fe/H]=–2.26 to –0.32, and in Figure 8 we find five peaks in the metallicity distribution function located at [Fe/H]\approx–1.75, –1.50, –1.15, –1.05, and –0.75. These peaks correspond to the RGB–MP, RGB–MInt, and RGB–a populations identified by Pancino et al. (2000) and Sollima et al. (2005), and also generally agree with Strömgren photometry estimates (Hilker & Richtler 2000; Hughes & Wallerstein 2000; Calamida et al. 2009). It is difficult to accurately deblend the two populations near [Fe/H]=–1.15 and –1.05 because the separation is comparable to the line–to–line dispersion of Fe abundance measurements in individual stars. Instead, we will combine these two populations during further analyses. Taking this into account, the (now four) stellar populations make up roughly 61\%, 27\%, 10\%, and 2\% of our sample, respectively. For brevity, we will follow a similar naming scheme used by Sollima et al. (2005) when referring to the different metallicity populations: RGB–MP ([Fe/H]\leq–1.6), RGB–Int1 (–1.6<[Fe/H]\leq–1.3), RGB–Int2+3 (–1.3<[Fe/H]\leq–0.9), and RGB–a ([Fe/H]>–0.9).

The most metal–poor stars ([Fe/H]\leq–2) make up about 2\% (17/867) of the full sample and only about 3\% (17/541) of the RGB–MP stellar population. However, the RGB–a stars are slightly underrepresented because of our V magnitude cutoff. To test for any selection effects, we rebinned the data to only include stars within \sim1 mag of each giant branch’s RGB tip, which is the approximate magnitude range over which we sampled the RGB–a. We did not find any significant differences in the relative population mix, and different magnitude cutoffs only raised the RGB–a population fraction to \sim5\%. These estimates are consistent with those derived from number counts in photometric analyses (Pancino et al. 2000; Sollima et al. 2005; Villanova et al. 2007; Calamida et al. 2009). It should also be noted that AGB contamination may affect the number counts of each population differently. Lee et al. (2005a) found that if the intermediate metallicity and most metal–rich stars are in fact He–rich then these stars will populate the “extreme” horizontal branch. Furthermore, D’Cruz et al. (2000) estimate that as much as 30\% of the cluster’s horizontal branch population may reside on the “extreme” horizontal branch, and it is likely that these stars evolve directly to white dwarfs rather than first ascending the AGB (e.g., Sweigart et al. 1974). Since it is difficult to differentiate between RGB and AGB stars in \omega Cen’s color–magnitude diagram, it is possible that the number counts for the two most metal–poor populations contain a disproportionate number of AGB stars compared to the more metal–rich populations. However, our estimated population fractions are consistent with those found along the main sequence and subgiant branch (e.g., Villanova et al. 2007) where AGB contamination is not an issue.

In addition to the existence of multiple, discrete stellar populations in \omega Cen, there is some evidence that the metal–rich stars are more centrally located than the more metal–poor populations (Norris et al. 1996; Suntzeff & Kraft 1996; Pancino et al. 2000; Hilker & Richtler 2000; Pancino et al. 2003; Rey et al. 2004; Sollima et al. 2005; Johnson et al. 2008; Bellini et al. 2009b; Johnson et al. 2009). In Figure 9, we plot our derived abundances as a function of projected distance from the cluster center. A two–sided Kolmogorov–Smirnov (K–S) test (Press et al. 1992) confirms that the metal–rich stars ([Fe/H]>–1.3) are more centrally located than the metal–poor stars at the 96\% level151515We adopt the notion that the null hypothesis (i.e., that the two distributions are the same) can be rejected if the p value is “small” (<0.05).. Additionally, all of the stars with [Fe/H]\geq–0.9 are located within 13\arcmin of the cluster center, with most of those residing inside 10\arcmin.

Further inspection of Figure 9 reveals another interesting radial distribution trend; all stars with [Fe/H]\leq–2 are located within 12\arcmin of the cluster core, and 88\% (15/17) of these stars reside inside 5\arcmin. A two–sided K–S test comparing the radial distribution of stars with –2.0<[Fe/H]\leq–1.60 versus those with [Fe/H]\leq–2 indicates that the two distributions are drawn from different parent populations at the 99\% level. Additionally, the star–to–star metallicity dispersion decreases with increasing distance from the cluster center, but this is mostly driven by the metallicity gradient and paucity of stars with [Fe/H]\geq–1.3 outside \sim15\arcmin from the cluster center. If one only considers stars with [Fe/H]<–1.3, the standard deviation in [Fe/H] between 0–10\arcmin and 10–20\arcmin differs by less than 0.02 dex. This indicates that the two most metal–poor stellar populations are well mixed inside the cluster.

4.2 Oxygen

The chemical evolution of oxygen in \omega Cen has previously been analyzed via high resolution spectroscopy in several studies containing sample sizes ranging from \sim5–40 RGB stars (e.g., Cohen 1981; Paltoglou & Norris 1989; Brown & Wallerstein 1993; Norris & Da Costa 1995; Zucker et al. 1996; Smith et al. 2000), and more recently in a sample of \sim200 RGB stars (Marino et al. 2010). The main results from past studies indicate that: (1) \omega Cen giants exhibit large star–to–star dispersions in [O/Fe] abundance, (2) many of the intermediate metallicity stars have [O/Fe]<0, (3) the majority of metal–poor stars are O–rich with [O/Fe]\sim+0.3, and (4) oxygen is anticorrelated with both sodium and aluminum. The results presented here add 848 new [O/Fe] abundance measurements.

Figure 9 includes a plot of our derived [O/Fe] abundances as a function of projected distance from the cluster center. Compared to the other elements in Figure 9, oxygen appears to exhibit a unique radial distribution. Stars with [O/Fe]\leq0, and especially those with [O/Fe]<–0.4, are more centrally concentrated than the bulk of stars with [O/Fe]>0. In our sample, 62\% (145/233) of stars with [O/Fe]\leq0 are located inside 5\arcmin from the core and 91\% (213/233) are inside 10\arcmin. This is compared to just 42\% (261/615) and 77\% (472/615) for the stars with [O/Fe]>0, respectively. A two–sided K–S test reveals that the O–poor stars exhibit a different spatial distribution than the O–rich stars at the 99\% level. This result may have important implications regarding the origin of the blue main–sequence, and will be discussed further in \lx@sectionsign5.2.2.

Figure 10 shows the chemical evolution of [O/Fe] plotted as a function of [Fe/H]. This plot reveals that the O–poor stars, in addition to being preferentially located near the cluster core, are also well separated from the O–rich stars over a large metallicity range. Figure 11 shows the [O/Fe] data binned in 0.10 dex increments and separated into the population subclasses defined in \lx@sectionsign4.1. The resultant histograms support the existence of two subpopulations, one O–rich ([O/Fe]>0) and the other O–poor ([O/Fe]<0), residing inside the RGB–Int1 and RGB–Int2+3 populations. Interestingly, neither the RGB–MP nor the RGB–a populations appear to exhibit this bimodal behavior. Instead, the RGB–MP stars are predominantly O–rich with a median [O/Fe]=+0.32, and the RGB–a stars are moderately O–poor with a median [O/Fe]=–0.15. In the RGB–MP population, the percentages of O–poor and O–rich stars are 13\% (71/535) and 87\% (464/535), respectively. The two intermediate metallicity populations show quite different distributions, with the percentages being 46\% (100/218) to 54\% (118/218) in the RGB–Int1 group and 64\% (47/74) to 36\% (27/74) in the RGB–Int2+3 group. The relative distribution in the RGB–a stars is 71\% (15/21) O–poor to 29\% (6/21) O–rich, respectively.

Examining the bulk properties of the [O/Fe] abundances reveals that, in all but the most metal–poor and metal–rich stars, a significant star–to–star dispersion is present with \Delta[O/Fe]>2 over a large metallicity range. The full range of [O/Fe] abundances found in our sample spans from [O/Fe]=–1.30 to +0.80. The stars with [Fe/H]\leq–2 are overwhelmingly O–rich with 94\% (15/16) having [O/Fe]>0 and \langle[O/Fe]\rangle=+0.38, and the single O–poor star is only moderately depleted at [O/Fe]=–0.13. The [O/Fe] abundance “ceiling” decreases for stars with [Fe/H]\gtrsim–1.3, dropping from [O/Fe]\approx+0.6 at [Fe/H]=–1.3 to [O/Fe]\approx+0.0 at [Fe/H]=–0.3. Additionally, the super O–poor stars ([O/Fe]\leq–0.4) are only found in the range –1.9\lesssim[Fe/H]\lesssim–1.0. When considering all stars in our sample, the relative percentages of O–rich ([O/Fe]>0), O–poor (–0.4<[O/Fe]\leq0.0), and super O–poor ([O/Fe]\leq–0.4) stars are 73\% (615/848), 14\% (118/848), and 13\% (115/848), respectively. We also find that in stars with [Fe/H]\lesssim–1, [O/Fe] is anticorrelated with both [Na/Fe] and [Al/Fe]. The implications of these anticorrelations, along with the possible significance of the super O–poor stars, will be discussed further in \lx@sectionsign5.

4.3 Sodium

Previous sodium abundance measurements support the idea that \omega Cen experienced a significantly different chemical evolutionary path than any other stellar system (Cohen 1981; Paltoglou & Norris 1989; Brown & Wallerstein 1993; Norris & Da Costa 1995; Zucker et al. 1996; Smith et al. 2000; Johnson et al. 2009; Villanova et al. 2009; Marino et al. 2010). The results from these studies have shown that: (1) [Na/Fe] appears to increase as a function of increasing [Fe/H], (2) \Delta[Na/Fe]>1 for most values of [Fe/H] in the cluster, (3) no strong [Na/Fe] abundance gradient is observed, and (4) [Na/Fe] is correlated with [Al/Fe] and anticorrelated with [O/Fe]. Our new results, combined with those from Johnson et al. (2009), give [Na/Fe] abundances for 848 cluster giants. Although it is likely that our derived sodium abundances suffer from moderate non–LTE (NLTE) effects, abundances derived from the 6154/6160 Å doublet used here are expected to have NLTE offsets <0.2 dex for giants in our metallicity regime (e.g., Gratton et al. 1999; Mashonkina et al. 2000; Gehren et al. 2004). Since no standard NLTE corrections are available in the literature, the abundances reported in Table 5 and shown in the figures do not include NLTE corrections.

Inspection of Figure 11 indicates that [Na/Fe] exhibits a similar bimodal abundance pattern as shown by [O/Fe]. That is, the most metal–poor and metal–rich stellar populations show a single primary peak in the [Na/Fe] distribution function, and the two intermediate metallicity populations may be best described as having two peaks in the [Na/Fe] distribution function. However, unlike the case with oxygen, we do not find an obvious centrally concentrated population that correlates with any [Na/Fe] abundance range. We do find that the most Na–rich stars in our sample ([Na/Fe]\geq+0.6) are all found inside 13\arcmin from the cluster center, but this observation is unlikely to be significant because (1) the two most metal–rich stellar populations contain 69\% (44/64) of the most Na–rich stars (see Figures 1011) and (2) these stellar populations are already known to be centrally concentrated. This is in contrast to the O–poor radial trend that is found in stars with –1.6<[Fe/H]\leq–1.3, which do not exhibit a preferred radial location. However, Figure 9 shows that a weak, declining [Na/Fe] gradient may exist such that the median [Na/Fe] values for 0–5\arcmin, 5–10\arcmin, 10–15\arcmin, and 15–20\arcmin are +0.22, +0.14, +0.08, and –0.03, respectively.

Figure 10 highlights the chemical evolution of [Na/Fe] as a function of [Fe/H]. We find that a large star–to–star dispersion is present at all metallicities, and that the full range extends from [Na/Fe]=–1.02 to +1.36. Since we have many stars of the same temperature, surface gravity, and metallicity, the line strength differences confirm that the observed abundance spread is a real effect and not due to possible underlying NLTE effects. In addition to displaying a significant star–to–star dispersion, the sodium abundances also exhibit a strong metallicity dependence such that the median [Na/Fe] value increases with increasing [Fe/H]. The median [Na/Fe] value rises from +0.08 in the RGB–MP population to +0.78 in the RGB–a population. As mentioned above, the two most metal–rich populations contain the most Na–rich stars in the cluster. Despite the complex nature of sodium’s evolution in \omega Cen, the O–Na anticorrelation and Na–Al correlation are present in all but the most metal–rich stars.

4.4 Aluminum

Except for iron and calcium, aluminum has been the most highly studied element in \omega Cen. Previous high resolution spectroscopic work has targeted more than 200 RGB stars (Cohen 1981; Brown & Wallerstein 1993; Norris & Da Costa 1995; Zucker et al. 1996; Smith et al. 2000; Johnson et al. 2008; Johnson et al. 2009) and shown: (1) \Delta[Al/Fe]>0.5 at all metallicities and exceeds more than a factor of ten in the most metal–poor stars, (2) the range of observed [Al/Fe] abundances decreases at [Fe/H]>–1.3, (3) there is a paucity of stars with [Al/Fe]<+0.3 at intermediate and high metallicities, and (4) a Na–Al correlation and O–Al anticorrelation are present in most, if not all, cluster stars. In this paper we present 133 new [Al/Fe] abundance measurements, and when combined with the data from Johnson et al. (2008; 2009) provide [Al/Fe] values for 332 \omega Cen giants. As with sodium (see \lx@sectionsign4.3), we have not applied any NLTE corrections to our derived aluminum abundances. However, all aluminum abundances determined here utilized the non–resonance 6696/6698 Å lines, which are not expected to have large NLTE offsets in the temperature, gravity, and metallicity range of stars in our sample (e.g., Gehren et al. 2004; Andrievsky et al. 2008).

Unlike oxygen, and to a lesser extent sodium, aluminum does not show any obvious correlation between [Al/Fe] abundance and radial location. However, aluminum does show the same bimodal abundance distribution for the RGB–Int1 and RGB–Int2+3 populations (see Figure 11). By dividing the samples at [Al/Fe]=+0.6, we find that the percentage of “Al–enhanced” ([Al/Fe]\geq+0.6) stars in the RGB–Int1 population is 50\% (50/100) compared to 50\% (50/100) as well for the “Al–normal” stars ([Al/Fe]<+0.6). Similarly, the RGB–Int2+3 stars are distributed as 69\% (31/45) enhanced and 31\% (14/45) normal, respectively. Interestingly, the [Al/Fe] distribution also shows complex substructure in the RGB–MP population, which is not observed in the [O/Fe] and [Na/Fe] data. In this population, 41\% (70/172) of the stars are Al–enhanced and 59\% (102/172) are Al–normal. Furthermore, this is the only \omega Cen population that contains a significant number of stars over the full [Al/Fe] range. For the RGB–a population, a single peak is observed at [Al/Fe]=+0.5 in the [Al/Fe] distribution function.

The full range of [Al/Fe] abundances observed here spans from –0.34 to +1.37, but only 4\% (12/332) of the stars have [Al/Fe]<0. Similarly, we find that \Delta[Al/Fe]\sim1.5 dex for [Fe/H]<–1.3. However, the star–to–star dispersion decreases noticeably at higher metallicities. Inspection of Figure 10 shows that [Al/Fe] exhibits an interesting trend as a function of [Fe/H]. The maximum value reached for stars with [Fe/H]\lesssim–1.3 remains steady near [Al/Fe]\approx+1.3, but above [Fe/H]\sim–1.3 the maximum abundance decreases to only [Al/Fe]\approx+0.6 in the RGB–a stars. Furthermore, the number of stars with [Al/Fe]<+0.3 strongly decreases at [Fe/H]>–1.3. In the RGB–MP and RGB-Int1 populations, stars with [Al/Fe]<+0.3 constitute 25\% (69/272) of the distribution, but this decreases to only 7\% (1/15) of the RGB–a population.

4.5 Silicon

Previous analyses (Cohen 1981; Paltoglou & Norris 1989; Brown & Wallerstein 1993; Norris & Da Costa 1995; Smith et al. 2000; Pancino et al. 2002; Villanova et al. 2009) have used the heavy \alpha element (Si, Ca, and Ti) abundances to assess the dominance of Type II versus Type Ia supernovae in \omega Cen and other clusters. In terms of silicon abundances, it has been shown that: (1) silicon is enhanced with [Si/Fe]>+0.3 in nearly all cluster stars, (2) the star–to–star dispersion in [Si/Fe] is significantly smaller than for the lighter \alpha and odd–Z elements, and (3) the most metal–rich stars may have appreciably lower [Si/Fe] abundances compared to the more metal–poor populations. From this study, we add 821 new [Si/Fe] measurements over \omega Cen’s full metallicity range.

While we find that the lighter \alpha element oxygen shows a distinctly unique distribution versus distance from the cluster center, [Si/Fe] does not show the same trend. Figure 9 suggests that a weak [Si/Fe] gradient may be present such that the stars inside 5\arcmin have a higher average silicon abundance than those outside 5\arcmin. We find that stars inside 5\arcmin have \langle[Si/Fe]\rangle=+0.37, which is noticeably higher than the \langle[Si/Fe]\rangle=+0.29 for those at r>5\arcmin. This result does not change even if we limit examination to stars only between 0–5\arcmin and 5–10\arcmin. Except near the cluster core, the average [Si/Fe]\approx+0.3 at all radii. It should be noted that Villanova et al. (2009) find \langle[Si/Fe]\rangle=+0.5 in the outer 20–30\arcmin of \omega Cen, which is larger by about 0.2 dex than we find in the same region. However, we do not presently have sufficient data to assess whether the average [Si/Fe] ratio increases at larger radii or if this merely reflects a systematic offset.

The full range of [Si/Fe] abundances in our data span from –0.30 to +1.15, but the average over all stars is [Si/Fe]=+0.33 (\sigma=0.17). While we do find a few Si–poor stars ([Si/Fe]<0), these stars comprise only 2\% (16/821) of the total sample. Similarly, the very Si–rich stars ([Si/Fe]>+0.6) only represent 6\% (52/821) of the total sample. Figure 10 reveals that [Si/Fe] may have a more complex morphology as a function of [Fe/H] than previously thought. The average [Si/Fe] ratio decreases from \langle[Si/Fe]\rangle=+0.46 (\sigma=0.19) in stars with [Fe/H]\leq–2 to \langle[Si/Fe]\rangle=+0.29 (\sigma=0.16) in the stars that comprise the majority of the RGB–MP population (–2.0<[Fe/H]\leq–1.6). In the subsequent populations, the average [Si/Fe] abundance monotonically increases with [Fe/H] to \langle[Si/Fe]\rangle=+0.45 (\sigma=0.23) in the RGB–a population. This is in agreement with Norris & Da Costa (1995) and Smith et al. (2000), but contrasts with the claims by Pancino et al. (2002) and Origlia et al. (2003) that stars with [Fe/H]>–1 have lower [\alpha/Fe] abundances (see \lx@sectionsign3.2.3 for a brief discussion).

4.6 Calcium

In addition to iron, calcium abundances have been analyzed in great detail for \omega Cen stars. Previous analyses have used calcium as a proxy metallicity indicator (Freeman & Rodgers 1975; Cohen 1981; Norris et al. 1996; Suntzeff & Kraft 1996; Rey et al. 2004; Sollima et al. 2005; Stanford et al. 2006; Lee et al. 2009) and as an \alpha element tracer (Paltoglou & Norris 1989; Norris & Da Costa 1995; Smith et al. 2000; Pancino et al. 2002; Kayser et al. 2006; Villanova et al. 2007; Johnson et al. 2009; Villanova et al. 2009). These studies have shown: (1) there is a large spread of at least 1 dex in [Ca/H] with multiple peaks in the distribution function (i.e., confirms the different populations found when using [Fe/H] as a metallicity tracer), (2) nearly all stars have enhanced [Ca/Fe]\approx+0.3 at all metallicities, (3) the star–to–star dispersion is significantly smaller than for the lighter elements, and (4) there may be a downturn in [Ca/Fe] at [Fe/H]>–1. Combining our new data with that of Johnson et al. (2009), we add 857 [Ca/Fe] abundance measurements.

Unlike silicon, which provides some evidence for a weak radial abundance gradient, [Ca/Fe] does not vary ostensibly between the inner and outer regions of the cluster. When considering all stars in our sample, the majority are Ca–rich with \langle[Ca/Fe]\rangle=+0.29 (\sigma=0.12). However, the full range of observed [Ca/Fe] abundances is smaller than for [Si/Fe], with [Ca/Fe] varying between –0.13 and +0.65. Figure 10 shows that [Ca/Fe] displays a similar morphology to [Si/Fe] when plotted as a function of [Fe/H]. That is, stars with [Fe/H]\leq–2 tend to be more Ca–rich with \langle[Ca/Fe]\rangle=+0.37 (\sigma=0.16) compared to the majority of stars in the RGB–MP population with \langle[Ca/Fe]\rangle=+0.26 (\sigma=0.11). Similarly, the average [Ca/Fe] abundance rises for the RGB–Int1 and RGB–Int2+3 populations to \langle[Ca/Fe]\rangle=+0.34 (\sigma=0.11; see also Figure 12). However, unlike the case for [Si/Fe], the average [Ca/Fe] abundance decreases for [Fe/H]\gtrsim–1, and the RGB–a stars have \langle[Ca/Fe]\rangle=+0.26 (\sigma=0.12).

Further inspection of Figure 10 reveals that the distribution of [Ca/Fe] among the RGB–Int2+3 stars may be bimodal. Figure 12 also suggests that the RGB–Int2+3 stars may exhibit a bimodal distribution, and shows that the other populations appear to exhibit a mostly unimodal [Ca/Fe] distribution. Interestingly, the two RGB–Int2+3 subsets occur in nearly equal proportions with the stars peaked near [Ca/Fe]=+0.45 constituting 47\% (36/76) of the subsample and the stars peaked near [Ca/Fe]=+0.25 making up 53\% (40/76) of the subsample. However, a two–sided K–S test does not rule out that the [Ca/Fe] distributions for the RGB–Int1 and RGB–Int2+3 are different at more than the 95\% level. While we caution the reader that the apparent bimodality may be a product of small number statistics, it would be interesting to investigate this possible trend further with additional calcium abundance indicators (e.g., HK index).

4.7 Scandium

Scandium is typically used as a tracer of Fe–peak element production in stellar populations, and Galactic halo and globular cluster stars with [Fe/H]>–2.5 tend to exhibit solar–scaled [Sc/Fe] abundances. Although scandium has been analyzed in only a handful of studies for \omega Cen stars (Cohen 1981; Paltoglou & Norris 1989; Norris & Da Costa 1995; Zucker et al. 1996; Smith et al. 2000; Johnson et al. 2009), the results typically show that: (1) the observed star–to–star scatter in [Sc/Fe] is significantly smaller than for lighter elements and (2) \langle[Sc/Fe]\rangle\approx0 at all metallicities. Combined with the results from Johnson et al. (2009), we are able to add 821 [Sc/Fe] abundance measurements.

As can be seen in Figure 9, we do not find any evidence for a radial [Sc/Fe] abundance gradient. Similarly, Figure 10 indicates that the [Sc/Fe] ratio is approximately constant over the full metallicity regime. However, a weak metallicity dependence may be present such that the average [Sc/Fe] abundance decreases from \langle[Sc/Fe]\rangle=+0.08 (\sigma=0.13) in the RGB–MP population to \langle[Sc/Fe]\rangle=–0.07 (\sigma=0.19) in the RGB–a stars. The full range of observed [Sc/Fe] abundances spans from –0.49 to +0.44, but most stars exhibit a solar–scaled [Sc/Fe] ratio. When considering the entire sample, we find \langle[Sc/Fe]\rangle=+0.05 (\sigma=0.15).

4.8 Titanium

Titanium is generally considered either the heaviest \alpha element or one of the lightest Fe–peak elements. Previous titanium abundance measurements for \omega Cen stars (Cohen 1981; Paltoglou & Norris 1989; Brown & Wallerstein 1993; Norris & Da Costa 1995; Smith et al. 2000; Villanova et al. 2007; Johnson et al. 2009; Villanova et al. 2009) have shown: (1) the star–to–star dispersion in [Ti/Fe] is comparable to that found in [Si/Fe] and [Ca/Fe], (2) the titanium abundance is generally enhanced at [Ti/Fe]\sim+0.3, and (3) there may be evidence for an increase in [Ti/Fe] with increasing [Fe/H]. Our new results, combined with Johnson et al. (2009), provide 826 [Ti/Fe] measurements.

Inspection of Figure 9 confirms that we do not find any correlation between our determined [Ti/Fe] abundance and a star’s radial location. In a similar fashion to the behavior of silicon and calcium, Figure 10 shows that titanium also exhibits a metallicity dependent morphology. The average [Ti/Fe] ratio is roughly constant across the RGB–MP population’s full metallicity range ([Fe/H]\leq–1.6) at \langle[Ti/Fe]\rangle=+0.13 (\sigma=0.12), which is \sim0.2 dex lower than the [Si/Fe] and [Ca/Fe] ratios in those same stars. However, the average [Ti/Fe] abundance rises monotonically to \langle[Ti/Fe]\rangle=+0.34 (\sigma=0.25) in the RGB–a population (see also Figure 12). The full range of abundances in our sample spans from [Ti/Fe]=–0.42 to +0.85, but most stars are at least moderately Ti–enhanced with \langle[Ti/Fe]\rangle=+0.18 (\sigma=0.16).

4.9 Nickel

Aside from iron, nickel is the only other “true” Fe–peak element analyzed here. The chemical evolution of nickel in a stellar population often tracks very closely to iron, and \omega Cen appears to follow that trend (Cohen 1981; Paltoglou& Norris 1989; Norris & Da Costa 1995; Smith et al. 2000; Johnson et al. 2009; Villanova et al. 2009). Previous studies agree that: (1) the derived [Ni/Fe] abundances show the smallest intrinsic dispersion of any element and (2) the average [Ni/Fe] abundance is nearly solar at all metallicities and locations in the cluster. We add to these results 806 new [Ni/Fe] abundance determinations.

Figure 9 shows that, like the other transition metals, [Ni/Fe] abundances do not exhibit any signs of a radial gradient. Similarly, Figure 10 indicates that the distribution of [Ni/Fe] is essentially constant as a function of [Fe/H] with a small intrinsic scatter, but there may be a slight decrease in [Ni/Fe] at [Fe/H]\gtrsim–1.3. The full spread of [Ni/Fe] values found in our sample ranges from –0.48 to +0.69, and the cluster as a whole gives \langle[Ni/Fe]\rangle=–0.03 (\sigma=0.12).

4.10 Lanthanum

The heavy element lanthanum is often used as a tracer of the slow neutron–capture process (s–process), and its evolution has proved to be particularly interesting in \omega Cen. Previous analyses (Cohen 1981; Paltoglou & Norris 1989; Norris & Da Costa 1995; Smith et al. 2000; Johnson et al. 2009; Marino et al. 2010) have examined the [La/Fe] ratios in \sim100 RGB stars and found: (1) the most metal–poor stars tend to have [La/Fe] abundances consistent with those found in monometallic globular clusters, (2) a large increase in [La/Fe] is seen between [Fe/H]\approx–1.7 and –1.4, (3) the intermediate metallicity stars are almost exclusively La–rich, and (4) the average [La/Fe] ratio remains super–solar in the most metal–rich stars. When combined with the data from Johnson et al. 2009, we add to these past results 810 new [La/Fe] abundances.

As can be seen in Figure 9, we find no evidence supporting the existence of a radial [La/Fe] gradient, and the star–to–star dispersion remains approximately constant across all radii sampled here. On the other hand, our data shown in Figure 10 support previous claims that [La/Fe] abundances exhibit an unusual morphology when plotted as a function of [Fe/H]. There is a strong increase in [La/Fe] for stars with [Fe/H]\gtrsim–1.7, and a large intrinsic scatter of \Delta[La/Fe]\geq1 is present an nearly all metallicities. Furthermore, the average [La/Fe] abundance monotonically increases from +0.05 in the RGB–MP population to +0.49 in the RGB–Int2+3 population (see also Figure 12). However, the RGB–a stars have \langle[La/Fe]\rangle=+0.43, which suggests either a leveling off or slight decline in [La/Fe] at [Fe/H]\gtrsim–1.

The full range of [La/Fe] abundances observed here spans from –0.78 to +1.17, and it is worth noting that the proper accounting of hyperfine structure in the [La/Fe] derivations has decreased the maximum abundance values found in Johnson et al. (2009) from [La/Fe]\sim+2 to [La/Fe]\sim+1.2. These lower abundance ratios suggest that a large fraction of binary transfer systems may not be required to account for the significant lanthanum enhancements. However, we still find that only 29\% (232/810) of the stars in our sample have [La/Fe]<0, and 94\% (217/232) of those stars reside in the RGB–MP population. Interestingly, the stars with [Fe/H]\leq–2 tend to exhibit rather high [La/Fe] abundances. These stars have \langle[La/Fe]\rangle=+0.19, which is distinctly larger than the \langle[La/Fe]\rangle=+0.05 found for the full sample of RGB–MP stars. Unfortunately, a two–sided K–S test indicates that the data are insufficient to reject the null hypothesis with more than 94\% confidence.

4.11 Europium

In an analogous fashion to lanthanum, the heavy element europium is often used as an indicator of the rapid neutron–capture process (r–process). However, europium has been analyzed in far fewer stars than lanthanum (Norris & Da Costa 1995; Zucker et al. 1996; Smith et al. 2000; Johnson et al. 2009). The primary results from these studies are: (1) [Eu/Fe] tends to be somewhat underabundant relative to monometallic globular clusters of similar metallicity, (2) a significant intrinsic scatter is observed, but it is smaller than that found in [La/Fe], and (3) [Eu/Fe] remains relatively constant as a function of [Fe/H]. Combined with the data from Johnson et al. (2009), we provide [Eu/Fe] abundances for 194 stars.

Given the significantly smaller sample for europium compared to the other elements analyzed here, it is difficult to assess whether any true radial trends exist. Figure 9 provides weak evidence that the average [Eu/Fe] abundance may increase away from the cluster center. The available data support this by showing an increase from \langle[Eu/Fe]\rangle=+0.12 for stars between 0–5\arcmin to \langle[Eu/Fe]\rangle=+0.23 for stars between 5–10\arcmin from the core. Unfortunately, the sample size becomes too small outside \sim10\arcmin to conclude whether this trend continues.

Figure 10 reveals that [Eu/Fe] exhibits a significantly different behavior than [La/Fe] when plotted as a function of [Fe/H]. The full range is somewhat smaller with [Eu/Fe] spanning –0.46 to +0.83, and the average [Eu/Fe] abundance appears to decrease in the metallicity range where [La/Fe] shows its greatest increase. While the intermediate metallicity populations generally contain the lowest [Eu/Fe] abundances, the average [Eu/Fe] ratios differ by only \sim+0.1 dex among the different stellar populations.

5 DISCUSSION

The results of our analyses support previous observations that \omega Cen hosts multiple stellar populations exhibiting a complex history of chemical enrichment. To briefly summarize, we have confirmed five peaks in the metallicity distribution function located at [Fe/H]\approx–1.75, –1.50, –1.15, –1.05, and –0.75; however, for discussion purposes the [Fe/H]=–1.15 and –1.05 populations are treated as a single group. The RGB–MP, RGB–Int1, RGB–Int2+3, and RGB–a populations constitute 61\%, 27\%, 10\%, and 2\% of stars in our sample, respectively. We also find large intrinsic abundance dispersions for O, Na, and Al, and, except for perhaps in the most metal–rich stars, these elements exhibit the well–known abundance correlations and anticorrelations found in “normal” globular clusters. Additionally, the O–poor ([O/Fe]\leq0) stars are located almost exclusively within \sim5–10\arcmin of the cluster center, but the O–rich ([O/Fe]\sim+0.3) stars are rather evenly distributed at all cluster radii. The heavier \alpha elements Si, Ca, and Ti exhibit smaller star–to–star dispersions than the lighter elements and are generally enhanced by about a factor of two. The average [\alpha/Fe] ratio tends to increase with metallicity up to [Fe/H]\approx–1, and above this metallicity the average [Ca/Fe] ratio begins to decline while the average [Si/Fe] and [Ti/Fe] abundances remain roughly constant. The two Fe–peak elements scandium and nickel exhibit little star–to–star dispersion and their [X/Fe] ratios are nearly constant as a function of metallicity. We find a strong increase in the [La/Fe] abundances when comparing stars in the RGB–MP and RGB–Int1 populations, but the average [La/Fe] ratios for stars in the RGB–Int2+3 and RGB–a populations remain roughly the same. In contrast, [Eu/Fe] does not vary strongly with metallicity and is only modestly enhanced. We now aim to interpret what these results reveal about \omega Cen’s complex evolutionary history.

5.1 Supernova Nucleosynthesis: Evidence from Heavy \alpha and Fe–peak Elements

The standard theory of Galactic chemical evolution suggests that massive stars (\gtrsim10 M{}_{\sun}) produce the majority of elements up to the Fe–peak during various hydrostatic and/or explosive burning stages, and return the newly synthesized material to the interstellar medium (ISM) primarily through Type II SN explosions (e.g., Arnett & Thielemann 1985; Thielemann & Arnett 1985; Woosley & Weaver 1995; Nomoto et al. 2006). Theoretical yields indicate that stellar populations where Type II SNe have played the dominant role in polluting the ISM should produce future generations of stars with [\alpha/Fe] ratios that are about 0.3–0.5 dex larger than the solar–scaled value, and exhibit abundance ratios in the range –0.5\lesssim[X/Fe]\lesssim+0.3 for other elements lighter than about zinc. The massive stars provide chemical enrichment on time scales of \sim2\times10{}^{\rm 7} years or less, and are believed to be the dominant production sources of most elements in the Galactic halo and disk up to [Fe/H]\approx–1 (e.g., Timmes et al. 1995; Samland 1998). In contrast, Type Ia SNe primarily produce Fe–peak elements, and can contribute to a stellar population’s ISM about 5\times10{}^{\rm 8} to 3\times10{}^{\rm 9} years after the onset of star formation (e.g., Yoshii et al. 1996; Nomoto et al. 1997). Significant contributions from Type Ia SNe are believed to drive the observed decrease in the Galactic [\alpha/Fe] abundance trend at [Fe/H]>–1.

Figure 13 shows our measured [X/Fe] ratios as a function of [Fe/H], and overplots the expected abundance trends if (1) Type II SNe are responsible for all of \omega Cen’s chemical enrichment and (2) Type Ia ejecta are mixed with Type II ejecta in a 75/25\% ratio. For consistency, we show only the supernova yields from Nomoto et al. (1997; Type Ia) and Nomoto et al. (2006; Type II), but the theoretical yields from other groups (e.g., Woosley & Weaver 1995) follow approximately the same trends. We find that the \alpha and Fe–peak abundance distributions are generally well described by pollution from Type II SNe. However, Figures 10 and 13 indicate that the behavior of [Si/Fe], [Ca/Fe], and [Ti/Fe] as a function of increasing [Fe/H] is more complex than for [Sc/Fe] and [Ni/Fe]. For all three \alpha elements, the average [\alpha/Fe] abundance noticeably increases between the most metal–poor and intermediate metallicity populations. Additionally, the stars with [Fe/H]<–2 tend to exhibit larger [Si,Ca/Fe] ratios than the rest of the RGB–MP stars, but the [Ti/Fe] abundances are mostly uniform across the full RGB–MP metallicity range.

Some of this behavior may be at least qualitatively explained by examining the mass and/or metallicity dependent yields of massive stars. In Figure 14, we plot the predicted production factors from Woosley & Weaver (1995) for various elements as a function of progenitor mass. The increase in the average [Si/Fe] and [Ca/Fe] abundances for \omega Cen stars at [Fe/H]>–1.6 may be explained by the metallicity dependence of the Si and Ca yields, especially for stars more massive than about 18–20 M{}_{\sun}. As can be seen in Figure 14, the most massive stars are predicted to produce higher yields as the metallicity increases from [Fe/H]=–2 to –1, but the difference between the Si and Ca yields are expected to remain roughly constant. This means that as long as \omega Cen was able to retain and mix the ejecta of \gtrsim18 M{}_{\sun} stars, we should expect (1) that the average [Si/Fe] and [Ca/Fe] abundances should increase with [Fe/H] and (2) that both Si and Ca should exhibit the same general morphology until at least [Fe/H]\approx–1. Both of these predictions are seen in Figures 10 and 13. However, the similar increase found for [Ti/Fe] may not be due to Type II SNe. The theoretical yields do not predict a significant increase in [Ti/Fe] as a function of either progenitor mass or metallicity, and the situation does not improve if >25 M{}_{\sun} stars are included (e.g., McWilliam 1997). Instead, it seems likely that titanium has additional production sources. We should note that this all follows the assumption that the observed abundances trace {}^{\rm 48}Ti, in addition to {}^{\rm 28}Si and {}^{\rm 40}Ca, but an increase in the production of other stable isotopes could alter this scenario.

Mass dependent yields may also be responsible for explaining the discrepancy in [Si,Ca/Fe] between the stars with [Fe/H]<–2 and the rest of the RGB–MP population. As noted in \lx@sectionsign4, the average [Si/Fe] and [Ca/Fe] abundances are 0.17 and 0.11 dex larger for the [Fe/H]<–2 stars. This trend can be reconciled if the most metal–poor stars in the cluster, which represent only 3\% of the RGB–MP population, preferentially formed from the ejecta of \gtrsim20 M{}_{\sun} stars. However, this would require very rapid enrichment of the early \omega Cen environment because >20 M{}_{\sun} stars live \lesssim10{}^{\rm 7} years (e.g., Schaller et al. 1992). Note that this scenario is compatible with the observation that the [Fe/H]<–2 stars have the same mean [Ti/Fe] abundance as the rest of the RGB–MP population because, as mentioned above, the titanium yields from >20 M{}_{\sun} stars are comparable to those of lower mass stars. Additionally, if a monotonic relationship between [Fe/H] and formation time exists for at least the RGB–MP stars, then the mass dependent yields may also explain the apparent decrease in [Si,Ca/Fe] as [Fe/H] increases from \sim–2 to –1.6, as well as, the steeper decline for [Si/Fe] compared to [Ca/Fe]. As indicated by Figure 14, the decline in Si yield is a stronger function of progenitor mass between 18–25 M{}_{\sun} than for Ca. Therefore, forming stars from gas polluted by progressively less massive SNe should qualitatively reproduce the observed trend. The sudden increase in [Si,Ca/Fe] in the RGB–Int1 population would then make sense if a new round of star formation began with >20 M{}_{\sun} stars contributing once again.

5.1.1 Are Type Ia SNe Required?

Since previous analyses have estimated that the age spread among the various \omega Cen populations is \sim2–4 Gyr (e.g., Stanford et al. 2006), it would seem reasonable to assume that Type Ia SNe could have contributed to the cluster’s chemical enrichment. However, the consistently elevated [\alpha/Fe] ratios observed for nearly all stars in the cluster suggests that Type Ia enrichment has been limited. Pancino et al. (2002) and Origlia et al. (2003) found in a small sample of \omega Cen giants that the RGB–a stars had noticeably lower [\alpha/Fe] and higher [Cu/Fe] abundances than the lower metallicity stars, and attributed these trends to the onset of Type Ia SNe at [Fe/H]>–1. On the other hand, Cunha et al. (2002) analyzed [Cu/Fe] abundances in a larger sample spanning [Fe/H]\sim–2 to –0.8, and did not find evidence for an increase in [Cu/Fe]. Similarly, Norris & Da Costa (1995) and Smith et al. (2000) did not find evidence for a decrease in [\alpha/Fe] or an increase in [Cu/Fe].

While the primary production source of Cu is uncertain (e.g., Sneden et al. 1991b; Matteucci et al. 1993), it is clear that ambiguity remains regarding the significance of Type Ia SNe to \omega Cen’s chemical evolution. Our data are generally inconsistent with the rather extreme 75\% Type Ia to 25\% Type II mixture plotted in Figure 13, especially at [Fe/H]<–1. Although we find a slight decrease in [Ca/Fe] at [Fe/H]>–0.7, at least part of this decrease may be explained by a reduction in calcium yields from more metal–rich Type II SNe (e.g., see Figures 1314). Interestingly, the [Si/Fe] and [Ti/Fe] ratios do not exhibit similar decreases at [Fe/H]>–0.7. However, the larger measurement error for silicon compared to calcium may be masking any subtle trends, and although titanium is often enhanced like other \alpha elements in globular cluster stars its dominant isotope {}^{\rm 48}Ti is not an \alpha isotope. Additionally, analyzing different mixtures of Type II versus Ia ejecta requires inherent assumptions about the massive star IMF and the source of Type Ia SNe, which in Figure 13 is the “standard” white dwarf deflagration model. The model values shown in Figure 13 could easily be changed by using different assumptions and adjusting the aforementioned parameters.

A more empirical approach is to compare the evolution of \alpha and Fe–peak elements with other stellar populations exhibiting different levels of Type Ia enrichment. In Figures 1517 we plot our derived abundances for \omega Cen stars as a function of [Fe/H], and compare with data from the literature tracing the chemical evolution of other globular clusters, the Galactic thin/thick disk, halo, bulge, and nearby dwarf galaxies (see Table 8 for literature references). Focusing on the heavy \alpha and Fe–peak elements at the metal–rich end of the distribution shows that, at least for stars with [Fe/H]<–0.7, \omega Cen generally follows a morphology similar to that found in monometallic globular clusters, the Galactic halo, and the Galactic bulge. In contrast, the most metal–rich \omega Cen stars ([Fe/H]>–0.7) exhibit [Ca/Fe] ratios that are more similar to those found in Galactic thick disk stars (e.g., see Brewer & Carney 2006). Additionally, the most metal–rich \omega Cen stars tend to exhibit [Ca/Fe] ratios that are, on average, at least 0.1–0.2 dex lower than those found in the more metal–poor stars. This may indicate that the level of Type Ia enrichment in the most metal–rich \omega Cen stars and the thick disk were comparable. However, at [Fe/H]>–0.7 the [Ni/Fe] ratios are noticeably low in the \omega Cen stars, and as mentioned previously the [Si/Fe] and [Ti/Fe] data do not exhibit similar abundance decreases in concert with [Ca/Fe]. Although \omega Cen is widely believed to be the remnant core of a dwarf spheroidal galaxy, the heavy \alpha elements are enhanced in \omega Cen stars by a factor of 2–3 compared with other dwarf galaxies, at least for [Fe/H]\gtrsim–1.5.

In addition to the heavy \alpha and Fe–peak elements, the lighter elements O, Na, and Al are also inconsistent with significant contributions from Type Ia SNe. Figure 13 shows that nearly all of the stars with [Fe/H]>–1 have [Na/Fe] and [Al/Fe] abundances that are well above even the levels predicted by Type II SNe, but [O/Fe] is abnormally low. The abundance patterns expected from Type Ia production should lead to an overall decrease in the average abundance of all three elements as [Fe/H] increases. However, these elements can be altered by either in situ mixing or pollution from other sources, and therefore may not be reliable indicators of a star’s original composition. While the heavy \alpha element data, in particular [Ca/Fe], provide some evidence for Type Ia SN contributions in the most metal–rich stars, the light element data are in better agreement with a Type II SN pollution model that includes an additional proton–capture production mechanism. The apparent suppression of Type Ia SNe in \omega Cen remains an open problem, but it may be at least partially tied to the cluster’s several Gyr relaxation time scale (e.g., van de Ven et al. 2006) and low (\sim3–4\%) binary frequency (Mayor et al. 1996).

5.2 Proton–Capture Processing: Light Element Variations

The light elements oxygen through aluminum provide sensitive diagnostics for determining the chemical enrichment history of stellar populations. These elements are primarily produced in the hydrostatic helium, carbon, and/or neon burning stages of massive (\gtrsim10 M{}_{\rm\sun}) stars (e.g., Arnett & Thielemann 1985; Thielemann & Arnett 1985; Woosley & Weaver 1995). Stars forming out of gas that has been primarily polluted by Type II SNe should have [O/Fe]\sim+0.4 and exhibit increasing [Na/Fe] and [Al/Fe] abundances with increasing metallicity. However, these elements can also be produced (or destroyed) in lower mass stars that reach internal temperatures high enough to activate the proton–capture ON, NeNa, and MgAl cycles. If this processed material is mixed to the surface, then some stars may return gas to the ISM that is O–poor and Na/Al–rich compared to the material ejected by Type II SNe. This scenario is believed to occur in the RGB and AGB phases of low and intermediate mass (\lesssim8 M{}_{\rm\sun}) stars (e.g., Sweigart & Mengel 1979; Cottrell & Da Costa 1981; Denisenkov & Denisenkova 1990; Langer et al. 1993; Ventura & D’Antona 2009; Karakas 2010), but also in the cores of massive, rapidly rotating main sequence stars (e.g., Decressin et al. 2007).

Figures 1518 highlight the distinct light element abundance patterns found in several different stellar populations. Examination of these trends indicates that although \omega Cen shares some abundance patterns with other globular cluster, Galactic disk, halo, bulge, and nearby dwarf galaxy stars, it differs from all of these both in the extent of its star–to–star abundance variations and its individual abundance ratios. Approximately half of the RGB–MP stars have O, Na, and Al abundances that are consistent with those found in similar metallicity halo, and to a lesser extent, dwarf galaxy stars. The chemical composition of these stars is believed to be primarily a result of Type II SN enrichment, and the chemical similarities among these populations is not unexpected. It seems likely that \omega Cen would have had considerable interaction with the primordial gas that formed the Galactic halo, and it has been shown that reproducing the cluster’s metallicity distribution function is only possible in an open box scenario (e.g., Ikuta & Arimoto 2000; Romano et al. 2007). However, the remaining RGB–MP stars exhibit [O/Fe], [Na/Fe], and [Al/Fe] abundances that are significantly different than those found in metal–poor halo and dwarf galaxy stars. In particular, the “enhanced” RGB–MP stars are O–poor and Na/Al–rich. Similar chemical compositions are only found in some monometallic globular cluster stars (e.g., see reviews by Kraft 1994; Gratton et al. 2004). Interestingly, the number of stars in \omega Cen that are O–poor and Na/Al–rich increases to 60–95\% at higher metallicities. The RGB–Int2+3, and especially the RGB–a, stars have [O/Fe], [Na/Fe], and [Al/Fe] ratios that differ significantly even from individual globular clusters by at least a factor of two. Figure 18 shows that this is true even when considering [O/Na], [O/Al], and [Na/Al] ratios instead of [X/Fe]. Our data indicate that the \omega Cen stars at [Fe/H]\gtrsim–1.3 experienced an additional enrichment process that is not observed in any other stellar system studied so far, but the combined populations of M54 and the Sagittarius dwarf galaxy may share some similar trends (Carretta et al. 2010).

The light element abundance patterns in other globular clusters are typically believed to be the result of high temperature proton–capture nucleosynthesis operating in an environment where a combination of the ON, NeNa, and MgAl cycles are or were active. Material that has been processed through these proton–capture cycles is expected to exhibit a deficiency in [O/Fe] concurrent with supersolar [Na/Fe] and [Al/Fe] ratios, which should naturally lead to O–Na and O–Al anticorrelations along with a Na–Al correlation. In Figures 1921, we plot [O/Fe], [Na/Fe], and [Al/Fe] against each other for the major \omega Cen populations described in \lx@sectionsign4.1. We find that the O, Na, and Al abundance relations found in the RGB–MP, RGB–Int1, and RGB–Int2+3 populations are consistent with the abundance patterns that are characteristic of high temperature proton–capture processing. Furthermore, the impact of proton–capture nucleosynthesis appears to increase as a function of increasing metallicity. Both the extent of the light element variations and the percentage of stars that are O–poor and Na/Al–rich increases monotonically with [Fe/H]. However, the same O–Na, O–Al, and Na–Al relations are not observed in the RGB–a population. Instead, the RGB–a, as well as a few RGB–Int2+3, stars exhibit a rather uniform composition that is moderately O–poor ([O/Fe]\sim–0.15), very Na–rich ([Na/Fe]\sim+0.78), and is unlike any of the more metal–poor \omega Cen stars.

A common interpretation of the light element abundance trends in monometallic globular clusters is that the O–rich, Na/Al–poor stars represent the first generation of stars formed from the ejecta of Type II SNe, and the O–poor, Na/Al–rich stars represent a subsequent generation formed from gas that had been chemically enriched by intermediate mass AGB stars or some other polluting source in which the ON, NeNa, and/or MgAl cycles were active (e.g., D’Ercole et al. 2008; Carretta et al. 2009b). The first generation stars are often referred to as “primordial” stars, and the enriched populations are referred to as either “intermediate” or “extreme”, depending on the level of O–depletion and Na–enrichment (e.g., Carretta et al. 2009a; but see also Lee 2010 for a different interpretation).

The \omega Cen data can be divided into similar subpopulations. Here we follow a similar definition to that used in Carretta et al. (2009a) where the primordial component is defined as having [O/Fe]\geq0 and [Na/Fe]\leq+0.1, the intermediate component includes stars with [O/Fe] ratios satisfying the relation [O/Fe]\geq[0.62([Na/Fe])–0.65], and the extreme component consists of the remaining most O–poor stars. Monometallic globular clusters typically consist of \sim20–40\% of stars belonging to the primordial component, \sim30–80\% in the intermediate component, and \lesssim20\% in the extreme component (e.g., Carretta et al. 2009a). As can be seen in Figures 1921, the RGB–MP stars follow the general trend observed in monometallic globular clusters with a primordial:intermediate:extreme distribution of 50\%:43\%:7\%, respectively. The RGB–Int1 population contains roughly an equal proportion of primordial, intermediate, and extreme abundance stars with a distribution of 30\%:32\%:38\%. However, the RGB–Int2+3 and RGB–a stars contain far more extreme abundance stars than are found in any globular cluster with distributions of 11\%:15\%:74\% and 5\%:14\%:81\%, respectively. The large number of intermediate and extreme abundance stars indicates that \omega Cen likely experienced a similar enrichment process to that in monometallic globular clusters during each round of star formation, and it is interesting to note that the populations expected to be He–rich exhibit the largest fraction of extreme abundance stars. While there is a clear delay in the onset of whichever mechanism drives the O–poor, Na/Al–rich abundance phenomenon, it is worth noting that we find a very low incidence of carbon stars161616While we do not provide explicit carbon abundance measurements in this paper, the possible carbon stars listed in Figure 1, Figure 3, and Table 2 were identified by visual inspection of their spectra. However, all three of the possible carbon stars identified here that also overlap with the van Loon et al. (2007) survey (LEID 32059, 41071, and 52030) are confirmed carbon stars based on the presence of strong C{}_{\rm 2} bands in their spectra. (<2\%; see Figure 1) despite the large population of O–poor stars. Unfortunately, we cannot distinguish between in situ carbon stars and those formed from mass transfer, but the frequency of carbon stars on the giant branch is consistent with the expected binary fraction of \sim3–4\% (Mayor et al. 1996).

5.2.1 Enrichment by Pollution and in situ Processing

Although we have identified the major light element abundance trends for \omega Cen, the information so far has only led us to conclude that proton–capture nucleosynthesis has likely played a significant role in the cluster’s chemical enrichment. Further examination is required in order to understand the possible location(s) where these processes are or were active. The comparatively small star–to–star dispersion in [X/Fe] exhibited by the heavy \alpha and Fe–peak elements (see Figure 10) indicates that the >1 dex variations observed for [O/Fe], [Na/Fe], and [Al/Fe] are not due to incomplete mixing of SN ejecta, as is suspected for [Fe/H]<–3 halo stars (e.g., McWilliam 1997). Previous studies have found that many of the light element abundance patterns exhibited by monometallic globular cluster stars, which are subsequently shared by many \omega Cen stars, may be best explained by proton–capture nucleosynthesis operating at temperatures near 70\times10{}^{\rm 6} K (e.g., Langer et al. 1997; Prantzos et al. 2007). If at least part of the abundance patterns found in \omega Cen and other globular cluster stars are due to pollution from external sources, then the currently favored production mechanisms are: (1) hot bottom burning in >5 M{}_{\sun} AGB stars (e.g., Ventura & D’Antona 2009; Karakas 2010), (2) hydrogen shell burning in now extinct but slightly more massive RGB stars (Denissenkov & Weiss 2004), and (3) core hydrogen burning in rapidly rotating massive stars (Decressin et al. 2007).

While massive, rapidly rotating stars and extinct \sim0.9–2 M{}_{\sun} RGB stars may also reproduce many of the observed light element trends, presently there are no detailed theoretical yields spanning a fine grid of metallicities similar to those available for intermediate mass AGB stars. Furthermore, the time scale of pollution from extinct low mass RGB stars is at least 2–3 times longer than the estimated age spread among the different \omega Cen populations, but this does not rule out possible mass transfer pollution from these objects. Additionally, the massive, rapidly rotating star scenario is expected to produce a continuum of polluted stars with varying He abundances (Renzini 2008), which is inconsistent with the singular Y=0.38 value that seems required to fit the blue main sequence (e.g., Piotto et al. 2005). Romano et al. (2010) also point out that if the winds from massive main sequence stars are also responsible for the anomalous light element abundance variations in the current generations of \omega Cen stars, it is not clear why the He enrichment was delayed until higher metallicities. However, Renzini (2008) and Romano et al. (2010) find that intermediate mass AGB stars may provide a reasonable explanation for the high He content in some stars, in addition to the average behavior of [Na/Fe], and to a lesser extent [O/Fe], in \omega Cen. Therefore, we will only consider the AGB pollution scenario here, but we caution the reader that several qualitative and quantitative hurdles remain in order for AGB pollution to be a viable explanation of light element variations in globular clusters (e.g., Denissenkov & Herwig 2004; Denissenkov & Weiss 2004; Fenner et al. 2004; Ventura & D’Antona 2005; Bekki et al. 2007; Izzard et al. 2007; Choi & Yi 2008).

In Figure 22, we plot our derived O, Na, and Al abundances as a function of [Fe/H], and overplot the metallicity dependent theoretical yields from Type II SNe, as well as, 3–6 M{}_{\sun} AGB stars. While the \omega Cen stars with chemical compositions similar to the Galactic disk and halo appear well bounded by production from Type II SNe, the enhanced stars at least qualitatively follow the general trends predicted by production from >5 M{}_{\sun} AGB stars. In particular, the depletion of oxygen concurrent with the rise in sodium and decline in the maximum [Al/Fe] ratio with increasing metallicity are all consistent with the predicted patterns exhibited by material that has been processed via hot bottom burning in >5 M{}_{\sun} AGB stars. However, the theoretical AGB yield curves shown in Figure 22 do not include lifetime estimates for the polluting AGB stars, and one could envision sliding the various curves along the abscissa to account for age differences among the different populations. In other words, plots similar to Figure 22 lend insight into whether the abundance trends are possibly consistent with AGB pollution, but numerical chemical evolution models are required to fully constrain which mass ranges have contributed to the chemical composition of stars in a given population.

Despite this limitation, we can use Figure 22 to elicit some constraints. We find that while 5–6 M{}_{\sun} AGB ejecta are generally consistent with the abundance trends observed at all metallicities, 3–4 M{}_{\sun} AGB stars likely did not contribute significantly to \omega Cen’s chemical enrichment until about [Fe/H]=–1.3. This is most evident by examining the [O/Al] and [Na/Al] ratios in Figure 22. The <5 M{}_{\sun} AGB stars produce [O/Fe] and [Na/Fe] ratios that are too high and [Al/Fe] ratios that are too low to fit the data, even when diluted with SN or >5 M{}_{\sun} AGB ejecta. Figures 1921 also support the rejection of 3–4 M{}_{\sun} AGB ejecta, which originate from AGB stars of comparable metallicity, from contributing significantly to the chemical composition of stars with [Fe/H]<–1.3. However, Figures 1922 do not rule out that <5 M{}_{\sun} AGB stars with [Fe/H]\lesssim–1.5 impacted enrichment of the RGB–Int2+3 and RGB–a populations. The [Na/Fe] and [Al/Fe] yields from metal–poor AGB stars are mostly consistent with the trends observed in the intermediate and most metal–rich \omega Cen giants, but it seems that an additional mechanism may be required to explain the [O/Fe] abundances. Note that our conclusions are not drastically altered if we adopt the theoretical AGB yields from Karakas (2010)171717This statement is based on using the average mass fraction data from Tables A2–A6 in Karakas (2010)., which uses mixing length theory for convection, instead of the Ventura & D’Antona (2009) yields, which use the full spectrum of turbulence theory for convection and are shown in Figures 1922. Unfortunately, Karakas (2010) does not provide yield information for metallicities between [Fe/H]=–2.3 and –0.7, which makes direct comparison with \omega Cen difficult because most stars fall in the missing range.

One of the most puzzling aspects concerning the abundance patterns of light elements in \omega Cen is the strongly bimodal distribution at intermediate metallicities (see Figure 11). If ISM pollution was driven by AGB stars, then it is unclear why (1) only the RGB–MP stars exhibit a continuous distribution of [O/Fe], [Na/Fe], and [Al/Fe] abundances and (2) more than 70\% of the more metal–rich stars have envelope material that has experienced significant proton–capture processing. As can be seen in Figures 1922, the [O/Fe] yields from AGB stars are by far the most inconsistent with our data, but the full mass range of AGB stars may reproduce the [Na/Fe] and [Al/Fe] abundances at nearly all metallicities. Depleting the oxygen abundance from [O/Fe]=+0.4 to [O/Fe]<–0.4 via hot bottom burning in AGB stars is generally not achieved for any mass or metallicity range. However, D’Ercole et al. (2010) showed that including the ejecta of “super–AGB” (>6.5 M{}_{\sun}) stars may reproduce the super O–poor ([O/Fe]<–0.4) abundances found in some globular clusters under the assumption that the massive AGB stars deplete to [O/Fe]\approx–1. Despite this, it is unlikely that more massive AGB stars are the culprits behind the large contingent of super O–poor \omega Cen stars because one would have to assume an IMF strongly weighted toward \sim5–9 M{}_{\sun} stars in order to produce so many super O–poor stars. Note that this is not as much of a problem in monometallic globular clusters because the number of super O–poor stars is <20\% (e.g., Carretta et al. 2009a). It seems that invoking some degree of in situ proton–capture processing is required to explain the observed abundance patterns of \omega Cen stars with [Fe/H]\gtrsim–1.6, in order to avoid unrealistic requirements such as IMFs strongly weighted toward intermediate mass stars or forming a majority of the RGB–Int1, RGB–Int2+3, and RGB–a stars almost entirely out of a narrow mass range of AGB stars.

A key assumption when considering in situ processing in low mass RGB stars is that the material being enriched near the hydrogen burning shell must be able to mix into the convective envelope and be brought to the surface. In stars with normal helium abundances, it is not believed that this can occur until the hydrogen burning shell erases the molecular weight barrier left behind by the convective envelope after first dredge–up (e.g., see review by Salaris et al. 2002). However, some or all of the intermediate metallicity stars in \omega Cen are thought to be quite He–rich, and D’Antona & Ventura (2007) found that stars with Y=0.35–0.40 should contain a much more shallow molecular weight gradient that might not inhibit deep mixing. Instead, deep mixing in He–rich stars might be active over a wide range of luminosities on the giant branch, which would be consistent with our observation that the degree of light element enrichment is not strongly correlated with luminosity. These authors also find that reproducing the abundance patterns exhibited by the super O–poor stars can be achieved by in situ mixing if the RGB stars are already polluted by the ejecta of intermediate mass AGB stars. In their scenario, in situ mixing should decrease the envelope [O/Fe] ratio by up to a factor of 10 while only increasing the [Na/Fe] ratio by about 0.2 dex. While the evolution of [Al/Fe] is not reported by D’Antona & Ventura (2007), we can speculate that the enhancement in [Al/Fe] is smaller than that experienced by [Na/Fe] given the higher temperatures required to convert Mg to Al.

As mentioned above, the proposed deep mixing scenario only works if the intermediate metallicity RGB stars in \omega Cen formed from material that was already enriched by hot bottom burning in intermediate mass AGB stars. Our current data set does not provide direct evidence of this, but we may look to the behavior of silicon as a proxy indicator because {}^{\rm 28}Si can be produced through leakage from the MgAl cycle at temperatures >65\times10{}^{\rm 6} K (e.g., Yong et al. 2005; Carretta et al. 2009b). In Figure 23, we plot our [X/Fe] abundances as a function of [Fe/H] color coded by the primordial, intermediate, and extreme abundance components described above. While most of the \alpha and Fe–peak elements do not display any particular dependence on light element abundance, the RGB–MP and RGB–Int1 extreme component stars exhibit silicon enhancements of nearly 0.3 dex compared to the primordial and intermediate component stars. Furthermore, in Figure 24 we plot [O/Fe], [Na/Fe], and [Al/Fe] versus [Si/Fe], [Ca/Fe], and [Ti/Fe] and find that only silicon shows any semblance of a correlation with O, Na, and Al, as is indicated by the respective Pearson correlation coefficients shown in Figure 24. This suggests that silicon may have undergone an additional production process not experienced by the heavier \alpha elements. The existence of an Al–Si correlation concurrent with an O–Si anticorrelation suggests that the O–poor stars were likely polluted by material that had been processed at temperatures exceeding \sim65\times10{}^{\rm 6} K. These conditions are reached during hot bottom burning in intermediate mass AGB stars, but not in the hydrogen burning shells of low mass RGB stars.

Since the \omega Cen stars likely satisfy the prerequisites needed for in situ mixing to occur, we may attribute a large portion of the [O/Fe], and to a lesser extent the [Na/Fe], variations to this process. The relatively small number of RGB–MP stars that are super O–poor suggests that the helium content had not yet been significantly increased in the cluster to allow the formation of He–rich stars. In fact, there are very few super O–poor stars at [Fe/H]<–1.7. The radial segregation of O–poor stars (see Figure 9) is also consistent with the idea that additional time was needed to increase the cluster He content, and may indicate that He–rich gas was preferentially funneled into the cluster core, as is suggested in the models by D’Ercole et al. (2008). We find that the light element abundance trends in the intermediate metallicity and RGB–a stars are consistent with an AGB pollution plus in situ mixing scenario. In these stars, the high [Na/Fe] and [Al/Fe] abundances are consistent with production in comparable metallicity or more metal–poor AGB stars because in situ mixing is not expected to significantly increase [Na/Fe] or [Al/Fe] in He–rich RGB stars that are already O–poor and Na/Al–rich (D’Antona & Ventura 2007). Additionally, the increasing minimum [O/Fe] abundance at [Fe/H]\gtrsim–1 is consistent both with the increase in the [O/Fe] yields for >5 M{}_{\sun} AGB stars and the fact that in situ mixing should produce less advanced proton–capture processing at higher metallicities. This is due primarily to the lower temperatures achieved in the interiors of more metal–rich stars, but may also occur if the He mass fraction in the RGB–a stars is smaller than in the RGB–Int2+3 stars, which could lead to more shallow mixing. Lastly, we note that because the [Na/Fe] and [Al/Fe] abundances do not share the same correlation as [O/Fe] with radial location, it may be the case that some stars producing high Na and Al yields do not necessarily produce large He yields.

One of the most important effects of including in situ mixing in the chemical enrichment picture is that it reduces the necessity for AGB stars to account for all abundance patterns, and also increases the mass range of available AGB polluters to more than just those with favorable yields. The inferred high He–content of the blue main sequence population and the observed large increase in s–process enrichment in this cluster indicate that the large degree of ISM pollution required for the above scenario to work is not unreasonable. A detailed comparison of the {}^{\rm 24}Mg, {}^{\rm 25}Mg, and {}^{\rm 26}Mg isotopes may be particularly illuminating in order to investigate whether hot bottom burning, in situ processing, or both played an active role in shaping the abundance patterns of \omega Cen giants. Note that fluorine is also expected to be strongly depleted in the proposed deep mixing scenario. Furthermore, a large sample spectroscopic abundance analysis of stars at lower luminosities could provide an interesting test for the impact of in situ mixing.

5.2.2 Oxygen Abundances and a Possible Connection to the Blue Main Sequence

The discovery and subsequent detailed analyses of \omega Cen’s blue main sequence (Anderson 1997, 2002; Bedin et al. 2004; Norris 2004; Piotto et al. 2005; Sollima et al. 2007; Bellini et al. 2009b) have revealed that this population represents \sim30\% of all main sequence stars, is preferentially located near the cluster center, and perhaps most importantly is more metal–rich than the dominant red main sequence. As mentioned in \lx@sectionsign1, the commonly accepted reason for the existence of the blue main sequence is that these stars are significantly more He–rich than the dominant population of more metal–poor stars. In fact, Norris (2004) and Piotto et al. (2005) find that the blue main sequence is best fit with an extreme helium abundance of Y\approx0.38. One of the most interesting characteristics of the blue main sequence is that it is well detached from the red main sequence in color, and almost no stars are found in between the two sequences (e.g., see Bedin et al. 2004; their Figure 1). From this and the information above, we might expect the current RGB stars that were once part of the blue main sequence to be chemically conspicuous, preferentially located near the cluster center, and more metal–rich that the dominant stellar population.

Examination of the abundance patterns in the RGB–Int1 and RGB–Int2+3 stars reveals that the [O/Fe] ratio stands out as a possible indicator of which stars once belonged to the blue main sequence. At intermediate metallicities, a majority of the stars have [O/Fe]\leq0, and the radial distribution of these stars shows that more than 90\% are located inside 10\arcmin from the cluster center while only 70\% of those with [O/Fe]>0 are located in the same range (see Figure 9). However, in order for the [O/Fe] abundance to be considered as a chemical tracer of the blue main sequence it must qualitatively and quantitatively agree with the observed trends of blue main sequence stars. In Figure 25, we plot the number ratio of O–poor to O–rich stars out to \sim15\arcmin, and also plot the measured number ratios of blue to red main sequence stars from Bellini et al. (2009b). Although we are plotting an indirect measurement of the ratio of blue to red main sequence stars with N{}_{\rm O-poor}/N{}_{\rm O-rich} and the Bellini et al. (2009b) data represent direct measurements, we find that the two trends are in reasonable agreement. Both data sets indicate that the majority of O–poor (blue main sequence) stars are inside \sim5\arcmin of the cluster center, and the relative ratio of O–poor/O–rich (blue/red main sequence) stars decreases at larger radii. Note that Sollima et al. (2007) come to a similar conclusion when considering stars located at \sim7–23\arcmin from the cluster center.

Since the relative ratios of O–poor to O–rich stars follow those observed for the blue and red main sequences, we may expect the absolute number of O–poor stars to also be consistent with that of the blue main sequence stars due to our high completion percentage (see Figure 2). As mentioned previously, it is estimated that the blue main sequence constitutes \sim25–35\% of all main sequence stars, and we find in agreement with this estimate that 27\% of all RGB stars in our sample are O–poor. Additionally, Piotto et al. (2005) showed that the blue main sequence is best fit by a metallicity similar to that of the RGB–Int1 and RGB–Int2+3 populations. We find that at least 65\% of the O–poor stars in our sample are located in the appropriate metallicity range. This percentage may in fact be somewhat larger if we consider that (1) very few O–poor stars are found at [Fe/H]<–1.7, (2) the average [Fe/H] abundance error is roughly \pm0.1 dex, and (3) the boundary between the RGB–MP and RGB–Int1 populations is not uniquely defined. However, we would still find that \sim20–30\% of intermediate metallicity stars are O–rich. Note that a significant number of O–rich, intermediate metallicity stars (i.e., stars in the correct metallicity range that would not lie on the blue main sequence) would be consistent with the observation by Sollima et al. (2006) that many RR Lyrae stars with [Fe/H]\sim–1.2 have standard helium abundances.

In any case, we have demonstrated that the O–poor giants are spatially similar, found mostly in the same metallicity range, and are present in nearly identical proportions to those found on the blue main sequence. It is not entirely clear why the [O/Fe] ratio in the giants shares a similar sensitivity to radial location and metallicity with the blue main sequence stars, but we speculate that the oxygen deficient stars are connected with the blue main sequence through helium enrichment. That is, the He–rich main sequence stars are pushed blueward on the color–magnitude diagram, and the He–rich giants experience in situ mixing that strongly depletes oxygen without similarly large increases in sodium and aluminum. Comparison between the 7770 Å oxygen triplet line strengths in blue and red main sequence stars would provide a direct confirmation of our hypothesis. Although we have invoked in situ mixing to explain the very large O–depletion in these stars, note again that the scenario proposed by D’Antona & Ventura (2007) requires that these star were already somewhat O–poor.

5.3 Neutron–Capture Processing

While the isotopes of most elements lighter than about zinc are produced primarily through charged particle reactions, the isotopes of elements beyond the Fe–peak are mostly produced through neutron–capture reactions. Neutron–capture nucleosynthesis is believed to proceed through two main channels: (1) the s–process where the neutron–capture rate is slow compared to the \beta–decay rate of unstable nuclei and (2) the r–process where the neutron–capture rate is fast compared to the \beta–decay rate of unstable nuclei (e.g., see recent review by Sneden et al. 2008). The large difference in neutron fluxes required for the two processes points to different operational environments. The main component of the s–process is widely believed to be active in thermally pulsing low and intermediate mass AGB stars, but theoretical models indicate that most of the s–process element production is probably constrained to stars in the range \sim1.3–3 M{}_{\sun} (e.g., Busso et al. 1999; Herwig 2005; Straniero et al. 2006). AGB stars \lesssim1.3 M{}_{\sun} have envelope masses that are too small for third dredge–up to occur, and more massive AGB stars are only believed to experience a few third dredge–up episodes. Conversely, the exact location(s) where the r–process operates is (are) not well defined, but significant circumstantial evidence suggests an explosive origin associated with core collapse SNe (e.g., Mathews & Cowan 1990; Cowan et al. 1991; Wheeler et al. 1998; Arnould et al. 2007; Sneden et al. 2008).

The solar system abundances indicate that \sim70–75\% of lanthanum is produced via the s–process and more than 95\% of europium is produced by the r–process (e.g., Sneden et al. 1996; Bisterzo et al. 2010). Therefore, we adopt lanthanum as an s–process indicator and europium as an r–process indicator. As can clearly be seen in Figure 17, the average [La/Fe] ratio increases by more than a factor of three between the RGB–MP and intermediate metallicity populations. Similar increases are not found for any other elements in our sample. This indicates that the s–process has played a significant role in the chemical evolution of \omega Cen, and is a dominant process at [Fe/H]\gtrsim–1.6. Comparison with the other stellar populations plotted in Figure 17 shows that the level of s–process enrichment was far greater in \omega Cen. It is interesting to note that the [La/Fe] ratio does not continue to increase beyond [Fe/H]\geq–1.5 despite the fact that s–process production appears to peak in the metallicity range –1.5\lesssim[Fe/H]\lesssim–0.8, at least for the “standard” {}^{\rm 13}C pocket (e.g., see Bisterzo et al. 2010, their Figure 8). This may indicate that a large fraction of the gas was swept out of the cluster through interaction with the Galaxy before low mass AGB stars with [Fe/H]\gtrsim–1.5 had a chance to contribute to \omega Cen’s chemical enrichment. Comparison between the RGB–Int2+3 and RGB–a stars shows that the average [La/Fe] ratio decreases by \sim0.2 dex (see Figure 12) for higher metallicities, but is still significantly enhanced compared to the Galactic disk and bulge trends. This suggests that s–process production still continued at high metallicities, but the rate of production did not exceed that of iron.

For the RGB–MP stars, the average [Eu/Fe] abundances are similar to those found in halo, dwarf galaxy, and individual globular cluster stars. At higher metallicities, the average [Eu/Fe] abundance of \omega Cen stars actually decreases while the average [La/Fe] abundance shows a significant increase. In fact, many intermediate metallicity \omega Cen stars have [Eu/Fe] abundances that are lower than those found in halo and dwarf galaxy stars, and are especially Eu–deficient compared to globular cluster stars. However, the average [Eu/Fe] abundance increases again at [Fe/H]\gtrsim–1.2 toward values similar to those found in the Galactic disk and bulge. The cause of the decrease in [Eu/Fe] at intermediate metallicities, and the low [Eu/Fe] abundances in general, is not entirely clear. It is believed that \sim8–10 M{}_{\sun} SNe may produce a large portion of the r–process elements (e.g., Mathews & Cowan 1990), but other processes such as neutron star and black hole mergers may be important as well (e.g., see review by Sneden et al. 2008 and references therein). It may be the case that either the IMF did not favor a large number of stars in the 8–10 M{}_{\sun} range or that one or more of the typical r–process production mechanisms was not active at “normal” levels in the intermediate metallicity range. Interestingly, the metallicity range at which the [Eu/Fe] abundance is lowest is also where Cunha et al. (2002; 2010) find low [Mn/Fe] and [Cu/Fe] values. Since Cunha et al. (2010) attributes the low [Cu/Fe] and [Mn/Fe] abundances to metallicity dependent SN yields, we can speculate that the low [Eu/Fe] values might also be due to a related effect. Although manganese and europium are produced through different processes, their production may be tied to similar progenitor objects and/or environments.

Despite the obvious differences in [La/Fe] and [Eu/Fe] abundances for \omega Cen stars compared to those in other populations, the ratio of these elements provides a better diagnostic for analyzing the impact of the s– and r–processes. In the Galactic disk and halo, the [La/Eu] ratio slowly increases with metallicity, and this is believed to be primarily due to the longer time scales required for low and intermediate mass stars to evolve into AGB stars (e.g., Simmerer et al. 2004). Dwarf galaxies also tend to exhibit an increase in s–process elements at higher metallicities, but are typically more s–process enhanced than similar metallicity halo and disk stars (e.g., Geisler et al. 2007). In contrast, most globular clusters follow the disk/halo trend and are generally r–process rich (e.g., Gratton et al. 2004). Figure 18 plots the [La/Eu] ratio as a function of [Fe/H] for these populations and also illustrates the relatively rapid transition in \omega Cen from being r–process to s–process dominated. Many stars in the RGB–MP population exhibit [La/Eu] ratios that are identical to those found in halo, dwarf galaxy, and globular cluster stars. However, almost all of the more metal–rich stars have [La/Eu]>0, and many of these stars have [La/Eu] ratios matching those expected for pure s–process production. Note that proper accounting of hyperfine structure for both the La and Eu lines has revised our [La/Eu] ratios downward, at least for the most La–rich stars, from those found in Johnson et al. (2009). The new results are consistent with the more metal–rich stars forming from gas that was already heavily polluted with s–process elements, but does not require surface pollution from mass transfer. This is in agreement with the results from Stanford et al. (2010), which suggest that the strontium abundances (a light s–process element) in several \omega Cen stars are the result of primordial pollution rather than surface accretion.

Although AGB stars of about 1.3–8 M{}_{\sun} may be able to produce s–process elements, Smith et al. (2000) used the [Rb/Zr] ratio to show that AGB stars between \sim1.5–3 M{}_{\sun} were likely the dominant s–process enrichment sources in \omega Cen. Since these stars have lifetimes of 3\times10{}^{\rm 8}–2\times10{}^{\rm 9} years, the time delay between the formation of RGB–MP stars and subsequent generations had to be at least this long. This delay is consistent with the estimated 2–4 Gyr age range of \omega Cen stars (e.g., Stanford et al. 2006), and is also consistent with the time required for >4–5 M{}_{\sun} AGB stars to have polluted the ISM, as seems required to explain at least part of the light element abundance trends.

In addition to analyzing the behavior of elements produced exclusively through neutron–capture processes, we can also examine how neutron–capture nucleosynthesis may have affected the abundances of lighter elements. In Figure 26, we plot multiple elements as a function of lanthanum abundance. As expected, the [Ni/Fe] and [Eu/Fe] ratios do not exhibit any correlation with [La/Fe]. This confirms our assumption that europium is produced almost exclusively through the r–process, and that nickel, along with other Fe–peak elements, is not significantly affected by the s–process. Additionally, we find that all other elements exhibit a mild correlation with [La/Fe]. Given the strong enhancement in lanthanum, it is not surprising that the lighter elements might also be mildly affected. Unfortunately, it is difficult to disentangle the production of these elements from other sources. We suspect that much of the correlation between the heavy \alpha elements and lanthanum may be due to the combined effects of Type II SN and AGB s–process production overlapping in the same metallicity regime. In particular, the largest increase in [La/Fe] occurs at the transition between the RGB–MP and RGB–Int1 populations. The elevated [Si/Fe] and [Ca/Fe] ratios concurrent with an increase in [Fe/H] strongly suggests that Type II SNe were the major producers of these elements. As mentioned in \lx@sectionsign5.1, the increase in Si and Ca abundances may be the result of metallicity dependent Type II SN yields rather than additional production from the s–process. At present, we do not have a definitive explanation for the increase in [Ti/Fe] or its correlation with [La/Fe]. However, we point out that the stable isotope {}^{\rm 50}Ti is a neutron magic nucleus, and it has been predicted that the helium shell of thermally pulsing AGB stars may exhibit a large {}^{\rm 50}Ti/{}^{\rm 48}Ti ratio (e.g., Gallino et al. 1994). If at least some AGB stars that eject large amounts of s–process elements also eject material with a high {}^{\rm 50}Ti/{}^{\rm 48}Ti ratio, then this may provide an explanation for the Ti–La correlation.

It is interesting to note that while the O–rich stars exhibit a correlation with [La/Fe], the same relation appears to be mostly absent from the O–poor stars. This supports the idea that the depletion of oxygen is driven by an additional process, such as in situ mixing, that does not alter the [La/Fe] ratio. Although we find that nearly all of the O–poor stars also have [La/Fe]>–0.2, we point out that this may be mostly related to the fact that the O–poor (He–rich?) stars formed at a time when the average lanthanum abundance was already becoming significantly enhanced in the cluster ISM. Also note that we do not find any correlation between lanthanum abundance and radial location in the cluster, which does not match the observed trend for the O–poor stars (see Figure 9). We therefore conclude that the simultaneous rise in the number of O–poor and La–rich stars are not due to the exact same mechanisms. However, we believe that both phenomena are at least in some way related to pollution from low and/or intermediate mass AGB stars.

5.4 Final Remarks

The data presented here and in previous analyses indicate that \omega Cen experienced a unique chemical enrichment history. The occurrence of at least 4–5 discrete star formation episodes spanning >1–2\times10{}^{\rm 9} years seems required to rectify the breadth of the main sequence turnoff, the metallicity distribution function, and the large enhancement of s–process elements. Despite \omega Cen’s rather extensive chemical enrichment, the most metal–poor stars ([Fe/H]<–2) exhibit abundance patterns and star–to–star dispersions that are nearly identical to those found in similar metallicity halo and dwarf galaxy stars. These signatures strongly suggest a rapid enrichment time scale in which only massive stars had time to contribute to \omega Cen’s chemical composition. Additionally, at least half of the RGB–MP stars exhibit abundance trends that are consistent with the metal–poor halo, and the heavy \alpha element trends seem to indicate that the initial chemical enrichment occurred on a time scale that was sensitive to Type II SNe of different masses. However, a significant portion of the RGB–MP stars have [O/Fe], [Na/Fe], and [Al/Fe] abundances that are unlike stars found in the halo, and are instead more similar to those found in monometallic globular clusters. A clear delay in the presence of O–poor, Na/Al–rich stars until [Fe/H]\sim–1.7 suggests that new generations significantly polluted by the ejecta of \lesssim8 M{}_{\sun} stars did not form until about the same time as the second major episode of star formation. Furthermore, the neutron–capture data indicate that at least 1 Gyr had to have elapsed between the formation of the RGB–MP and RGB–Int1 populations.

Since a majority of RGB–MP stars have abundance patterns matching those predicted for Type II SN pollution, it seems likely that \omega Cen was able to retain and mix a significant percentage of SN ejecta at early times in the cluster’s evolution. However, at intermediate metallicities \omega Cen’s overall chemistry experienced a dramatic shift that strongly deviates from trends observed in the Galactic halo and most dwarf galaxies. The products of proton– and neutron–capture nucleosynthesis began to dominate the chemical composition of progressively more metal–rich stars, despite obvious contributions from Type II SNe. The significant pollution of intermediate metallicity stars by O–poor (He–rich?), Na/Al–rich, and s–process enhanced gas is undoubtedly the result of the RGB–MP stars evolving and enriching the cluster ISM. In order for pollution to occur at the levels observed in \omega Cen, the cluster must not have strongly interacted with the Galaxy until after at least the formation of the RGB–Int1 population. Otherwise, it is likely that the gas would have been removed by ram pressure stripping. The radial concentration of the RGB–Int2+3 and RGB–a stars near the cluster core indicates that enriched gas was funneled toward the cluster center and/or the central region was the only location where the escape velocity was large enough to retain gas ejected by SNe or AGB stars. The rapid decline in the relative number of “primordial” composition stars in the RGB–Int2+3 and RGB–a populations may be evidence that \omega Cen began to lose mass at [Fe/H]\gtrsim–1.3. Significant mass loss from the cluster may also help explain the minimal impact Type Ia SNe have played in \omega Cen’s chemical enrichment.

6 SUMMARY

We have measured chemical abundances of O, Na, Al, Si, Ca, Sc, Ti, Fe, Ni, La, and Eu for 855 RGB stars in the globular cluster \omega Cen. The abundances were obtained using moderate resolution (R\approx18,000), high S/N (>100) spectra obtained with the Hydra multifiber spectrograph on the Blanco 4m telescope at CTIO. The data set covers more than 80\% of stars with V\leq13.5, more than 90\% of stars with V\leq13.0, and samples the full breadth of the giant branch to include the most metal–poor and most metal–rich stars in the cluster. Similarly, we have achieved a completion fraction of \sim50–100\% at radii extending out to \sim24\arcmin from the cluster center. All abundances were determined using either equivalent width or spectrum synthesis analyses along with the inclusion of blended molecular lines, hyperfine structure, and/or isotope broadening when appropriate. An empirical hyperfine structure correction for the 6774 Å La II line is also provided.

We find in agreement with past photometric and spectroscopic studies that \omega Cen contains multiple, discrete stellar populations with large star–to–star abundance variations for all elements. The metallicity distribution function contains five peaks centered at [Fe/H]=–1.75, –1.50, –1.15, –1.05, and –0.75. However, for the analysis we have combined the [Fe/H]=–1.15 and –1.05 peaks into a single population. The (now four) stellar populations are identified as the RGB–MP ([Fe/H]\leq–1.6), RGB–Int1 (–1.6<[Fe/H]\leq–1.3), RGB–Int2+3 (–1.3<[Fe/H]\leq–0.9), and RGB–a ([Fe/H]>–0.9, which constitute 61\%, 27\%, 10\%, and 2\% of our sample, respectively. The metallicity distribution function also exhibits a sharp cutoff at the metal–poor end such that only 2\% of the stars in our sample have [Fe/H]<–2. The RGB–MP and RGB–Int1 populations appear to be uniformly mixed in the cluster, but the RGB–Int2+3 and RGB–a stars are preferentially located near the cluster core. Additionally, almost 90\% of the most metal–poor stars ([Fe/H]<–2) reside within 5\arcmin of the cluster center.

The abundance trends exhibited by the heavy \alpha (Si, Ca, and Ti) and Fe–peak elements (Sc and Ni) are generally well described by production from Type II SNe at all metallicities. That is, the \alpha elements are typically enhanced at [\alpha/Fe]\approx+0.3 and [Sc,Ni/Fe]\approx0. While the Fe–peak element [X/Fe] ratios and star–to–star variations remain mostly constant over \omega Cen’s full metallicity range, the heavy \alpha elements show a more complicated morphology. Over the metallicity range spanned by the RGB–MP, there is a noticeable decrease in the average [Si/Fe] and [Ca/Fe] abundances with increasing [Fe/H], but the average [Ti/Fe] abundance remains essentially constant. However, the decrease in [Si/Fe] is a stronger function of [Fe/H] than for [Ca/Fe]. The average [X/Fe] ratios for all three heavy \alpha elements increase with metallicity between the RGB–MP and RGB–Int1 populations and remains mostly enhanced at higher metallicities. It seems that many of these abundance trends may be driven by mass and/or metallicity dependent Type II SN yields and a new round of star formation creating the RGB–Int1 and subsequent populations. The simultaneous rise in [Ti/Fe] at [Fe/H]\gtrsim–1.6 may be driven by a different production mechanism because theoretical Type II SN yields do not predict a large increase in titanium with either progenitor mass or metallicity.

Although some previous analyses have suggested that Type Ia SNe may have become significant contributors to \omega Cen’s chemical enrichment at [Fe/H]>–1, we do not find particularly strong evidence supporting this claim. In the more metal–rich RGB–Int2+3 and RGB–a populations, we find that the average [\alpha/Fe] abundances remain elevated above the level found in disk and dwarf galaxy stars of similar metallicity. While there does appear to be a decrease in [Ca/Fe] at [Fe/H]>–1, this may be attributed to metallicity dependent Type II SN yields. Additionally, the strong rise in the average [Na/Fe] ratio for the RGB–Int2+3 and RGB–a stars seems inconsistent with Type Ia SNe production. The maximum [O/Fe] abundance also begins to decrease at [Fe/H]\gtrsim–1.2; however, this element, as well as Na and Al, may be altered by in situ mixing or pollution from sources other than Type II or Ia SNe. Therefore, the [X/Fe] ratios for these light elements may not directly trace SN production or even reflect a star’s original composition. We cannot explicitly rule out that Type Ia SNe have contributed to \omega Cen’s chemical enrichment, but it seems that their involvement has been mostly limited.

Unlike the heavy \alpha and Fe–peak elements, the light elements (O, Na, and Al) exhibit >0.5 dex star–to–star abundance variations at all metallicities. Although roughly half of the RGB–MP stars exhibit light element abundance patterns that are consistent with those found in similar metallicity halo and dwarf galaxy stars, the remaining RGB–MP stars, as well as >70\% of more metal–rich stars, show light element abundance patterns that are more similar to those found in individual globular clusters (i.e., O–poor and Na/Al–rich). Interestingly, the presence of these stars is a strong function of metallicity, and the [X/Fe] distribution functions are bimodal at intermediate metallicities. While very few O–poor, Na/Al–rich stars are found at [Fe/H]<–1.7, the majority of stars in the RGB–Int1 and subsequent populations exhibit these characteristics. We find that many of the metallicity dependent light element trends can be at least qualitatively reproduced by hot bottom burning in intermediate mass AGB stars. This is evidenced by the pervasive O–Na and O–Al anticorrelations and concurrent Na–Al correlation present in all stars with [Fe/H]\lesssim–1. Interestingly, the RGB–a stars no longer exhibit the light element relations and instead appear to have a roughly uniform composition. In any case, the light element trends in stars with [Fe/H]\lesssim–1 are similar to what is found in monometallic globular clusters, but the relative fraction of O–poor, Na/Al–rich stars in \omega Cen at [Fe/H]>–1.6 is significantly larger than those found in other globular clusters. Since a wide mass range of AGB stars seem able to reproduce the observed [Na/Fe] and [Al/Fe] trends but only a narrow range eject O–poor material, we conclude that the [Na/Fe] and [Al/Fe] ratios in the “enhanced” \omega Cen stars may be explained solely by pollution from intermediate mass AGB stars. However, the strongly depleted [O/Fe] ratios in many stars appear to require an additional process. Interestingly, we find a low incidence of carbon stars (<2\%) in our sample despite the large population of O–poor giants.

It seems that some degree of in situ processing must be invoked in order to interpret the large population of O–poor stars. We find an interesting parallel between O–poor giants and blue main sequence stars that may explain at least part of this phenomenon. The two populations share strikingly similar radial locations, metallicities, and number fractions. In particular, the O–poor and blue main sequence stars are both predominantly found inside \sim10\arcmin from the cluster center, are mostly found at intermediate metallicities, and constitute \sim30\% of the RGB and main sequence by number. Since the blue main sequence stars are believed to be He–rich, it seems likely that the O–poor stars may also be He–rich. Previous theoretical analyses of He–rich, globular cluster RGB stars predict that significant in situ mixing can occur more easily in He–rich compared to He–normal stars. Furthermore, it is predicted that the surface [O/Fe] abundance may be significantly depleted, but [Na/Fe] (and presumably [Al/Fe]) should be mostly unaffected. However, this scenario assumes that the O–poor, Na/Al–rich stars were already polluted by material that was moderately processed by proton–capture nucleosynthesis before ascending the RGB. The observed O–Si anticorrelation and Al–Si correlation may support this scenario. These relations can naturally arise due to leakage from the MgAl cycle at temperatures exceeding \sim65\times10{}^{\rm 6} K; temperatures this high are achieved in hot bottom burning conditions but not in the interiors of low mass RGB stars. If we assume that the observed O–poor stars are also He–rich and therefore more apt to experience in situ deep mixing, then this may explain why only the [O/Fe] ratio is correlated with radial location. Since the Na and Al abundances do not strongly correlate with radial location like O, this may be an indication that the stars responsible for producing the high Na and Al abundances do not necessarily produce high He yields as well.

A majority of RGB–MP stars have [La/Fe], [Eu/Fe], and [La/Eu] ratios indicating that the r–process was the primary production mechanism early in \omega Cen’s history. This is similar to what is found in metal–poor halo, globular cluster, and dwarf galaxy stars, and is consistent with a rapid formation time scale of the RGB–MP population. However, the [La/Fe], [Eu/Fe], and [La/Eu] abundance patterns indicate that the s–process became the dominant neutron–capture production mechanism at [Fe/H]>–1.6, and was active at a level above that observed in any other stellar population to date. In fact, almost no stars with [Fe/H]>–1.6 have [La/Fe]<0, and many stars in the intermediate metallicity populations exhibit [La/Eu] ratios suggesting pure s–process production. However, proper accounting of hyperfine structure in determining both La and Eu abundances has revised our [La/Eu] ratios downward from those in Johnson et al. (2009), and we now find that surface pollution from mass transfer is not generally required to explain the stars with large [La/Eu] ratios. Interestingly, the typical [Eu/Fe] abundances in the RGB–Int1 and RGB–Int2+3 stars are well below those observed in similar metallicity halo and globular cluster stars. This suggests that typical r–process production mechanisms may have been suppressed in \omega Cen.

While we find that both the [Ni/Fe] and [Eu/Fe] ratios are independent of a star’s [La/Fe] abundance, all other elements exhibit a mild correlation with [La/Fe]. Since the <3 M{}_{\sun} AGB stars believed to produce most of the s–process elements in \omega Cen are also predicted to produce some light elements, the correlation with La is not entirely unexpected. Interestingly, the O–rich stars show a correlation with [La/Fe], but the O–poor stars do not. This suggests that the O–depletion phenomenon is driven by an additional process, such as in situ mixing, that does not alter the envelope [La/Fe] ratio. With regard to the heavy \alpha elements, we suspect that the correlation with La may be due to the combined effects of Type II SNe producing \alpha elements and low/intermediate–mass AGB stars producing s–process elements at approximately the same time. This is supported by the observation that the rise in s–process and \alpha elements occurs in the same metallicity range. We do not have a definitive explanation for the correlation between [Ti/Fe] and [La/Fe] because the [Ti/Fe] ratio is not believed to be significantly enhanced in Type II SNe. However, we point out that the stable isotope {}^{\rm 50}Ti is a neutron magic nucleus and that the He shell of thermally pulsing AGB stars are predicted to exhibit large {}^{\rm 50}Ti/{}^{\rm 48}Ti ratios. Therefore, if at least some AGB stars that eject large amounts of s–process elements also eject material with a high {}^{\rm 50}Ti/{}^{\rm 48}Ti ratio, this may explain both the rise [Ti/Fe] at [Fe/H]\gtrsim–1.6 and the Ti–La correlation.

This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. Support of the College of Arts and Sciences and the Daniel Kirkwood fund at Indiana University Bloomington for CIJ and CAP is gratefully acknowledged. We would like to thank Bob Kraft and Chris Sneden for many helpful discussions, Katia Cunha for sending an electronic version of her paper in advance of publication, and TalaWanda Monroe for her assistance in obtaining these observations. We would also like to thank Frank and Janet Winkler and the CTIO staff for their generous hospitality. We also thank the referee for his/her careful reading and thoughtful comments that led to improvement of the manuscript.

Appendix A Empirical Lanthanum 6774 Å Hyperfine Broadening Correction

The 6774 Å La II line is often measurable in the spectra of [Fe/H]\gtrsim–2 RGB and AGB stars, but accurate La abundance determinations from this line can be hampered by hyperfine broadening if the EW exceeds \sim50 mÅ. Unfortunately, we are not aware of any publicly available linelists that include log gf values for the individual hyperfine components of the 6774 Å line. However, the spectra used here and in Johnson et al. (2009) provide EW measurements of the 6774 Å line and spectrum synthesis abundance determinations from the 6262 Å line in 85 giants. Since the 6262 Å abundance determinations properly account for hyperfine broadening, we can use these data to derive an empirical correction factor for EW–based abundance measurements that use the 6774 Å line. In Figure 27, we plot [La/Fe]{}_{\rm syn}–[La/Fe]{}_{\rm EW} (\Delta[La/Fe]{}_{\rm EW}) as a function of EW. The least–squares fit to the data gives the empirical correction factor as,

\Delta[La/Fe]_{EW}=[(5.0\times 10^{-6})(EW^{2})]-[(0.0068)(EW)]+0.1084(\sigma=% 0.07), (A1)

where the EW is measured in units of mÅ. This relation is qualitatively expected because it shows that a straight–forward EW analysis will overestimate the La abundance by an increasingly larger amount as one moves up the curve–of–growth to larger EWs. Since this is an empirical correction, it is difficult to predict how the relation might change outside the T{}_{\rm eff} (3800–5000 K), log g (\lesssim2), and metallicity (–2.5\lesssim[Fe/H]\lesssim–0.5) regime of our sample.

Facilities: CTIO

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Figure 1: A color–magnitude diagram of \omega Cen’s RGB with photometry taken from van Leeuwen et al. (2000). The filled red circles represent the stars observed for this study. The filled blue squares indicate possible carbon stars. Note that the identifiers for the carbon stars are provided in Table 2. The filled green triangles show stars that were observed for Johnson et al. (2008; 2009), but do not overlap with the current sample. The complete sample from van Leeuwen et al. is represented by the small black circles.
Figure 2: The three panels illustrate the observed completion fraction of our sample in terms of V magnitude, B–V color, and distance from the cluster center relative to the van Leeuwen et al. (2000) observations. For the bottom left and top right panels, the completion fraction only includes stars with V\leq13.5, as discussed in \lx@sectionsign2.
Figure 3: This figure shows the coordinate positions of our sample. The cross indicates the cluster center defined by van Leeuwen et al. (2000) as 201.691\arcdeg, –47.4769\arcdeg (J2000; 13{}^{\rm h}26{}^{\rm m}45.9{}^{\rm s}, –47\arcdeg28\arcmin37.0\arcsec). The ellipses represent 1, 5, and 10 times the core radius of 1.40\arcmin (Harris et al. 1996). The symbols are the same as those in Figure 1, and the van Leeuwen et al. data only represent stars with V\leq13.5 and a membership probability \geq70\%.
Figure 4: The top three panels overplot sample spectra with nearly identical atmospheric parameters and metallicity, but which exhibit significant differences in their derived [La/Fe], [O/Fe], and [Al/Fe] abundances. The middle set of panels show sample spectrum syntheses of La and O for star 50259 in the left and middle panels and Al for star 40123 in the right panel. In all three of the middle panels the solid line indicates the best fit to the spectra and the dotted lines indicate changes of \pm0.30 dex for the indicated elements. The bottom set of panels show sample spectrum syntheses, but the dotted lines in these cases illustrate changes to the synthetic spectra when the blended features of CN, Co, Sc, or Fe are altered by \pm0.50 dex. Note that the right panels have a different intensity scale than the left and middle panels.
Figure 5: The four panels show comparisons of our adopted model atmosphere parameters versus those in the literature. In all panels the solid straight line indicates perfect agreement.
Figure 6: The different panels show the [X/Fe] abundance comparisons between this study and those in the literature. The dashed line indicates perfect agreement, and the symbols are the same as those in Figure 5.
Figure 7: Spectrum synthesis fits to the RGB–a stars LEID 48099 (ROA 300) and LEID 48116 (WFI 222068). The two left panels show the synthetic spectrum fits using our measured abundances, model atmosphere parameters, and linelist. The two right panels show the synthetic spectrum fits using the Pancino et al. (2002) abundances and model atmosphere parameters but our linelist. In all panels, the solid red line shows the synthesis results using the predetermined abundances, and the solid blue lines show changes of \pm0.3 dex to [Si/Fe] and [Ca/Fe]. Note that the abundances of elements other than silicon and calcium were set to the values listed in Table 5.
Figure 8: The top panel shows the metallicity distribution function for our complete sample, including data from Johnson et al. (2008; 2009). For this panel, the solid red line shows a least–squares fit to the distribution using five Gaussian profiles, and the dashed blue lines illustrate the individual Gaussian component fits. The bottom panel compares our distribution function (solid black line) to those of Norris et al. (1996; dotted red line) and Suntzeff & Kraft (1996; dashed blue line).
Figure 9: Chemical abundance ratios of all elements are plotted as a function of distance from the cluster center. The defined cluster center is the same as that used in Figure 3. The plotted abundances contain the results from this study and Johnson et al. (2008; 2009). In all panels, the black dashed line indicates the solar–scaled abundance values.
Figure 10: [X/Fe] abundances are plotted as a function of [Fe/H] for all elements analyzed in this study, including non–repeat stars from Johnson et al. (2008; 2009). The ordinate axis in all panels spans the same range, and the dashed line indicates the solar–scaled abundance values.
Figure 11: Histograms showing the abundance distributions of [O/Fe], [Na/Fe], and [Al/Fe]. Each histogram is binned in 0.10 dex increments, and the panels are broken down by the metallicity subclasses described in \lx@sectionsign4.1.
Figure 12: Histograms showing the abundance distributions of [Ca/Fe], [Ti/Fe], and [La/Fe]. Each histogram is binned in 0.10 dex increments, and the panels are broken down by the metallicity subclasses described in \lx@sectionsign4.1.
Figure 13: [X/Fe] abundances for \omega Cen stars plotted as a function of [Fe/H]. The solid blue lines indicate the combined Type II SNe yields of Nomoto et al. (2006) weighted by a standard IMF integrated from 0.07–50 M{}_{\sun}, including contributions from hypernovae. The dotted red lines represent the expected abundance trends if the Type Ia SN yields from Nomoto et al. (1997) are mixed with the Type II yields in a with a 75\% Type Ia and 25\% Type II ratio. Note that the Type II yields have been systematically adjusted for [Sc/Fe], [Ti/Fe], and [Ni/Fe] to match the average abundances of the RGB–MP stars.
Figure 14: Production factors for 12–25 M{}_{\sun} Type II SNe from Woosley & Weaver (1995). The production factors are calculated as the ratio of an isotope’s mass fraction in the ejecta compared to its mass fraction in the Sun. Note that the isotopes plotted here are {}^{\rm 16}O, {}^{\rm 23}Na, {}^{\rm 27}Al, {}^{\rm 28}Si, {}^{\rm 40}Ca, {}^{\rm 45}Sc, {}^{\rm 48}Ti, {}^{\rm 56}Fe, and {}^{\rm 58}Ni.
Figure 15: [O/Fe], [Na/Fe], [Al/Fe], and [Si/Fe] abundances for individual stars in \omega Cen (filled red circles), other globular clusters (filled grey circles), Galactic halo (black stars), thin/thick disk (open blue boxes), bulge (open green boxes), and dwarf galaxies (open cyan triangles). The left panels show the [X/Fe] abundances as a function of [Fe/H] for \omega Cen’s full metallicity range. The right panels show the same abundance trends for [Fe/H]\geq–1.2, but the \omega Cen points are plotted on top. The literature references are listed in Table 8.
Figure 16: Similar plot to Figure 15 showing [Ca/Fe], [Sc/Fe], [Ti/Fe], and [Ni/Fe] abundances. The symbols are the same as those in Figure 15.
Figure 17: Similar plot to Figure 15 showing [La/Fe] and [Eu/Fe] abundances. The symbols are the same as those in Figure 15.
Figure 18: [O/Na], [O/Al], [Na/Al], and [La/Eu] abundances are plotted as a function of [Fe/H] for \omega Cen (left panels) and the literature (right panels). The symbols are the same as those in Figure 15. The dotted lines in the [La/Eu] panels indicate the abundance ratios expected for pure r– and s–process enrichment given in McWilliam (1997).
Figure 19: [Na/Fe] versus [O/Fe] abundances for the four primary \omega Cen populations (see \lx@sectionsign4.1). The filled grey circles represent the full sample, and the filled black circles represent only the stars residing in the designated metallicity range. Individual yields from Ventura & D’Antona (2009) are shown for 3 (dot–dashed cyan lines), 4 (long dashed green lines), 5 (dashed magenta lines), and 6 M{}_{\sun} (dotted red lines) AGB stars of varying [Fe/H]. The filled blue squares indicate the approximate Type II SN+Hypernova yields from Nomoto et al. (2006) expected for the given metallicity regime.
Figure 20: Similar plot to Figure 19 showing the run of [Al/Fe] versus [O/Fe] abundances for the different populations. The symbols are the same as those in Figure 19.
Figure 21: Similar plot to Figure 19 showing the run of [Al/Fe] versus [Na/Fe] abundances for the different populations. The symbols are the same as those in Figure 19.
Figure 22: The abundances of O, Na, and Al are plotted as a function of [Fe/H] for the full sample that includes our new results and those from Johnson et al. (2008; 2009). The solid blue lines illustrate the Salpeter IMF–weighted Type II SN yields from Nomoto et al. (2006), and the other curves are the same as those in Figure 19.
Figure 23: Similar plot to Figure 10 showing the abundance distribution of all elements as a function of [Fe/H]. The stars are broken down into the primordial (filled red circles), intermediate (filled blue circles), and extreme (filled green circles) components defined in \lx@sectionsign5.
Figure 24: The light elements O, Na, and Al plotted as a function of the heavier \alpha elements Si, Ca, and Ti for all \omega Cen giants. The Pearson correlation coefficient (R{}_{\rm P}) is also calculated and displayed for each panel.
Figure 25: A plot illustrating the change in N{}_{\rm O-poor}/N{}_{\rm O-rich} (our results) or N{}_{\rm BMS}/N{}_{\rm RMS} (Bellini et al. 2009b) as a function of radial distance from the cluster center. Our results are shown as the filled circles, and the results from Bellini et al. (2009b) are shown as the open circles. Note that N{}_{\rm BMS} refers to the number of blue main sequence stars and N{}_{\rm RMS} the number of red main sequence stars in the Bellini et al. (2009b) sample.
Figure 26: A plot of multiple elements as a function of [La/Fe]. The dashed lines indicate the solar–scaled abundance values.
Figure 27: A plot of the difference between the [La/Fe] abundances derived using an EW approach for the 6774 Å La II line and a spectrum synthesis approach for the 6262 Å La II line. The solid red line shows the least–squares fit to the data, and the horizontal dashed line indicates perfect agreement.
Table 1: Hydra Observation Log
Field UT Date Wavelength Center Filter Exposure
(Å) (s)
1 2008 March 25 6250 E6257 3\times3600
2 2008 March 25 6250 E6257 2\times3600
2008 March 29 6250 E6257 1\times2200
3 2008 March 26 6250 E6257 3\times3600
4 2008 March 26 6250 E6257 3\times3600
5 2008 March 26 6250 E6257 1\times3600
2008 March 26 6250 E6257 1\times1800
2008 March 27 6250 E6257 2\times2700
6 2008 March 27 6250 E6257 3\times3600
7 2008 March 28 6250 E6257 3\times3600
8 2008 March 28 6250 E6257 3\times3600
9 2008 March 28 6250 E6257 1\times3600
2008 March 29 6250 E6257 1\times3600
2008 March 29 6250 E6257 1\times3000
10 2008 March 29 6250 E6257 3\times3600
11 2009 March 06 6250 E6257 3\times3600
12 2009 March 06 6250 E6257 1\times3600
2009 March 06 6250 E6257 1\times3000
13 2009 March 07 6250 E6257 3\times3000
14 2009 March 08 6700 E6757 3\times3000
15 2009 March 08 6700 E6757 2\times3000
2009 March 08 6700 E6757 1\times2700
2009 March 08 6700 E6757 1\times1800
Table 2: Star Identifiers, Photometry, and Atmospheric Parameters
Star Alt. ID V B–V J H K{}_{\rm s} T{}_{\rm eff} log g [Fe/H] v{}_{\rm t} S/N S/N
LEIDaaIdentifier from van Leeuwen et al. (2000). ROAbbIdentifier from Woolley (1966). (K) (cgs) Avg. (km s{}^{\rm-1}) 6250 Å 6650 Å
9 370 12.529 1.250 10.382 9.755 9.627 4500 1.20 -1.35 1.95 250
5009 548 12.912 1.080 10.752 10.185 10.040 4525 1.25 -1.86 1.75 200
6017 240 12.233 1.420 9.717 8.982 8.808 4145 0.85 -1.19 1.90 200
8014 6734 13.365 1.013 11.353 10.781 10.705 4700 1.75 -1.73 1.60 200
9013 6771 13.269 0.973 11.261 10.717 10.603 4700 1.50 -1.67 1.80 200 150
10009 12.573 1.234 10.331 9.664 9.520 4390 1.15 -1.43 1.70 150
10012 43 11.529 1.618 8.684 7.895 7.706 3930 0.25 -1.44 2.10 200
11019 537 12.841 1.223 10.595 9.952 9.823 4405 1.25 -1.54 1.65 225
11021 400 12.600 1.268 10.285 9.621 9.464 4330 1.10 -1.49 1.75 150 150
11024 91 11.738 1.333 9.294 8.639 8.410 4220 0.70 -1.76 1.90 300
12013 394 12.579 1.319 10.242 9.560 9.402 4300 1.10 -1.20 1.80 175
12014 6602 13.300 0.992 11.293 10.754 10.644 4710 1.60 -1.70 1.80 80 125
14010 435 12.807 0.993 10.803 10.255 10.131 4700 1.45 -1.89 1.80 200 100
15022 180 11.982 1.243 9.730 9.087 8.952 4405 0.95 -1.76 1.70 250
15023 234 12.182 1.166 9.964 9.352 9.231 4460 1.05 -1.80 1.95 200
15026 245 12.234 1.329 9.853 9.120 9.004 4260 0.95 -1.31 1.90 250 250
16009 252 12.232 1.201 9.915 9.286 9.117 4345 1.00 -1.76 1.80 275
16015 213 12.127 1.122 9.979 9.373 9.210 4510 1.05 -1.92 2.00 275
16019 6460 13.217 1.039 11.268 10.742 10.618 4775 1.65 -1.74 1.90 175 150
16027 6497 13.499 0.948 11.532 10.993 10.857 4740 1.70 -1.86 1.85 100
17014 212 12.120 1.363 9.747 9.077 8.936 4285 0.90 -1.60 1.75 150 200
17015 325 12.430 1.156 10.235 9.610 9.497 4470 1.15 -1.79 1.80 175
17027 6461 13.388 0.880 11.524 11.028 10.913 4900 1.75 -2.00 1.80 100
17029 6465 13.129 0.915 11.201 10.668 10.543 4795 1.60 -1.98 1.60 125 125
17032 605 12.989 1.150 10.841 10.226 10.106 4515 1.40 -1.54 1.75 150
17046 6545 13.266 0.873 11.364 10.858 10.738 4850 1.70 -1.84 1.35 90 100
18017 448 12.699 1.048 10.620 10.061 9.899 4600 1.35 -1.84 2.10 150
18020 146 11.917 1.360 9.529 8.838 8.681 4260 0.80 -1.71 2.05 >350 200
18035 581 12.922 1.061 10.855 10.227 10.123 4590 1.40 -1.66 1.70 125
18040 465 12.708 1.267 10.448 9.736 9.596 4355 1.20 -1.31 1.70 200 150
18047 408 12.570 1.104 10.450 9.844 9.698 4535 1.25 -1.85 1.85 175
19022 6442 13.075 0.929 11.212 10.689 10.576 4885 1.65 -1.80 1.80 150
19062 464 12.803 1.144 10.601 10.001 9.872 4470 1.30 -1.84 1.90 175
20018 6259 13.384 1.099 11.348 10.757 10.598 4615 1.60 -1.60 1.60 85 75
20037 6316 13.153 1.172 11.033 10.442 10.306 4545 1.50 -1.58 1.75 225 125
20042 6327 13.093 0.999 11.099 10.541 10.402 4695 1.55 -1.87 1.80 100
20049 6355 13.273 1.058 11.184 10.559 10.464 4570 1.55 -1.80 1.70 225
21032 172 11.947 1.394 9.550 8.782 8.620 4215 0.80 -1.50 1.80 >350
21035 362 12.457 1.151 10.343 9.716 9.547 4520 1.20 -1.87 1.95 200
21042 348 12.494 1.179 10.322 9.700 9.575 4485 1.20 -1.73 1.70 175
21063 6342 13.263 1.023 11.285 10.709 10.571 4700 1.60 -1.88 1.70 150
22023 6137 13.312 1.122 11.308 10.727 10.568 4660 1.60 -1.23 1.53 175 100
22037 307 12.339 1.186 10.178 9.559 9.402 4485 1.10 -1.76 1.80 215
22042 415 12.607 1.120 10.543 9.930 9.832 4605 1.30 -1.74 1.95 200
22049 6207 13.419 0.989 11.442 10.840 10.711 4685 1.65 -1.86 1.55 125
22063 6234 13.358 1.006 11.312 10.799 10.623 4655 1.60 -1.81 1.75 175
23022 6119 13.396 0.983 11.450 10.875 10.799 4765 1.70 -1.93 1.75 150
23033 558 12.877 1.089 10.846 10.266 10.156 4655 1.45 -1.73 1.60 100 75
23042 570 12.906 1.053 10.891 10.278 10.179 4655 1.45 -1.84 1.80 150 150
23050 6179 13.106 1.020 11.132 10.539 10.459 4720 1.55 -1.84 1.80 225
23061 296 12.337 1.188 10.158 9.472 9.390 4460 1.10 -1.72 1.75 250
23068 96 11.658 1.459 9.084 8.344 8.191 4115 0.60 -1.64 2.10 300 250
24013 56 11.596 1.589 8.816 7.991 7.801 3950 0.40 -1.64 2.15 150
24027 5969 13.013 1.099 10.952 10.344 10.226 4600 1.45 -1.55 1.60 150
24040 5993 13.129 0.952 11.230 10.713 10.605 4850 1.65 -1.75 1.55 100
24046 74 11.657 1.367 9.263 8.574 8.406 4260 0.70 -1.76 1.95 300
24056 364 12.474 1.145 10.363 9.708 9.584 4525 1.20 -1.77 1.75 125
24062 352 12.628 1.307 10.304 9.691 9.469 4325 1.15 -1.41 1.60 150
25006 5941 13.444 0.835 11.620 11.106 11.016 4950 1.80 -1.78 1.60 150 75
25026 569 12.875 1.067 10.807 10.238 10.137 4630 1.40 -1.89 2.00 150
25043 89 11.734 1.500 9.239 8.449 8.257 4130 0.60 -1.50 2.05 250
25062 46 11.583 1.545 8.788 7.985 7.839 3965 0.40 -1.60 2.30 >350
25065 12.101 1.689 9.231 8.407 8.175 3900 0.55 -1.11 2.05 100
25068 58 11.542 1.434 9.052 8.354 8.176 4180 0.60 -1.71 2.00 175
26010 5759 12.972 0.998 11.088 10.571 10.442 4855 1.55 -1.68 1.25 125 125
26014 387 12.605 1.107 10.517 9.923 9.808 4585 1.30 -1.91 2.00 175
26022 5788 13.095 1.071 11.071 10.486 10.380 4660 1.50 -1.76 1.50 175
26025 61 11.411 1.591 8.671 7.877 7.757 4000 0.40 -1.63 2.45 275
26030 5809 13.403 0.960 11.527 10.975 10.887 4855 1.75 -1.87 1.65 100
26069 528 12.893 0.998 10.919 10.365 10.254 4735 1.45 -1.87 1.45 175
26072 303 12.415 1.163 10.258 9.632 9.503 4495 1.15 -1.73 1.75 200 150
26086 295 12.787 1.313 10.330 9.650 9.464 4205 1.10 -1.07 1.75 175
26088 161 11.895 1.379 9.484 8.791 8.616 4240 0.80 -1.59 1.85 175
27048 313 12.442 1.241 10.253 9.566 9.468 4445 1.15 -1.44 1.60 150
27050 5823 13.030 0.964 11.125 10.529 10.455 4795 1.55 -1.93 2.00 150 125
27073 566 12.959 1.109 10.848 10.207 10.064 4520 1.40 -1.68 1.60 175
27094 5880 13.381 1.019 11.393 10.824 10.708 4705 1.65 -1.80 1.90 90 100
27095 139 11.817 1.452 9.378 8.632 8.470 4195 0.70 -1.52 2.05 200
28016 5585 13.177 1.038 11.077 10.481 10.371 4575 1.50 -1.71 1.45 150
28020 424 12.690 1.008 10.638 10.062 9.972 4650 1.35 -1.84 1.55 150
28044 246 12.323 1.169 10.071 9.392 9.286 4395 1.05 -1.69 1.75 250
28069 185 12.084 1.296 9.799 9.156 8.995 4365 0.95 -1.76 1.85 250 150
28084 497 12.910 1.113 10.734 10.101 10.011 4490 1.35 -1.69 1.75 200 150
28092 380 12.521 1.207 10.301 9.649 9.522 4425 1.15 -1.69 1.85 225
29029 545 12.911 1.139 10.811 10.197 10.068 4555 1.40 -1.54 1.50 200
29031 375 12.584 1.047 10.568 9.983 9.863 4665 1.30 -1.80 1.75 175
29037 5640 13.213 0.982 11.303 10.795 10.684 4840 1.70 -1.74 1.80 125
29059 458 12.820 1.140 10.662 10.007 9.868 4475 1.30 -1.55 1.80 125
29067 84 11.793 1.663 8.879 8.092 7.826 3880 0.40 -1.25 1.90 150
29069 206 12.313 1.232 9.893 9.151 8.992 4215 0.95 -1.54 1.75 200 225
29072 385 12.665 1.119 10.486 9.875 9.754 4490 1.25 -1.84 1.70 175
29085 450 12.839 1.039 10.802 10.228 10.074 4635 1.40 -1.68 1.55 200
29089 5686 13.439 1.008 11.446 10.874 10.732 4685 1.65 -1.76 1.50 90
29099 184 11.934 1.445 9.506 8.788 8.597 4210 0.75 -1.62 2.00 175 175
29106 209 11.951 1.317 9.657 9.007 8.827 4350 0.90 -1.92 1.90 175
30013 540 12.895 1.249 10.737 10.116 9.955 4485 1.35 -1.32 1.75 100
30019 5588 13.204 1.059 11.029 10.392 10.279 4480 1.45 -1.51 1.65 225
30022 496 12.793 0.998 10.775 10.214 10.096 4680 1.40 -1.80 1.75 150 200
30031 95 11.634 1.544 9.051 8.326 8.118 4100 0.55 -1.52 2.00 275 250
30069 5644 13.430 0.900 11.641 11.138 11.021 4985 1.80 -2.01 1.65 200
30094 512 12.934 1.145 10.722 10.070 9.935 4430 1.30 -1.54 1.60 100
30124 5707 13.299 1.077 11.167 10.583 10.423 4530 1.55 -1.54 1.50 175
31016 526 13.097 1.016 10.996 10.453 10.313 4595 1.50 -1.93 1.60 125
31041 361 12.596 1.091 10.378 9.762 9.637 4450 1.20 -1.69 1.65 175
31047 13.216 0.995 11.245 10.701 10.558 4725 1.60 -1.83 1.85 200
31048 504 12.770 1.020 10.840 10.302 10.166 4785 1.45 -1.60 1.45 150
31075 5413 13.487 0.992 11.588 11.006 10.876 4785 1.90 -1.74 1.60 50
31079 200 12.151 1.202 9.957 9.325 9.211 4470 1.05 -1.84 1.95 250
31094 292 12.405 1.130 10.288 9.690 9.570 4555 1.20 -1.74 1.80 250 150
31095 5434 13.103 1.059 11.100 10.524 10.372 4665 1.55 -1.77 1.65 75 125
31104 5446 13.160 0.953 11.284 10.739 10.619 4845 1.65 -1.83 1.60 125
31109 5451 13.482 1.056 11.446 10.829 10.719 4625 1.65 -1.48 1.65 150
31110 195 12.242 1.354 9.721 9.042 8.846 4160 0.85 -1.49 1.95 200
31119 327 12.586 1.234 10.159 9.484 9.308 4235 1.05 -1.53 1.75 175
31133 5489 13.311 0.922 11.445 10.949 10.827 4895 1.70 -1.87 1.55 100
31139 373 12.621 1.113 10.486 9.828 9.701 4500 1.25 -1.77 1.70 300
31141 261 12.368 1.159 10.077 9.434 9.284 4365 1.05 -1.66 1.65 200
31147 5511 13.298 0.997 11.286 10.747 10.634 4700 1.65 -1.56 1.75 100
31152 5522 13.195 1.046 11.170 10.576 10.442 4640 1.55 -1.75 2.15 75
32014 474 12.809 1.042 10.732 10.174 10.048 4620 1.40 -1.78 1.90 125
32026 544 12.978 1.083 10.858 10.241 10.126 4540 1.40 -1.44 1.55 125
32027 5367 13.054 1.030 10.994 10.407 10.300 4620 1.50 -1.81 1.85 85
32043 5394 13.269 0.985 11.370 10.860 10.746 4850 1.70 -1.71 1.70 75
32063 382 12.613 1.151 10.446 9.822 9.689 4485 1.20 -1.72 1.75 250 150
32069 5411 13.268 0.947 11.483 10.963 10.853 4980 1.75 -1.77 1.50 125
32100 5448 13.105 1.051 11.124 10.519 10.410 4690 1.55 -1.73 1.65 200
32101 502 12.940 1.117 10.761 10.150 10.026 4485 1.35 -1.65 1.85 150 150
32125 262 12.352 1.174 10.116 9.479 9.360 4425 1.10 -1.71 1.90 300
32130 5478 13.253 0.956 11.372 10.815 10.714 4840 1.65 -1.74 1.55 150
32138 48 11.402 1.579 8.750 8.035 7.844 4065 0.45 -1.76 2.40 200
32140 390 12.687 1.126 10.529 9.892 9.793 4500 1.25 -1.75 1.75 250
32144 5490 13.154 1.111 11.051 10.392 10.288 4535 1.45 -1.48 1.55 175
32165 5501 13.172 1.027 11.068 10.463 10.365 4570 1.50 -1.87 1.95 125
32169 5510 13.331 1.173 10.975 10.289 10.128 4285 1.35 -1.06 2.05 200
32171 251 12.189 1.383 9.897 9.176 9.051 4330 0.95 -1.46 1.80 175
33006 11.403 1.659 8.924 8.064 7.929 4125 0.50 -1.61 2.10 250
33011 159 11.879 1.337 9.537 8.844 8.715 4305 0.80 -1.75 2.05 300
33018 379 12.647 1.125 10.339 9.724 9.572 4365 1.15 -1.79 1.70 150 150
33030 5056 13.260 0.975 11.246 10.691 10.593 4695 1.60 -1.71 1.55 100
33051 11.979 1.213 9.778 9.150 8.993 4450 0.95 -1.65 1.75 300
33064 5108 13.197 1.051 11.220 10.587 10.503 4685 1.55 -1.76 1.55 175
33099 175 12.100 1.483 9.615 8.848 8.691 4155 0.80 -1.02 1.90 150
33114 71 11.645 1.531 9.092 8.344 8.125 4105 0.55 -1.58 2.05 200 325
33115 5198 13.417 1.051 11.400 10.812 10.658 4640 1.65 -1.24 1.35 100
33126 5216 13.447 1.073 11.362 10.775 10.572 4555 1.60 -1.50 1.70 125
33129 397 12.644 1.122 10.583 9.976 9.869 4605 1.30 -1.76 1.85 225
33138 560 13.032 1.057 10.966 10.375 10.234 4595 1.45 -1.74 1.85 100
33145 561 13.007 0.993 11.056 10.528 10.364 4750 1.55 -1.95 1.75 100
33154 5243 13.329 0.902 11.507 11.018 10.914 4965 1.75 -1.42 1.10 125
33167 5268 13.451 0.984 11.494 10.951 10.856 4765 1.70 -1.51 1.65 125
33177 5290 13.420 1.008 11.349 10.789 10.688 4630 1.65 -1.69 2.00 125
34008 434 12.629 1.174 10.510 9.897 9.749 4530 1.25 -1.71 1.80 175 100
34029 243 12.107 1.452 9.635 8.878 8.719 4170 0.80 -1.28 1.90 150
34040 503 12.748 1.098 10.662 10.061 9.949 4585 1.35 -1.70 1.75 150
34056 576 12.976 0.942 11.099 10.603 10.466 4875 1.60 -1.63 1.40 150
34069 254 12.357 1.192 10.131 9.500 9.340 4420 1.10 -1.63 1.80 250
34075 157 11.937 1.403 9.617 8.873 8.669 4270 0.80 -1.49 1.75 >350 150
34081 436 12.774 1.168 10.632 9.987 9.851 4495 1.30 -1.67 1.70 >350
34129 559 13.045 1.019 11.100 10.536 10.415 4750 1.55 -1.80 1.85 150
34130 5176 13.242 0.956 11.390 10.883 10.793 4920 1.70 -1.74 1.20 150
34134 45 11.483 1.497 9.009 8.301 8.139 4190 0.60 -1.69 1.75 300
34143 419 12.904 1.229 10.556 9.895 9.746 4310 1.25 -1.16 1.80 200 150
34163 494 12.928 1.007 11.008 10.434 10.321 4775 1.50 -1.73 1.50 100
34166 12.927 1.097 10.811 10.200 10.059 4535 1.35 -1.71 2.00 125
34169 467 12.760 1.179 10.482 9.861 9.737 4395 1.25 -1.56 1.80 175
34175 119 11.994 1.430 9.540 8.872 8.686 4215 0.80 -1.56 2.05 225
34180 517 13.030 1.503 10.336 9.593 9.329 4015 1.05 -0.79 1.95 200 150
34187 468 12.830 1.106 10.741 10.130 9.996 4565 1.35 -1.88 1.90 125
34193 111 12.048 1.207 9.662 8.958 8.787 4255 0.85 -1.78 1.80 >350
34207 229 12.221 1.266 9.844 9.181 9.011 4280 0.95 -1.48 1.70 175 150
34214 5256 13.210 0.946 11.313 10.794 10.672 4840 1.65 -1.74 1.30 100
34225 557 13.017 1.229 10.608 9.932 9.820 4265 1.25 -1.09 1.65 200
34229 402 12.616 1.067 10.521 9.936 9.815 4585 1.30 -1.86 2.05 225
35029 4676 13.264 1.015 11.212 10.635 10.514 4630 1.55 -1.65 1.55 200
35035 4686 13.234 0.993 11.194 10.607 10.488 4635 1.55 -1.89 1.70 250
35046 257 12.398 1.091 10.112 9.504 9.348 4390 1.10 -1.79 1.80 225
35053 275 12.303 1.084 10.107 9.485 9.370 4475 1.10 -1.86 1.95 200
35056 69 11.439 1.625 8.712 7.929 7.816 4015 0.40 -1.69 2.00 >350
35061 208 12.202 1.270 9.832 9.165 8.999 4285 0.95 -1.50 1.85 300 125
35066 67 11.444 1.486 8.891 8.194 8.000 4135 0.50 -1.76 1.90 300
35071 4735 13.459 0.990 11.576 11.035 10.965 4840 1.75 -1.39 1.34 75
35074 326 12.627 1.120 10.458 9.870 9.727 4505 1.25 -1.74 1.70 125
35087 5089 13.321 1.020 11.377 10.816 10.693 4755 1.65 -1.72 1.75 125
35090 174 11.977 1.451 9.496 8.737 8.613 4175 0.75 -1.38 1.95 300
35093 4775 13.158 0.839 11.501 10.999 10.874 5165 2.30 -1.36 0.85 75
35124 4817 13.395 1.054 11.309 10.737 10.606 4595 1.60 -1.32 1.35 200
35157 13.164 1.135 10.908 10.244 10.098 4380 1.40 -1.25 1.55 200 150
35165 12.259 1.097 10.146 9.502 9.371 4530 1.10 -1.78 1.70 200
35172 237 12.414 1.399 10.043 9.310 9.127 4245 1.00 -1.30 2.15 175
35190 452 12.862 1.129 10.755 10.154 9.997 4545 1.35 -1.78 1.65 125
35201 263 12.530 1.360 10.268 9.530 9.389 4335 1.10 -1.06 1.90 125
35204 420 12.932 1.025 10.922 10.338 10.202 4660 1.45 -2.00 1.85 75
35216 54 11.469 1.489 8.955 8.199 8.065 4150 0.55 -1.82 2.10 225 175
35228 518 12.951 1.077 10.852 10.263 10.130 4570 1.40 -1.77 1.55 150
35230 141 11.922 1.266 9.614 8.994 8.824 4360 0.85 -1.90 2.10 250
35235 125 11.693 1.393 9.250 8.553 8.367 4210 0.70 -1.73 1.75 >350
35240 115 11.671 1.356 9.197 8.450 8.328 4190 0.65 -1.80 2.00 200
35248 4937 13.165 1.027 11.160 10.609 10.465 4685 1.55 -1.70 1.85 150
35260 377 12.522 1.148 10.445 9.827 9.701 4575 1.25 -1.69 1.65 250
35261 4961 13.330 1.084 11.239 10.599 10.488 4555 1.55 -1.56 1.45 200
36028 535 12.871 1.001 10.872 10.349 10.239 4730 1.45 -1.65 1.30 175 115
36036 65 11.425 1.498 8.875 8.209 7.934 4130 0.50 -1.87 2.25 275
36048 4748 13.264 1.016 11.234 10.699 10.536 4660 1.60 -1.73 1.65 125
36059 4763 13.308 1.028 11.340 10.784 10.657 4730 1.65 -1.75 1.55 100
36061 592 13.064 1.140 10.967 10.363 10.228 4560 1.45 -1.37 1.65 175
36087 4797 13.186 1.028 11.218 10.603 10.539 4715 1.60 -1.81 1.65 125
36106 392 12.858 1.036 10.670 10.057 9.946 4485 1.30 -1.83 1.65 150
36110 13.272 0.980 11.255 10.691 10.524 4655 1.60 -1.97 2.05 75
36113 343 12.872 1.092 10.830 10.307 10.148 4660 1.45 -1.62 1.50 150
36134 12.567 1.220 10.436 9.783 9.635 4495 1.20 -0.96 1.70 150 175
36156 11.643 1.343 9.363 8.698 8.519 4355 0.75 -1.89 2.00 250 250
36179 148 12.108 1.554 9.568 8.781 8.645 4115 0.75 -1.13 2.00 150 200
36182 215 12.352 1.302 9.939 9.265 9.099 4250 0.95 -1.66 1.80 250
36191 336 12.808 1.369 10.518 9.816 9.619 4315 1.20 -0.75 1.65 150
36206 308 12.499 1.151 10.292 9.626 9.518 4435 1.15 -1.90 1.78 175
36228 49 11.365 1.661 8.742 8.042 7.829 4085 0.45 -1.77 2.25 275
36239 281 12.492 1.222 10.186 9.515 9.382 4340 1.10 -1.56 1.75 150 150
36259 355 12.568 1.112 10.365 9.725 9.600 4450 1.20 -1.84 1.85 275
36260 4912 13.491 1.006 11.472 10.884 10.792 4670 1.70 -1.40 1.35 75
36280 395 12.565 1.268 10.378 9.668 9.564 4430 1.15 -1.64 1.80 125 125
36282 290 12.351 1.155 10.179 9.575 9.449 4500 1.15 -1.88 1.95 225
37022 4437 13.395 0.930 11.477 10.935 10.821 4800 1.71 -1.60 1.70 100
37024 447 12.719 1.638 9.575 8.687 8.471 3800 0.60 -0.79 1.80 150
37051 349 12.795 1.030 10.752 10.232 10.062 4660 1.40 -1.94 1.95 175
37052 4738 13.195 1.070 11.145 10.601 10.467 4650 1.55 -1.58 1.75 100
37055 562 13.036 1.092 10.954 10.358 10.221 4580 1.45 -1.46 1.60 175
37062 507 13.009 1.166 10.731 10.087 9.931 4370 1.30 -1.14 1.85 150
37071 391 12.621 1.054 10.571 9.995 9.897 4645 1.30 -1.78 1.55 100
37082 4770 13.231 1.020 11.233 10.666 10.513 4675 1.60 -1.86 1.80 100
37087 309 12.550 1.150 10.420 9.816 9.645 4520 1.20 -1.87 1.95 225
37094 443 12.988 1.089 10.879 10.292 10.222 4590 1.45 -1.90 1.75 175
37105 514 13.234 0.954 11.320 10.798 10.617 4790 1.65 -1.60 1.45 200
37110 12.077 1.574 9.345 8.577 8.359 3990 0.65 -0.79 2.35 125
37119 12.212 1.246 9.787 9.072 8.896 4220 0.90 -1.71 1.90 150
37136 12.631 1.118 10.624 10.065 9.895 4665 1.35 -1.88 1.75 125
37139 12.519 1.222 10.144 9.442 9.292 4265 1.05 -1.37 1.95 200
37143 12.794 1.143 10.684 10.093 9.943 4550 1.35 -1.76 1.50 200
37147 13.008 1.190 10.730 10.007 9.967 4370 1.30 -1.35 1.60 250 150
37157 12.396 1.132 10.207 9.573 9.385 4440 1.10 -1.85 1.65 150
37169 13.458 0.969 11.242 10.718 10.570 4525 1.60 -1.91 1.40 125
37179 12.793 1.040 10.759 10.206 10.075 4660 1.40 -1.92 1.60 150 150
37184 12.257 1.221 10.096 9.443 9.327 4480 1.10 -1.83 2.00 225 135
37196 12.752 1.113 10.625 10.019 9.864 4525 1.30 -1.95 1.95 125
37198 12.680 1.189 10.444 9.789 9.649 4405 1.20 -1.58 1.75 200 115
37215 12.868 1.038 10.830 10.292 10.169 4670 1.45 -1.97 1.65 125
37232 11.529 1.593 8.813 8.041 7.848 4005 0.45 -1.63 2.25 300
37247 238 12.430 1.163 10.191 9.506 9.363 4385 1.05 -1.88 1.75 200
37253 104 11.758 1.409 9.324 8.586 8.461 4215 0.70 -1.81 1.75 300 225
37271 169 12.080 1.294 9.655 8.978 8.802 4235 0.85 -1.74 1.90 200 175
37275 439 13.230 1.151 10.984 10.379 10.256 4430 1.45 -1.43 1.85 100
37318 324 12.510 1.538 9.716 8.919 8.704 3950 0.75 -0.88 1.75 100 250
37322 4938 13.450 0.887 11.583 11.078 10.989 4905 1.80 -1.93 1.70 150
37329 351 12.458 1.188 10.264 9.642 9.505 4465 1.15 -1.75 1.75 225
38011 253 12.217 1.365 9.940 9.250 9.092 4345 1.00 -1.31 1.75 175
38018 4429 13.139 1.032 11.062 10.456 10.371 4600 1.50 -1.60 1.65 175
38049 44 11.520 1.459 9.041 8.279 8.085 4155 0.55 -1.74 2.10 250 200
38052 77 11.635 1.434 9.179 8.471 8.274 4195 0.65 -1.71 1.90 >350
38056 515 12.905 1.107 10.821 10.199 10.138 4595 1.40 -1.79 1.85 175
38057 584 13.220 1.120 11.065 10.458 10.296 4495 1.45 -1.19 1.40 75
38059 151 11.964 1.555 9.443 8.604 8.476 4110 0.70 -1.15 1.95 100 250
38061 4495 13.299 0.941 11.461 10.928 10.870 4930 1.75 -1.72 1.30 100
38096 13.256 1.051 11.151 9.506 10.428 4565 1.55 -1.82 1.90 100
38097 12.271 1.383 9.568 8.748 8.599 4025 0.75 -1.14 1.65 200
38105 12.549 1.146 10.331 9.747 9.493 4420 1.15 -1.84 1.90 150
38112 12.942 1.161 10.712 10.039 9.888 4395 1.30 -1.51 1.70 150
38115 130 11.995 1.343 9.515 8.845 8.638 4190 0.80 -1.51 1.90 200
38129 12.284 1.187 9.897 9.195 9.000 4245 0.95 -1.68 1.50 275
38147 12.507 1.184 10.287 9.655 9.481 4420 1.15 -1.49 1.65 125
38149 11.762 1.579 9.197 8.460 8.213 4095 0.60 -1.27 1.95 275
38156 12.223 1.262 9.960 9.338 9.159 4390 1.00 -1.76 1.65 200
38166 12.242 1.206 9.949 8.688 8.489 4100 0.25 -2.03 1.60 225
38168 11.799 1.536 9.201 8.303 8.142 4030 0.55 -1.29 1.75 175 175
38169 12.561 1.361 10.199 9.506 9.365 4285 1.05 -1.53 1.70 200
38195 11.743 1.478 9.266 8.457 8.357 4160 0.65 -1.70 1.95 250 200
38198 12.474 1.374 10.122 9.425 9.242 4275 1.05 -1.44 1.95 175
38204 12.008 1.411 9.581 8.849 8.738 4225 0.80 -1.79 2.10 200 150
38206 13.159 1.066 11.160 9.292 10.495 4710 1.55 -1.61 1.60 150
38215 12.953 1.120 10.763 10.133 9.977 4455 1.35 -1.20 1.60 200
38223 12.520 1.169 10.290 9.625 9.462 4395 1.15 -1.74 1.75 175
38225 13.000 1.120 10.870 10.283 10.180 4555 1.40 -1.67 1.70 225
38226 13.007 1.100 10.867 10.285 10.163 4540 1.40 -1.64 1.55 100
38232 12.236 1.449 9.724 9.021 8.834 4160 0.85 -1.45 1.80 250
38255 12.561 1.240 10.359 9.671 9.524 4410 1.45 -1.22 1.70 175
38262 127 11.856 1.362 9.496 8.817 8.660 4290 0.80 -1.70 1.85 125
38276 168 12.283 1.342 10.014 9.277 9.141 4335 1.00 -1.61 1.90 275
38303 293 12.476 1.238 10.153 9.507 9.365 4340 1.10 -1.64 1.95 150
38319 416 12.764 1.182 10.583 9.985 9.832 4480 1.30 -1.50 1.70 175
38323 4578 13.340 1.118 11.163 10.530 10.376 4465 1.50 -1.11 1.45 225
38330 550 12.957 1.033 10.874 10.300 10.169 4595 1.45 -1.72 1.60 150 150
39026 287 12.333 1.373 9.943 9.208 9.059 4240 0.95 -1.48 1.65 200
39033 580 13.452 0.972 11.231 10.774 10.599 4525 1.20 -2.02 1.55 75
39034 334 12.513 1.087 10.278 9.640 9.535 4435 1.15 -1.67 1.60 150
39037 94 11.629 1.393 9.188 8.480 8.320 4215 0.65 -1.72 2.10 275
39043 604 13.139 1.002 11.109 10.574 10.475 4695 1.55 -1.58 1.75 150
39044 258 12.263 1.157 9.945 9.318 9.185 4360 1.00 -1.78 1.85 300
39048 451 12.887 1.420 10.106 9.335 9.114 3965 0.95 -0.65 1.75 150
39056 519 13.180 0.984 9.661 9.058 8.878 4800 1.85 -1.76 1.50 150
39063 4476 13.056 0.955 11.176 10.650 10.535 4860 1.60 -1.82 1.40 250
39067 86 11.545 1.480 9.306 8.531 8.383 4335 1.15 -1.34 1.70 300
39086 249 12.191 1.277 9.929 9.253 9.121 4375 1.00 -1.61 1.70 275
39088 304 12.324 1.214 10.127 9.506 9.346 4450 1.10 -1.79 1.85 150
39102 563 13.127 1.053 11.034 10.463 10.370 4605 1.50 -1.66 1.35 100
39119 12.651 1.128 10.473 9.883 9.728 4490 1.25 -1.79 1.70 200
39123 12.786 1.034 10.794 10.212 10.094 4690 1.40 -1.75 1.70 175
39129 12.843 1.361 10.639 9.982 9.833 4430 1.30 -1.34 1.75 200
39141 101 11.852 1.270 9.612 8.909 8.753 4375 0.85 -1.77 2.00 >350 325
39149 12.472 1.275 9.966 9.285 9.118 4180 0.95 -1.08 1.70 150
39165 80 11.620 1.422 9.207 8.570 8.414 4275 0.70 -1.97 2.15 200 225
39186 11.960 1.306 9.694 9.019 8.873 4370 0.90 -1.66 2.00 275 200
39187 12.546 0.724 9.737 9.053 8.907 4040 0.25 -2.13 1.80 250
39198 11.353 1.311 9.104 8.405 8.279 4385 1.00 -1.66 1.85 300
39204 12.673 1.108 10.452 9.856 9.712 4455 1.25 -1.85 1.95 125
39215 12.715 1.137 10.493 9.864 9.750 4445 1.25 -1.97 1.85 150
39216 12.916 1.048 10.790 10.171 10.069 4540 1.40 -1.78 1.55 125
39225 13.302 1.079 11.326 10.744 10.670 4725 1.65 -1.65 1.75 100
39235 12.400 1.225 9.972 9.267 9.147 4240 0.75 -1.59 1.70 250
39245 11.806 1.471 9.154 8.367 8.175 4035 0.60 -1.50 1.90 275 250
39257 11.934 1.582 9.234 8.472 8.242 4005 0.60 -1.47 1.95 275
39259 12.483 1.271 10.228 9.547 9.377 4365 1.10 -1.70 1.70 200
39284 11.598 1.486 9.041 8.350 8.169 4140 0.50 -1.76 2.05 >350 275
39289 12.714 1.174 10.533 9.966 9.782 4490 1.30 -1.84 1.45 250
39298 13.078 1.015 11.086 10.498 10.405 4695 1.55 -1.95 1.80 100
39301 12.863 1.128 10.747 10.125 10.013 4540 1.35 -1.90 1.65 175
39306 123 11.918 1.328 9.569 8.857 8.721 4290 0.80 -1.81 1.85 225 200
39325 117 11.906 1.592 9.370 8.530 8.404 4100 0.65 -1.40 2.05 200
39329 13.209 1.059 11.166 10.598 10.391 4605 1.55 -1.90 1.90 75
39345 356 12.734 1.076 10.677 10.116 9.944 4615 1.35 -1.77 1.65 175
39346 13.132 1.270 10.791 10.078 9.916 4285 1.30 -1.24 1.65 175
39352 97 11.740 1.380 9.401 8.680 8.502 4275 0.75 -1.79 1.85 150
39384 4570 13.296 1.069 11.231 10.673 10.565 4635 1.60 -1.36 1.75 150
39392 4579 13.413 1.194 11.108 10.440 10.265 4330 1.45 -0.75 1.90 150
39401 345 12.625 1.186 10.320 9.636 9.544 4350 1.15 -1.52 1.80 250
39921 12.700 1.199 10.400 9.692 9.586 4335 0.95 -1.56 1.60 150
40016 359 12.550 1.253 10.260 9.633 9.468 4365 1.15 -1.47 1.75 200 150
40031 501 12.850 1.037 10.730 10.150 10.041 4570 1.35 -1.80 1.85 250
40041 585 13.012 1.093 10.883 10.287 10.181 4550 1.40 -1.57 1.60 150 150
40108 13.081 1.038 11.050 10.444 10.326 4630 1.50 -1.86 1.60 100
40123 107 11.850 1.499 9.259 8.511 8.288 4080 0.65 -1.46 2.05 250 175
40135 78 11.773 1.353 9.341 8.552 8.421 4195 0.70 -1.92 2.20 250
40139 12.105 1.421 9.654 8.871 8.719 4175 0.75 -1.46 2.10 150
40162 12.878 1.008 10.842 10.203 10.068 4600 1.55 -1.59 1.55 300
40166 12.890 1.169 10.609 9.965 9.845 4380 1.10 -1.48 1.70 300
40168 12.860 1.096 10.726 10.128 9.997 4535 1.35 -1.71 1.65 150
40170 12.736 1.134 10.577 9.938 9.798 4480 1.25 -1.86 1.75 250
40207 12.444 1.226 9.952 9.239 9.095 4180 0.70 -1.54 1.90 150
40210 12.606 1.118 10.446 9.886 9.689 4510 1.25 -1.92 1.45 200
40216 11.943 1.398 9.457 8.653 8.564 4160 0.65 -1.63 1.75 275 250
40220 13.080 0.877 11.038 10.490 10.236 4565 1.45 -1.64 1.40 100
40232 12.130 1.649 9.520 8.678 8.495 4040 0.75 -1.04 1.90 225
40235 12.441 1.236 10.161 9.490 9.339 4355 0.90 -1.84 2.10 175
40237 12.607 1.202 10.196 9.540 9.366 4255 0.80 -1.65 1.80 150
40275 12.508 1.131 10.237 9.605 9.441 4385 0.95 -1.88 1.90 250
40291 12.098 1.331 9.751 9.059 8.917 4295 0.90 -1.64 1.75 200
40318 13.333 1.145 11.014 10.349 10.251 4345 1.40 -1.26 1.95 150
40339 12.261 1.583 9.597 8.681 8.572 4000 0.70 -1.25 2.15 200
40349 12.591 1.184 10.182 9.515 9.353 4255 0.80 -1.68 1.70 250
40358 12.808 1.323 10.140 9.351 9.171 4025 0.70 -1.03 1.90 150 200
40361 12.761 1.094 10.633 10.049 9.874 4530 1.30 -1.93 1.60 300
40371 12.324 1.324 9.765 9.033 8.820 4110 0.85 -1.45 1.85 300
40372 12.062 1.252 9.706 9.061 8.889 4305 0.90 -1.91 1.85 325
40373 12.584 1.187 10.431 9.803 9.628 4480 1.20 -1.78 1.60 150
40409 552 13.276 1.044 10.974 10.776 10.312 4480 1.15 -1.88 1.95 100
40420 374 12.996 1.260 11.031 10.825 10.330 4750 1.70 -2.05 1.25 100 75
40424 521 12.989 1.088 11.013 10.440 10.301 4700 1.85 -1.49 1.40 100
40472 73 11.463 1.608 8.698 7.877 7.748 3975 0.25 -1.69 2.10 250
40479 4369 13.063 1.105 10.848 10.250 10.114 4460 1.40 -1.61 1.60 250
41015 571 12.935 1.064 10.904 10.305 10.180 4635 1.45 -1.64 1.55 125
41025 4159 13.059 0.996 11.020 10.478 10.358 4670 1.50 -1.63 1.65 100
41033 463 12.900 1.258 10.257 9.503 9.330 4060 0.80 -1.03 2.00 150
41034 319 12.396 1.211 10.165 9.463 9.371 4400 1.10 -1.64 1.85 200 150
41035 233 12.141 1.219 9.854 9.204 9.055 4365 0.95 -1.82 2.00 175
41039 256 12.251 1.230 9.977 9.295 9.190 4375 1.00 -1.73 1.95 250
41060 178 11.906 1.474 9.418 8.671 8.517 4165 0.75 -1.50 1.95 >350 200
41061 235 12.159 1.304 9.810 9.123 8.997 4305 0.95 -1.59 1.60 275 200
41063 404 12.649 1.116 10.517 9.888 9.789 4530 1.25 -1.76 1.80 175
41164 13.034 1.101 10.851 10.246 10.017 4445 1.15 -1.63 1.80 200
41186 12.398 1.184 10.094 9.419 9.285 4345 0.85 -1.82 1.65 300
41201 13.320 0.946 11.333 10.772 10.550 4660 1.60 -2.08 1.45 75
41230 12.726 1.143 10.528 9.907 9.784 4465 1.25 -1.82 1.45 125
41232 12.946 0.987 10.970 10.426 10.309 4735 1.50 -2.06 1.75 75
41241 11.741 1.401 9.277 8.472 8.364 4170 0.65 -1.84 1.95 300
41243 12.519 1.121 10.307 9.676 9.521 4435 1.15 -1.80 1.65 300
41246 12.531 1.123 10.352 9.698 9.594 4470 1.20 -1.75 1.70 175
41258 12.711 1.018 10.602 10.006 9.844 4525 1.30 -2.16 1.80 125
41259 11.977 1.234 9.692 9.003 8.854 4350 0.90 -1.78 1.90 200
41262 13.112 0.863 11.373 10.949 10.790 5105 1.75 -1.17 1.40 100
41310 12.879 1.106 10.796 10.180 10.088 4585 1.40 -1.65 1.30 125
41312 12.977 1.072 10.790 10.182 10.092 4495 1.40 -2.13 0.90 100
41313 12.219 1.147 9.770 9.124 8.948 4240 0.65 -1.91 1.95 275
41321 12.378 1.115 9.972 9.340 9.209 4290 0.75 -1.89 2.25 175
41348 12.267 1.014 9.928 9.293 9.104 4330 0.95 -1.73 1.60 225
41366 12.987 1.092 10.838 10.184 10.086 4500 1.40 -1.74 1.70 100
41375 11.621 1.607 8.872 8.143 7.961 4005 0.25 -1.75 2.25 225
41380 11.810 1.661 9.054 8.315 8.061 3980 0.55 -1.23 1.95 150
41387 12.791 1.152 10.488 9.864 9.691 4355 1.00 -1.72 1.70 150
41389 12.799 1.114 10.663 9.999 9.899 4505 1.30 -1.89 1.50 150
41402 12.729 1.117 10.537 9.935 9.813 4485 1.15 -1.95 1.95 150
41435 202 12.331 1.240 9.857 9.132 9.001 4195 0.90 -1.59 1.75 200
41455 11.566 1.558 8.854 8.112 7.899 4015 0.45 -1.22 2.30 300
41476 179 12.031 1.651 9.020 8.188 7.960 3830 0.20 -1.41 1.90 175
41494 4339 13.328 1.080 11.140 10.563 10.453 4505 1.50 -1.54 1.45 275
42012 3875 13.379 1.089 11.299 10.705 10.613 4605 1.60 -1.58 1.65 125
42015 3881 13.057 1.138 10.879 10.249 10.105 4465 1.40 -1.59 1.75 200 100
42023 170 11.949 1.275 9.619 8.916 8.801 4315 0.85 -1.80 2.00 >350
42039 205 12.013 1.246 9.712 9.063 8.892 4350 0.90 -1.76 1.95 200
42049 533 12.926 1.175 10.641 9.968 9.857 4365 1.30 -1.32 1.60 300
42054 72 11.484 1.436 8.989 8.297 8.097 4175 0.55 -1.83 2.05 275 200
42056 3957 13.140 0.941 11.235 10.717 10.625 4850 2.05 -1.86 1.65 150
42079 3976 13.204 1.067 11.094 10.487 10.361 4550 1.50 -1.42 1.40 125
42084 259 12.236 1.297 9.993 9.314 9.165 4385 1.00 -1.52 1.90 225
42106 346 13.209 1.075 10.831 10.373 10.149 4390 1.10 -1.72 1.55 100
42114 12.192 1.229 9.823 9.147 9.019 4295 0.95 -1.55 1.75 >350
42120 12.570 1.088 10.390 9.764 9.517 4430 1.20 -1.52 1.50 300
42134 13.208 0.999 11.211 10.618 10.519 4685 1.60 -1.74 1.65 125
42161 11.816 1.328 9.317 8.609 8.445 4175 0.55 -1.84 2.00 >350 150
42162 12.763 1.262 10.222 9.482 9.258 4110 1.00 -1.09 1.85 250
42169 12.640 1.213 10.481 9.810 9.655 4455 1.20 -1.34 1.60 200
42174 13.153 1.070 11.119 10.481 10.351 4600 1.50 -1.58 1.45 125
42175 12.402 1.226 10.129 9.468 9.289 4360 1.05 -1.66 1.60 275
42179 11.875 1.354 9.450 8.676 8.561 4210 0.60 -1.81 1.90 275 200
42182 12.992 1.037 10.932 10.363 10.264 4640 1.45 -1.77 1.25 125
42187 12.547 1.216 10.248 9.590 9.392 4330 0.95 -1.62 1.75 200
42196 12.950 1.046 10.824 10.184 9.950 4435 1.35 -2.13 1.65 125
42198 13.085 1.064 10.901 10.441 9.914 4330 0.80 -2.03 1.75 150
42205 11.996 1.567 9.310 8.592 8.283 4015 0.65 -1.35 2.30 275
42221 13.032 1.089 10.833 10.233 10.092 4470 1.15 -1.84 1.55 200
42260 12.986 1.165 10.769 10.145 10.016 4445 1.35 -1.78 1.80 125
42271 12.445 1.090 10.072 9.522 9.242 4310 0.70 -2.26 1.60 225
42302 11.584 1.513 8.992 8.363 8.076 4115 0.55 -1.81 2.05 300 250
42303 12.593 1.184 10.616 9.967 9.739 4610 1.70 -1.49 1.65 150
42309 13.123 1.034 11.164 10.689 10.412 4680 1.55 -0.80 1.45 125
42339 12.683 1.250 10.544 9.839 9.667 4445 1.45 -1.18 1.45 175
42345 12.891 1.026 10.905 10.333 10.209 4700 1.65 -2.00 1.80 225
42361 12.588 1.078 10.426 9.787 9.697 4500 1.20 -1.90 1.75 200
42384 12.316 1.313 9.569 8.847 8.656 4010 0.40 -1.51 1.95 200
42385 12.686 1.126 10.606 9.983 9.853 4565 1.30 -1.86 1.55 275
42407 13.358 1.048 11.378 10.790 10.699 4710 1.65 -1.48 1.20 75
42415 12.531 1.195 10.155 9.452 9.297 4265 0.85 -1.55 1.80 200
42438 538 13.067 1.159 10.811 10.149 10.020 4390 1.35 -1.32 1.60 200
42457 4047 13.314 1.072 11.183 10.629 10.482 4555 1.55 -1.66 1.65 75
42461 51 11.617 1.441 9.137 8.324 8.149 4135 0.55 -1.75 1.95 >350 150
42473 414 12.852 1.186 10.489 9.832 9.666 4295 1.05 -1.38 1.80 275
42497 398 12.619 1.147 10.407 9.766 9.636 4440 1.10 -1.84 1.90 250 150
42501 305 12.512 1.242 10.248 9.582 9.427 4370 1.10 -1.72 1.55 175
42503 4095 13.497 1.027 11.415 10.841 10.703 4595 1.65 -1.61 1.55 150
42508 600 13.041 1.137 10.783 10.144 9.990 4390 1.35 -1.72 1.90 225
43010 591 13.009 1.042 10.902 10.326 10.209 4580 1.45 -1.77 1.75 175
43024 3911 13.133 1.016 11.076 10.486 10.358 4615 1.50 -1.65 1.50 200
43036 440 12.716 1.133 10.489 9.842 9.729 4430 1.25 -1.40 1.55 100
43040 3937 13.226 1.009 11.207 10.630 10.520 4670 1.60 -1.62 1.70 150
43060 3952 13.200 1.068 11.089 10.518 10.399 4575 1.50 -1.68 1.60 175
43061 357 12.602 1.431 9.744 8.973 8.780 3930 0.55 -1.12 2.15 150
43064 140 11.821 1.259 9.563 8.906 8.769 4395 0.85 -1.58 1.80 225 150
43068 405 12.756 1.167 10.509 9.858 9.758 4415 1.25 -1.43 1.60 175
43071 427 12.720 1.098 10.611 9.984 9.847 4535 1.30 -1.70 1.50 175
43079 3977 13.196 1.036 11.309 10.781 10.580 4800 1.65 -1.04 1.30 75
43087 360 12.675 1.173 10.448 9.813 9.671 4425 1.15 -1.64 1.80 250
43091 314 12.789 1.154 10.399 9.754 9.629 4295 1.00 -1.50 1.65 200
43095 116 11.997 1.232 9.618 8.972 8.794 4290 0.85 -1.83 1.90 150
43096 35 11.419 1.593 8.473 7.670 7.578 3900 0.20 -1.88 2.25 325
43099 39 11.600 1.625 8.565 7.683 7.549 3825 0.15 -1.47 1.90 275
43101 210 12.387 1.148 10.158 9.534 9.392 4430 1.10 -1.77 1.85 300
43104 12.855 1.166 10.707 10.059 9.952 4500 1.35 -1.51 1.65 200
43108 13.033 1.024 10.973 10.422 10.266 4625 1.45 -1.69 1.45 125
43111 12.918 1.065 10.836 10.256 10.146 4605 1.40 -1.59 1.75 125
43134 12.755 1.106 10.805 10.202 9.926 4645 1.40 -1.95 1.85 150
43139 12.565 1.050 10.687 10.051 9.923 4770 1.35 -1.72 1.30 125
43158 12.555 1.120 10.229 9.621 9.442 4345 0.90 -1.90 1.70 300
43189 12.085 1.486 9.521 8.829 8.582 4115 0.75 -1.43 2.15 200
43216 12.414 1.348 9.650 8.965 8.689 3990 0.40 -1.40 1.95 250 225
43233 12.817 1.093 10.610 10.009 9.837 4450 1.30 -1.92 1.45 200
43241 11.629 1.530 8.805 8.142 7.970 3995 0.25 -1.91 2.55 >350
43258 12.693 1.143 9.848 8.885 9.116 4070 0.20 -2.23 2.00 200
43261 11.612 1.411 8.931 8.231 8.068 4065 0.30 -1.80 2.00 250
43278 12.996 1.059 11.018 10.488 10.395 4790 1.55 -1.93 1.75 75
43326 12.103 1.528 9.321 8.413 8.258 3925 0.40 -1.24 1.85 150 200
43330 11.779 1.401 9.284 8.567 8.411 4175 0.60 -1.87 1.90 125
43351 11.686 1.574 9.206 8.391 8.224 4135 0.60 -0.98 2.40 200
43367 11.603 1.477 9.003 8.264 8.100 4095 0.40 -1.82 2.05 300 275
43389 12.856 1.301 10.387 9.686 9.500 4190 1.10 -1.38 1.75 200
43397 13.300 0.982 11.354 10.817 10.680 4760 1.65 -1.88 1.45 100
43399 12.785 1.140 10.757 10.149 10.024 4630 1.60 -1.77 1.60 150
43412 88 11.740 1.436 9.249 8.561 8.407 4190 0.60 -1.78 2.15 300
43433 12.461 1.224 10.075 9.413 9.238 4270 0.80 -1.80 1.65 200
43446 564 13.133 1.071 11.067 10.486 10.401 4630 1.50 -1.64 1.75 100
43458 522 12.941 0.967 10.994 10.389 10.280 4730 1.50 -1.28 1.55 175
43463 410 12.746 1.087 10.678 10.114 9.971 4615 1.35 -1.77 1.90 200
43475 593 13.376 1.044 11.181 10.676 10.457 4500 1.85 -0.60 1.60 300
43485 265 12.520 1.183 10.254 9.437 9.482 4360 0.95 -1.74 1.55 200
43539 4106 13.264 1.081 11.097 10.507 10.378 4510 1.40 -1.57 1.60 200
44026 341 12.607 1.185 10.192 9.536 9.368 4255 1.05 -1.33 1.75 250
44042 136 11.785 1.215 9.555 8.886 8.777 4420 0.85 -1.83 1.80 >350 225
44056 578 13.032 1.111 10.856 10.241 10.142 4495 1.40 -1.51 1.60 125
44065 350 12.434 1.132 10.279 9.651 9.505 4490 1.15 -1.78 1.80 200
44067 310 12.332 0.987 10.489 9.957 9.831 4900 2.25 -1.66 1.45 100
44115 64 11.632 1.464 9.122 8.414 8.229 4160 0.60 -1.71 2.10 >350
44120 13.117 0.958 11.069 10.503 10.355 4630 1.50 -1.88 1.40 125
44143 11.876 1.197 9.674 9.008 8.858 4430 0.90 -1.79 1.85 300 200
44163 12.707 1.140 10.387 9.822 9.540 4335 0.95 -1.84 1.80 250
44188 13.299 1.151 11.056 10.414 10.294 4415 1.45 -1.60 1.70 150
44189 12.863 1.217 10.497 9.845 9.671 4290 1.20 -1.45 1.65 175
44198 12.179 1.258 9.933 9.302 9.132 4400 1.00 -1.79 2.10 225
44219 12.194 1.162 9.886 9.237 9.086 4350 1.00 -1.77 1.95 250
44231 12.691 1.140 10.616 9.986 9.834 4560 1.55 -1.46 1.35 250
44253 12.656 1.223 10.296 9.645 9.479 4300 0.90 -1.58 1.65 150
44271 13.069 0.989 10.995 10.464 10.288 4615 1.50 -1.80 1.90 100
44277 11.556 1.839 8.537 8.106 7.495 3900 0.25 -1.37 2.10 300
44304 12.864 1.140 10.465 9.807 9.686 4280 0.75 -1.85 1.65 200
44313 12.255 1.301 9.902 9.239 9.089 4305 0.95 -1.75 1.95 150 200
44327 11.823 1.276 9.491 8.742 8.628 4290 0.80 -1.87 1.75 275 215
44337 12.118 1.299 9.751 9.044 8.854 4260 0.75 -1.79 1.80 300
44343 12.446 1.230 10.130 9.473 9.248 4310 0.90 -1.79 1.60 275
44380 13.120 0.973 11.130 10.620 10.455 4725 1.55 -1.83 1.35 75
44424 12.737 1.049 10.646 10.073 9.910 4580 1.35 -1.83 1.70 150
44426 12.598 1.188 10.292 9.607 9.476 4335 1.05 -1.48 1.65 150
44435 433 12.938 1.179 10.667 10.026 9.879 4380 1.10 -1.49 1.65 200
44446 529 13.174 1.033 11.097 10.481 10.355 4575 1.50 -1.77 1.75 75
44449 100 11.789 1.584 9.207 8.471 8.267 4095 0.60 -1.37 2.35 200
44462 321 12.559 1.403 9.918 9.110 8.942 4040 0.90 -1.18 1.65 225
44488 3813 13.319 0.922 11.388 10.870 10.754 4805 1.70 -1.71 1.40 100
44493 499 12.863 1.073 10.762 10.171 10.001 4555 1.35 -1.72 1.45 200
45082 318 12.606 1.082 10.403 9.816 9.670 4475 1.20 -1.83 1.65 250
45089 197 12.288 1.074 10.107 9.531 9.408 4515 1.10 -1.85 2.00 175
45092 406 12.828 1.134 10.546 9.907 9.720 4360 1.25 -1.30 1.65 300
45093 573 13.149 1.040 11.186 10.579 10.519 4730 1.60 -1.61 1.45 100
45126 13.081 1.064 10.933 10.352 10.227 4530 1.45 -1.76 1.70 200
45177 11.736 1.418 9.207 8.501 8.307 4145 0.50 -1.83 2.00 300
45180 12.704 1.138 10.410 9.754 9.589 4350 1.00 -1.73 1.60 275
45206 12.390 1.114 10.313 9.740 9.582 4595 1.20 -1.74 1.60 150
45215 12.993 1.430 10.617 9.881 9.696 4240 1.20 -1.06 1.45 200 175
45232 11.409 1.384 8.600 7.957 7.710 4000 0.30 -1.91 2.45 300
45235 13.297 1.015 11.171 10.574 10.448 4540 1.55 -1.88 1.45 125
45238 12.485 1.188 10.089 9.405 9.276 4270 0.80 -1.73 1.75 250
45240 12.918 1.085 10.614 10.004 9.862 4375 1.30 -1.62 1.55 75
45246 12.488 1.244 9.904 9.227 9.050 4130 0.65 -1.55 1.80 200
45249 12.714 1.251 10.190 9.486 9.271 4140 0.60 -1.64 1.80 300
45272 12.207 1.336 9.567 8.849 8.659 4070 0.45 -1.76 1.90 250 200
45285 12.955 1.323 10.749 10.096 9.883 4405 1.30 -0.95 1.50 150
45292 12.901 1.155 10.605 9.952 9.821 4360 1.25 -1.59 1.55 150
45309 12.980 1.066 10.802 10.239 10.065 4500 1.15 -1.96 1.55 150
45322 12.358 1.466 9.503 8.880 8.515 3945 0.25 -1.71 2.00 175
45326 13.043 1.108 10.794 10.139 10.025 4405 1.15 -1.53 1.50 175
45342 12.995 1.300 10.734 10.019 9.847 4340 1.30 -1.12 1.95 200
45343 12.493 1.187 10.184 9.545 9.395 4350 1.00 -1.63 1.65 250
45359 12.241 1.241 9.849 9.164 9.024 4270 0.80 -1.79 1.65 300
45373 12.434 1.247 9.929 9.231 9.056 4170 0.65 -1.68 1.75 225
45377 12.656 1.139 10.443 9.816 9.678 4445 1.20 -1.61 1.55 200
45389 12.181 1.219 9.810 9.124 8.958 4275 0.80 -1.72 1.65 >350
45410 13.056 1.048 10.991 10.347 10.278 4610 1.50 -1.80 1.60 100
45418 13.052 1.122 10.923 10.354 10.154 4525 1.40 -1.44 1.40 125
45453 144 12.252 1.310 9.599 8.830 8.710 4060 0.35 -1.86 1.95 >350 200
45454 42 11.644 1.495 8.945 8.226 8.046 4040 0.40 -1.78 2.25 200
45463 444 12.962 1.166 10.670 10.040 9.891 4370 1.15 -1.48 1.65 150
45482 586 13.071 1.084 10.883 10.283 10.147 4480 1.40 -1.49 1.45 125
46024 40 11.291 1.479 8.813 8.073 7.954 4190 0.50 -1.69 2.10 >350
46055 344 12.535 1.145 10.310 9.671 9.542 4430 1.15 -1.52 1.75 200
46062 62 11.494 1.595 8.680 7.918 7.696 3950 0.20 -1.81 2.20 >350
46073 267 12.544 1.242 10.038 9.368 9.182 4180 1.00 -1.09 1.75 175 200
46090 454 12.950 0.979 10.923 10.387 10.282 4695 1.50 -1.97 1.80 150
46092 92 11.830 1.571 9.113 8.297 8.128 3990 0.45 -1.45 2.10 >350
46121 12.891 1.400 10.101 9.400 9.175 3985 0.65 -0.96 2.00 >350
46140 12.478 1.129 10.254 9.583 9.482 4425 1.15 -1.67 1.80 250
46150 11.867 1.505 9.269 8.515 8.274 4065 0.65 -1.39 1.90 275
46166 12.605 1.160 10.345 9.910 9.661 4475 1.20 -1.69 1.55 150
46172 12.717 1.189 10.357 9.695 9.526 4290 0.90 -1.51 1.80 200
46194 12.267 1.173 9.675 9.022 8.840 4135 0.50 -1.80 1.80 >350
46196 13.103 0.952 11.173 10.658 10.553 4815 1.60 -1.79 1.50 75
46223 12.725 1.220 10.215 9.528 9.287 4150 0.60 -1.68 1.80 275
46248 11.354 1.393 8.805 8.121 7.980 4165 0.50 -1.87 1.75 >350
46279 13.146 0.868 11.171 10.628 10.519 4745 1.60 -1.78 1.40 125
46289 12.281 1.214 9.899 9.209 9.059 4270 0.75 -1.84 1.65 300 175
46301 12.283 1.175 10.050 9.377 9.235 4400 1.05 -1.76 1.80 250
46318 12.804 1.128 10.568 9.952 9.755 4405 0.95 -1.87 1.75 200
46323 12.341 1.227 9.930 9.294 9.104 4265 0.80 -1.75 1.70 300
46325 12.872 1.090 10.721 10.085 9.868 4460 1.10 -1.97 1.95 175
46348 12.914 1.094 10.701 10.059 9.938 4440 1.05 -1.91 1.90 200
46350 12.291 1.316 9.776 9.102 8.914 4170 0.70 -1.44 1.95 >350
46381 329 12.607 1.192 10.226 9.568 9.401 4280 0.90 -1.52 1.70 250
46388 574 13.034 1.050 10.938 10.316 10.227 4570 1.40 -1.81 1.95 250
46391 469 12.846 1.107 10.692 10.080 9.947 4505 1.35 -1.50 1.85 200
46398 3534 13.139 0.938 11.247 10.729 10.626 4860 1.65 -1.80 1.40 75
46405 3545 13.208 1.103 11.309 10.779 10.674 4835 1.65 -1.71 1.35 125
46438 3588 13.142 0.962 11.166 10.608 10.516 4740 1.60 -1.67 1.65 100
47012 155 11.890 1.415 9.480 8.791 8.588 4230 0.75 -1.63 1.75 >350
47039 489 12.807 1.063 10.723 10.122 10.014 4590 1.35 -1.67 1.60 275
47055 3449 13.266 1.067 11.224 10.627 10.511 4665 1.60 -1.72 2.20 200
47074 459 13.009 1.041 10.660 10.436 10.323 4690 1.50 -1.62 1.55 125
47096 3489 13.259 1.086 11.101 10.483 10.350 4495 1.50 -1.22 1.50 125
47107 12.053 1.308 9.657 9.016 8.737 4240 0.75 -1.70 2.20 300 150
47110 12.444 1.148 10.101 9.474 9.355 4345 0.95 -1.81 1.75 275
47146 12.357 1.254 9.912 9.072 8.913 4150 0.65 -1.57 1.95 250 250
47150 12.731 1.203 10.199 9.469 9.322 4145 0.70 -1.48 2.05 250
47151 13.074 1.053 10.823 10.289 10.299 4620 1.50 -1.82 1.40 125
47153 11.945 1.620 9.129 8.330 8.141 3940 0.55 -1.14 2.20 300
47176 12.608 1.156 10.264 9.615 9.485 4325 1.00 -1.56 1.75 275
47186 11.868 1.609 9.091 8.235 8.041 3940 0.45 -1.23 2.05 >350
47187 12.641 1.319 10.316 9.628 9.475 4310 1.10 -1.17 1.65 275
47199 11.566 1.531 8.884 8.116 7.960 4035 0.35 -1.68 1.90 >350 250
47269 12.957 1.202 10.709 10.070 9.915 4400 1.20 -1.36 1.65 200
47299 13.412 1.053 11.362 10.761 10.670 4630 1.65 -1.73 1.65 100
47307 41 11.583 1.483 8.921 8.173 8.008 4055 0.50 -1.77 2.00 325 225
47331 13.187 0.991 11.245 10.716 10.592 4780 1.65 -1.76 1.40 100
47338 12.628 1.173 10.316 9.696 9.539 4355 0.95 -1.67 1.75 175
47339 13.024 0.943 11.047 10.463 10.317 4695 1.50 -1.47 1.40 150
47348 12.592 1.206 10.222 9.523 9.387 4275 0.90 -1.51 1.70 300
47354 13.147 1.282 10.911 10.247 10.065 4385 1.35 -0.95 1.70 175 175
47387 247 12.286 1.224 9.988 9.321 9.140 4335 1.00 -1.71 1.80 225 125
47399 85 11.701 1.588 8.943 8.173 7.957 3975 0.40 -1.44 2.00 300
47400 376 12.643 1.229 10.258 9.580 9.397 4260 0.95 -1.42 1.65 300
47405 75 11.668 1.338 9.226 8.500 8.377 4220 0.70 -1.89 2.10 300
47420 530 12.969 1.094 10.803 10.177 10.065 4495 1.35 -1.38 1.40 200
47443 597 13.052 1.005 11.000 10.432 10.306 4635 1.50 -1.83 1.55 250
47450 3606 13.504 0.979 11.471 10.893 10.791 4655 1.65 -1.67 1.60 175
48028 193 12.062 1.244 9.744 9.061 8.954 4340 0.90 -1.78 1.85 300
48036 3433 13.324 1.006 11.297 10.750 10.623 4675 1.60 -1.58 1.50 125
48049 76 11.525 1.511 8.825 8.098 7.912 4035 0.35 -1.76 2.10 >350
48060 52 11.316 1.622 8.635 7.952 7.763 4065 0.40 -1.88 2.50 >350
48067 498 12.931 1.151 10.720 10.114 9.958 4450 1.30 -1.52 1.80 225
48083 191 12.044 1.376 9.719 9.056 8.894 4320 1.10 -1.35 1.80 225
48099 300 12.443 1.684 9.503 8.691 8.444 3890 0.70 -0.68 1.65 >350
48116 12.847 1.474 10.129 9.342 9.109 3990 0.80 -0.74 1.95 175 200
48120 11.622 1.676 8.665 7.869 7.673 3875 0.15 -1.61 2.10 250
48150 11.727 1.740 8.599 7.886 7.582 3800 0.25 -1.15 2.15 250
48151 12.825 1.079 10.650 10.031 9.911 4490 1.20 -1.94 1.75 275
48186 12.968 1.068 10.777 10.221 10.053 4495 1.35 -1.97 1.85 150
48197 12.939 1.126 11.029 10.467 10.305 4770 2.00 -1.56 1.45 125
48221 13.022 1.143 10.721 10.050 9.926 4350 1.20 -1.28 1.55 250
48228 12.456 1.159 10.184 9.565 9.380 4380 0.95 -1.95 1.85 175
48235 12.020 1.468 9.474 8.650 8.529 4100 0.60 -1.41 1.85 300 150
48247 12.757 1.135 10.584 9.972 9.810 4475 1.25 -1.64 1.65 175
48259 12.966 1.090 10.864 10.278 10.160 4575 1.40 -1.78 1.90 125
48281 106 11.797 1.357 9.431 8.719 8.592 4280 0.80 -1.78 1.65 150
48305 11.880 1.593 9.018 8.212 7.962 3900 0.40 -1.13 1.70 300
48323 500 13.081 1.461 10.286 9.458 9.273 3945 0.65 -0.73 2.00 250 250
48367 59 11.588 1.511 8.901 8.151 7.989 4040 0.40 -1.54 2.15 >350 175
48370 239 12.355 1.245 9.923 9.209 9.054 4220 0.85 -1.44 1.75 225
48392 120 11.802 1.391 9.367 8.645 8.483 4210 0.70 -1.71 1.90 300
48409 457 12.717 1.022 10.672 10.129 10.008 4665 1.35 -1.91 1.85 300 100
49013 312 12.325 1.299 10.046 9.399 9.231 4365 1.10 -1.56 1.70 >350
49022 430 12.726 1.076 10.560 9.941 9.821 4495 1.20 -1.83 1.60 225
49037 509 12.864 0.994 10.839 10.313 10.175 4690 1.45 -1.79 1.80 200
49056 231 12.305 1.511 9.382 8.613 8.404 3895 0.55 -0.66 2.10 300
49072 479 12.821 1.107 10.721 10.083 9.983 4550 1.35 -1.74 1.55 225
49088 3174 13.287 1.061 11.228 10.637 10.520 4615 1.55 -1.60 1.45 225
49111 3199 13.381 1.081 11.253 10.608 10.474 4505 1.55 -1.06 1.45 200
49123 11.292 1.599 8.776 8.113 7.911 4175 0.50 -1.96 2.35 >350
49134 12.627 1.226 10.236 9.542 9.425 4270 0.85 -1.61 1.75 325 125
49148 12.398 1.331 9.933 9.177 9.038 4180 0.80 -1.37 1.75 300
49177 12.851 1.173 10.517 9.883 9.736 4335 1.10 -1.43 1.65 225
49179 12.817 1.104 10.699 10.114 9.969 4550 1.35 -1.85 1.95 225
49188 13.170 0.980 11.174 10.703 10.574 4790 1.60 -1.81 1.10 100
49193 11.755 1.447 9.299 8.574 8.417 4195 0.70 -1.65 1.95 300 100
49205 12.983 1.100 10.806 10.234 10.104 4510 1.40 -1.80 1.70 175
49212 12.540 1.446 10.025 9.295 9.114 4145 0.90 -1.00 2.00 200
49238 12.421 1.194 10.179 9.536 9.334 4385 1.00 -1.82 1.85 125
49249 12.457 1.319 9.904 9.195 9.014 4130 0.60 -1.51 1.80 200
49252 12.615 1.145 10.424 9.818 9.638 4460 1.20 -1.77 1.45 100
49255 13.014 1.049 10.947 10.374 10.229 4605 1.45 -1.79 1.70 125
49293 244 12.305 1.255 9.900 9.226 9.041 4250 0.90 -1.54 1.70 250
49322 485 12.797 1.104 10.651 10.044 9.881 4505 1.20 -1.89 1.80 250
49333 3292 13.044 1.049 10.939 10.384 10.230 4580 1.45 -1.83 1.80 225
50022 3109 13.400 0.968 11.371 10.815 10.716 4680 1.65 -1.54 1.25 125
50037 568 13.013 1.050 10.820 10.216 10.055 4465 1.25 -1.53 1.70 250
50046 588 13.195 1.032 10.822 10.265 10.450 4650 1.70 -1.64 1.60 150
50066 428 12.900 1.179 10.592 9.942 9.786 4345 1.05 -1.38 1.70 250
50078 167 12.038 1.291 9.658 8.984 8.871 4295 0.85 -1.69 2.10 250
50108 330 12.591 1.117 10.407 9.712 9.593 4435 1.20 -1.35 1.65 200
50109 328 12.644 1.136 10.467 9.875 9.730 4495 1.25 -1.83 1.70 175
50133 11.601 1.449 9.035 8.296 8.157 4125 0.50 -1.76 1.90 >350
50163 13.427 1.038 11.358 10.876 10.493 4490 1.15 -2.11 1.60 100
50167 12.326 1.258 10.029 9.355 9.237 4355 1.00 -1.69 1.95 225 200
50172 12.999 1.101 10.765 10.158 9.998 4425 1.20 -1.61 1.60 200
50187 12.364 1.548 9.502 8.762 8.609 3945 0.50 -1.08 1.70 250 125
50191 12.293 1.247 10.314 9.729 9.494 4645 1.75 -1.41 1.50 200
50193 11.906 1.580 9.314 8.567 8.329 4075 0.65 -1.19 2.15 175
50198 12.984 1.176 10.758 10.153 10.024 4445 1.30 -1.46 1.55 275
50218 188 12.290 1.304 9.819 9.103 8.945 4190 0.75 -1.41 1.80 200 150
50228 12.670 1.196 10.397 9.770 9.597 4380 1.05 -1.68 1.70 275
50245 203 12.297 1.194 10.037 9.356 9.212 4370 1.00 -1.72 1.80 150 200
50253 79 11.658 1.375 9.293 8.555 8.374 4250 0.70 -1.72 1.95 250
50259 108 11.714 1.668 8.865 8.043 7.859 3920 0.30 -1.45 2.10 300
50267 224 12.138 1.232 9.760 9.081 8.938 4280 0.85 -1.85 1.80 250 150
50291 221 12.380 1.188 10.083 9.479 9.304 4375 1.05 -1.76 1.65 125 150
50293 401 12.794 1.153 10.499 9.901 9.730 4380 1.10 -1.57 1.70 275
50294 589 12.974 1.069 10.918 10.320 10.223 4620 1.45 -1.62 1.70 200
50304 3311 13.332 1.026 11.242 10.672 10.514 4580 1.50 -1.63 1.75 150
51021 171 11.984 1.470 9.391 8.633 8.424 4075 0.60 -1.42 2.05 325
51024 516 12.895 1.123 10.562 9.932 9.762 4330 1.05 -1.48 1.60 275
51074 372 12.706 1.300 10.241 9.505 9.338 4180 1.05 -1.09 1.90 250
51079 301 12.504 1.229 10.157 9.500 9.338 4310 1.05 -1.39 1.70 325 200
51080 236 12.317 1.428 9.809 9.058 8.900 4150 0.75 -1.39 1.85 >350
51091 198 12.320 1.143 10.132 9.516 9.353 4465 1.10 -1.88 2.05 275
51121 285 12.473 1.115 10.352 9.741 9.636 4550 1.20 -1.74 1.95 250
51132 421 12.874 1.365 10.267 9.503 9.375 4090 1.05 -1.02 2.00 250
51136 2926 13.089 1.008 11.180 10.627 10.532 4815 1.60 -1.67 1.65 75 150
51156 122 11.855 1.395 9.561 8.902 8.732 4345 0.85 -1.59 1.85 >350
51254 12.402 1.316 10.110 9.407 9.289 4340 1.05 -1.33 1.70 >350
51257 602 12.955 1.022 10.925 10.338 10.231 4655 1.45 -1.90 1.85 250
51259 423 12.597 1.135 10.486 9.867 9.756 4550 1.25 -1.75 1.75 250
52017 66 11.435 1.616 8.639 7.880 7.730 3980 0.25 -1.72 2.15 >350
52035 11.498 1.574 9.026 8.330 8.128 4185 0.60 -1.46 2.35 >350
52039 2850 13.326 0.944 11.472 10.936 10.890 4920 1.75 -1.64 1.30 125
52103 286 12.551 1.378 9.937 9.192 9.007 4075 0.65 -1.41 1.90 300 150
52105 486 12.870 1.134 10.744 10.124 10.019 4535 1.40 -1.69 1.60 225
52106 2899 13.304 1.049 11.293 10.743 10.629 4695 1.60 -1.39 1.60 100
52109 121 12.009 1.149 9.580 8.993 8.790 4280 0.75 -1.98 1.95 250
52110 2903 13.260 1.038 11.286 10.680 10.619 4735 1.65 -1.66 1.30 100
52111 166 12.347 1.522 9.360 8.562 8.329 3850 0.60 -1.12 2.15 250 250
52133 411 12.984 1.082 10.901 10.317 10.172 4585 1.45 -1.77 1.70 175
52139 276 12.473 1.380 9.869 9.078 8.940 4075 0.60 -1.27 1.90 300 200
52151 311 12.485 1.178 10.495 9.885 9.733 4655 1.40 -1.67 1.80 300
52154 2944 13.278 0.960 11.447 10.929 10.811 4920 1.75 -1.64 1.45 125
52167 131 11.735 1.392 9.367 8.745 8.513 4290 0.75 -1.77 2.00 >350
52180 441 12.733 1.169 10.571 9.953 9.837 4500 1.35 -1.67 1.80 200
52192 554 12.930 1.100 10.861 10.282 10.157 4610 1.40 -1.34 1.90 100
52204 3000 13.305 0.911 11.483 10.956 10.833 4925 1.75 -1.81 1.55 125
52222 12.447 1.097 10.339 9.747 9.611 4560 1.20 -1.72 1.75 250
53012 483 12.742 1.063 10.657 10.063 9.977 4605 1.35 -1.83 1.90 300
53054 599 12.981 1.076 10.916 10.340 10.216 4615 1.45 -1.78 1.90 200
53058 422 12.678 1.126 10.579 9.982 9.836 4560 1.30 -1.74 1.85 200
53067 163 11.941 1.303 9.586 8.886 8.743 4290 0.80 -1.74 1.75 >350
53076 455 12.797 1.192 10.607 9.974 9.850 4465 1.30 -1.42 1.70 200
53114 138 12.037 1.390 9.378 8.631 8.495 4065 0.50 -1.45 1.90 225
53119 2928 13.385 0.984 11.477 10.930 10.810 4805 1.70 -1.57 1.65 75
53132 315 12.532 1.160 10.354 9.754 9.598 4485 1.20 -1.73 1.85 275
53178 337 12.407 1.154 10.219 9.575 9.455 4465 1.15 -1.77 1.65 >350
53185 124 11.776 1.380 9.284 8.569 8.395 4175 0.60 -1.64 1.90 >350 150
53203 2785 13.200 1.008 11.152 10.628 10.467 4650 1.55 -1.78 1.85 225
54018 2588 13.475 1.042 11.363 10.779 10.646 4560 1.60 -1.45 1.50 275
54022 2594 13.360 1.412 10.825 10.069 9.910 4135 1.15 -0.46 1.80 250
54031 332 12.560 1.507 9.970 9.235 9.023 4090 0.75 -1.15 1.85 >350 250
54064 2661 13.273 1.048 11.293 10.749 10.625 4725 1.60 -1.71 1.75 150
54073 456 12.756 1.072 10.755 10.185 10.140 4725 1.50 -1.65 1.65 175
54084 2674 13.201 1.044 11.226 10.656 10.557 4725 1.60 -1.50 1.55 100
54095 437 12.768 1.124 10.731 10.117 10.010 4625 1.50 -1.72 1.70 125
54105 386 12.771 1.293 10.194 9.473 9.277 4105 1.00 -1.00 1.90 250
54132 266 12.275 1.184 10.100 9.468 9.300 4465 1.10 -1.65 1.60 250
54148 105 11.593 1.547 9.087 8.309 8.171 4145 0.60 -1.54 2.00 >350 200
54154 2737 13.000 1.023 11.055 10.512 10.422 4785 1.55 -1.66 1.70 225
55028 270 12.247 1.520 9.738 8.981 8.821 4145 0.80 -1.19 1.80 300 200
55029 339 12.387 1.356 10.082 9.357 9.244 4320 1.05 -1.33 1.80 275
55056 2655 13.437 1.044 11.464 10.904 10.816 4740 1.70 -1.43 1.25 150
55063 177 11.955 1.414 9.603 8.875 8.724 4270 0.80 -1.48 1.80 >350
55071 248 12.150 1.695 9.239 8.410 8.185 3875 0.55 -0.75 2.00 >350
55089 277 12.268 1.203 10.110 9.501 9.333 4490 1.10 -1.70 2.00 300
55101 480 12.923 1.252 10.505 9.832 9.650 4240 1.15 -0.96 1.80 >350
55102 268 12.560 1.184 10.348 9.765 9.560 4445 1.20 -1.52 1.90 200
55111 182 11.969 1.476 9.502 8.804 8.591 4185 0.75 -1.49 1.90 325
55114 132 11.654 1.705 8.787 7.948 7.735 3895 0.20 -1.45 1.95 >350
55121 135 11.957 1.673 9.306 8.465 8.286 4015 0.60 -1.05 2.35 300
55122 220 12.315 1.296 9.923 9.201 9.081 4255 0.95 -1.36 1.80 200 175
55131 2732 13.414 1.086 11.453 10.885 10.707 4705 1.65 -1.52 1.50 125
55142 367 12.442 1.445 10.008 9.257 9.086 4195 1.20 -0.73 1.80 300
55149 505 12.894 1.321 10.581 9.883 9.708 4310 1.35 -0.83 1.75 275
55152 541 12.905 1.107 10.712 10.092 9.936 4455 1.30 -1.58 1.85 150 100
55165 418 12.649 1.118 10.529 9.897 9.775 4530 1.25 -1.65 1.65 150
56024 378 12.716 1.158 10.353 9.705 9.539 4300 1.00 -1.42 1.65 300
56028 473 12.825 1.042 10.617 9.983 9.921 4475 1.15 -1.86 1.95 275 125
56040 204 12.379 1.162 10.204 9.606 9.423 4475 1.15 -1.80 2.05 200
56056 2450 13.488 0.989 11.568 11.039 10.931 4810 1.75 -1.62 1.40 125
56070 445 12.957 1.116 10.773 10.154 10.026 4475 1.35 -1.44 1.60 275
56087 81 11.404 1.543 8.763 8.059 7.893 4085 0.45 -1.84 2.25 250
56106 534 12.860 1.118 10.809 10.197 10.062 4600 1.40 -1.64 1.90 200 100
56114 417 12.729 1.152 10.552 9.906 9.785 4470 1.25 -1.52 1.55 175
56118 532 12.890 1.084 10.838 10.279 10.108 4620 1.40 -1.64 1.70 125
56128 2518 13.336 1.042 11.364 10.770 10.663 4705 1.85 -1.55 1.55 125
57010 207 12.154 1.412 9.744 9.001 8.864 4225 0.85 -1.52 1.85 >350
57029 2427 13.282 0.976 11.358 10.827 10.770 4835 1.70 -1.77 1.65 225
57054 110 11.589 1.595 8.972 8.190 7.989 4055 0.60 -1.32 2.05 275
57058 2462 13.230 1.064 11.235 10.673 10.542 4695 1.60 -1.71 1.70 150 125
57067 302 12.373 1.188 10.205 9.570 9.415 4470 1.10 -1.68 1.75 175 150
57073 368 12.470 1.151 10.355 9.746 9.608 4540 1.20 -1.76 1.75 225
57076 278 12.311 1.170 10.089 9.461 9.319 4435 1.10 -1.72 1.75 250
57083 2483 13.152 1.039 11.192 10.630 10.511 4735 1.60 -1.77 1.70 150
57085 2484 13.035 1.074 11.082 10.493 10.330 4705 1.50 -1.73 1.50 200
57091 2491 13.425 1.074 11.388 10.782 10.657 4620 1.65 -1.31 1.70 250
57114 2530 13.473 1.010 11.462 10.886 10.789 4685 1.70 -1.72 1.80 125
57127 2367 13.504 0.988 11.454 10.892 10.787 4650 1.65 -1.62 1.65 150
58043 531 12.923 1.079 10.863 10.294 10.165 4625 1.45 -1.77 1.85 250
58059 508 13.133 0.986 11.097 10.536 10.344 4625 1.45 -1.94 1.85 150
58077 2297 13.370 1.027 11.417 10.872 10.757 4760 1.70 -1.79 1.75 100
58087 133 11.760 1.337 9.438 8.724 8.609 4315 0.80 -1.69 1.75 >350
59016 2229 13.068 0.970 11.135 10.587 10.479 4785 1.60 -1.77 1.70 250
59024 11.855 1.629 9.113 8.322 8.143 3985 0.55 -0.82 2.55 250
59036 289 12.396 1.182 10.209 9.554 9.433 4455 1.15 -1.63 1.75 250
59047 192 11.975 1.413 9.653 9.001 8.794 4315 0.85 -1.44 1.80 300
59085 183 11.918 1.328 9.570 8.927 8.750 4310 0.85 -1.72 2.10 125
59089 363 12.694 1.212 10.468 9.827 9.670 4415 1.20 -1.45 1.65 175
59090 271 12.316 1.255 10.081 9.451 9.267 4405 1.05 -1.70 1.75 300
59094 164 12.174 1.157 10.091 9.527 9.386 4605 1.15 -1.91 1.75 175 125
60034 2059 13.394 1.018 11.451 10.891 10.792 4765 1.70 -1.76 1.70 125
60058 594 13.103 1.475 10.562 9.802 9.658 4130 1.15 -0.32 1.80 250 200
60059 2104 13.235 1.020 11.262 9.592 10.466 4655 1.55 -1.84 1.80 100
60064 2109 13.003 1.035 11.092 10.598 10.455 4830 1.60 -1.58 1.65 200
60065 288 12.335 1.226 10.156 9.538 9.393 4475 1.25 -1.75 1.75 150
60066 2118 13.086 1.253 11.067 10.470 10.330 4640 1.75 -0.98 1.55 200
60067 490 12.893 1.027 10.963 10.404 10.283 4775 1.80 -1.83 1.85 150
60069 556 13.022 1.171 11.041 10.448 10.352 4705 1.55 -1.41 1.80 100
60073 211 12.266 1.613 9.556 8.741 8.525 3985 0.75 -0.82 2.00 200
60088 2158 13.275 1.081 11.282 10.684 10.604 4695 1.60 -1.43 1.55 175
60101 446 12.680 1.092 10.579 9.962 9.830 4550 1.30 -1.76 1.85 200
61015 53 11.503 1.644 8.667 7.854 7.694 3935 0.35 -1.71 2.30 275
61026 2042 12.994 1.070 10.950 10.410 10.240 4640 1.45 -1.76 1.75 150
61042 260 12.209 1.306 9.927 9.220 9.096 4345 1.00 -1.56 1.70 >350 150
61046 543 12.878 1.062 10.841 10.252 10.134 4640 1.40 -1.73 1.70 175 100
61050 160 11.884 1.542 9.353 8.609 8.411 4125 0.70 -1.14 1.95 300 250
61067 371 12.528 1.605 9.875 9.096 8.899 4035 0.85 -0.94 1.90 300
61070 255 12.161 1.310 9.979 9.348 9.224 4470 1.05 -1.55 1.90 275 125
61075 2132 12.987 1.089 10.997 10.431 10.308 4700 1.50 -1.79 1.70 200
61085 158 11.846 1.699 9.088 8.287 8.081 3965 0.55 -1.26 2.30 >350
62018 1879 13.271 0.939 11.331 10.839 10.692 4800 1.65 -1.87 1.70 125 100
62058 407 12.564 1.280 10.416 9.786 9.626 4490 1.20 -1.37 1.70 250
63021 1878 13.169 1.181 11.031 10.389 10.293 4515 1.45 -1.46 1.65 275
63027 1898 13.024 1.058 10.993 10.417 10.310 4660 1.50 -1.64 1.85 150
63052 461 12.709 1.235 10.616 9.956 9.837 4535 1.30 -1.50 1.75 175 100
64023 1890 13.405 0.933 11.514 10.989 10.879 4850 1.75 -1.77 1.45 150
64049 181 12.015 1.346 9.769 9.130 8.952 4395 0.95 -1.68 1.75 250
64057 1957 13.469 1.027 11.579 11.025 10.906 4820 1.75 -1.66 1.50 150
64064 1978 13.348 1.005 11.370 10.817 10.720 4735 1.65 -1.74 1.75 100
64067 269 12.259 1.223 10.030 9.367 9.245 4415 1.05 -1.59 1.65 150 125
64074 1830 13.467 1.000 11.418 10.848 10.719 4635 1.65 -1.66 1.65 125
65042 579 12.882 1.076 10.983 10.440 10.332 4825 1.90 -1.83 1.30 150 125
65046 601 12.904 1.098 10.873 10.312 10.193 4665 1.45 -1.80 1.85 200
65057 1802 13.476 1.042 11.441 10.802 10.675 4600 1.65 -1.81 1.90 150
66015 1595 13.412 0.977 11.444 10.872 10.787 4735 1.70 -1.68 1.75 225
66026 438 12.672 1.130 10.585 9.986 9.873 4585 1.30 -1.68 1.80 250
66047 472 12.704 1.351 10.452 9.779 9.628 4375 1.30 -1.30 1.75 250
66054 232 12.111 1.290 9.908 9.226 9.123 4435 1.00 -1.59 1.80 >350
67049 1754 13.318 1.013 11.363 10.812 10.676 4740 1.65 -1.71 1.75 100
67063 199 12.084 1.348 9.756 9.056 8.873 4295 0.90 -1.50 1.90 175
68044 470 12.673 1.056 10.744 10.184 10.064 4775 1.65 -1.59 1.70 150
69007 1422 13.412 1.000 11.523 11.004 10.860 4835 1.75 -1.60 1.55 150
69012 109 11.666 1.390 9.268 8.555 8.414 4250 0.70 -1.78 1.95 >350
69027 1471 13.365 1.399 10.944 10.229 10.050 4225 1.35 -0.76 2.05 250
70032 449 12.690 1.124 10.571 9.937 9.832 4535 1.30 -1.70 1.55 >350
70035 595 12.969 1.229 10.850 10.177 10.035 4495 1.35 -1.45 1.95 150
70041 1493 13.221 1.102 11.237 10.636 10.550 4700 1.60 -1.54 1.70 175
70049 389 12.621 1.137 10.417 9.806 9.651 4455 1.20 -1.35 1.50 75
71013 1409 13.435 0.866 11.574 11.028 10.963 4895 1.75 -1.69 1.00 150
73025 150 11.864 1.685 9.194 8.360 8.166 4005 0.55 -1.42 2.35 >350
75021 442 12.630 1.164 10.473 9.863 9.718 4500 1.25 -1.74 1.80 275
76027 297 12.366 1.280 10.049 9.389 9.249 4335 1.05 -1.69 1.80 250 125
76038 316 12.535 1.411 10.009 9.238 9.049 4120 0.95 -1.24 1.85 >350
77025 194 12.197 1.339 9.861 9.171 9.008 4300 0.95 -1.58 1.85 300
77030 354 12.547 1.133 10.384 9.788 9.665 4515 1.20 -1.73 1.60 250
80026 481 12.803 1.106 10.702 10.084 9.950 4570 1.35 -1.86 1.95 125
80029 218 12.273 1.293 9.949 9.248 9.111 4310 1.00 -1.67 1.70 250
81018 217 12.282 1.174 10.015 9.377 9.244 4395 1.00 -1.81 1.95 275
81019 1209 13.401 1.097 11.336 10.747 10.618 4605 1.60 -1.49 1.65 150
81028 1241 13.332 0.899 11.312 10.712 10.580 4645 1.60 -1.74 1.60 200
82015 1026 13.277 0.980 11.383 10.818 10.702 4810 1.70 -1.70 1.65 200
82029 1107 13.469 0.813 11.608 11.070 10.973 4885 1.80 -1.76 1.05 150
85027 264 12.370 1.260 10.035 9.358 9.217 4315 1.00 -1.56 1.75 200
85031 369 12.634 1.045 10.389 9.771 9.615 4420 1.20 -1.77 1.80 175
89009 403 12.650 1.126 10.497 9.890 9.753 4510 1.25 -1.76 1.90 150

Note. – The possible carbon stars shown in Figures 1 and 3 are: LEID 32059, 33062, 35250, 37199, 39105, 41071, 42044, 43199, 43368, 44126, 44262, 44361, 44484, and 52030. Coordinates and photometry for these stars can be found in van Leeuwen et al. (2000).

Table 3a: Fe Atomic Parameters, Equivalent Widths, and Solar Abundances
Wavelength (Å) 6151.62 6157.73 6165.36 6173.34 6180.20 6187.99 6200.32 6219.28 6226.74 6229.23 6232.64 6246.32 6252.56 6265.14
Ion Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I
E.P. (eV) 2.18 4.07 4.14 2.22 2.73 3.94 2.61 2.20 3.88 2.84 3.65 3.60 2.40 2.18
Log gf -3.33 -1.22 -1.51 -2.89 -2.66 -1.69 -2.41 -2.42 -2.19 -3.00 -1.23 -0.85 -1.71 -2.56
Log \epsilon{}_{\rm\odot} 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52 7.52
Star (LEID) Equivalent Widths (mÅ)
9 73 55 35 107 68 99 136 14 37 81 110 162 137
5009 36 22 16 59 30 10 58 90 23 45 77 116 95
6017 103 46 133 100 46 123 158 69 113 130
8014 30 27 11 51 28 17 58 87 18 45 67 113 85
9013 29 26 12 48 27 8 56 88 40 74 110 88
10009 66 31 103 61 31 95 123 15 40 78 107 147
10012 119 80 42 148 105 48 140 183 26 81 106 142 192 165
11019 64 55 26 92 59 28 91 119 19 39 73 100 147 123
11021 72 66 28 99 75 33 96 128 20 44 81 103 151 134
11024 69 39 21 100 59 24 90 135 11 36 68 96 162 139
12013 91 78 46 121 93 45 114 148 32 59 100 126 170 163
12014 35 26 7 48 19 52 90 14 47 71 98 76
14010 22 10 42 18 6 42 72 60
15022 50 24 14 69 38 12 62 109 7 23 49 77 128
15023 44 23 17 69 37 11 67 105 8 24 49 84 136 109
15026 88 82 41 121 84 44 109 137 57 105 135 157
16009 45 28 15 86 46 18 72 112 10 27 53 89 132 111
16015 32 19 8 58 29 11 57 93 5 15 40 75 122 95
16019 21 22 10 46 28 15 51 80 4 13 42 70
16027 21 32 20 44 71 7 51 99 75
17014 69 60 38 105 71 23 92 132 19 36 78 109 148 144
17015 43 27 13 69 41 16 68 99 6 20 49 81 129 100
17027 18 33 44 13 46 81 36
17029 15 10 31 10 8 27 60 10 23 50 83 61
17032 53 51 27 89 62 17 79 104 28 68 94 139 124
17046 11 13 15 37 54 41 90 52
18017 21 50 19 7 49 81 13 32 68 112 84
18020 67 49 24 99 63 24 94 141 10 36 74 106 173 135
18035 32 25 11 73 27 14 61 89 46 74 114 100
18040 76 75 38 107 78 37 103 133 20 51 83 110 148 151
18047 33 23 11 64 33 10 63 89 13 46 77 124 87
19022 16 13 8 35 13 5 37 67 10 27 55 62
19062 40 24 13 69 37 13 68 98 25 51 83 128
20018 48 32 76 55 69 97 51 90 113 100
20037 56 50 83 55 18 81 102 30 67 98 135 119
20042 17 19 52 40 72 35 62 100 73
20049 27 25 10 57 28 57 81 17 43 73 108 87
21032 84 64 34 111 77 37 110 138 20 54 87 115 168 142
21035 40 21 64 37 14 64 97 17 47 75 124 94
21042 44 30 18 75 48 21 67 101 25 56 87 124 105
21063 24 23 51 17 10 47 74 6 37 60 100 77
22023 63 60 31 93 59 28 88 106 13 37 83 95 123
22037 43 27 16 66 39 14 64 112 21 47 74 115 103
22042 30 29 14 64 37 14 64 96 17 45 75 124 93
22049 21 43 31 42 81 12 37 71 98 77
22063 28 23 10 49 21 51 80 13 39 68 109
23022 14 34 16 7 37 69 9 31 51 95 69
23033 31 24 66 37 61 80 41 63 107 92
23042 25 50 21 8 51 84 16 38 66 108 79
23050 18 16 48 20 7 45 80 5 8 31 61
23061 46 26 14 76 45 15 70 104 13 25 53 80 139 104
23068 87 52 29 120 80 31 117 162 17 52 84 114 181 149
24013 110 68 40 137 97 36 122 159 21 68 85 126 203 170
24027 45 45 15 73 43 18 68 100 25 57 91 116
24040 18 34 18 35 65 47 56
24046 68 38 17 94 58 19 87 127 12 33 70 97 154 127
24056 36 21 62 34 13 62 89 9 21 48 78 125 89
24062 69 61 35 102 75 35 103 123 21 48 87 104 151 133
25006 11 26 11 7 25 62 7 42 51
25026 26 53 25 49 80 38 67 108 83
25043 93 75 39 130 90 40 114 160 21 60 93 126 200 167
25062 104 54 32 130 92 36 130 165 21 60 93 127 204
25065 136 156 120 188 116 151
25068 78 42 22 109 68 23 106 137 16 44 74 100 161
26010 27 27 10 52 62
26014 28 13 9 57 28 7 57 82 14 37 72 107 89
26022 31 48 53 80 6 13 65 107
26025 99 52 25 130 83 30 124 170 15 52 195 163
26030 20 10 42 10 30 64 26 59 95 72
26069 22 37 18 42 70 9 30 53 94
26072 48 23 72 33 72 103 23 50 72 125
26086 105 53 136 95 50 116 80 117 145
26088 74 50 29 108 70 29 97 136 11 34 68 103 163 138
27048 63 52 27 96 62 26 91 116 33 76 104 138
27050 38 15 34 68 24 58 95 66
27073 44 30 15 70 39 15 63 99 8 25 50 85 119 99
27094 43 23 53 82 81 115 86
27095 82 35 124 78 34 117 146 48 100 126 174
28016 39 31 67 39 73 98 25 51 83 119 100
28020 27 16 52 25 46 87 35 59 112 86
28044 52 36 18 80 51 17 80 113 12 32 63 87 144 110
28069 57 33 15 86 55 18 80 109 30 64 93 142 121
28084 42 27 73 45 21 77 98 32 51 87 127 105
28092 50 37 84 46 18 74 114 28 62 91 133 116
29029 48 34 16 75 49 20 71 98 30 63 86 120
29031 25 17 46 11 44 79 37 67
29037 19 10 45 20 45 76 37 61 66
29059 57 41 20 89 51 19 78 114 35 59 95 140 117
29067 132 89 158 129 78 167 102 101 129 187
29069 75 60 32 107 68 25 99 131 40 84 103 157
29072 46 23 63 36 11 56 91 16 41 70 117 87
29085 24 32 11 57 32 55 80 16 40 70 107
29089 32 18 9 48 64 79 46 66 105
29099 89 67 32 123 81 33 117 147 13 49 100 117 184
29106 50 27 12 82 47 15 74 111 22 60 89 146 119
30013 69 33 99 76 35 93 119 51 94 114
30019 60 53 29 89 57 25 83 109 33 70 97 145 122
30022 27 45 26 10 43 78 39 66 104
30031 98 73 34 133 90 36 120 156 24 60 99 128 180
30069 9 8 21 47 40 69
30094 71 45 26 83 44 15 80 111 15 33 72 88 125 124
30124 43 42 73 47 15 76 95 12 24 61 84 121 98
31016 28 15 6 42 19 42 74 11 54 90 65
31041 47 37 70 45 17 65 99 23 52 85 125 105
31047 16 8 47 22 81 32 65 98 73
31048 23 46 23 47 14 37 64
31075 15 37 16 47 79 29 60 97
31079 40 22 10 68 38 64 101 20 51 76 132 91
31094 34 22 16 66 35 14 63 14 48 74
31095 29 55 23 52 80 13 47 72 106
31104 18 7 33 14 31 65 21
31109 45 31 69 43 19 76 98 32 65 83 121 94
31110 91 77 36 121 84 39 112 143 17 50 96 119 157
31119 78 43 108 76 36 106 142 22 49 92 112 162
31133 14 28 14 33 56 8 50 53
31139 37 24 12 65 34 11 63 100 24 50 75 126
31141 52 37 18 79 45 18 74 110 27 58 90 128 111
31147 40 11 64 19 71 102 50 92 125 78
31152 66 41 12 57 104 77 132 87
32014 29 14 8 52 32 9 51 85 36 70 116
32026 54 24 80 66 26 78 114 40 63 90 130
32027 27 32 10 67 37 54 80 49 67 116 91
32043 19 7 48 76 11 38 75
32063 46 33 13 80 40 15 71 101 25 60 90 121 105
32069 9 17 24 43 42 48
32100 26 21 53 30 9 54 79 36 70 103
32101 52 43 19 76 45 18 78 103 21 61 93 135 113
32125 53 34 13 79 48 16 77 119 9 27 62 134 109
32130 11 9 35 8 39 65 52 90
32138 94 48 25 127 82 28 118 160 14 50 120 194 163
32140 41 31 71 45 11 62 97 19 44 77 126 95
32144 47 31 19 74 45 18 78 107 15 34 63 93 124
32165 26 15 9 58 27 50 89 19 38 77 113 87
32169 110 62 143 103 49 131 150 30 67 125 135
32171 74 26 108 67 28 99 46 97 108 152
33006 96 58 31 127 91 37 126 173 23 55 88 116 178 153
33011 66 35 17 88 61 20 84 124 9 33 63 96 158 127
33018 59 29 22 73 50 16 87 108 29 54 82 94
33030 15 47 56 77 64 66 98 84
33051 53 40 18 83 49 21 76 112 26 63 85 135 116
33064 32 22 50 32 50 81 15 39 76 105 79
33099 106 109 60 150 105 52 156 82 148
33114 88 62 34 122 85 34 114 170 21 52 83 119 178 157
33115 54 65 37 58 25 87 101 31 79 96 129
33126 43 45 23 73 46 19 77 102 10 25 79 96 122 112
33129 34 20 10 59 31 12 60 85 8 13 38 70 118 85
33138 39 33 62 38 92 52 82 118 96
33145 16 9 37 19 5 70 6 35
33154 23 67 74
33167 39 30 16 48 33 14 54 96 21 67 80 114 88
33177 40 22 19 61 100 45 86 115 93
34008 38 78 48 14 75 106 16 61 86 135 109
34029 98 87 52 134 97 54 122 168 33 75 105 138 187
34040 36 27 67 36 13 61 91 52 83 121 97
34056 17 17 43 71 33 55 65
34069 55 28 21 92 51 19 82 108 31 59 91 132 109
34075 81 59 34 113 85 34 109 144 19 49 85 112
34081 49 35 17 77 44 22 73 98 10 25 54 86 131 109
34129 21 11 7 42 30 40 72 28 63 97 73
34130 7 17 37 28 44
34134 77 41 25 109 71 23 102 124 13 41 74 110 112
34143 47 119 88 50 106 147 60 103 136 188
34163 24 18 49 48 81 13 24 62
34166 42 37 81 14 74 60 83 123
34169 61 24 88 53 22 83 111 8 38 84 100 132 127
34175 87 62 24 127 84 30 113 152 50 91 110 173
34180 121 156 123 85 77 140 144
34187 22 51 28 10 59 79 5 13 35 76 112 88
34193 52 33 19 84 54 18 82 124 15 31 58 88 115
34207 65 55 27 97 73 29 96 135 15 44 72 106 154 124
34214 13 29 27 65 57 64
34225 55 134 93 51 126 145 66 119 131 164
34229 23 21 11 51 25 50 85 11 32 71 117 86
35029 32 24 15 53 34 12 84 22 39 72 105 82
35035 24 18 47 27 47 80 4 10 37 63 102 81
35046 46 35 15 79 45 15 72 112 12 24 54 79 132
35053 34 24 7 57 29 11 63 97 20 38 76 117 95
35056 96 61 42 129 81 32 122 154 61 79 121 186 150
35061 74 65 34 110 79 30 103 18 44 85 114 166
35066 76 43 21 107 71 25 104 133 15 40 66 107 155 128
35071 34 49 79 11 19 55 92
35074 39 33 66 36 12 59 96 20 47 82 115 99
35087 19 11 39 27 7 40 79 12 36 68 98
35090 94 39 123 92 43 123 159 20 63 108 127
35093 16 23 13 31 46 51 80
35124 50 51 26 79 54 21 83 94 15 33 66 96 127
35157 73 36 116 78 34 96 121 49 97 113
35165 41 22 11 65 39 13 62 88 7 18 45 72 122 101
35172 47 136 107 51 127 66 113 141
35190 37 13 63 33 19 57 98 7 24 49 70 118 85
35201 58 135 102 52 120 67 112 125
35204 15 20 35 12 37 65 8 27 64 90 73
35216 66 42 25 108 61 20 102 146 15 41 69 104 156 140
35228 30 25 60 24 15 55 87 48 77 112 92
35230 52 29 78 44 11 75 112 24 53 93 147 116
35235 67 41 20 93 59 24 101 115 35 67 113 143 116
35240 72 45 21 104 63 14 91 140 28 69 104 144
35248 28 10 59 28 10 57 87 7 20 41 83 115
35260 36 25 11 71 36 14 62 98 16 47 87
35261 49 41 20 69 43 15 72 97 23 55 85 118 100
36028 22 9 58 43 77 18 39 69
36036 82 40 18 118 69 25 109 137 13 37 66 115 182
36048 27 23 65 24 20 56 84 37 71 104 82
36059 23 52 32 16 53 76 14 42 62 105 74
36061 53 51 21 85 61 24 87 108 9 34 74 97 132
36087 18 44 25 9 44 69 15 29 65 102 78
36106 39 30 11 65 14 66 89 8 20 40 80 109 101
36110 12 24 45 85 60 98 70
36113 32 27 55 28 12 56 82 10 70 110 86
36134 89 93 50 121 88 55 25 63 90 127 159
36156 55 27 19 92 53 16 82 110 7 26 59 84 140 122
36179 64 148 110 56 137 178 80 146
36182 69 52 26 103 64 27 93 120 37 75 103 149 131
36191 99 63 145 117 60 123 151 78 119 139
36206 35 23 71 37 16 67 97 23 48 84 124 98
36228 88 46 24 115 75 30 115 145 16 46 77 121 191 156
36239 61 96 60 24 90 113 31 80 106 142
36259 35 11 68 36 11 60 99 21 47 80 123 101
36260 52 71 17 66 87 30 61 80 113 84
36280 61 52 23 93 56 87 118 9 38 70 94
36282 36 20 61 32 59 95 6 15 40 73 119 93
37022 12 57 31 54 86 15 40 70 114
37024 148 163 101 179 134
37051 22 14 10 37 25 46 79 35 69 107
37052 46 28 16 66 27 15 62 93 22 42 86 117 83
37055 49 42 79 47 77 97 31 65 90 122 107
37062 78 41 122 84 42 112 53 92 128
37071 51 45 102 78
37082 21 41 38 75 32 62 98 72
37087 34 26 10 70 37 67 93 47 76 120
37094 27 18 10 53 25 13 48 74 13 42 63 109 82
37105 27 23 51 22 11 44 73 8 42 64 99 72
37110 144 90 194 148 74 170 244 48 111 164 172 231
37119 72 41 23 101 65 27 99 133 13 37 70 104 153 125
37136 22 18 46 12 37 75 5 13 35 61 105 79
37139 83 59 33 122 80 35 115 144 20 55 89 127
37143 45