A NEW ABUNDANCE SCALE FOR THE GLOBULAR CLUSTER 47 Tuc

For the Arcturus T_eff we adopted the value of 4290 K derived by F06 from the angular diameter of Perrin et al. (1998) and the bolometric flux reported by Griffin & Lynas-Gray (1999). We note that the uncertainties on the bolometric flux, cited by Griffin & Lynas-Gray led F06 to assign a total 1σ T_eff uncertainty of only 10 K. We now believe that Griffin & Lynas-Gray's flux uncertainty was too optimistic, as it is based on essentially the same observational data as numerous other studies (Mozurkewich et al. 2003; Alonso et al. 1999; Bell & Gustafsson 1989; Augason et al. 1980), yet those studies gave a range of bolometric flux values inconsistent with Griffin & Lynas-Gray's stated flux uncertainty. Here we adopt a 1σ uncertainty in the bolometric flux of 2.6% from the standard deviation of the fluxes estimated from the five investigations listed above. This translates to a 1σ T_eff uncertainty of 28 K for Arcturus from the flux; the angular diameter contributes a temperature uncertainty of 8 K, thus indicating a total temperature uncertainty of 29 K.

F06 estimated log g = 1.6 and a microturbulent velocity parameter of 1.67 km s⁻¹ for Arcturus. The Fe abundances in Arcturus, found using this initial set of stellar parameters, are shown in Figure 2. For this purpose, we consider the results relative to the Sun, for which we derived each line's abundance using the EWs of F06, measured from the atlas of Kurucz et al. (1984) and the canonical solar parameters of T_eff = 5777 K, log g = 4.44 and ξ = 0.93 km s⁻¹. A comparison of the Arcturus EWs measured from the Hinkle et al. (2000) Arcturus atlas with EW measurements of an Arcturus spectrum obtained with the MIKE spectrograph indicated that the MIKE EWs are ∼2% larger; this corresponds to ∼0.008 dex in abundance, which is smaller than the computational uncertainties.

Figure 2 (top panel) shows that the run of abundance versus excitation potential (henceforth "excitation plot") has essentially no slope, thus confirming the accuracy of the adopted temperature scale. The investigation of the differences between abundance analyses using plane-parallel and spherical geometry model atmospheres by Heiter & Eriksson (2006) predicts increased calculated abundances for low-excitation lines of neutral iron-peak elements by up to ∼0.3 dex. If the predictions are correct then the Arcturus excitation plot, using solar gf values, should show a slope when the correct temperature is adopted for Arcturus. However, Figure 2, indicates that, empirically, the absolute effect for Arcturus is rather small (∼0.05 dex), and therefore, the differential effect between Arcturus and the 47 Tuc stars must be negligible. This supports the validity of the excitation plots to constrain the temperatures of the 47 Tuc red giants. The same arguments apply to the possible effects of granulation on the derived abundances of Fe i lines as a function of excitation potential (see Steffen & Holweger 2002): Figure 2 shows that the difference in this effect is not detected between the Sun and Arcturus and so should be negligible when taken differentially between the 47 Tuc giants and Arcturus.

Our initial data showed, however, a considerable trend of iron abundance in Arcturus with EWs. This prompted us to lower the microturbulence to 1.54 km s⁻¹ in order to remove any such remaining slope (lower panel of Figure 2). One noteworthy feature in these plots is, however, the lack of ionization equilibrium: while the mean iron abundance, [Fe/H], from the neutral stage is −0.49 ± 0.01 dex and thus consistent with the value of −0.50 from Peterson et al. (1993) and F06, the ionized species yield an abundance [Fe ii/H] higher by 0.08 ± 0.03 dex.

Our measured deficiency of Fe i, relative to Fe ii, is similar to the 0.03 to 0.06 dex non-LTE effect predicted for the K0III star Pollux by Steenbock (1985): the non-LTE correction for Fe i lines of high-excitation potential were ∼0.02 dex, while low-excitation lines required corrections of ∼0.05 dex, and the Fe ii correction was approximately −0.01 dex. Thus, a non-LTE excitation temperature for Pollux would be lower than the LTE value (a trend of increasing correction with line EW was also predicted, but in an LTE abundance analysis this would be absorbed into the microturbulent velocity parameter). For iron in the Sun, Steenbock (1985) found non-LTE corrections of 0.01 and 0.03 dex for weak high and low-excitation Fe i lines, respectively. More recent non-LTE calculations by Korn et al. (2003) found that collisions of hydrogen atoms with iron in the solar atmosphere are enhanced over the Darwin (1968, 1969) formalism by a factor of 3 (S_H = 3); since Steenbock (1985) employed the Darwin formulae (i.e., S_H = 1) Steenbock's non-LTE corrections for the Sun and Pollux are probably overestimated. Pollux is 560 K hotter than Arcturus (McWilliam 1990) and more metal-rich by ∼0.4 dex, so the non-LTE corrections may differ. However, F07 showed that the Fe i/Fe ii and Ti i/Ti i abundance ratios for bulge and disk red giants are approximately constant in the [Fe/H] interval from −1.5 to +0.5 dex and for T_eff from 4000 to 5000 K; this suggests that the non-LTE corrections for Pollux and Arcturus are probably very similar. If we assume similar non-LTE correction for Arcturus and Pollux for an equal mix of low and high-excitation lines, and if we include the solar non-LTE corrections from Steenbock (1985) and Korn et al. (2003), then our estimate for the non-LTE-corrected Arcturus [Fe/H] from the neutral lines is −0.49 dex. The non-LTE corrected Fe ii lines indicate [Fe/H] of −0.46; this iron ionization difference, at 0.03 dex, is comparable to the 1σ random error on the mean Fe ii abundance, derived from a mere five lines.

In order to explore the effect of gravity of iron ionization equilibrium we opted to re-derive the mass of Arcturus by comparing its location in the T_eff-luminosity diagram with theoretical isochrones. The luminosity was obtained from its Hipparcos-catalog-based apparent magnitude and distance of (−0.04 ± 0.02) mag, (11.25 ± 0.09) pc, respectively. A bolometric correction (BC) of (−0.78 ± 0.02) was adopted from an interpolation of the predicted photometry from the Kurucz-atmosphere grid. For consistency it is also necessary to employ the predicted BCs with the Kurucz-based bolometric magnitude for the Sun, at 4.62, when computing stellar photometric gravities. The BCs implied by the Teramo group (BaSTI; Pietrinferni et al. 2004) could have been used with the standard M_bol of 4.74 for the Sun (e.g., Cox 2000) to give the same result. Unfortunately, F06; F07 did not appreciate this problem, so their computed gravity for Arcturus was too small by 0.04 dex.

We employed the solar composition and α-enhanced BaSTI isochrones (Pietrinferni et al. 2004; including the revised α-opacities from Ferguson et al. 2005) to estimate the mass and age of Arcturus, as indicated by its location in the T_eff versus M_V plane. Our analysis involved the use of cubic spline interpolation of the BaSTI grid to the metallicity, Z, and (O/Fe) of Arcturus, taken from the abundances of F07. In particular we interpolated to the Arcturus Z value (of 0.00954) for solar composition and α-enhanced BaSTI isochrones, followed by interpolation to the Arcturus (O/Fe) value of 1.67 dex. It is important to note that although the α-enhancements of Mg, Si and Ca employed in the BaSTI models are similar to the values seen in Arcturus, the O/Fe value of the models is 0.2 dex higher than observed; presumably this resulted from early high estimates of the solar oxygen abundance (e.g. Grevesse & Noels 1993) used in the BaSTI models.

Our results indicate a best-fitted age of 9.0^+3.0_−1.8 Gyr and a mass of 1.00^+0.05_−0.09 M_☉ for Arcturus. The uncertainties on age and mass include estimates for the uncertainties of T_eff, distance, magnitude, metallicity and O/Fe ratio.

The BaSTI results are well consistent with the value derived from the α-enhanced Padova isochrones (Salasnich et al. 2000), from which we obtain (0.92 ± 0.09) M_☉ and (10.5 ± 1.0) Gyr. Lastly, we employed the Yonsei–Yale (Yi & Demarque 2003) set of isochrones, again accounting for enhanced α-element abundances of [α/Fe]=+0.4 dex. As Maraston (2005) argues, the BaSTI models tend to produce higher T_eff for a given luminosity and mass compared to the other sets of isochrones. Hence the latter will necessarily result in lower age estimates. Concordant with this view, the Yonsei–Yale tracks provide a "best-fitted" mass of (1.22 ± 0.2) M_☉ and a corresponding younger age of (5 ± 1.5) Gyr. In the following, we will use the BaSTI based mass estimate, since these tracks incorporate a sophisticated, i.e., varying with metallicity, treatment of the mixing length and have succeeded best in matching the observations of Galactic globular clusters (Maraston 2005). Higher adopted mass, and accordingly log g, would aggravate the departure from ionization equilibrium, whereas coincidence of the neutral and ionized stage would require log g ∼ 1.44, which is established with a lower mass of 0.71 M_☉.

If we appeal to errors in the basic parameters of α Boo to lower its mass, then an increase in T_eff of ∼190 K, or an increase in the metallicity, Z, by 0.2 dex are required; these changes are far greater than the uncertainty in these two parameters, and so can be eliminated. Another possibility is that Arcturus has experienced mass loss, perhaps related to its metallicity and evolutionary phase, or as the result of interactions with a putative companion (e.g., Soderhjelm & Mignard 1998; Verhoelst et al. 2005; but see Griffin 1998). While this extra-ordinary mass loss is feasible, and may reflect lack of certainty of mass loss in metal-rich RGB stars, it seems a rather ad hoc assumption. Also, it remains unlikely that the observed temperature and luminosity are consistent with a lower mass of Arcturus.

We note in passing that the isochrone mass-loss parameter is not sufficient to reduce the derived Arcturus mass enough to obtain Fe ionization equilibrium. At the location of Arcturus on the RGB the mass-loss parameter values, η, of 0.2 and 0.4 (Reimers 1977) hardly affect the stellar mass; however, at the tip of the RGB and on the AGB these parameters do have a significant effect. Although it would enable ionization equilibrium the luminosity and temperature of Arcturus eliminate it as a possible AGB star. In the following, we adopt a mass of 1.00 M_☉ for Arcturus, based on the BaSTI isochrones, which corresponds to a gravity of 1.64 ± 0.03.

The T_eff values of the target stars were calibrated using the empirical color–temperature relations from Alonso et al. (1999). For this purpose, we exploited the V and I photometry from Kaluzny et al. (1998), complemented by infrared J and K data from the 2MASS (Skrutskie et al. 2006). The 2MASS photometry was converted to the TCS system, employed in the Alonso et al. (1999) T_eff calibration, using the Carpenter (2005, unpublished) 2MASS–CIT transformation³ and the CIT–TCS conversion of Alonso et al. (1998).

In addition to the color transformations it is necessary to correct for interstellar extinction; we employ the extinction law of Winkler (1997) throughout this work. Harris (1996) obtained a reddening for 47 Tuc of E(B − V) = 0.05 mag, while the reddening maps of Schlegel et al. (1998) indicate E(B − V) = 0.032 mag. Gratton et al. (2003) obtained E(B − V) = 0.035 ± 0.009 from B−V colors and E(B − V) = 0.021 ± 0.005 from b−y colors. The average of all four estimates is 0.035 ± 0.006; if the unusually low reddening from b−y colors by Gratton et al. (2003) is ignored, the average reddening becomes 0.039± 0.007 mag. Considering this distribution of reddening estimates for 47 Tuc for our initial reddening value we adopt E(B − V) = 0.04 ± 0.01 mag.

The large baseline of the V − K color and the steep color–temperature gradient for red giant stars makes this T_eff estimate the least susceptible to potential photometric uncertainties. As a result temperatures derived from V − K color are generally expected to be the most accurate and we shall use these values as the photometric T_eff in the following. The typical uncertainty on V − K temperatures, given by the photometry and calibration errors, is ∼40 K.

We chose to employ the Alonso et al. (1999) (V − K) color temperatures differentially, relative to the known (V − K) and T_eff of Arcturus, in order to remove possible zero-point systematics in the calibration. The average of photometry from Lee (1970) and Johnson et al. (1966) were used to determine the Arcturus V − K color of 2.925 mag (in the Johnson–Cousins system); we note that the V − K color from the two studies differ from the mean by 0.025 mag. The Johnson V − K color, when converted to the CIT system using the relations in Elias et al. (1985) and then to the TCS system, as described above, indicate T_eff = 4252 K using the Alonso et al. (1999) calibration; this is 38 K cooler than the directly measured effective temperature of 4290 ± 29 K, based on absolute flux and angular diameter measurements. Thus, in order to place our 47 Tuc photometric V − K temperatures onto the physical T_eff scale for Arcturus it is necessary to add a zero point of 38 K to the values indicated by the Alonso et al. (1999) V − K calibration. In this way our photometric T_eff values are differential to the Arcturus value. We note that the ±0.025 mag range of the observed (V − K) Arcturus color corresponds to 17 K.

In addition to the V − K photometric temperatures we derived spectroscopic temperatures by demanding excitation equilibrium for Fe, i.e. that there is no slope in the plot of iron abundance versus excitation potential. Since each individual 47 Tuc line abundance is differential to the same line in Arcturus we ensured that our spectroscopically determined temperatures are on the same physical T_eff scale as Arcturus. The differential V − K photometric and spectroscopic temperatures in this work are listed in Table 5. The mean difference between the two temperatures, T(V − K) − T(spec), is −5 K with an rms scatter of 41 K; this suggests a random error on the mean difference from the eight RGB stars of only ±15 K. We note that a reddening change of 0.01 mag. in E(B − V) leads to a ∼19 K change in photometric T_eff; thus, the agreement between our photometric and spectroscopic T_eff values is consistent with the range of reddening values cited in the literature, from 0.03 to 0.04 mag.

We adopted physical gravities for the 47 Tuc stars based on Equation (1):

$$\begin{equation} \log {g} = \log {M/M_{\odot }} - \log {L/L_{\odot }} + 4\log {(T/T_{\odot }}) + \log {g_{\odot }}. \end{equation} \tag{ 1 }$$

For the luminosities we used the dereddened V-band photometry of Kaluzny et al. (1998), BC from the Kurucz Web site and a distance modulus of (m − M)₀ = 13.22 ± 0.06. Our adopted distance modulus is the average from six studies (Zoccali et al. 2001; Percival et al. 2002; Gratton et al. 2003; Weldrake et al. 2004; McLaughlin et al. 2006; Thompson et al. 2008, in preparation) that used numerous techniques, including HST proper motions, the white dwarf cooling sequence, empirical CMD fitting, and eclipsing binaries.

Masses for the 47 Tuc stars were determined by comparison with the latest version of the Teramo α-enhanced isochrones (with α-element opacities from Ferguson et al. 2005). In Figure 1 we compare the observed 47 Tuc color–magnitude diagram with the α-enhanced, [Fe/H] = −0.70 dex, Teramo 12 Gyr isochrone; this is the average of the ages estimated by Zoccali et al. (2001) and Percival et al. (2002). This comparison suggests a typical mass of 0.89 M_☉ for our 47 Tuc RGB stars.

For a more precise comparison of the isochrones with the 47 Tuc giants we interpolated the isochrones to match the overall metallicity, Z, and the measured O/Fe ratio from a previous iteration on the abundances (Z = 0.0062, (O/Fe) = 1.77). The observed M_V values of our 47 Tuc RGB stars were closest to the interpolated isochrones with ages in the range of 12–14 Gyr. However, these interpolated isochrones were all brighter than the observed M_V values by a few hundredths of a magnitude, although the differences are well within the systematic uncertainties. For example: a T_eff increase of 10 to 30 K, or a reddening increase of 0.01 mag (slightly more than the uncertainty on the observed Arcturus V magnitude) could account for the difference. This range of isochrone ages gave masses (for η = 0.4) of 0.87 M_☉ for the 12 Gyr isochrone to 0.81 M_☉ for 14 Gyr.

These isochrone-based masses compare favorably with the direct measurement of 0.871 ± 0.006 M_☉ for a subgiant in a double-lined, eclipsing, spectroscopic binary in 47 Tuc by Thompson et al. (2008, in preparation). Inspection of the 12 Gyr, α-enhanced, Teramo isochrones shows that the masses of the subgiant and our RGB stars should be equal to within 0.01 M_☉. This is the case because the mass loss experienced by the RGB stars reduces their slightly higher original mass to the mass of the subgiant, according to the η = 0.4 prescription of the Teramo isochrones. Given the consistency of these methods we adopt the direct measurement of Thompson et al. (2008, in preparation), at 0.87 M_☉ for the mass of our 47 Tuc RGB stars. Since star #3 is closer to the AGB track in the CMDs shown in Figure 1 we adopt the AGB mass of 0.65 M_☉ for this star, as indicated by the interpolated Teramo isochrones, interpolated to the Z and O/Fe measured from the spectra. In the abundance iterations the overall metallicity parameter, [M/H], for the input model atmospheres, is equated to [Fe i/H] abundance from the previous iteration.

As an initial guess for the microturbulence parameter, ξ, for the model atmospheres, we used the same value as in Arcturus, due to the expected similarity in the spectral type of our target stars and α Boo. This value of 1.54 km s⁻¹ provides a reasonable estimate for four of our eight stars in terms of no apparent trend of Fe i abundance with EW. The weakest lines with EWs below 12 smÅ were neglected for this part of the analysis. Nevertheless, stars #6–#8 required a ξ lower by ∼0.1 km s⁻¹, while for star #3, this parameter had to be significantly increased (see Figure 3) to eliminate any such slope, as might be expected from its AGB star evolutionary status. Usually, ξ could be determined to within ±0.1 km s⁻¹ accuracy.

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Ionization equilibrium is not obtained for any of our eight red giants in 47 Tuc; the mean [Fe i/Fe ii] ratio is +0.083 ± 0.015 dex with a scatter of the eight stars of σ = 0.040 dex. The giant that comes closest to (Fe i)=(Fe ii) is star #7 with [Fe i/Fe ii] = +0.03 dex. This issue will be addressed in detail in Section 4.4.

The final chemical abundance ratios derived for the 47 Tuc red giant sample, using the spectroscopic excitation T_eff values are listed in Table 6.

The atmospheric parameters of the unevolved 47 Tuc TO star differ substantially from those of the red giant sample, so Arcturus can no longer be employed as a reference for differential abundance analysis. The 47 Tuc TO star was selected with T_eff similar to the Sun, in order to perform a solar differential abundance analysis. However, due to its low-metallicity lines in the TO star are considerably weaker than the same lines in the Sun. As a result of the low S/N of the TO star spectrum lines that are measurable in the TO star are saturated in the Sun, thus reducing the effectiveness of a differential abundance analysis.

To solve this difficulty we employed a two-step differential abundance analysis using a bright Galactic halo field TO star, Hip 66815. Its parameters (5850 K, log g = 4.5, ξ = 0.95 km s⁻¹, [Fe/H] = −0.64; Fulbright 2000; Sobeck et al. 2006) are comparable to those expected for the 47 Tuc TO star, judging from its location in color–magnitude space and the previously discussed red giant sample. Our S/N ∼ 500 spectrum of Hip 66815 enabled us to measure very weak lines, down to ∼5 mÅ, in this star that are not saturated in the solar spectrum. Thus, we used unsaturated lines in the 47 Tuc TO star and Hip 66815 for the first step, and then compared very weak, but well-measured, lines in Hip 66815 to unsaturated lines in the solar spectrum for the second step of the differential analysis. These lines and their EWs are listed in Table 4.

We refined the stellar parameters of Hip 66815 and the 47 Tuc TO star in the same manner as discussed above for the red giant sample. Thus it turned out that the temperature of Hip 66815 needed to be lowered by 100 K from the photometric value. Contrary to the red giants, damping issues such as Stark and van der Waals broadening play a progressively dominant role in the dense atmospheres of the dwarf stars. For the case of hydrogen we matched the observed Hα-line profile with a spectral synthesis, in which the damping constants in the classical Unsöld approximation were multiplied by a constant factor of 6.5, which provided the best fit to the line wings. In this case we obtained an independent, reddening-free estimate of the stellar T_eff by synthesizing the temperature-sensitive wings of the Hα line. From this we found a T_eff value in agreement with the photometric temperature to within 40 K. In the following we employed this damping factor enhancement of 6.5 over the Unsöld approximation for all the absorption lines. It should be noted that errors due to this approximate treatment will be absorbed by a change in the best-fitted microturbulence parameter.

In this way we found a [Fe/H] of −0.76 for the reference star Hip 66815, which is about 0.1 dex more metal poor than derived in earlier studies (Fulbright 2000; Sobeck et al. 2006); it should be noted that the Sobeck et al. (2006) work assumed the Fulbright T_eff value. Fulbright's excitation T_eff was based on laboratory log gf values, which may constitute a significant source of uncertainty, whereas our differential analysis is largely insensitive to the systematic effects induced by such atomic parameters. The photometric and excitation temperature of the 47 Tuc TO star agree remarkably well to within ≲20 K.

Ionization equilibrium is well established in Hip 66815, it does, however, not hold in the 47 Tuc TO star. We address this issue in detail in the next section. Our final abundance ratios for the 47 Tuc TO star are presented in Table 7.

As can be seen from Table 6 the mean difference between Fe i and Fe ii abundances (ΔFe = (Fe i) − (Fe ii)) for our 47 Tuc giants (relative to Arcturus) is 0.08 dex. In this section we investigate possible resolutions of this apparent inconsistency. We note that the differential [Fe i/H] and [Fe i/H] values were computed based on an assumed [Fe/H] for Arcturus of −0.51 dex, from the Fe i lines alone. It is interesting that if we employ our Arcturus [Fe ii/H] value to compute the differential [Fe ii/H] for the 47 Tuc giants, and Fe i lines to compute [Fe i/H], the ionization equilibrium problem is reduced to only ΔFe = 0.03 dex; i.e. consistent to within 1σ of satisfying ionization equilibrium for Fe. Thus, it appears that the differential abundances of 47 Tuc relative to the Sun provides ionization equilibrium, while iron ionization equilibrium for Arcturus is not satisfied.

We remind the reader that the purpose of employing results differential to Arcturus was to avoid systematic errors in the model atmospheres, due to errors and the use of incomplete physical description in the 1D Kurucz model grid. Hence, it is also the difference between the Arcturus and 47 Tuc atmospheric parameters that determine whether ionization and excitation equilibrium are achieved. To explain the ionization imbalance it is then necessary to find an unaccounted systematic difference between the Arcturus and 47 Tuc red giant atmospheres.

In the mean, ionization equilibrium could be achieved by an average increase in log g for the 47 Tuc giants of ∼0.16 dex. As indicated by Equation (1), mass, luminosity, and temperature determine the gravity. If a systematic error in log g is the source of the apparent under-ionization of Fe, the change in log g cannot be due to mass, as this would indicate the presence of main sequence stars with M∼1.4 M_☉ (late F-type), which are not seen in 47 Tuc. For luminosity to create this change in log g would require a 0.5 mag decrease in the distance modulus, implying a distance to 47 Tuc closer by 500 pc, or (m − M)₀ = 12.72. This value lies 8σ below the mean value, and 0.3 mag lower than the lowest recent measurement of the distance modulus. Uncertainties in the photometry are less than a few hundredths of a magnitude, given the consistency of the Kaluzny et al. (1998) CMD with other published work (e.g., Armandroff 1988). We estimate the uncertainty on the Kurucz BCs at 0.05 mag, based on the uncertainties in temperature, gravity, and metallicity. Finally, the published reddening values for 47 Tuc cite uncertainties of 0.01 mag. The quadrature sum of these uncertainties affecting the luminosity amount to 0.04 dex in log g, much less than the 0.16 dex in log g required to explain the apparent under-ionization of iron.

At first glance it may seem that the required changes in log g cannot be due to temperature either, given the excellent agreement of the two sets of independent differential temperatures for our red giants on the Arcturus scale; it would be necessary to investigate how both temperature measures could be in error. However, the Fe ionization imbalance could be resolved with a modest systematic T_eff decrease of ∼60 K, as can also be seen from Table 8. This would, however, lower the Fe i abundances by only ∼0.01 dex, and fortunately does not affect our conclusion on the [Fe/H] scale of our 47 Tuc red giants. The main effect is the enhanced temperature sensitivity of the Fe ii abundance, most likely due to a rapid change in the degree of Fe ionization at the T_eff of Arcturus. Because of the differential nature of both the photometric and spectroscopic temperatures, relative to Arcturus, a shift in the adopted Arcturus T_eff does not affect the relative derived temperatures of the 47 Tuc giants; thus, the ionization equilibrium is not directly affected by any reasonable change in the Arcturus temperature.

Next, we investigated the sensitivity of ionization equilibrium to the adopted model atmosphere [α/Fe] ratio. An increase from scaled-solar composition to the 0.4 dex enhancement of the Castelli/Kurucz α-enhanced model atmospheres raised the computed Fe ii/Fe i abundance ratio by ∼0.10 dex. This suggests that models with [α/Fe] enhancements of ∼0.8 dex for 47 Tuc would solve the Fe ionization problem—a value that has not been detected that highly in any globular cluster so far. Inspection of the abundances in Table 6 shows average α-element (O, Mg, Si, Ca, Ti) enhancement of 0.41 dex. In this regard it is interesting that the average α-enhancement for Arcturus is 0.34 dex; if Na and Al are included then the 47 tuc stars are enhanced by 0.39 dex and Arcturus is enhanced by 0.31 dex. To estimate the effect of the difference in composition of the light metals between Arcturus and 47 Tuc we computed the electron densities (e.g. see Mihalas 1978) for the Arcturus and 47 Tuc compositions at the T_eff of star #8, with gas pressures indicated by the scaled solar and α-enhanced models. The change in electron density due to the composition difference was about one third of the change from scaled-solar to α-enhanced models, which suggests that the composition difference could account for ∼ 0.03 dex of the difference between Fe i and Fe ii abundances in the 47 Tuc stars. Thus, with the correction for composition difference between Arcturus and the 47 Tuc giants we only need to explain an ionization difference of 0.068 dex, which corresponds to a temperature decrease of ∼40 K.

If we adopt the Lee (1970) V − K for Arcturus, at 2.90 mag, rather than the average of the Lee (1970) and Johnson et al. (1966) results, the 47 Tuc V − K colors, differential to Arcturus, appear cooler, by 16 K. Next, if we employ a reddening for 47 Tuc of E(B − V) = 0.027 mag, instead of the previously adopted 0.040, then our 47 Tuc photometric temperatures are reduced by an additional 24 K. This is not an unreasonable assumption: if the notably high reddening value of Harris (1996) is omitted, the unweighted average of the Schlegel et al. (1998) value and the two values from Gratton et al. (2003) gives E(B − V) = 0.029 ±0.005. Unfortunately, we cannot find a satisfactory fit to the observed CMD with E(B − V) = 0.02 and the standard theoretical isochrones of the Teramo group: in order to fit the RGB an older age is required with the lower reddening, but this then creates a poor fit for the core helium burning, red clump stars. On the other hand a reddening of E(B − V) = 0.04 gave a good fit to the observed CMD (see Figure 1).

If the differential photometric V − K temperatures are in fact cooler by 50–60 K we need to understand why the excitation of Fe i lines indicates a higher temperature. Because our excitation analysis is differential to the Arcturus line abundances, the excitation temperatures are themselves differential to the adopted Arcturus temperature; thus, if we lower the Arcturus T_eff value the excitation temperatures will decline accordingly. One possibility is that there are systematic measurement differences between the Arcturus spectrum and the 47 Tuc spectra, since we did not obtain a spectrum of Arcturus with the same instrument as the 47 Tuc spectra; rather, we employed EWs measured from the high-S/N, high-resolving-power Hinkle et al. (2000) Arcturus atlas.

Another possibility is that the Kurucz models approximate the 47 Tuc stars differently from Arcturus, resulting from real physical differences between Arcturus and 47 Tuc stars. The difference between Fe ii and Fe i abundances could be understood if Arcturus is reddened by E(B − V) ∼ 0.03 mag, or if Arcturus is an AGB star, and thus less massive than our CMD fit indicated. However, there is no evidence for this amount of reddening, and the V magnitude of Arcturus is too faint, by 0.15 mag, for it to be an AGB star. These possibilities would affect the derived excitation temperatures, but not the differential photometric temperatures.

It is also not possible to correct the inconsistency between Fe i and Fe ii abundances in 47 Tuc by altering the helium mass fraction, Y, of the cluster, because it would be necessary to drastically reduce Y—a reduction from Y = 0.20 to an unrealistically low value of Y = 0.10 changes the gravity by less than 0.1 dex (Green et al. 1987). Not only would such a low-Y value be inconsistent with big bang nucleosynthesis theory, but it is still insufficient to resolve the observed abundance differences in our 47 Tuc giants. On the other hand, an appealing alternative is that the helium fraction of Arcturus is significantly higher than normal expectations. Helium-rich Teramo isochrones, with Y = 0.40, were kindly supplied to us by S. Cassisi (2008, private communication). These isochrones fit the Arcturus temperature, luminosity, and composition with an age of 14 Gyr and a mass of 0.67 M_☉. This old age offers a natural explanation for the enhanced [α/Fe] ratio in Arcturus, which would be difficult to understand if it is ∼3 Gyr younger than the globular clusters, as indicated from the isochrones with standard He composition (see Section 4.2), because supernovae (SNe) of Type Ia would be expected to have reduced the [α/Fe] ratio over that time. An increase in the He fraction of α Boo would, however, result in an opposite problem for the (differential) Fe i and Fe ii abundances for the bulge and disk giant stars in F06 and F07. Thus, it seems that the helium mass fraction cannot be altered to resolve the Fe ionization problem in our 47 Tuc red giants. Also, if Arcturus has log g near 1.44 dex, consistent with the Y = 0.40 tracks, then both its [Fe i/H] and [Fe ii/H] values decrease to −0.55 dex, while the mean of the [Fe/H] values for our 47 Tuc RGB stars remains unchanged, at −0.76 dex (see also Section 6).

It is possible that differential non-LTE effects, between Arcturus and the 47 Tuc giants, could result in over-estimated excitation temperatures of the 47 Tuc giants (see Section 4.1). Steenbock (1985) predicts that the non-LTE corrections for low excitation Fe i lines in Pollux are larger than for the high-excitation Fe i lines by about 0.03 dex. From our LTE calculations we estimate that the resulting excitation temperature difference would be of order 50 K. Thus, in order to obtain the over-estimated excitation temperatures in 47 Tuc giants, relative to Arcturus, it is necessary for the non-LTE abundance effect on Fe i in the 47 Tuc giants to be larger than Arcturus by about a factor of ∼2. Since 47 Tuc giants are more metal poor and slightly more luminous than Arcturus the 47 Tuc giants have more ionizing photons and fewer collisional de-excitations in the line-forming region than in Arcturus. Therefore, one might expect slightly greater non-LTE effects in the 47 Tuc giants, in the right sense to ultimately understand the LTE iron ionization equilibrium problem encountered here.

It is interesting to note that Ti ionization equilibrium does hold for our 47 Tuc stars, with a mean deviation Δ(Ti i–Ti ii) of 0.00 ± 0.02 dex. However, for the coolest 47 Tuc red giant in our sample, the Ti i abundance is higher than Ti ii by 0.08 dex (1.6 σ). If we lower the adopted T_eff of our 47 Tuc giants by ∼50 K then the Ti i–Ti ii abundance difference will decrease to −0.11 dex. Thus, we are unable to obtain ionization equilibrium for both Fe and Ti simultaneously, although a deficiency of Ti i relative to Ti ii might readily be understood as a consequence of non-LTE over-ionization of Ti. A more precise estimate of the effect of non-LTE on differential excitation temperatures in red giants, however, requires a detailed non-LTE study, which is beyond the scope of the current paper.

Finally, we note that the ionized species in the 47 Tuc TO star gives an abundance higher by 0.14 dex than the neutral one, while ionization equilibrium is well established in the reference dwarf star Hip 66815. Because of the similarity of Fe i and Fe ii, which deviate by a mere 0.02 dex, in the reference star, which has similar parameters to the 47 Tuc TO star, non-LTE can be eliminated as a possible explanation for the ionization imbalance in the 47 Tuc TO star. Thévenin & Idiart (1999) estimate that for subgiants and TO stars with T_eff and log g similar to our sample a non-LTE treatment of the iron lines yields a [Fe/H] higher by ∼0.1 dex, which is close to the order of magnitude of the discrepancy seen in our star. However, Thévenin & Idiart (1999) did not include line opacities in their non-LTE calculations, which magnified the predicted non-LTE effects. We suggest that either the measured Fe ii lines in the 47 Tuc TO star are affected by noise spikes that bring them into detection in the low-S/N spectrum, or that the electron density in this star is higher than in Hip 66815, perhaps due to an unusual α enhancement.

From our entire sample of nine stars we find a mean iron abundance of [Fe i/H] = −0.76 ± 0.01 ± 0.04, where the first value gives the internal error, i.e., the standard deviation of the mean and the second number incorporates the systematic errors. At 0.03 dex, the star-to-star scatter within this cluster is very small and fully consistent with our estimated measurement errors, as is also seen in the recent spectroscopic data of Carretta et al. (2004) and Alves-Brito et al. (2005) as well in the photometric estimates of Hesser et al. (1987). In particular, our stars cover a range in [Fe i/H] from −0.82 to −0.72, Moreover, it is reassuring that the TO star yields an iron abundance that is in excellent agreement with the red giant sample, indicating that the chemical iron abundance in this cluster is independent of the stars' evolutionary status.

Apart from the early work of Brown & Wallerstein (1992), who derived a lower iron abundance of −0.81 dex, all previous studies have placed 47 Tuc toward the more metal-rich regime. For instance, Alves-Brito et al. (2005) found a [Fe/H] of (−0.66 ± 0.12) dex, and Kraft & Ivans (2003) found [Fe ii/H] = −0.79, based on an empirical calibration of Ca-triplet metallicities, but from a re-analysis of both the Brown & Wallerstein (1992) and Carretta & Gratton (1997) EWs they obtained −0.70 dex, based on corrections for their preferred models and log gf values. Moreover, the recent AGB star study of Wylie et al. (2006) argues in favor of the metal-richer regime in terms of [Fe/H] = (−0.60 ± 0.20) dex. While these estimates can still be considered to coincide with our value to within the quoted errorbars, it is more difficult to reconcile the result of (−0.67 ± 0.04) dex by Carretta et al. (2004) from their accurate analysis of 12 subgiant and dwarf stars with our data. Recently, McWilliam & Bernstein (2008) have obtained [Fe i/H] = −0.75 ± 0.03 dex based on an integrated-light analysis of the core of 47 Tuc. While the agreement with the present result was encouraging, the analysis method was radically different, except that McWilliam & Bernstein also performed a differential analysis relative to α Boo.

The main reason for discrepancies between our results and other studies can be sought in the different analysis method employed. Virtually all the previous works performed their analyses relying on the accuracy of the oscillator strength. Despite the availability of accurate laboratory log gf values (e.g., Blackwell et al. 1995), the use of these values in abundance studies of red giants may be fraught with peril (e.g., Prochaska et al. 2000), in particular, when the derived abundances are referenced to the solar abundance scale. We sidestepped such difficulties by performing our line-by-line differential analysis relative to Arcturus so that unavoidable systematic uncertainties, which may affect the different approaches, can be expected to have canceled out to first order. Examples of effects on standard abundance analysis that may, to first order, cancel out in our differential technique include errors in gf values, non-LTE effects, spherical versus plane parallel atmosphere geometry, inhomogeneous photospheres (granulation), three-dimensional hydrodynamics, and the effect of chromospheres.

One might argue that all the studies under scrutiny have focused on stars in different evolutionary stages, reaching from the unevolved early subgiants and dwarfs in the Carretta et al (2004) sample to AGB stars in the case of Wylie et al. (2006) and evolved red giants in the data of Alves Brito et al. (2005). However, all these works agree in that they do not find any considerable abundance spread with evolutionary status, and also we cannot confirm a significant difference between our red giant sample and the TO star's abundance ratios. Moreover, also our likely AGB star candidate (#3) is entirely consistent with the remainder of our iron results. Hence we conclude that the difference between our results and the previous works is not due to any target-selection effects.

An overview of our resultant abundance ratios is provided in the Box-Whisker plot in Figure 4, which displays each element's mean, the 25- and 75% interquartile ranges as well as the full range covered. It turns out that each of Si, Ca, and Ti are similarly enhanced at ∼0.37 dex⁵. On the other hand, there is an indication that Mg shows even higher abundances for most of the stars, with an average of [Mg/Fe]∼0.45 dex. Oxygen is also enhanced more than Si, Ca, and Ti, in our 47 Tuc stars, with a mean [O/Fe] value, at +0.60 dex. These results are in excellent agreement with the abundances determined in the bulge giants of F07 with similar [Fe/H], as indicated by the filled circles in Figure 4. Overall, it is worth noticing that all of the [α/Fe] abundance ratios only show very little star-to-star variations, where the scatter does not exceed 0.06 dex for the elements considered here and can be purely explained by the random EW measurement errors of our analysis.

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The abundance ratios for the TO star are consistent with those in the red giant sample, with the exception of [Mg/Fe], where the TO star yields an abundance lower by 0.12 dex, and for the case of [Si/Fe], with an abundance higher by 0.07 dex in the dwarf. We note that Si and Mg in dwarf stars are both sensitive to damping and the adopted stellar gravity; an overestimate of gravity would result in overabundances of these two elements. The question of why these two species show opposite deviations remains open, but it may indicate over-estimated EWs for Si, due either to blends or noise effects (see also Cohen et al. 2004).

The production of the α-elements is generally believed to occur in SNe ii, which are associated with the death of massive, short-lived stars. However, while Mg and O are believed to be formed during the hydrostatic nuclear burning phase in the SNe ii progenitors, Si, Ca, and Ti are generally assigned to the explosive nucleosynthetic phase of the SNe ii (e.g., Woosley & Weaver 1995). It is thus natural to expect different trends of for instance [Mg/Fe] as compared to [Si, Ca, Ti/Fe] as a function of [Fe/H]. Following F07, we investigate to what extent these groups of α-elements track each others trends: we plot in Figure 5 the difference of Ca and Si, Ca, and Ti i, respectively, with metallicity. It is reassuring that all of the explosive α-elements follow the identical trends with [Fe/H], which is reflected in that the aforementioned abundance ratios exhibit flat slopes with metallicity near solar values. At 0.04 ([Ca/Si]) and 0.05 dex ([Ca/Ti i]), the scatter around zero is small.

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Again following F07 we consider the straight average [〈SiCaTi i〉/Fe] as a measure of explosive α-element abundance to reduce the overall scatter in these elements. Figure 6 shows this average abundance ratio in comparison with the bulge data of F07. Furthermore, this diagram incorporates a number of abundance ratios from the Galactic thin disk (Reddy et al. 2003; Bensby et al. 2005; Brewer & Carney 2006) and the thick disk (Prochaska et al. 2000; Fulbright 2000; Bensby et al. 2005; Brewer & Carney 2006).

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As was shown by F07 the Galactic bulge is clearly separated from the thin disk in the α-elements by ∼+0.2 dex, and the bulge [α/Fe] ratio shows a distinct decline with increasing metallicity. This picture is generally interpreted in terms of a higher SNe ii/SNe Ia ratio in the bulge, indicating an increased importance of massive stars for the evolution of the bulge, and addition of iron from long-lived SNe Ia at higher [Fe/H] than for the thin disk. The Galactic thick-disk α-abundances, on the other hand, are significantly lower than the bulge values at [Fe/H] ∼−0.5, while these two components converge toward the enhanced [α/Fe] ratio at metallicities around −1. How does 47 Tuc now fit into this picture? As Figure 6 implies, this cluster is clearly strongly enhanced in its α-elements and inconsistent with an association with the thin disk. At a metallicity of [Fe/H] = −0.76, the cluster stars occupy a region in [α/Fe] that is higher than most thick-disk stars, and consistent with the bulge composition. And yet, at this [Fe/H], the bulge [<SiCaTi i >/Fe] value is higher than the thick-disk population by only ∼0.1 dex. Thus, while the mean 47 Tuc [〈SiCaTi i〉/Fe] ratio is similar to the bulge, there is a small overlap with the composition of thick-disk stars.

The fact that [Mg/Fe] in the bulge is higher on average than the explosive α-elements' abundance ratios was first noted by McWilliam & Rich (1994) and later confirmed by F07. This enhancement as well as only a negligible decline of [Mg/Fe] with [Fe/H] was interpreted by a rapid formation of the bulge (Matteucci et al. 1999). Also [Mg/Fe] in the 47 Tuc stars shows an excess of ∼+0.1 dex relative to the [Si, Ca, Ti/Fe] group (Figure 4 and the bottom panel of Figure 7), while [O/Fe] has an excess of ∼0.2 dex. This is in accord with the conclusion of F07 that explosive and hydrostatic α-elements show different trends in the bulge, as is also seen in the dwarf galaxy abundances (see the review by Venn et al. 2004). As mentioned in F07 part of the reason for the lower enhancement of the [Si,Ca,Ti/Fe] relative to the hydrostatic alphas is that SNe Ia are thought to produce small amounts of Si, Ca, and Ti so that ratios taken relative to the solar composition are lower because of the SNe Ia contribution of these elements in the Sun.

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The first obvious thing to note is that both Na and Al are enhanced (by +0.2 and +0.45 dex, respectively) in 47 Tuc. While the [Na/Fe] enhancement is in good agreement with that found in previous studies (Brown & Wallerstein 1992; Norris & Da Costa 1995; Carretta et al. 2004; James et al. 2004; Alves-Brito et al. 2005), these works do not support evidence for an average [Al/Fe] in excess of 0.38 dex, with the exception of Brown & Wallerstein, who yield an estimate of +0.67. Generally, a wide range of [Al/Fe] ratios for various stellar systems is not uncommon and globular cluster giants have been reported to reach maximum enhancements in excess of +1 dex (McWilliam 1997; Ivans et al. 1999).

The top panel of Figure 7 shows our derived [Al/Fe] abundances; note that the raw [Al/Fe] bulge abundances of F07 are used the comparison. In a similar plot F07 shifted their [Al/Fe] ratios lower to account for zero-point differences between studies of disk dwarfs and giants. However, as indicated in F07, non-LTE effects on the [Al/Fe] ratios in the dwarf studies are probably to blame for the shift, so the dwarf results should have been corrected upward, although the amount depends on the stellar temperatures. The F07 bulge giant [Al/Fe] ratios should have remained unaltered. Thus, in the top panel of Figure 7 the thin- and thick-disk results, which were based on dwarf stars, should be increased by an average of 0.08 dex. Figure 7 shows that our mean [Na/Fe] and [Al/Fe] ratios for 47 Tuc are at the upper end of the distributions found in the bulge, but also compatible with the, few, thick-disk stars in this metallicity regime.

Although both the light elements Na and Al are also produced by SNe ii, the trends with metallicity are clearly distinguished from those found for the other α-elements discussed in the previous section (see F07 for a review). While the Galactic thin- and thick-disk abundance ratios exhibit a smooth but slow decline with increasing [Fe/H], which is due to the continuous pollution by SNe ii and a late addition of SNe Ia processed material into the ISM, [Al/Fe] in the bulge shows the opposite trend. This can be understood in terms of the production of significantly less iron in the Galactic bulge environment.

Given the same line of reasoning as for the traditional enhancement of Na and Al in the Galactic bulge, we can argue that the material, out of which 47 Tuc formed, had lesser iron contributions from SNe Ia, but more important, the Al and Na yields are slightly more increased at the metallicity of 47 Tuc. This could have occurred as a result of an overly high neutron excess (Arnett 1971) or an increased fraction of high-mass stars in the population that produced the 47 Tuc composition. In this context Vuissoz et al. (2004) suggest that rotating Wolf–Rayet stars can provide increased Al yields. However, the presence of material from more massive SNe ii events should result in higher [O&Mg] ratios in 47 Tuc than the bulge, which we do not observe.

Again, the lowest [Al/Fe] is found for the TO star and the AGB-star candidate #3. Non-LTE calculations for Al in dwarf stars by Baumueller & Gehren (1997) indicate a correction of +0.09 dex for the Al I lines we used in the TO star. If this correction is applied to the TO star, the [Al/Fe] ratio increases to +0.42 dex, similar to the mean value of +0.47 for the 47 Tuc giants. Similar calculations for Na (Baumueller et al. 1998; Takeda et al. 2003) indicate downward corrections to the TO star Na abundance of approximately 0.06 dex. While these non-LTE corrections bring the TO star and giants into better agreement it must be remembered that, in order to obtain absolute abundance ratios, non-LTE treatment needs to be considered for all element species, including Fe. This holds for the TO star, the RGB stars, and the Sun, but such a treatment is beyond the scope of the current paper.

We note in passing that there is no clear evidence of the Mg–Al anti-correlation (Langer & Hoffmann 1995) present in our data, which would be indicative of the occurrence of deep mixing processes in globular cluster stars. This finding is also consistent with the result of Carretta et al. (2004).

On the other hand, we cannot exclude the possibility that Na and O anti-correlate in 47 Tuc (Figure 8). Such a trend was suggested to occur also in this metal-rich cluster (e.g., Carretta et al. 2004), and to be present across all stellar evolutionary stages. The canonical picture to explain this abundance anomaly is the occurrence of internal deep mixing during the first dredge-up. Our data cover only a small range in the [O/Fe] abundances, but it is clear that the star with the highest depletion in oxygen is accordingly enhanced in Na by about 0.15 dex above average. All in all, there is a large scatter present in the [Na/O] abundance ratio (at an rms of 0.11 dex) and the object with the highest enhancement in [Na/Fe] appears to fall into the thin-disk regime. Moreover, in the phase space of sodium versus oxygen (Figure 8, bottom) the over-abundance of sodium coincides with the upper end of the bulge and thick-disk abundances, which is, however, hampered by the sparse sampling of thick-disk stars in this regime. The general enhancement of Na in 47 Tuc can then also be understood, if, as for the case of the Galactic bulge, there was a primordial source for the Na production available (F07).

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