CLUES TO THE METALLICITY DISTRIBUTION IN THE GALACTIC BULGE: ABUNDANCES IN MOA–2008–BLG–310S AND MOA–2008–BLG–311S^*

High-magnification microlensing events present a rare opportunity to obtain high-resolution spectra of otherwise extremely faint dwarfs in the Galactic bulge, which would require of order 100 hr of observations on 8 m class telescopes under ordinary circumstances. Microlensing is itself very rare, with only a fraction τ ∼ 10⁻⁶ of stars being microlensed at any given time, even toward the Galactic bulge where the density of lenses is exceptionally high. Events that are magnified by a factor A are rarer still by a factor A⁻¹. And finally, the high magnification lasts only A⁻¹t_E, where t_E ∼ 30 days is the Einstein timescale of the event. So there are formidable problems predicting high-magnification episodes sufficiently far in advance to arrange spectroscopic observations from 8 m class telescopes.

Nevertheless, two groups, Microlensing Observations in Astrophysics (MOA) and the Optical Gravitational Lens Experiment (OGLE) find a total of about 800 microlensing events per year, of which the Microlensing Follow-Up Network⁹ (μFUN) is able to identify about 10 as high-magnification events. During the 2008 season, the additional challenges posed by getting spectra on short notice were overcome for three of these events, bringing the total number of bulge dwarfs with high-magnification spectra to seven. There are four published analyses: OGLE–2006–BLG–265S (Johnson et al. 2007), OGLE–2007–BLG–349S (Cohen et al. 2008), MOA–2006–BLG–099S (Johnson et al. 2008), and OGLE–2008-BLG–209S (Bensby et al. 2009). In addition, there is a spectrum of OGLE-2007-BLG-514S taken by M. Rauch and G. Becker with an as yet unpublished analysis by C. Epstein et al.

Here, we analyze the two remaining high-mag bulge-dwarf spectra from the 2008 season, MOA–2008–BLG–310S and MOA–2008–BLG–311S, which, remarkably, peaked on successive nights over Africa and were both observed as they were falling from their peak at the beginning of the Chilean night using the Magellan Clay Telescope. With the addition of these two stars, the sample microlensed bulge main-sequence turnoff region stars with high-resolution, high-quality spectra and published detailed abundance analysis becomes six stars; we refer to them collectively as the six microlensed dwarfs.

The ability to obtain high-resolution, high-quality spectra of Galactic bulge stars and to carry out a detailed abundance analysis offers an unbiased way to determine the metallicity distribution of stars in the Galactic bulge, as well as their detailed chemical inventory. The goal of the present paper is to carry out detailed abundance analyses for the two additional microlensed bulge dwarfs (Section 4). Then in Section 5, we use the six microlensed dwarf sample to study the bulge metallicity distribution function as well as their abundance ratios, and to compare them to the results obtained by a number of surveys of giants in the Galactic bulge.

MOA–2008–BLG–310S and MOA–2008–BLG–311S were observed on two consecutive nights in 2008 July using the Magellan Inamori Kyocera Echelle (MIKE) spectrograph (Bernstein et al. 2003) on the 6.5 m Magellan Clay Telescope at the Las Campanas Observatory by I. Thompson and G. Burley. Details of the exposures are given in Table 1. Spectroscopic exposures for MOA–2008–BLG–311S began at UT 22:58 just after sunset at air mass 1.93 (4.1 hr east of the meridian, so the initially large air mass decreased quickly) when it was magnified by a factor of 190; the star was just past its maximum brightness of I ∼ 13.5 mag and fading at that time. The photometry of this microlensing event is consistent with a point source being magnified by a perfect point lens.

Spectroscopic exposures of MOA–2008–BLG–310S began with MIKE the following night at UT 22:51 at air mass 1.87 at the same hour angle as for MOA–2008–BLG–311S. MOA–2008–BLG–310S was brighter than MOA–2008–BLG–311S at the time of observation by ∼0.8 mag. A narrower slit 0.5 arcsec wide was used to isolate MOA–2008–BLG–310S from a close companion roughly 2 mag fainter. Fortunately, the seeing that night was very good (0.6 arcsec) after the first half hour (i.e., once the air mass became reasonable), and the companion rotated further away from the slit with time. Thus, even with the narrower slit and consequently higher spectral resolution, a high signal-to-noise ratio per spectral resolution element was achieved for the spectrum of this star.

The light curve of MOA–2008–BLG–310S shows pronounced finite-source effects, with the lens exiting the limb of the source about 20 minutes before the start of spectroscopic observations. In addition, the light curve shows much smaller deviations from standard point-lens microlensing due to a companion to the lens (J. Janczak et al. 2009, in preparation). J. A. Johnson et al. (2009, in preparation) has explored the impact of differential amplification across the surface of a dwarf near the main-sequence turnoff as it affects an abundance analysis; she finds it to be negligible compared with the uncertainties in the abundances.

The microlensed bulge dwarfs suffer from substantial reddening whose exact value is unknown. We therefore rely purely on their spectra to determine their stellar parameters. The classical technique of excitation equilibrium for the set of the many Fe i lines measured is used to find T_eff. Then the microturbulent velocity v_t is set by requiring the deduced Fe abundance to be independent of the equivalent width W_λ for the same set of lines. The surface gravity is set by requiring ionization equilibrium between neutral and singly ionized Fe; the ionization equilibrium for Ti in both of the stars is then extremely good. If the deduced [Fe/H] is substantially different from that assumed to construct the model atmosphere, the process is repeated with the [Fe/H] determined from the initial pass used for the model atmospheres. Throughout this process, we choose to ignore lines with W_λ exceeding 130 mÅ due to the difficulty of properly including their damping wings in the W_λ measurements. Features bluer than 5200 Å were ignored unless the species had very few other detected lines as the signal-to-noise ratio decreases rapidly at bluer wavelengths due to the high reddening along the line of sight to the Galactic bulge.

Because the spectra are not perfect, and being concerned about the convergence of this scheme onto the correct set of stellar parameters, we decided to develop a technique for determining [Fe/H], at least approximately, that might bypass some of these issues and indicate the magnitude of some of the uncertainties in a more direct fashion. Following in the spirit of the line ratio method developed by Gray & Johanson (1991) and used by Biazzo et al. (2007), we looked for something easy to measure based purely on aspects of the spectrum that have a strong dependence on metallicity, but little dependence on any other stellar parameter. As a guide we constructed plots based on detailed abundance analyses of the behavior of weak lines of species with many detected absorption lines as a function of the set of adopted stellar parameters T_eff, log(g), [Fe/H] of the model atmosphere, and v_t that would enable us to isolate metallicity from them. Figure 1 illustrates the best case we found for stars in the region of the main-sequence turnoff, namely, [Fe/H] derived from Fe i absorption lines with high excitation (χ>4 eV), which show low sensitivity to changes in T_eff of ±250 K or of log(g) of ±0.5 dex within the regime of interest. Although not shown in the figure, we note that increasing [Fe/H] of the model atmosphere by 0.5 dex increases the deduced [Fe/H] by only 0.05 dex. Using high excitation Fe i lines, the final derived [Fe/H] from a detailed abundance analysis is bound to be close to the true value even if the adopted stellar parameters are slightly off. The weak dependence of the behavior of such lines on T_eff is a result of the competition between ionizing Fe i when T_eff is increased versus increasing the population in the high excitation state from which the absorption features arise. Fe ii lines with χ ∼ 0 eV show a similar behavior with T_eff, but have much more sensitivity to changes in log(g) than do Fe i lines.

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The resulting stellar parameters for MOA–2008–BLG–310S and MOA–2008–BLG–311S are listed in Table 2, which also gives the slopes between deduced [Fe/H] abundances and the excitation potential, W_λ, and λ of the set of Fe i lines with W_λ <130 mÅ. We see that extremely good results (i.e., almost flat relations with slopes very close to 0) were obtained for the first two (primarily sensitive to T_eff and to v_t, respectively). The slope with wavelength for MOA–2008–BLG–310S is somewhat larger than ideal but the correlation coefficient is low (<0.15), and the total change over the span of 2600 Å covered is only 0.07 dex. The uncertainty in T_eff is related to the first slope, which decreases by ∼0.05 dev eV⁻¹ when T_eff is increased by 250 K in this regime. Assuming a reasonable sample of low excitation Fe i lines, so that the range of the measured lines covers ∼4 eV, we set the uncertainty in T_eff to 100 K. The uncertainty in log(g) then follows by considering the error resulting in ionization equilibrium of Fe i should T_eff be off by 100 K, which has to be compensated for by changing log(g). There is an additional smaller uncertainty in log(g) arising from the uncertainty in the value of [Fe/H](Fe i) – [Fe/H](Fe ii) itself. We find an uncertainty in log(g) of 0.2 dex in log(g) is appropriate.

We note that a fit to the Hα profile in MOA–2008–BLG–310S, the star with the higher SNR spectrum, indicates T_eff ∼5500 K, 120 K less than that derived from the Fe i line analysis. We also compare our derived values of T_eff with those that would be inferred from the photometry of the two microlensed bulge dwarfs. Light curves were obtained in two colors, V and I, by the μFUN Collaboration for MOA–2008–BLG–310S and for MOA–2008–BLG–311S during the microlensing event as part of an effort to detect planets. The color of red clump stars¹⁰ in the field around each of the microlensed stars is easily determined. The comparison of instrumental (V − I) and I of the red clump and the microlensed star then yield (V − I)₀ and I₀ of the star, under the assumption that it suffers the same extinction as the clump. If the microlensed star is further assumed to lie at the same distance as the clump, then the star's absolute magnitude M_I can be calculated. This yields (V − I)₀ = 0.70 mag for MOA–2008–BLG–310S and (V − I)₀ = 0.66 mag for MOA–2008–BLG–311S, with I₀ = 17.94 mag for MOA–2008–BLG–310S and 18.37 mag for MOA–2006–BLG–099S311; I is in the Cousins system. The Sun has V − I = 0.688 ± 0.014 mag (Holmberg et al. 2006), which would suggest that T_eff for these two microlensed stars is quite close to that of the Sun. Given the uncertainties in the photometry and the probability of small spatial variations in the reddening across the field, this is in good agreement with the T_eff derived directly from the spectra of MOA–2008–BLG–310S and of MOA–2008–BLG–311S of Table 2. These independent determinations of T_eff, together with their uncertainties, are summarized in Table 3.

We consider whether the derived parameters are consistent with the star being in the Galactic bulge by comparing log(g) derived from the spectra with that derived from the photometry. I₀ is converted into a total luminosity assuming a distance to the Galactic center of 8 kpc. Then using the derived T_eff, and assuming a mass of 1 M_☉, we predict log(g)(phot). The agreement between log(g)(phot) and log(g)(spec) is reasonable, with differences of 0.1 dex for MOA–2008–BLG–310S, and 0.3 dex for MOA–2008–BLG–311S.

The ages of the microlensed bulge dwarfs are determined by comparing M_I as a function of T_eff from the relevant [Fe/H] and [α/Fe] isochrones of the grid of the Dartmouth Stellar Evolution Database (Dotter et al. 2008), as shown in Figure 2. The results for MOA–2008–BLG–310S and MOA–2008–BLG–311S are given in the last column of Table 1; they are consistent to within the errors with that of the Galactic bulge population inferred from Hubble Space Telescope (HST) imaging, ∼10 Gyr, by Feltzing & Gilmore (2000), see also Zoccali et al. (2003).

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Once the stellar parameters were determined, the abundance analysis was carried out in a manner identical to that for OGLE–2007–BLG–349S as described in Cohen et al. (2008); in particular it was a differential analysis with respect to the Sun. In preparing the line list only features redder than 5200 Å were used, unless there were none that red for a particular species, due to increased crowding toward the blue and to the high reddening. Lines with W_λ >130 mÅ were rejected unless the species did not have at least a few suitably weak lines. The exceptions are the 5680 Å Na doublet¹¹ and the K i resonance line at 7700 Å in both stars. Also one Mg i, one Si i line, and the only two Cu i lines detected in MOA–2008–BLG–310S, each of which had W_λ <140 mÅ, were retained. The equivalent widths are given in Table 4; their major uncertainty in the W_λ results from the definition of the continuum level.

We used a current version of the local thermodynamic equilibrium (LTE) spectral synthesis program MOOG (Sneden 1973). We employ the grid of stellar atmospheres from Kurucz (1993) with [Fe/H] = 0.0 and +0.5 dex having solar abundance ratios without convective overshoot (Castelli & Kurucz 2003) and with the most recent opacity distribution functions. Non-LTE corrections were not included, as this is a differential analysis with respect to the Sun, and the stellar parameters of both of these stars are fairly close to those of the Sun. Hyperfine structure (hfs) corrections were used as appropriate; see Cohen et al. (2008) for details.

The deduced abundances for MOA–2008–BLG–310S and for MOA–2008–BLG–311S are given in Tables 5 and 6, respectively, with derived absolute abundances (second column), the abundances relative to the Sun (fifth column), and the abundance ratios [X/Fe] (seventh column). The abundance ratios use either Fe i or Fe ii as the reference depending on the ionization state and mean excitation potential of the measured lines of species under consideration. The 1σ dispersion around the mean for each species is given as σ_obs. This is calculated from the set of differences between the deduced solar abundance for the species in question and that found for a microlensed bulge dwarf for each observed line of the species. Thus, neither random nor systematic errors in the gf values contribute to σ_obs.

Table 5. Abundances in MOA–2008–BLG–310S

Species	log[(X)]a (dex)	σobsb (dex)	Number of Lines	log[(X)/(X)☉] (dex)	[X/Fe]c Colhead (dex)	σpred for [X/Fe] (dex)	Notes
C(CH)	8.89	0.15	Band	+0.30	−0.10	0.17	Syn
O i	9.09	0.16	4	+0.20	−0.22	0.19	High χ
Na i	6.63	0.16	4	+0.54	+0.12	0.09
Mg i	8.06	0.17	3	+0.59	+0.17	0.07
Al i	6.72	0.15	2	+0.54	+0.12	0.08
Si i	8.05	0.17	15	+0.52	+0.10	0.17	High χ
K i	5.45	...	1	+0.22	−0.20	0.12
Ca i	6.45	0.12	8	+0.34	−0.08	0.07
Sc ii	3.73	0.15	6	+0.50	+0.08	0.10	d
Ti i	5.31	0.13	31	+0.45	+0.03	0.11
Ti ii	5.32	0.04	2	+0.45	+0.03	0.10
V i	4.40	0.10	9	+0.61	+0.19	0.14	d
Cr i	6.17	0.15	5	+0.51	+0.09	0.07
Mn i	5.79	0.09	2	+0.42	+0.00	0.11	e
Fe i	7.90	0.14	100	+0.42	0.00	0.09g
Fe ii	7.87	0.14	13	+0.39	−0.03	0.17h
Co i	5.40	0.11	5	+0.63	+0.19	0.08	d
Ni i	6.74	0.15	37	+0.56	+0.14	0.05
Cu i	4.78	0.20	2	+0.81	+0.39	0.15	f
Zn i	4.92	...	1	+0.37	−0.05	0.13
Y ii	2.59	0.15	3	+0.53	0.11	0.12
Ba ii	2.60	0.04	3	+0.31	−0.11	0.17	d
Nd ii	1.77	...	1	+0.31	−0.11	0.12

Notes. ^aThis is log[(n(X)/n(H)] + 12.0 dex. ^brms dispersion about the mean abundance, using differential line-by-line abundances with respect to the Sun. ^cThe reference species (Fe i or Fe ii) is based on the level of excitation and ionization. See Table 4 in Cohen et al. (2008). ^dThe hfs corrections are small and not an issue. ^eThe hfs corrections are large and are a concern. ^fThe hfs corrections are very large and are a major concern. ^gThe uncertainty in [Fe/H] inferred from the 100 Fe i lines. ^hThe uncertainty in [Fe/H] inferred from the 13 Fe ii lines.

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Table 6. Abundances in MOA–2008–BLG–311S

Species	log[(X)]a (dex)	σobsb (dex)	Number of Lines	log[(X)/(X)☉] (dex)	[X/Fe]c Colhead (dex)	σpred for [X/Fe] (dex)	Notes
C(CH)	8.89	0.15	Band	+0.30	+0.05	0.17	Syn
O i	9.31	0.12	4	+0.42	+0.14	0.19	High χ
Na i	6.54	0.09	4	+0.45	+0.20	0.09
Mg i	7.91	0.14	4	+0.33	+0.08	0.07
Al i	6.72	0.09	2	+0.54	+0.29	0.08
Si i	7.94	0.12	15	+0.41	+0.16	0.17	High χ
K i	5.45	...	1	+0.22	−0.03	0.12
Ca i	6.49	0.18	9	+0.36	+0.11	0.07
Sc ii	3.47	0.11	6	+0.24	−0.04	0.10	d
Ti i	5.25	0.18	15	+0.42	+0.17	0.11
Ti ii	5.30	0.12	2	+0.43	+0.15	0.10
V i	4.10	0.10	8	+0.31	+0.06	0.14	d
Cr i	5.98	0.11	6	+0.32	+0.07	0.07
Mn i	5.66	0.12	2	+0.29	+0.04	0.11	e
Fe i	7.73	0.16	92	+0.25	0.00	0.09g
Fe ii	7.75	0.16	11	+0.28	+0.03	0.17h
Co i	5.14	0.08	4	+0.36	+0.11	0.08	d
Ni i	6.60	0.15	41	+0.42	+0.17	0.05
Cu i	4.35	0.09	2	+0.38	+0.13	0.15	f
Zn i	4.84	...	1	+0.29	+0.04	0.13
Y ii	2.34	...	1	+0.45	0.17	0.12
Ba ii	2.24	0.11	3	+0.12	−0.13	0.17	d

Notes. ^aThis is log[(n(X)/n(H)] + 12.0 dex. ^brms dispersion about the mean abundance, using differential line-by-line abundances with respect to the Sun. ^cThe reference species (Fe i or Fe ii) is based on the level of excitation and ionization. See Table 4 in Cohen et al. (2008). ^dThe hfs corrections are small and not an issue. ^eThe hfs corrections are large and are a concern. ^fThe hfs corrections are very large and are a major concern. ^gThe uncertainty in [Fe/H] inferred from the 92 Fe i lines. ^hThe uncertainty in [Fe/H] inferred from the 11 Fe ii lines.

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While the absolute abundance for a given species listed in Tables 5 and 6 will be affected by any systematic error in the gf values of the lines we use here, relative abundances [X/Fe] will not since we have carried out a differential analysis with respect to the Sun. An uncertainty for [X/Fe] for each species, σ_pred, is calculated summing five terms combined in quadrature representing a change in T_eff of 100 K, the corresponding uncertainty in log(g) of 0.2 dex, a change in v_t of 0.2 km s⁻¹, and a potential 0.25 dex mismatch between [Fe/H] of OGLE–2007–BLG–349S versus the value +0.5 dex of the model atmospheres we are using. (Tables 3 and 4 of Cohen et al. 2008 give the values of these four individual terms for each species.) The fifth term, the contribution for errors in W_λ, is set to 0.05 dex if only one or two lines were measured; for a larger number of detected lines we adopt $\sigma _{\rm obs}/\sqrt{N({\rm lines})}$ for this term. This is added in quadrature to the other four terms to determine our final uncertainty estimate given in the final column of Tables 5 and 6. We note that the total uncertainty in [Fe/H] so derived is 0.09 dex when the large set of Fe i lines is used.

The key result of the abundance analysis is the high Fe metallicity found for the two microlensed Galactic bulge stars in the region of the main-sequence turnoff, [Fe/H] =+0.41 dex for MOA–2008–BLG–310S and +0.26 dex for MOA–2008–BLG–311S. The abundance ratios are also of great interest. Figures 3–5 show selected abundance ratios as a function of [Fe/H] for the six microlensed bulge dwarfs. These are compared with abundance ratios from surveys of Galactic bulge giants by Fulbright et al. (2007), Rich & Origlia (2005), Rich et al. (2007), and Lecureur et al. (2007). The figures demonstrate that to within the uncertainties microlensed bulge dwarfs have abundance ratios [X/Fe] consistent with those of Galactic bulge giants at the same Fe metallicities. Comparisons between bulge giants and thick and thin disk stars are given by Fulbright et al. (2007) and Lecureur et al. (2007), while detailed studies separating thick and thin disk stars, as well as halo stars, via their abundance ratios and trends with [Fe/H] include Reddy et al. (2003), Mashonkina et al. (2004), and Bensby et al. (2005).

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We have presented detailed abundance analyses for two additional microlensed bulge main-sequence turnoff region stars, so there are now six that have been observed at high spectral resolution within the past three years and for which detailed abundance analyses have been completed; the references for the additional four are given in Section 1. Only one of the six falls below solar metallicity, at [Fe/H] = −0.32 dex; all the others are well above solar, with the mean of the six being 〈[Fe/H]〉 = +0.29 dex.

The positions on the sky of the six microlensed bulge dwarfs are shown in Figure 6. (The magnitude of their radial velocities are also indicated in this figure.) The location of Baade's window is marked. This is the field closest to the center of the Milky Way with reddening low enough that its bulge giants can be studied in detail in the optical with the current generation of large telescopes, and has thus been the subject of many recent surveys at the Very Large Telescope (VLT; see, e.g., Zoccali et al. 2008) and at Keck (Fulbright et al. 2006, among others). The circle marks the region with projected Galactocentric distance equal to that of Baade's window. It is important to note that five of the six microlensed bulge dwarfs are slightly outside that circle; only one is slightly within it. This means that the population we are sampling via microlensing should be essentially identical to the population sampled by studies of the giants in Baade's window. Zoccali et al. (2008) detected a small radial gradient in the mean metallicity with Galactocentric distance of 0.6 dex kpc⁻¹ (0.08 dex deg⁻¹ on the sky at the distance of the Galactic center). The gradient was established between Baade's window and bulge fields with larger projected R_GC. This would suggest that the mean Fe metallicity of the sample of microlensed bulge dwarfs should be ∼0.05 dex lower than that of Baade's window.

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Zoccali et al. (2008) recently redetermined the Fe-metallicity distribution function in Baade's window using a sample of 204 luminous K giants with 14.2 < I < 14.7 mag spanning a wide range in V − I color (1.53 < (V − I) < 2.62 mag) so as to cover the full metallicity range within the stellar population of the Galactic bulge. There is also a sample of ∼200 red clump giants in the Baade's window discussed in Lecureur et al. (2007). Red clump stars are biased against low metallicities, where RR Lyrae and blue horizontal branch stars would be expected instead, but should not be biased at the [Fe/H] values relevant here, [Fe/H] > − 1 dex. Zoccali et al. (2008) combine the two data sets for a total sample of ∼400 giants in this field.

Figure 7 compares the Fe-metallicity distribution function recently determined by Zoccali et al. (2008) in Baade's window with that of the six microlensed bulge dwarfs. The distributions are clearly different. The microlensed bulge dwarfs reveal a significantly higher mean Fe metallicity than do the giants studied by Zoccali et al. (2008), who find a mean [Fe/H] of −0.04 dex for the 204 K giants and +0.03 dex for the red clump stars from Lecureur et al. (2007). This is considerably lower than that of the six microlensed bulge dwarfs. Furthermore, K and M giants closer to the Galactic center than Baade's window at (l,  b) = (0°, − 1°) have been probed through high-resolution infrared spectroscopy by Rich et al. (2007), who also find a low mean Fe metallicity, −0.22 dex, and no sign of a radial gradient in metallicity for R_GC inward from Baade's window (see also Cunha & Smith 2006).

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To evaluate the statistical significance of this difference in Fe metallicity, we drew six stars at random from the sample of Zoccali et al. (2008), eliminating stars in the globular cluster NGC 6822, which is in Baade's window, and also those with highly uncertain [Fe/H] as indicated by the quality codes in their table. We took the average [Fe/H], which we call the six star mean. Note that the microlensed bulge star with by far the lowest [Fe/H] is actually a subgiant; it is the only subgiant among the six and is quite discrepant in [Fe/H] from the other five microlensed bulge dwarfs. The results for 40,000 such trials are given in Table 7 as the percentage of trials where the mean [Fe/H] for six stars drawn from the bulge giant sample equaled or exceeded that of the set of six microlensed bulge dwarfs.

If the [Fe/H] values of the large sample of bulge giants from Zoccali et al. (2008) are correct, and those of the six microlensed dwarfs are correct as well, then the probability that the two metallicity distribution functions are identical is very small, ∼4 × 10⁻³, ignoring any radial gradient, which would further reduce the tabulated probabilities for metallicity increasing as Galactocentric radius decreases. A Kolmogorov–Smirnov (K–S) test also indicates a very low probability that the two metallicity distributions are the same, 1.9%. However, if there are systematic errors in the metallicity scale of either (or of both), and they act in the right direction, the probability of this happening by chance increases. Therefore, Table 7 also contains the probability in the case of systematic offsets of the correct sign ranging from 0.05 to 0.20 dex in size. A systematic difference in Fe-metallicity scale between the two samples of 0.20 dex such that either the bulge giant metallicities are underestimated or those of the microlensed dwarfs are overestimated is required before the probability reaches 20%.

Zoccali et al. (2008) quotes a "conservative" uncertainty in [Fe/H] of an individual giant as ±0.2 dex, including possible systematic errors. A substantial systematic error in [Fe/H] is required to produce consistency between the microlensed bulge stars and the K (and M) giant samples. If only T_eff is changed and one looks at the Fe metallicity derived from Fe i lines (which is only logical, since there are far fewer Fe ii lines detectable), a 0.2 dex change corresponds to a 400 K systematic error for the microlensed stars near the main-sequence turnoff, as was shown in Figure 1, and to at least a 500 K systematic error if the problem lies in the cool giants, as at such low temperatures, iron is almost entirely neutral.

This level of systematic error is larger than the uncertainty in the absolute Fe metallicity of the microlensed dwarfs, as their spectra can be directly compared with the solar spectrum. Bensby et al. (2009) includes a comparison of [Fe/H] for the previously published four microlensed bulge dwarfs derived independently, with different codes, different grids of model atmospheres, and different schemes for determining the stellar parameters, by T. Bensby, J. Cohen, and J. A. Johnson; the agreement among the analyses by the three independent groups is quite good, ±0.06 dex. On the other hand, the analysis of the cool giants and the determination of their stellar parameters is much more difficult. However, the required error in T_eff for the bulge giants is even larger, and seems very unlikely. Furthermore, many independent groups have surveyed giants in the Galactic bulge, with similar results as to the mean Fe metallicity, so there is no reason to assign the required systematic error to them.

There are a number of consistency checks that have been or could be carried out to test the validity of the absolute Fe abundances between the bulge giants and the microlensed dwarfs. The scale of the Fe transition probabilities is not relevant for the dwarfs, as a differential solar analysis was used. But it is for the giants; Fulbright et al. (2006) used a differential analysis with respect to the well studied giant Arcturus, while Lecureur et al. (2007) use the spectrum of the metal-rich giant μ Leo to derive pseudo-gf values appropriate for their method of measuring W_λ and their grid of model atmospheres, while their absolute scale for [Fe/H] is set by taking [Fe/H] for this star as +0.30 dex. Checks of the determination of the continuum level in the giant spectra, where this is quite difficult, could be carried out with very high quality spectra of a few bulge giants. Differences between the model atmosphere grids are probably not the cause as several independent groups have participated both for the dwarfs and for the giants. However, systematic problems affecting all the chosen model atmosphere grids as T_eff decreases such as overionization of Fe could be contributing. Arguments that studies of members of a single open or globular cluster at a wide range of luminosities show no such effect (see, e.g., Santos et al. 2009 versus Boesgaard et al. 2009) are often not relevant to the present case when examined in detail. For example, Pasquini et al. (2004) studied giants and dwarfs in the open cluster IC 1651 with [Fe/H] +0.10 dex. However, their coolest and most luminous giant is several hundred K hotter in T_eff and 0.4 dex higher in log(g) than the hottest and least luminous of the bulge giants in the sample of Fulbright et al. (2006). Stars near the red giant branch (RGB) tip are very rare, and are unlikely to be found in any open cluster, while no globular cluster with [Fe/H] > + 0.1 dex is known in the Galaxy. Furthermore, the best abundances for the most metal-rich clusters come from dropping in luminosity to the RHB, where T_eff is considerably higher, and avoiding the RGB tip giants completely (see, e.g., Cohen et al. 1999).

There is thus a clear discrepancy between the metallicity distribution function in the Galactic bulge as sampled by microlensed main-sequence turnoff region stars and by luminous K and M giants. While still more microlensed dwarfs with detailed abundance analyses are highly desired to improve the statistics, we assume that this difference is real and is not the result of systematic errors producing suitable offsets in [Fe/H] derived from the abundance analyses.

In our earlier paper Cohen et al. (2008), we offered the suggestion that the highest metallicity giants have such high-mass-loss rates that they do not get to the RGB tip before losing their entire envelope. Possible evidence against this hypothesis is presented by Zoccali et al. (2008) on the basis of the luminosity function along the RGB; Clarkson et al. (2008) comment that the metallicity distribution of the bulge giants and of main-sequence stars inferred from ACS/HST photometry are consistent with each other. An additional possibility is that we are sampling a "young" and metal-rich stellar population such as that found within the inner 40 pc, where rather surprisingly massive young clusters exist (Figer et al. 2002), presumably fed, at least in part, by mass loss from bulge giants. This runs into the problem that the corresponding high-luminosity stars from such a population are not present in Baade's window, as reinforced by the very recent ACS/HST study of the Galactic bulge by Clarkson et al. (2008).

A similar argument applies for any proposed special component of the central region of our Galaxy such as an extension of the disk. Luck et al. (2006) determined the metallicity gradient for the Galactic disk from analysis of a large sample of Cepheid variables outside 4 kpc from the center to be −0.06 dex kpc⁻¹. It is interesting to note that their deduced [Fe/H] reached +0.3 dex at R_GC = 4 kpc, and if their linear fit is extrapolated inward, would reach +0.5 dex at R_GC = 1 kpc. A similarly metal-rich population of solar neighborhood disk stars whose highly eccentric orbits have pericentric distances as small as 3 kpc was identified by Grenon (1999) and Pompeia et al. (2002). These super-metal-rich old dwarfs have [Fe/H] reaching up to +0.4 dex and mean distance from the Galactic plane of only 220 pc. But a rather puffed up disk would be required to contribute significantly at Baade's window, which is at b ∼ −4° (560 pc). Certainly, over a very large range in R_GC the vertical scale height of the thin disk is smaller than that.

Another possibility is that the disk and/or halo contamination in the giant samples in Baade's window is larger than that calculated from Galactic models by Zoccali et al. (2008) and others. Little is known of the detailed structure of the disk and bulge in the region of the Galactic center. Although disk and halo contamination of the giant samples are believed to be small based on calculations using models of the stellar population of the Galaxy (see, e.g., Zoccali et al. 2008), the uncertainty in such corrections might be large. The extensive proper motion studies in bulge fields (see, e.g., Clarkson et al. 2008) give good determinations of the foreground disk contamination, but cannot easily address the possible presence of the disk within the bulge itself provided it makes a minor contribution to the total stellar population in the bulge. Disk contamination in the microlensed sample, which is a sample of background sources, must be smaller than that of the in situ giant samples, which probe the long line of sight to the center; the probability of microlensing for a foreground disk star is much smaller than for a star in the bulge itself, hence very biased strongly against disk stars.

We present detailed abundance analyses based on high dispersion and high signal-to-noise ratio MIKE spectra taken with the 6.5 m Magellan Clay Telescope of two highly microlensed Galactic bulge stars in the region of the main-sequence turnoff. Our stellar parameters were derived ignoring the available photometry out of concern for the high and uncertain reddening toward the bulge, and rely only on the spectra themselves. They are based on the classical criteria of Fe excitation equilibrium, and the ionization equilibrium of Fe and of Ti, and are consistent to within the adopted errors with that inferred from the Hα profile for the star with the higher quality spectrum, MOA–2008–BLG–310S. We deduce T_eff near 5650 K for both of these stars. MOA–2008–BLG–310S and MOA–2008–BLG–311S appear to be at the distance of the bulge with age ∼9 Gyr.

We suggest that the use of high excitation (χ>4 eV) Fe i lines is the measure of metallicity most independent of the exact choice of values for stellar parameters for such stars among the various possibilities we explored. We note that the available V,  I photometry for the two stars supports our choice of T_eff for each to within the photometric errors and the uncertainty of the reddening determination, which is based on red clump stars in the bulge in the field around each of the microlensed dwarfs.

We carry out a detailed classical abundance analysis using one-dimensional stellar model atmospheres and ignoring non-LTE. Since this is done differentially to the Sun and the two stars both have T_eff within 160 K of that of the Sun and log(g) within 0.3 dex of the Sun, these choices seem appropriate. We find that MOA–2008–BLG–310S has [Fe/H] = +0.41 ± 0.09 dex and MOA–2008–BLG–311S has +0.26 ± 0.09 dex. The abundance ratios for the ∼20 elements for which features could be detected in the spectra of each of the two stars follow the trends with [Fe/H] found among samples of Galactic bulge giants.

Combining these two bulge stars with the results from previous abundance analysis of four other Galactic bulge dwarfs, all highly magnified by microlensing, gives a mean [Fe/H] of +0.29 dex for the six microlensed dwarfs, which rises to +0.41 when the lowest metallicity dwarf, which is actually a subgiant with [Fe/H] very discrepant from the other five stars, is removed. On the other hand, the many large surveys of the metallicity distribution function in the Galactic bulge carried out at the VLT (Lecureur et al. 2007; Zoccali et al. 2008) and at Keck (Fulbright et al. 2006; Rich et al. 2007, among others) from samples of cool, luminous bulge giants give mean [Fe/H] ∼ −0.1 dex. This implies that there is an inconsistency between the Fe-metallicity distribution of the microlensed bulge dwarfs and that derived by the bulge giants. This difference is highly statistically significant assuming that both the abundance analyses of the giant samples and of the six microlensed dwarfs have been carried out correctly.

We provide statistical arguments suggesting that to produce consistency a substantial systematic error in the absolute metallicity of Fe in one or both of the two cases, bulge dwarfs versus bulge giants, is necessary. The required offset which must act to either underestimate the metallicities for the giants or overestimate those of the microlensed dwarfs, or both of these, is 0.2 dex in [Fe/H], ignoring a radial gradient, which would only increase this value. Were a systematic offset of this size present, the probability of the observed metallicity distribution functions for these two groups of bulge stars in very different evolutionary phases to be identical would rise to 15%.

Since the microlensed main-sequence region stars are usually analyzed differentially with respect to the Sun, to which they are fairly close in stellar parameters, the resulting systematic errors should be small. Furthermore, there are now multiple independent analyses for several of the microlensed dwarfs (see, e.g., Bensby et al. 2009), and there are several major independent surveys of bulge giants, suggesting that it is unlikely that either the dwarfs or the giants or both have major systematic errors in their [Fe/H] determinations. The contamination by foreground disk stars is predicted to be small for the giant samples; samples of bulge dwarfs selected through microlensing should contain a considerably smaller fraction of foreground disk stars.

A number of mechanisms for producing this difference are discussed, but none seems compelling. We clearly need a still larger sample of microlensed bulge dwarfs to refine the systematic offset required to achieve statistically identical Fe-metallicity distributions and to eliminate completely the possibility that a systematic error of the required size may have occurred in one or both of the Fe-metallicities between the bulge giants and the bulge microlensed dwarfs before indulging in further speculations of the cause of this discrepancy. The rising interest in time-domain phenomena has led to increased attention on how to handle these phenomena efficiently at large telescopes, increasing sensitivity for the handling of targets of opportunity. In the past three years, high dispersion spectra for six highly microlensed bulge dwarfs have been obtained at the Las Campanas or the Keck Observatory. With high hopes that the same will hold for the next three years, we eagerly await future larger samples of microlensed bulge turnoff region stars.

J.G.C. and W.H. are grateful to NSF grant AST-0507219 to J.G.C. for partial support. I.B.T. is grateful for support NSF grant AST-0507325. A.G. was supported by NSF grant 0757888. T. Sumi is grateful for a grant-in-aid for Young Scientists (B) and grant-in-aid for Scientific Research on Priority Areas, "Development of Extra-solar Planetary Science" by the Ministry of Education, Culture, Sports, and Technology (MEXT) of Japan. I. Bond is grateful to support from the Marsden Fund of the Royal Society of New Zealand.