VARIABLE STARS IN LARGE MAGELLANIC CLOUD GLOBULAR CLUSTERS. III. RETICULUM^*

This is the third in a series of papers focusing on the variable stars in Large Magellanic Cloud (LMC) globular clusters. The goal of this series of papers is to better understand the nature of the Oosterhoff dichotomy in the Milky Way and how Oosterhoff-intermediate (Oo-int) clusters in nearby dwarf galaxies fit into that picture. Globular clusters in the Milky Way are classified as either Oosterhoff I (Oo-I) or Oosterhoff II (Oo-II) objects based on the properties of their RR Lyrae stars. Oo-I objects are defined as having an average RRab period of 〈P_ab〉 < 0.58 days while Oo-II objects have 〈P_ab〉 > 0.62 days; the typical values of 〈P_ab〉 are 0.55 days and 0.65 days for Oo-I and Oo-II objects, respectively. Oo-I clusters also tend to be more metal-rich and have a smaller ratio of first overtone dominant to fundamental mode dominant RR Lyrae. The period range between the two groups, 0.58 ⩽ 〈P_ab〉 ⩽ 0.62 days, is referred to as the Oosterhoff gap and is essentially unoccupied by Milky Way globular clusters. The nearby dwarf galaxies and their globular clusters present a sharp contrast to this behavior as these extra-galactic clusters not only fall in the Oo-I and Oo-II groups, they also fall into the gap between these groups; in fact the extra-galactic objects seem to preferentially be located in the gap (Catelan 2009). These Oo-int objects, as objects that fall in the gap are called, present a challenge for models that propose that the Milky Way halo was formed through the accretion of objects similar to the present day nearby dwarf galaxies as we would expect to see similar Oosterhoff properties in both samples if that were the case.

The first two papers in this series discussed the variables in the globular clusters NGC 1466 (Kuehn et al. 2011) and NGC 1786 (Kuehn et al. 2012). These previous investigations, combined with the results presented here, build an inventory of updated RR Lyrae properties in a representative sample of LMC globular clusters. A future paper in the series will present a more detailed discussion of our present understanding of the Oosterhoff phenomenon and how the overall results from our study of LMC globular clusters fit into this picture.

Reticulum is an old globular cluster that is located ≈11° from the center of the LMC (Demers & Kunkel 1976). It has a metal abundance of [Fe/H]_ZW84 ≈ −1.66 (Mackey & Gilmore 2004) ([Fe/H]_UVES ≈ −1.61 in the new UVES scale; Carretta et al. 2009) and is not very reddened, E(B − V) = 0.016 (Schlegel et al. 1998). Mackey & Gilmore found that the age of Reticulum is similar to the ages of the oldest globular clusters in the Milky Way and the LMC, having an age that is approximately 1.4 Gyr younger than the classic nearby Milky Way halo globular cluster M3. Johnson et al. (2002) used Hubble Space Telescope observations to determine that Reticulum formed within 2 Gyr of the other old LMC clusters.

Reticulum is a sparsely populated cluster, but it does have a distinct horizontal branch that stretches across the instability strip (Figures 1 and 2). Twenty-two RR Lyrae stars were first found in the cluster by Demers & Kunkel (1976). Walker (1992a, hereafter Walker) later found an additional 10 RR Lyrae stars, bringing the total in the cluster to 32. The pulsation types include 22 RRab stars (fundamental-mode pulsators), 9 RRc's (first-overtone), and 1 candidate RRd (double-mode pulsators), although recently Ripepi et al. (2004) found evidence for RRd behavior in four of the previously discovered RR Lyrae stars.

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A total of 38 V, 33 B, and 35 I images were obtained using the SOI imager (5.2 × 5.2 arcmin field of view) on the SOAR 4 m telescope in February of 2008. ANDICAM (6 × 6 arcmin field of view) on the SMARTS 1.3 m telescope operated by the SMARTS consortium was used to obtain 45 V, 43 B, and 45 I images between 2006 September and the end of 2006 December. An additional 145 V and 146 B image were taken with the Tek2K (13.6 × 13.6 arcmin field of view) on the SMARTS 0.9 m telescope between 2008 December and 2009 November. SOAR exposure times were between 30 s and 600 s for V and I, and between 45 s and 900 s for B. SMARTS 1.3 m exposures were 450 s for the V and B filters and 300 s for the I filter. SMARTS 0.9 m exposures were 400 s in both the V and B.

Data reduction and variable identification for the SOAR and SMARTS 1.3 m data were carried out as described in Kuehn et al. (2011), the same method used for both NGC 1466 and NGC 1786. The SMARTS 0.9 m data was processed using the method described in Y.-B. Jeon et al. (2013, in preparation). The uncrowded nature of Reticulum was ideal for Daophot's profile fitting photometry (Stetson 1987, 1992, 1994) and while an image differencing method (Alard 2000) was run on the images for completeness, no additional variable stars were recovered. The photometry from Daophot was transformed to the standard system using the Landolt standard fields PG0231, SA95, and SA98 (Landolt 1992). We compared our resulting photometry to five of the local standard stars used by Walker, finding that for these five stars our photometry was 0.011  ±  0.010 mag brighter in V and 0.001  ±  0.018 in B.

All 32 RR Lyrae stars found by Walker were recovered: 22 RRab, 4 RRc, and 6 RRd stars. The 6 RRd stars were originally classified as RRc stars by Walker but the larger number of observations in our data set allowed for the identification of secondary pulsation modes. The RRab and RRc stars and their observed characteristics (periods, V, B, and I amplitudes, intensity-weighted V, B, and I mean magnitudes, and magnitude-weighted mean B − V color) are listed in Table 1; the stars that potentially show the Blazhko effect are identified with "BL" after their name. The RRd stars, their fundamental and first overtone periods and amplitudes, their period ratios, and their mean magnitudes and color are listed in Table 2. Periods for RRab and RRc stars are typically good to ±0.00001 or ±0.00002 days while periods for RRd stars are less well known, with uncertainties about an order of magnitude larger. Walker identified the variables in his paper using their star number in the catalog compiled in Demers & Kunkel (1976). We introduce a new naming system that features only the variable stars and is ordered based on increasing R.A. The names used by Walker are listed in the last column in Tables 1 and 2. Table 3 gives the photometry for the RR Lyrae stars and Figures 3, 4, and 5 show the light curves for the RRab, RRc, and RRd stars, respectively. The positions of the variable stars within the cluster are shown in Figure 6.

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The RRab stars have intensity-weighted mean magnitudes of 〈V〉 = 19.06  ±  0.01, 〈B〉 = 19.39  ±  0.01, and 〈I〉 = 18.61  ±  0.01 while the RRc stars have mean magnitudes of 〈V〉 = 19.05  ±  0.02, 〈B〉 = 19.26  ±  0.04, and 〈I〉 = 18.69  ±  0.01. The results for RRab stars are 0.02 mag brighter than the mean magnitudes found by Walker while our values for the RRc stars are consistent within the errors of those found by Walker.

In general our periods agreed with those of Walker to within 0.0002 days. V08 and V19 were the only stars for which a difference in period greater than 0.01 days was found. Walker found a period of 0.6566 days for V08 while we found a period of 0.64495 days, a decrease of 0.0117 days. For V19, Walker found a period of 0.469 days while we found a period of 0.48485 days, an increase of 0.016 days. We believe the periods adopted represent these stars more accurately, as our phase coverage and timespan of observation is significantly improved over those of Walker.

The first overtone periods for the RRd stars show good agreement with the periods that Walker had reported. Four of the six RRd stars (V03, V11, V15, V24) were also found by Ripepi et al. (2004). Figure 7 shows the Petersen diagram for the RRd stars in Reticulum along with those in the field of the LMC. The Reticulum RRd stars have similar period ratios to not only the LMC field RRd stars, but also to the RRd stars found in Milky Way Oo-I clusters (Clementini et al. 2004). The right-hand panel shows the results for models from Bragaglia et al. (2001) for three different combinations of metallicity, mass, and luminosity of the RRd stars. The RRd stars in Reticulum are fit very well by the line that corresponds to a metallicity of [Fe/H]_ZW84 = −1.53 ([Fe/H]_UVES = −1.45), a mass of M/M_☉ = 0.80, and a luminosity of log (L/L_☉) = 1.72. However, this gives a mass that is much higher than the masses of the RRc stars calculated through the Fourier decomposition method (see Section 4) or from fitting horizontal branch evolutionary tracks to the color–magnitude diagram (Section 5). The model tracks for a metallicity of [Fe/H]_ZW84 = −1.71 ([Fe/H]_UVES = −1.68) suggests that the Reticulum RRd stars could also be fit by a model of that metallicity with a mass in the range of 0.70 < M/M_☉ < 0.75 which would be closer to the masses obtained for the RRc stars.

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It has been shown that the Fourier parameters of RR Lyrae light curves can be used to estimate their physical properties (e.g., Jurcsik & Kovács 1996; Jurcsik 1998; Simon & Clement 1993). The RRab light curves were fit with a Fourier series of the form

$\begin{equation} m(t)=A_{0}+\sum _{j=1}^{n}A_{j}\sin (j\omega t+\phi _{j}), \end{equation} \tag{ 1 }$

while the RRc light curves were fit with a cosine series. The resulting Fourier coefficients were then used to calculate physical properties of the stars using the relations from Jurcsik & Kovács (1996), Jurcsik (1998), Kovács & Walker (1999, 2001), Simon & Clement (1993), and Morgan et al. (2007). We refer the reader to the first paper in this series, Kuehn et al. (2011), for further details.

Although a Fourier decomposition was attempted on all the RRab and RRc stars, only 14 RRab had light curves that allowed the reliable determination of Fourier parameters; all 4 RRc stars had reliable parameters determined but V12 stands out from the other RRc stars, see discussion below. Tables 4 and 5 give the Fourier coefficients for the RRab and RRc stars, respectively. The physical properties determined from these coefficients are given in Tables 6 and 7. Table 4 also lists the Jurcsik & Kovács D_max values (Jurcsik & Kovács 1996) for the RRab stars. D_max can be used to separate RRab stars with "regular" light curves from those with more "anomalous" light curves; lower values represent more regular light curves. Jurcsik & Kovács (1996) suggest that stars with D_max > 3 should not be trusted to provide reliable physical properties. We take a slightly more liberal approach and use the RRab stars with D_max < 5 to determine the average properties for the cluster; following the condition from Jurcsik & Kovács does not change the average values by a significant amount.

Table 6. Derived Physical Properties for RRab Variables

ID	[Fe/H]J95	〈MV〉	〈V − K〉	$\log T_{\rm eff}^{\langle V-K\rangle }$	〈B − V〉	$\log T_{\rm eff}^{\langle B-V\rangle }$	〈V − I〉	$\log T_{\rm eff}^{\langle V-I\rangle }$	log g
V02	−1.446	0.772	1.204	3.800	0.366	3.802	0.528	3.801	2.740
V05	−1.435	0.782	1.137	3.807	0.346	3.809	0.502	3.808	2.780
V13	−1.427	0.771	1.179	3.803	0.362	3.804	0.522	3.803	2.747
V18	−1.490	0.780	1.137	3.807	0.342	3.810	0.497	3.810	2.791
V21	−1.363	0.782	1.178	3.802	0.363	3.804	0.523	3.803	2.749
V07	−1.478	0.799	1.076	3.814	0.317	3.819	0.466	3.818	2.840
V14	−1.557	0.781	1.175	3.803	0.358	3.804	0.517	3.805	2.767
V16	−1.433	0.785	1.078	3.814	0.316	3.819	0.464	3.818	2.827
V17	−1.581	0.796	1.104	3.811	0.321	3.817	0.470	3.817	2.838
V22	−1.414	0.827	1.089	3.812	0.328	3.816	0.478	3.815	2.837
V27	−1.489	0.781	1.079	3.814	0.314	3.820	0.462	3.819	2.836
V29	−1.489	0.795	1.077	3.814	0.314	3.820	0.461	3.819	2.842
V30	−1.303	0.790	1.068	3.815	0.321	3.818	0.471	3.816	2.815
V31	−1.368	0.815	1.060	3.816	0.318	3.820	0.467	3.817	2.845
Mean	−1.432 ± 0.020	0.778 ± 0.003	1.167 ± 0.013	3.804 ± 0.001	0.356 ± 0.005	3.806 ± 0.002	0.514 ± 0.006	3.805 ± 0.002	2.762 ± 0.010

Notes. The properties in this table were calculated from the Fourier coefficients for the light curves using the equations described in Kuehn et al. (2011). The mean values were computed using only the first five stars, which have the lowest D_max values (Table 4).

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The mean metallicity of the RRab stars is [Fe/H]_J95 = −1.43  ±  0.02 which is [Fe/H]_ZW84 = −1.61  ±  0.02 on the Zinn & West (1984) scale and [Fe/H]_UVES = −1.55  ±  0.04 This value is in similar to the metallicity of [Fe/H]_UVES ≃ −1.61 found by Mackey & Gilmore (2004). On the other hand, the relation from Morgan et al. (2007) gives a metallicity for the RRc stars of [Fe/H]_ZW84 = −1.75  ±  0.03, [Fe/H]_UVES = −1.73  ±  0.06, which is more metal-poor than the values obtained from the RRab stars and the literature, but still within the 0.2 dex error estimation in their empirical relation. While this difference in metallicity could be caused by errors in the Fourier analysis, the fact that the other physical properties obtained for the RRc stars are consistent with expectations lends support to the validity of the obtained Fourier coefficients.

The Fourier parameters and physical properties for the RRc star V12 are listed in Tables 5 and 7 but were not included when calculating the average physical properties for the RRc stars in Reticulum. The physical properties calculated for V12 show a marked difference from the properties of the other RRc stars in the cluster; we obtained a metallicity of [Fe/H]_ZW84 = −1.98 for V12, more metal-poor than the other RRcs, and a mass of M/M_☉ = 0.89 which is very large for an RRc. The amplitudes of V12 in all three filters are significantly smaller than for the other RRc stars in the cluster, suggesting possible blending. V12 is slightly brighter in V and B and is bluer than the other RRc stars in the cluster, supporting the possibility that it is blended with a faint blue companion. Blending with a nearby star would alter the shape of the light curve and thus explain the unusual values obtained for the physical properties of V12.

The absolute magnitude–metallicity relationship from Catelan & Cortés (2008) is used to provide the absolute magnitude of the RR Lyrae stars in Reticulum. The disagreement between the metallicities for RRab and RRc stars raises an issue as to which metallicity to use for calculating the absolute magnitude. Since the metallicity obtained from the RRab stars is consistent with what has been reported in the literature and is drawn from a larger number of stars, that value is used, [Fe/H]_ZW84 = −1.61  ±  0.02. This value gives an absolute magnitude of M_V = 0.61  ±  0.20. The average magnitude of the RRab stars, 〈V〉 = 19.064  ±  0.008, and the reddening value of E(B − V) = 0.016 from Schlegel et al. (1998) are used, along with a standard extinction law of A_V/E(B − V) = 3.1, to obtain a reddening-corrected distance modulus of (m − M)₀ = 18.40  ±  0.20, which agrees with the value of 18.39  ±  0.12 found by Ripepi et al. (2004). This is shorter than the distance modulus of (m − M)_LMC = 18.44  ±  0.11 that Catelan & Cortés (2008) derived for the LMC, though the two distance moduli agree within the errors. This is not necessarily a surprise as Reticulum is widely separated from the disk of the LMC, having a location that is about 11 degrees from the center of the LMC (Walker 1992a).

We can also use the period–metallicity–luminosity relationship for the I-band from Catelan et al. (2004) to determine the distance modulus. We used the Fourier derived individual metallicities for the stars that we were able to successfully fit; we used the average metallicity of [Fe/H]_ZW84 = −1.61 for the remaining stars. Using the E(B − V) = 0.016 from Schlegel et al. (1998) and a standard extinction law of A_I/A_V = 0.482 gives an I-band extinction of A_I = 0.024. This gives a reddening-corrected distance modulus of (m − M)₀ = 18.47  ±  0.06 which is longer than value obtained from the V-band magnitudes; the smaller error bar for the I-band based distance modulus is due to there being no systematic zero point uncertainty in the I-band.

Despite the changes in color during the pulsation cycle of RR Lyrae stars, RRab stars show a very small range of intrinsic B − V and V − I colors during their minimum light phase (Mateo et al. 1995). We compare the B − V and V − I colors of our RRab stars to the expected colors in order to calculate the reddening to the cluster. We calculate the expected B − V colors of the RRab stars using the method devised by Sturch (1966) which gives the expected color as a function of period and metallicity. We use the calibration of Sturch's method from Walker (1992b) which gives the color excess as

$\begin{eqnarray} E(B-V) &=& (B-V)_{{\rm min}}-0.336-0.24P\nonumber \\ && -0.056{\rm [Fe/H]_{ZW84}} \end{eqnarray} \tag{ 2 }$

where P is the period of the star in days. Table 8 lists the (B − V)_min colors and the reddening, E(B − V) for each of the RRab stars in Reticulum. The Fourier derived individual metallicities were used for the stars for which they were successfully determining, we used the average cluster metallicity of [Fe/H]_ZW84 = −1.61 for the remaining RRab stars. The average reddening is E(B − V) = 0.05  ±  0.01 which is larger than the E(B − V) = 0.016 from Schlegel et al. (1998) but in agreement with the value of E(B − V) = 0.05  ±  0.02 found by Walker (1992a) using the same method. Unlike the expected B − V color, the expected V − I color at minimum light does not appear to vary significantly with the period or metallicity of the RRab and we use the value of (V − I)_{0, min} = 0.58  ±  0.02 from Guldenschuh et al. (2005); Table 8 lists the (V − I)_min colors and the reddening, E(V − I) for each of the RRab stars in Reticulum. The average reddening from the RRab stars is E(V − I) = −0.01  ±  0.02; this is less than the reddening value of E(V − I) = 0.026 that is expected based on the reddening from the Schlegel dust maps.

Table 8 shows that V06 has an E(B − V) that is significantly larger than the values for any of the other RRab stars and an E(V − I) value that is one the smallest. V06 potentially shows the Blazhko effect and the light curve modulations that result from this effect could potentially make impact its color at minimum light. If we exclude V06 from our calculations, we obtain an E(B − V) = 0.04  ±  0.01 and an E(V − I) = −0.01  ±  0.01; moving both values closer to what is expected from the Schlegel values.

Our color–magnitude diagram (CMD) is compared to theoretical isochrones from the Princeton–Goddard–PUC (PGPUC) stellar evolutionary code (Valcarce et al. 2012). The RR Lyrae distance modulus of (m − M)_V = 18.45 mag is adopted; assuming a reddening of E(B − V) = 0.016 Schlegel et al. (1998), the true distance modulus is (m − M)_{V, 0} = 18.40 mag, as discussed in Section 5. Although there have been some suggestions that the reddening toward Reticulum is larger than that adopted here (e.g., Mackey & Gilmore 2004), as shown below, we find little evidence to support a larger reddening value than reported by Schlegel et al. (1998); the reddening value obtained from the B − V colors of the full sample of the RRab stars at minimum light does support the larger reddening value of Mackey & Gilmore but the V − I colors do not support such a large reddening. Isochrones with a "normal" [α/Fe] ratio (e.g., Mateluna et al. 2012), Y = 0.245 and Z = 0.0006 (corresponding to [Fe/H]_UVES ∼ −1.61 dex) are overplotted.

Figure 8 shows that the best fit isochrones have ages of ∼14  ±  2 Gyr, consistent with the ages of other LMC globular clusters (Olsen 1999; Mackey & Gilmore 2004; Bekki et al. 2008). The observed red giant branch (RGB) fits the CMD well. In contrast, a larger reddening value would shift the isochrones to the red. A smaller [α/Fe] or a more metal-poor [Fe/H] would shift the isochrones to the blue, as would a smaller reddening value. We therefore see no need to adopt a larger value of reddening than that that found by Schlegel et al. (1998). A small reddening value is also in agreement with the E(B − V) = 0.03 derived by Walker (1992a). We believe Figure 8 provides evidence that our derived RR Lyrae distance modulus fits the CMD remarkably well and supports an old age of Reticulum.

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Figure 9 shows the V, (V − I) CMD for Reticulum centered on the RR Lyrae instability strip. A zero-age horizontal branch (ZAHB) from the BaSTI HB tracks (Pietrinferni et al. 2004, 2006) with Z = 0.0006 is over-plotted, as well as the BaSTI evolutionary tracks for 0.65 M_☉, to 0.68 M_☉ HB stars. As shown by Gallart et al. 2005, the deviation of the mean RR Lyrae magnitudes from the ZAHB is δ(V_ZAHB − 〈V〉)_RR ∼ 0.1 mag at the metallicity of Reticulum, and hence we adopt (m − M)_{V0, ZAHB} = 18.50 mag. The BaSTI tracks indicate that most of the Reticulum RR Lyrae stars have a mass range of 0.65–0.68 M_☉. These RR Lyrae masses are a little larger than those found from the Fourier decomposition of the RRc stars (see Table 7), although the mass of V28 derived from the BaSTI tracks and from the Fourier decomposition technique agrees remarkably well. We note that changing (m − M)_{V0, ZAHB} does not affect the derived RR Lyrae masses. In contrast, a change in Z affects the theoretical RR Lyrae masses in a sense that a more metal-rich Z shifts the RR Lyrae masses to smaller values.

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The average periods for the RR Lyrae stars in Reticulum are 〈P_ab〉 = 0.552 days and 〈P_c〉 = 0.325 days. The 22 RRab, 4 RRc, and 6 RRd stars give the cluster a number fraction of N_{c + d}/N_{c + d + ab} = 0.31. The average periods for the RRab and RRc stars strongly indicate an Oo-I classification and, while the number fraction is high, it is still consistent with the cluster being an Oo-I object. The minimum period for an RRab star in Reticulum is P_{ab, min} = 0.46862 days, which is also consistent with an Oo-I classification for Reticulum (Catelan et al. 2013).

Figure 10 shows the V, B, and I band period–amplitude diagrams for Reticulum. Both diagrams show that the RRab stars cluster along the line that indicates the typical location for RRab stars in Oo-I clusters. There is more scatter in the positions of the RRc stars but most of them still are located near the Oo-I locus, confirming the classification of Reticulum as an Oo-I object.

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We have conducted a photometric study of the Reticulum globular cluster in order to identify and classify the variable stars in that cluster; our data set consists of 228 V, 222 B, and 80 I images, making it the largest such data set on Reticulum. We found a total of 32 RR Lyrae stars (22 RRab, 4 RRc, and 6 RRd) in the cluster. While all 32 stars had been previously discovered, we were able to discover secondary pulsation periods in 2 stars that had previously been classified as RRc stars.

We calculated Fourier parameters for a sub-sample of the RRab and RRc stars and used these to determine the physical properties of the RR Lyrae stars in Reticulum for the first time. A future paper in this series will compare these physical properties to those obtained for other clusters in order to look at the differences between clusters of different Oosterhoff type.

We calculated a reddening-corrected distance modulus of (m − M)₀ = 18.40  ±  0.20 which agrees with the literature values for Reticulum.

The V, (V − I) CMD of the cluster was used to calculate an age of ∼14  ±  2 Gyr for Reticulum, consistent with the age of the other old globular clusters in the LMC. The CMD, along with the V − I colors of the RRab stars at minimum light, do not support the suggestions that the reddening toward Reticulum is larger than the value of E(B − V) = 0.016 from Schlegel et al. (1998); however, the B − V colors of the RR Lyrae at minimum light support the larger reddening value of E(B − V) = 0.04  ±  0.01 from Mackey & Gilmore (2004).

The average periods for the RRab and RRc stars indicate that Reticulum is an Oo-I cluster. This is confirmed by the location of the RRab and RRc stars on the Bailey diagram and the location of the RRd stars on the Petersen diagram.

Support for H.A.S. and C.A.K. is provided by NSF grants AST 0607249 and AST 0707756. M.C. and J.B. are supported by the Chilean Ministry for the Economy, Development, and Tourism's Programa Iniciativa Científica Milenio through grant P07-021-F, awarded to the Milky Way Millennium Nucleus, and by the BASAL Center for Astrophysics and Associated Technologies (PFB-06). M.C. is also supported by Proyecto Fondecyt Regular 1110326 and by Proyecto Anillo ACT-86. J.B. is also supported by Proyecto Fondecyt Regular 1120601. Y.B.J. was supported by the KASI (Korea Astronomy and Space Science Institute) grant 2013940000. We would like to thank an anonymous referee for helpful comments which improved this paper.