TOWARD THE GENERAL RED GIANT BRANCH SLOPE–METALLICITY–AGE CALIBRATION. I. METALLICITIES, AGES, AND KINEMATICS FOR EIGHT LARGE MAGELLANIC CLOUD CLUSTERS^*

Short exposure images of eight LMC clusters were observed with FORS2 VLT through the filters V and R under excellent atmospheric conditions (seeing <0.7 arcsec) on 2006 October 5 and 2006 November 17. FORS2 was used in normal resolution with the pixel size of 025 pixel⁻¹ and field of view of 68 × 68, which allowed us to sample, in the outermost field regions, a good portion of the background LMC field. The coordinates of the clusters as well as the total exposure times are listed in Table 1.

De-biasing and flat fielding were performed with standard IRAF packages, using the calibration frames (bias and sky flat fields) obtained during the same nights as the target observations. Photometric reduction was carried out with the DAOPHOT II/ALLFRAME package (Stetson 1987, 1994). Stellar point-spread function models for each frame were obtained by means of a large set of uncrowded and unsaturated stars. The mean photometric errors are 0.003–0.009 mag for (V, R) <20 mag and between 0.01 mag and 0.03 mag for the fainter magnitudes. The nights were photometric and the calibration to the Johnson standard photometric system was performed by comparison of the stars in the Landolt (1992) field PG2213-006. The maximum zero-point errors are calculated as ±0.01–0.02 mag.

The spectroscopic observations were carried out with FORS2 in visitor mode at the Antu (VLT–UT1) 8.2 m telescope at ESO's Paranal Observatory during the night of 2006 November 16–17. We used the FORS2 spectrograph in mask exchange unit (MXU) mode, with the 1028z+29 grism and OG590+32 order blocking filter. The MXU slit mask configuration allows the placement of more slits (in this case 37) on the sky than the 19 movable slits provided in the multiobject spectrograph mode. Targets were selected so as to maximize the number of likely cluster members observed; typically 20 stars inside our estimated cluster radius (see Section 5) were observed, with an additional 15 stars outside of this radius that appeared to be LMC field red giants based on our IR photometry with the du Pont telescope.

We used slits that were 1'' wide and 625 long. In all fields, we obtained three to four separate 600 s exposures, taken under seeing less than 1''. They were average combined to form the final spectra. Pixels were binned 2 × 2, yielding a plate scale of 025 pixel⁻¹. We used the upper (master CCD) of FORS2 for observations of the target clusters which has a readout noise of 2.9 e⁻ and inverse gain of 0.7 e⁻ ADU⁻¹. The spectra have a dispersion of ∼0.85 Å pixel⁻¹ (which corresponds to a resolution of 2–3 Å) with a characteristic rms scatter of 0.06 Å, and cover a range of ∼1600 Å in the region of the CaT (8498 Å, 8542 Å, and 8662 Å). For the final spectra, the S/N is typically 40–60 pixel⁻¹ with some stars as high as ∼100 pixel⁻¹ and, in some few cases, as low as ∼20 pixel⁻¹. For the present study we use spectra having S/N ⩾35 pixel⁻¹. Calibration exposures, bias frames and flat fields were also taken as a part of the standard calibration plan.

We used the IRAF task ccdproc to fit and subtract the over-scan region, trim the images, and flat-field each image. Flats were corrected for the lamp shape by the task response. We used the task apall to define the sky background and extract the stellar spectra onto one dimension. The sky level was defined by performing a linear fit across the dispersion direction to sky windows on each side of the star. When the star fell near the top or bottom of the slitlet, the sky regions were chosen interactively. The tasks identify and dispcor were used to calculate and apply the dispersion solution for each spectrum. Finally, the spectra were continuum normalized by fitting a polynomial to the stellar continuum. Examples of the final spectra in the CaT region can be seen in Figure 1. Clearly, the three Ca ii lines dominate the red giant's spectra in this region. Also note the stronger Ca lines in the bottom spectrum, which, given the very similar T_eff and log g values (as indicated by their virtually identical V − V_HB values, i.e., the mag difference between the star and the horizontal branch), graphically illustrates the higher metallicity of the bottom spectrum and the power of the CaT technique.

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Figure 6 shows the CMDs of the eight LMC clusters. All the stars measured with good precision (error in mag <0.1) in the whole FORS2 frames are plotted here; therefore, the CMDs include both cluster and field stars. To check the zero point of our calibrations, we overplotted the fiducial lines of RGB stars, field RR Lyrae, and Red Clump (RC) stars as defined from MACHO database (Alcock et al. 2000, see their Table 1).

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The clusters from our sample are located in areas densely populated by field stars. In order to obtain a cleaner cluster CMD, we proceeded in the following way. For each cluster, an annulus around the center was selected with the criterion of being large enough to contain most cluster stars, but small enough to minimize the background contribution. The small circular region containing the very center of some of the clusters was excluded because these areas were too crowded, and therefore the photometry was rather poor. The photometry around very bright stars projected close to the objects NGC 1786, SL 826, and NGC 1754 is also removed. A CMD typical of LMC field stars was extracted from a second region, well outside a given radius around the cluster center, selected with the criterion of containing a number of stars large enough to ensure good statistics, but far enough from the cluster not to contain a significant fraction of cluster stars. The cluster and reference fields cover the same area. The full range of magnitude and colors of a given CMD was divided into grids and we computed the expected number density of field stars in each cell based on the number of comparison field stars. After that the expected number of field stars is randomly subtracted from each cell. The statistically decontaminated CMDs are plotted in Figure 6 as dark dots.

To check our decontamination procedure we calculated the stellar surface-density distributions (number of stars per arcmin²; Bonatto & Bica 2006). They are computed for a mesh size of 0.2 × 0.2 arcmin², centered on the apparent cluster center. Figure 7 (left panel) shows observed photometry of NGC 1795, while on the right-hand panel only the stars selected by means of the color–magnitude filter described above are plotted. As can be seen, most of the field stars have been removed, although a small number of field stars still fall in the cluster main-sequence locus region.

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The decontaminated CMDs outline the basic features of the clusters. Most of them show typical diagrams of intermediate-age clusters. As can be seen in Figure 8, we cannot reach the Turnoff/Termination Point (TO) for NGC 1795, NGC 1754, NGC 1786, and Hodge 2 because of the crowding and short exposure times. For the rest of the clusters from our sample, NGC 1900, SL 509, SL 817, and SL 862, the main sequence can be followed up to 4 mag bellow the TO. The RC stars are located between ≈19 mag and 19.3 mag and the RGB extends between 2 mag and 4 mag brightward of the RC. NGC 1754, and to a lesser extent NGC 1786, show well-populated horizontal branches (HB).

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The goal of this project is to obtain homogeneous [Fe/H] values and ages to be used for calibration of the near-IR K_s-band RGB slope–metallicity–age relation. The determination of the metallicities is described in Section 4. The most reliable technique for age determination is to examine the luminosity of the main-sequence turnoff and compare it to the predictions of theoretical isochrones. Unfortunately, it is not possible for half of our objects, since the photometry is just not deep enough and we could not reach the TO and main-sequence region. We choose to compare the rest of our CMD with the Padova set of theoretical isochrones (Marigo et al. 2008), because they are based on models with a moderate amount of convective overshooting, asymptotic giant branch evolution, and circumstellar dust around the coolest evolved stars. For the clusters NGC 1795, NGC 1754, and NGC 1786 much deeper, better HST data are available in the literature and we adopted the age determination from the corresponding papers. Since in these papers different sets of theoretical isochrones are used, we plotted the corresponding isochrone from the Padova set to check the coincidence. To determine the best models, we applied a statistical tool to compare the observed and theoretical main sequence and/or RC. We compared the differences along the observed and theoretical fiducial lines of each cluster using a ξ² statistic.

NGC 1795. Because of the crowding, incompleteness, and short exposure times of our images, the CMD of NGC 1795 does not reach the TO. The RGB and RC stars however are clearly visible and the corresponding branches are well populated. To determine the RC brightness we adopted the method described in Pietrzyński et al. (2003): we selected the stars with V-band magnitudes and V − R colors in the range around the RC stars and fit the derived V-band magnitude histogram with a complex function involving a Gaussian function (representing the distribution of RC stars) superimposed on a second-order polynomial component (for the stellar background; see, e.g., Stanek & Garnavich 1998; Alves et al. 2002; Pietrzyński & Gieren 2002). Such a described procedure finds the RC at V = 19.13 ± 0.07. The latest photometric investigation based on the archival HST images of the cluster is given in Milone et al. (2009). The observed deep (V, V − I) CMD is compared with a set of BaSTI isochrones and gives the following parameters: (M − m)₀ = 18.45, E(B − V) = 0.10, z = 0.008, and age 1.3 Gyr. Since we have accurately determined metallicity [Fe/H] = −0.47 we adopted their distance, reddening, and age values and plot the corresponding isochrone from Padova set which fit well the luminosity and color of the RC region (Figure 8, upper left panel).

NGC 1754. NGC 1754 is a well-known old LMC cluster (Olsen et al. 1998). The main features visible on our CMD are well-populated RGB, long blue HB, typical for metal-poor clusters, and a sub-giant branch (SGB) down to V = 22 mag. The TO point and RC regions are not visible. In our photometry, the RC is determined at V = 19.25 ± 0.17. The level of the HB calculated as lower envelope is found at V = 19.55 ± 0.11. Olsen et al. (1998) derived (M − m)₀ = 19.00 (based on the MW globular cluster stars comparison) and (M − m)₀ = 18.62 (based on the level of the HB stars); E(B − V) = 0.10 and age 15.6 Gyr. We adopted their average distance value of (M − m)₀ = 18.66 and plotted the Padova isochrone of 15.6 Gyr, but the deviation from the observed CMD is very large. Taking into account our metallicity [Fe/H] = −1.48, the best fit of the Padova isochrones (Marigo et al. 2008) favors an age of 14 Gyr. To check this age determination, we retrieve the HST V, I photometry of Olsen et al. (1998). As can be seen in Figure 8 (right corner of the NGC 1754 plot), an age of 14 Gyr fits well the TO region of the Olsen et al. (1998) CMD. Obviously, this is slightly older than the well-determined age of the universe from WMAP and therefore an overestimate.

NGC 1786. This object is another example of an old, metal-poor cluster in the LMC (Brocato et al. 1996). In our CMD the RGB is well defined, the HB is populated on the blue side of the instability trip at V = 19.44 ± 0.08 (lower envelop). The fundamental properties of NGC 1786 are taken from Table 7 of Grocholski et al. (2007) and are based on the mean apparent V-band magnitude of RR Lyrae stars (Walker 1985; Walker & Mack 1988; Walker 1989, 1990, 1992a, 1992b, 1993). With (M − m)₀ = 18.62, E(B − V) = 0.06, and [Fe/H] = −1.77, we plotted Brocato et al. (1996) isochrone of 12.3 Gyr. As can be seen in Figure 8, the isochrone for the adopted age fits our CMD well.

Hodge 2. There is no photometric information for this cluster in the literature. Our CMD does not clearly reach the TO point; however, the RGB is well defined and the RC can be located at V_RC = 19.12 ± 0.17. To determine the age of the cluster, we need reddening and distance. We calculate the distance using the Population II Cepheid star SV*HV 2439 (OGLE LMC-SC7 21841), a confirmed cluster member (Hodge & Wright 1963; Udalski et al. 1999). According to the OGLE III database (Soszynski et al. 2008) the apparent mean V magnitude of the star is V = 15.58, with a period of pulsation P = 4.81308 days. The reddening E(B − V) = 0.14 is adopted from the OGLE database as a mean value of the SC7 field. The distance modulus (M − m)₀ = 18.62 is calculated as a difference between the reddening corrected mean V magnitude of SV*HV 2439 and the absolute M_V magnitude of Cepheid stars given in Benedict et al. (2002). The cluster has a metallicity value [Fe/H] = −0.49 ± 0.11 and the best-fit isochrone favors an age of 1.6 Gyr.

NGC 1900. The CMD presented here is the only photometric investigation up to the moment and shows typical features of an intermediate-age stellar cluster: a long and well-populated main sequence reaching about 4 mag below the turnoff point and some evolved RGB stars. The distance of (M − m)₀ = 18.47 ± 0.07 is calculated from the mean RC K_S brightness derived from our high-quality J, K_S IR photometry (R. Kurtev et al. 2010, in preparation). We used the absolute RC magnitude M_K = −1.644, calibrated in Alves et al. (2002). To calculate the distance a correction for population effects has to be applied (Gullieuszik et al. 2007) because of the differences in the stellar content of LMC and Galactic RC stars on which the Alves et al. (2002) calibration is based. Salaris & Girardi (2002) estimated the population effects on the RC absolute magnitude in the K band of ΔM^RC_K = −0.03. Using [Fe/H] = −0.55 ± 0.09 obtained in Section 5, we derive an age of 800 Myr.

SL 509. The only photometric investigation up to the moment is reported by Bica et al. (1998) and Piatti et al. (2003) and is based on the Washington photometric system. The derived age in Piatti et al. (2003) is 1.2 Gyr and the metallicity corrected for age effects is [Fe/H] = −0.65. They also reported a secondary clump 0.45 mag fainter and bluer than the main RC, which also can be noted in our CMD. In Figure 9 (left panel) we zoomed the RC and TO regions of the CMD, marking with boxes the suspected clumps. The luminosity function of the RC region is shown in the middle panel of Figure 9, and finally the last panel of Figure 9 represents the positions of the stars with respect to the cluster center. As can be seen there is a strong hint of two populations, as pointed out by Piatti et al. (2003), but the sample is too small with only 66 stars and more data are necessary to confirm the reality of these populations. If confirmed, according to Girardi et al. (2009), the secondary clump could be a result of He-ignition in stars just massive enough to avoid e⁻ degeneracy in their H-exhausted cores. The TO can be located at V_TO = 19.40 ± 0.11. Using the same method as for NGC 1900, we derived (M − m)₀ = 18.48 ±  0.05. The E(B − V) = 0.03 is taken from the OGLE database. The best isochrone fit gives 1.2 Gyr, in excellent agreement with Piatti et al. (2003) result.

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SL 817. The cluster has only Washington photometry (Bica et al. 1998; Piatti et al. 2003) and shows morphology similar to that of SL 509. Using the same technique as for SL 509 we derived the TO at V_TO = 20.20 ± 0.11, the RC is calculated at V_RC = 18.96 ± 0.17. For the distance, reddening, and age, we determined (M − m)₀ = 18.38 ± 0.07, E(B − V) = 0.12, and 2.2 Gyr, respectively.

SL 862. And finally for SL 862 we have TO at V_TO = 20.10 ± 0.11, the RC at V_RC = 19.07 ± 0.09, (M − m)₀ = 18.45 ± 0.07, E(B − V) = 0.10, and an age of 1.7 Gyr. Piatti et al. (2003) give an age of 1.7 Gyr and the metallicity of −0.75 from Washington photometry, in agreement with our values.

We estimated the errors in the age determination as an upper limit of the various factors: errors in the photometry, errors in the transformation to the standard system, errors due to incompleteness, field decontamination, metallicity determination, and errors of the fit to the theoretical isochrones. For the clusters without good main-sequence photometry, ages can be estimated to within ±1.4–1.7 Gyr, while for the younger clusters with prominent main sequences we estimate an error of ±0.5 Gyr. In Table 3, we have listed the obtained value of age for all the target clusters. The radial velocity and metallicity along with standard deviation is also given in Table 3, which has been obtained by taking the mean of the individual values of cluster members.

We compared the values of the metallicities obtained in the present work with previously published values. Since our method relies on high S/N spectroscopy of a large number of stars per cluster, the individual and mean errors are in general smaller as compared to the previously determined values (e.g., O91 have used in general two stars per cluster, while we have on average 10 identified cluster members). Four of our target clusters have metallicity values given in O91 using CaT spectroscopy of some individual giants. Five of our target clusters also have photometrically determined values of metallicity (see Table 3). As indicated by G06, although O91 used CaT lines as a proxy for measuring Fe abundance directly and is thus similar to our work, it is inappropriate to directly compare the O91 values to our work due to differences in the details of the metallicity determination (see for detail G06). C05 find that one can estimate the abundance of O91 clusters on the metallicity system we have used via the following conversion:

$$\begin{equation*} [{\rm Fe}/{\rm H}] \simeq - 0.212 + 0.498[{\rm Fe}/{\rm H}]_{\rm O91} - 0.128[{\rm Fe}/{\rm H}]^2_{\rm O91}. \end{equation*}$$

In Table 3, Columns 6, 7, and 9 give the [Fe/H] values obtained in the present study, values given by O91 (spectroscopically), and the photometrically determined values, respectively. In Column 8, we give the transformed values of [Fe/H] given by O91 to our system using the above relation. In Figure 10, we have plotted the difference "[Fe/H]_present − [Fe/H]_literature" as a function of age for O91 clusters (filled circles: original O91 values; open circles: transformed O91 values) and photometrically observed clusters (open triangles).

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The difference of metallicity between the present value and the transformed value of O91 are of the order of 0.15–0.23 dex. O91 give their [Fe/H] errors for individual stars as 0.2 dex, therefore, deviations between these data sets as large as ±0.2 are not unexpected, suggesting that these results are in relative agreement with no offset. We note, however, that even with the use of the above equation, it is very difficult to directly compare the derived cluster abundances because of the difference in calibration strategy. Comparison of our [Fe/H] values with the photometrically determined values for each cluster is given below.

NGC 1754. This cluster has been studied by Olsen et al. (1998) using HST CMDs quoting a metallicity of −1.42 ± 0.15. Olsen et al. (1998) commented that the abundances they obtained are on average higher than previously measured spectroscopic abundances. They have used the method of Sarajedini (1994) to determine abundances from the measurement of the height of the RGB above the level of HB.

NGC 1786. This cluster has been studied by Brocato et al. (1996) using VI data from the 3.6 ESO NTT. They have determined a lower value of −2.1 but with a large error (0.3 dex) using the Sarajedini (1994) method. Recently, this cluster was also studied by Mucciarelli et al. (2009) using high-resolution spectroscopy of giant stars. Their value of [Fe/H] = −1.75 ± 0.01 is virtually identical to our metallicity determination ([Fe/H] = −1.77 ± 0.08), lending confidence to our results.

SL509, SL817, and SL862. These clusters have been studied by Piatti et al. (2003) using Washington photometry. Our [Fe/H] values for SL509 and SL817 (i.e., −0.54 ± 0.09, −0.41 ± 0.05) are comparable to their reported values of −0.65 ± 0.2 and −0.35 ± 0.2, respectively. For SL862, they gave [Fe/H] = −0.75 ± 0.2, which is lower than the present estimation of −0.47 ± 0.07.

For all eight clusters, we have used the very reliable CaT method as the [Fe/H] indicator, with significantly more cluster members and less scatter in individual [Fe/H] value compared to previous studies.

It is important to have significant numbers of data points to make a definitive analysis of the AMR of LMC clusters. Over the past few decades, nearly a hundred LMC star clusters have had both accurate age estimated from isochrone fitting to their CMDs (Sagar & Pandey 1989; Balbinot et al. 2009, and references therein), and a metallicity measurement from either spectroscopy and/or isochrone fitting (G06). Recently, Harris & Zaritsky (2009) have compiled the age and metallicity of 85 clusters from their literature search. Out of these 85, 5 are in common with our sample and 15 are in common with G06. We have excluded our 5 and 15 G06 clusters from this sample and generate a new sample of 101 clusters [(85 −5 −15) + 8 + 28 = 101]. The present work combined with G06 makes a homogeneous data set of 36 clusters using the same method for metallicity determination. In the case of G06 clusters, out of 28, 15 have ages from the sample of Harris & Zaritsky (2009). For the other 13 clusters, we converted the given SWB type (Searle et al. 1980, hereafter SWB) into age from the conversion given in Bica et al. (1996). These 13 clusters have either SWB type V or VI. Based on published data, we have taken the mean age of SWB type V and VI as 1.5 Gyr and 2.5 Gyr, respectively. Here it is important to mention that the Harris & Zaritsky (2009) compilation is heterogeneous, using a variety of different age and metallicity scales, so in fact it is a bit dangerous lumping them all together, although this effect is minimal for the present study.

The cluster metallicity distribution (hereafter MD) is an important diagnostic of the global chemical evolution of a galaxy and is useful for an overall comparison of the cluster systems of different galaxies (P09).

In Figure 11, we have shown first the distribution of the ages of all 101 clusters. The black, gray, and open regions represent the data from the present study, from G06, and from Harris & Zaritsky (2009), respectively. Broadly, we can classify the population in three age bins: <1 Gyr, 1–3 Gyr, and >12 Gyr, i.e., youngest, intermediate-age, and old-age populations. In Table 4, we have presented the statistics for the value of [Fe/H] and age in these bins along with the number of clusters using the CaT method or clusters from the literature survey. We can easily see the change in the value of [Fe/H] with age. Globally, for clusters having mean age ∼0.2 Gyr, the [Fe/H] value is −0.35, for age ∼2 Gyr, the [Fe/H] value is −0.55 and for age ∼14 Gyr, the [Fe/H] value is −1.62. This change is more prominent in second and third bin of clusters having used the CaT method (we have only one cluster in the first bin). We found that the younger clusters are generally more enriched than older clusters with the youngest bin [Fe/H] value comparable to the present-day LMC value of "−0.31 ± 0.04" given by Rolleston et al. (2002) and "−0.27 ± 0.06" given by Hill et al. (1995). The MD is shown in Figure 12, where the color code is the same as Figure 11. We can easily see the strong peak in the distribution of clusters having [Fe/H] = −0.5 to −0.4 and rest of them are distributed approximately uniformly with metallicity. The metallicity of the six young clusters obtained in the present study, having a mean age of 1.5 Gyr, is −0.49 with a scatter of 0.04, in excellent agreement with the previous finding of G06, which shows a very tight distribution with mean metallicity of −0.49 (σ = 0.09) for the younger clusters, which formed after the age gap ended some 3 Gyr ago. The narrow metallicity distribution of LMC young-intermediate-age clusters has also been observed previously, based on high-resolution spectroscopy (i.e., NGC 1866: [Fe/H] = −0.5 ± 0.1 (Hill et al. 2000) and mean [Fe/H] = −0.38 ± 0.09 for four LMC globular clusters (Mucciarelli et al. 2008)). This agrees well with the theoretical work of Bekki et al. (2004), which indicates that a close encounter between the LMC and SMC caused not only the restart of cluster formation in the LMC but also the generation of the central bar (mean [Fe/H] = −0.37 ± 0.15; C05). We can easily see the two separate distributions in the age of the clusters (Figure 11) and older clusters are showing a much larger spread in [Fe/H] value as compared to younger ones (see also Figure 12). The sample size is near the limit of drawing statistically significant results of this kind. It is not clear why the SMC cluster age and metallicity distribution are distinct from that of the LMC. It is of great interest to enlarge the present homogeneous sample in order to ascertain the LMC cluster MD. Note that the CaT data shows a much tighter metallicity distribution than that of Harris & Zaritsky (2009) or O91.

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The AMR is a record of the progressive chemical enrichment of the star-forming local interstellar medium during the evolution of the galaxy, and so provides useful clues about the SFH and CEH of the local environment (Carraro et al. 1998). All existing AMR studies suffer from uncertainties due to either inhomogeneous data sets or photometry-based abundances. In Figure 13, we make an updated AMR using homogeneous set of data using the CaT method for [Fe/H] measurement (36 clusters, 8 from the present work (star symbols) and 28 from G06 (closed circles)). We have also plotted, for comparison, the data from the sample of Harris & Zaritsky (2009) (open circles) which are not in common with either the present work or the work done by G06. We can easily see that there is less scatter in [Fe/H] values for the clusters using the CaT method.

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The essential features of the AMR have not changed (see also Harris & Zaritsky 2009): there is still a long age gap, which is also a metallicity gap, especially if one only looks at the CaT data. Prior to the age gap, the LMC formed a number of low-metallicity populous clusters, analogous to the MW's globular cluster population. Following the age gap, cluster formation resumed in the LMC, and proceeded roughly continuously to the present day. The clusters formed following the age gap have less dispersion in metallicity and are significantly more enriched than the ancient cluster population, and there is some evidence for further enrichment with time for ages <1 Gyr.

C05 have obtained stellar metallicities for almost 400 stars in the bar of the LMC, also using CaT lines. Their obtained AMR shows a similar behavior to that of the clusters for the oldest population. However, while for the clusters the metallicity has increased over the last 2 Gyr, this has not happened in the bar. Recently, Carrera et al. (2008) have examined the AMR for field stellar populations, based on CaT spectroscopy of individual red giants in four LMC fields. They find that the disk AMR is similar to that of the LMC star clusters: there was rapid initial enrichment to [Fe/H] ∼−0.8 by about 10 Gyr ago. Following this, the metallicity increased only slowly until 3 Gyr ago, when it began a more rapid increase to its present-day value of [Fe/H] ∼−0.2. However, the lack of objects with ages between 3 Gyr and 10 Gyr is not observed in the field population. Their reconstructed SFH (for their inner disk fields) indicates there was a relatively quiescent epoch between 5 Gyr and 10 Gyr ago but some star formation occurred. These conclusions differ in detail from those derived from the AMR of the central region of the LMC (C05), but the observed AMRs are entirely consistent.

Carrera et al. (2008) also showed that the bar AMR differs from that of the disk in the last 3 Gyr; while in the disk the metallicity has increased during this time, in the bar it has remained approximately constant. This would be in agreement with the prediction that a typical bar instability pushes the gas of the disk toward the center (Sellwood & Wilkinson 1993), so the infall gas is expected to be previously pre-enriched by the disk chemical evolution. This would be also the case in the scenario suggested by Bekki & Chiba (2005), in which the bar would have formed from disk material as a consequence of tidal interactions between the LMC, the SMC, and the MW about 5 Gyr ago, the epoch when the bar AMR differed from that of the disk. Also, a bar is expected to destroy any metallicity gradient within a certain radius, as is observed (e.g., G06). Harris & Zaritsky (2009) recently found that the CEH for the LMC is qualitatively similar to the one derived for the SMC (see Harris & Zaritsky 2004). In both galaxies, the mean metallicity remained at an almost constant, low value, from ∼10 Gyr until about 4 Gyr ago when the metallicity began a steady ascent to the present-day value. In both galaxies, the AMR is consistent with the bursting enrichment model proposed by Pagel & Tautvaisienė (1999) (P09).

The galactic distribution of elemental abundances is central to studying the chemical evolution of the galaxy. The relative abundances of the elements are sensitive to the SFH, the number of massive stars, the ratio of SN Ia to II, the importance of AGB stars, the relative yield of the elements, and the exchange of matter between the galactic disk, bar, and halo through infall or ejection. Measurements of elemental abundances throughout the galaxy provide vital input to model the formation and evolution of the galaxy. From observations of clusters, O91 and Santos et al. (1999) found no evidence for the presence of a radial metallicity gradient in the LMC. The only evidence for a radial metallicity gradient in the LMC cluster system was reported by Kontizas et al. (1993) based on six outer LMC clusters (⩾ 8 kpc). Hill et al. (1995) were the first to report evidences of a gradient in the field population from high-resolution spectroscopy, using a sample of nine stars in the bar and in the disk. They found that the bar is on average 0.3 dex more metal-rich than the disk population, but the disk stars studied are located within a radius of 2°. Subsequent work by Cioni & Habing (2003) also implies a decrease in metallicity while moving away from the bar within radius of 6°. Finally, an outward radial gradient of decreasing metallicity was also found by Alves (2004) from IR CMDs using the 2MASS. Recently, Carrera et al. (2008) concluded that the lower mean metallicity in the outermost field is a consequence of it having a lower fraction of young stars, which are more metal-rich. They found that there is a change in the age composition of the disk population beyond a certain radius, while the chemical enrichment history seems to be shared by all fields.

It is necessary to further investigate the presence, or absence, of an abundance gradient in the LMC. We have used the current sample of 101 clusters in this regard. Positions on the sky for each cluster are shown in Figure 14 along with the metallicity bin into which each cluster falls represented by the color of the plotting symbol. We have used the same color scheme as used by G06. Figure 14(a) represents clusters with [Fe/H] determined using CaT method. Star and dot symbols represent data from the present work and from G06, respectively. Figure 14(b) represents the sample of all 101 clusters. The adopted center of the LMC (α = 5^h27^m36^s, δ = −69°52'12''; van der Marel et al. 2002) is marked by the cross and the dashed oval represents the 2° near-IR isopleth from van der Marel (2001), which roughly outlines the location of the LMC bar. Conversion from right ascension and declination to Cartesian coordinates was performed using a zenithal equidistant projection (e.g., van der Marel & Cioni 2001, their Equations (1)–(4)).

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In Figures 15 and 16, we further explore the metallicity–position relationship for LMC clusters by plotting metallicity as a function of de-projected position angle and radial distance (in kpc), respectively. The symbols are the same as in Figure 13. We can very easily see the tight distribution of the clusters with CaT-based [Fe/H] determination. This is an important factor in constraining the SFH of the galaxy. We have corrected for projection effects by adopting 347 as the inclination and 1225 for the position angle of the line of nodes of the LMC (van der Marel & Cioni 2001; G06). In this rotated coordinate system, a cluster with a position angle of zero lies along the line of nodes, and angles increase counterclockwise (see G06); radial distances were converted from angular separation to kpc by assuming an LMC distance of (m − M₀) = 18.5 (∼50 kpc); at this distance, 1° is ∼870 pc. In Figure 16, we have overplotted both the MW open cluster metallicity gradient from Friel et al. (2002, dashed line) and the M33 gradient from Tiede et al. (2004, solid line). Neither of these disk abundance gradients resembles what we see among the LMC clusters, which shows no evidence for a gradient.

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Combined, these three figures illustrate that, similar to what was found by O91 (and Geisler et al. 2003; G06), there is no [Fe/H] gradient in terms of either position angle or radial distance for the higher metallicity clusters in our sample. It is well known that a number of metal-poor clusters ([Fe/H] ⩽−1.5) exist in the inner portions of the LMC (e.g., O91), suggesting that neither the metal-rich nor the metal-poor clusters exhibit a metallicity gradient. In the case of the LMC, the presence of a strong bar component may have diluted the metallicity gradient originally present in the star clusters, leading to a cluster population that is well mixed (see G06).

Geisler et al. (2009) also found that the cluster distribution is similar to what has been found for red giant stars in the bar, which indicates that the bar and the intermediate-age clusters have similar SFHs. This is in good agreement with recent theoretical models that suggest the bar and intermediate-age clusters formed as a result of a close encounter with the SMC. Our findings also confirm previous results which show that the LMC lacks the metallicity gradient typically seen in non-barred spiral galaxies, suggesting that the bar is driving the mixing of stellar populations in the LMC.

The kinematical properties of the LMC provide important clues to its structure. They have been obtained from many tracers such as H i gas (e.g., Rohlfs et al. 1984; Luks & Rohlfs 1992; Kim et al. 1998), star clusters (Freeman et al. 1983; Schommer et al. 1992), planetary nebulae (Meatheringham et al. 1988), H ii regions and supergiants (Feitzinger et al. 1977), and carbon stars (Kunkel et al. 1997; Graff et al. 2000; Alves & Nelson 2000; van der Marel et al. 2002). All these studies imply that the LMC is kinematically cold, and must therefore to first approximation be a disk system (van der Marel 2006). G06 also found their cluster sample has motions consistent with that of a single rotating disk system, with no indication of halo kinematics.

To study the kinematics of the LMC, we followed the approach of G06 and Schommer et al. (1992) using star clusters as a tracers. To characterize the rotation of their clusters, Schommer et al. (1992) fit an equation of the form

$$\begin{equation*} V(\theta) = \pm V_m \lbrace [{\tan }(\theta -\theta _0) {\rm sec }\, i]^2 +1 \rbrace ^{-0.5} + V_{{\rm sys}} \end{equation*}$$

to their radial velocity data using a least-squares technique to derive the systemic velocity (V_sys), the amplitude of the rotation velocity (V_m), and the orientation of the line of nodes; they adopted an inclination of 27°. Their best-fit parameters give a rotation amplitude and dispersion consistent with the LMC clusters having disk-like kinematics, with no indications of the existence of a pressure-supported halo.

In Figure 17, we have plotted galactocentric radial velocity versus position angle on the sky for our sample (8 from present work + 28 from G06), along with velocity data for all clusters listed in Schommer et al. (1992). To be consistent with the approach of Schommer et al. (1992), we have adopted the galactocentric velocity corrections given by Feitzinger & Weiss (1979). In addition, for this figure only, we have adopted their LMC center (α = 5^h20^m40^s, δ = −69°14'10'' [J2000]) for use in calculating the position angles of our clusters (see also G06). We have used the standard astronomical convention in which north has a position angle of zero and angles increase to the east (G06); data from Schommer et al. (1992) are plotted as open circles, present data are plotted as star symbols, and data from G06 are given by solid points. Overplotted in this figure (dashed line) is the rotation curve solution number 3 from Schommer et al. (1992). Derived velocities for the present eight target clusters show that their motions are consistent with the findings of Schommer et al. (1992) in that the LMC cluster system exhibits disk-like kinematics that are very similar to the H i disk and has no obvious signature of a stellar halo. Carrera et al. (2008) argued that failure to find evidence of a hot stellar halo is related to a low contrast of the halo population with respect to that of the disk, even at the large galactocentric radius of their outermost field. Curiously, both old, metal-poor clusters as well as intermediate-age, metal-rich clusters share the same disk rotation.

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