Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud: II. Relative ages and distances for six ancient globular clusters
R. Wagner-Kaiser, Dougal Mackey, Ata Sarajedini, Brian Chaboyer, Roger E. Cohen, Soung-Chul Yang, Jeffrey D. Cummings, Doug Geisler, Aaron J. Grocholski
MMon. Not. R. Astron. Soc. , 1– ?? (2002) Printed 7 April 2018 (MN L A TEX style file v2.2)
Exploring the nature and synchronicity of early clusterformation in the Large Magellanic Cloud: II. Relative agesand distances for six ancient globular clusters
R. Wagner-Kaiser , Dougal Mackey , Ata Sarajedini , , Brian Chaboyer ,Roger E. Cohen , Soung-Chul Yang , Jeffrey D. Cummings , Doug Geisler ,Aaron J. Grocholski University of Florida, Department of Astronomy, 211 Bryant Space Science Center, Gainesville, FL, 32611 USA Australian National University, Research School of Astronomy & Astrophysics, Canberra, ACT 2611, Australia Florida Atlantic University, Department of Physics, 777 Glades Rd, Boca Raton, FL, 33431 USA Dartmouth College, Department of Physics and Astronomy, Hanover, NH, 03755, USA Space Telescope Science Institute, Baltimore, MD 21218, USA Korea Astronomy and Space Science Institute (KASI), Daejeon 305-348, Korea Center for Astrophysical Sciences, Johns Hopkins University, Baltimore MD 21218 Departamento de Astronomia, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile Department of Physics and Astronomy, Swarthmore College, Swarthmore, PA 19081, USA
ABSTRACT
We analyze Hubble Space Telescope observations of six globular clusters in the LargeMagellanic Cloud from program GO-14164 in Cycle 23. These are the deepest availableobservations of the LMC globular cluster population; their uniformity facilitates aprecise comparison with globular clusters in the Milky Way. Measuring the magnitudeof the main sequence turnoff point relative to template Galactic globular clustersallows the relative ages of the clusters to be determined with a mean precision of8.4%, and down to 6% for individual objects. We find that the mean age of our LMCcluster ensemble is identical to the mean age of the oldest metal-poor clusters in theMilky Way halo to 0.2 ± ± Key words: globular clusters: individual: NGC 1466 NGC 1841 NGC 2210 NGC2257 Reticulum Hodge 11, Magellanic Clouds.
Globular clusters (GCs) have long been a crucial tool to un-derstand star formation processes in the early Universe aswell as the buildup of galactic halo populations. In recentyears, high-precision photometry from the Hubble SpaceTelescope (HST) has facilitated accurate and consistentanalyses of such clusters. In particular, the ACS GalacticGlobular Cluster Treasury Program has provided a deep anduniform photometric database for a large sample of GalacticGCs. Its enduring contribution to the literature includes awide range of studies of GC properties, such as mass func-tions, binary fractions, and horizontal branch morphology,among others (Dotter et al. 2010; Mar´ın-Franch et al. 2009; Milone et al. 2012; Paust et al. 2010; Sarajedini et al. 2007;Wagner-Kaiser et al. 2017).However, to fully untangle the nature and role of GCsin the formation and evolution of galaxies, it is necessary tolook beyond the thoroughly-studied Galactic globular clus-ter (GGC) system. The population of old globular clustersin the Large Magellanic Cloud (LMC) provides the logicalnext step in expanding the sample of targets for which ex-tremely high quality photometry can be obtained. We haverecently obtained very deep, uniform HST observations ofsix ancient LMC clusters – NGC 1466, NGC 1841, NGC2210, NGC 2257, Hodge 11, and Reticulum – resulting inphotometry extending well down their main sequences forthe first time (Mackey et al. 2017). We can now begin to c (cid:13) a r X i v : . [ a s t r o - ph . GA ] J u l Wagner-Kaiser et al. explore with unprecedented precision how the timing of theearliest epoch of star cluster formation in the LMC com-pares to that in the Milky Way, and search for evidence ofan age spread and/or a well-defined age-metallicity relation-ship (AMR) in the ancient LMC cluster system.These goals are of particular significance because re-cent proper motion measurements have demonstrated thatthe Magellanic system is likely on its first passage aboutthe Milky Way (e.g., Kallivayalil, van der Marel & Alcock2006; Kallivayalil et al. 2013; Besla et al. 2007). The impli-cation is that at the time of globular cluster formation thetwo galaxies were widely separated. Moreover, the large dif-ference in halo mass and observed star-formation historiesbetween the LMC and the Milky Way suggests that theirinternal environments are likely to have been substantiallydifferent from each other. Thus, examining the relative agesof the oldest GCs in the LMC and the Milky Way allowsus to begin to quantitatively probe how the earliest epochsof star formation might vary as a function of location andenvironment.The past several decades have seen a strong push tobetter understand the chronology of globular cluster forma-tion in the LMC. Brocato et al. (1996) studied NGC 1786,NGC 1841 and NGC 2210 and determined ages to ∼ ∼ ∼ . − ≈ ω Centauri, Bedin et al. 2004), asthe main effects of multiple populations are concentratedin the blue-uv part of the spectrum (e.g. Sbordone et al.2011). Thus, approximating both our LMC targets and thereference Galactic GCs as single populations for the presentanalysis is a valid approach.This paper is arranged as follows. In Section 2, we dis-cuss the dataset and the relevant photometry. We analyzethe clusters to derive their relative ages in Section 3 anddetermine distances via subdwarf and HB fitting in Section4. Section 5 lists our conclusions.
The data for our analysis come from HST Cycle 23 programGO-14164 (PI: Sarajedini). Deep imaging was obtained forsix ancient LMC globular clusters – NGC 1466, NGC 1841,NGC 2210, NGC 2257, Hodge 11, and Reticulum – throughthe F606W and F814W filters with the Advanced Camerafor Surveys (ACS) Wide Field Channel (WFC), and throughthe F336W filter with the Wide Field Camera 3 (WFC3)Ultraviolet and Visual (UVIS) channel. In this paper wewill consider only the F606W and F814W data. These sixclusters were chosen as they comprise the complete sam-ple of LMC globular clusters outside the confusion-limitedcrowded stellar fields of the LMC bar region, as well as span-ning a range of galactocentric radius, luminosity, and struc-ture. The locations of the clusters relative to the LMC areshown in Figure 1.Full details of the data acquisition and photometricanalysis can be found in Mackey et al. (2017); here we pro-vide a brief description for completeness. Each cluster wasobserved for two orbits in the F606W filter resulting in either13 or 14 images (depending on the visibility of the target),and for three orbits in the F814W filter resulting in either19 or 20 images. Of these image sets, two each per filterper cluster were short exposures ( ≈ −
70s per frame)while the remainder were much longer ( ∼ − dolphot software package (e.g., Dol-phin 2000) to photometer the images, performing one runon the long exposures and one on the short exposures, andthen merging the two quality-filtered output catalogues. To c (cid:13) , 1– ?? elative ages and distances for LMC GCs Figure 1.
The LMC and surrounding region. The six clustersfrom HST Cycle 23 program GO-14164 (PI: Sarajedini) are indi-cated on the image. ensure that our photometry was minimally affected by im-perfect charge transfer efficiency (CTE) in the ACS/WFCchips, we utilised the images from the calacs pipeline cor-rected using the pixel-based algorithm of Anderson & Be-din (2010). Our final measurements are on the calibratedVEGAmag scale of Sirianni et al. (2005). For each clusterthe photometry reaches from the top of the red-giant branch(RGB) to more than 4 magnitudes below the main sequenceturn off point (MSTOP). The signal-to-noise ratio aroundthe HB level is ∼ ∼
300 perstar, and remains at at least ∼
30 four magnitudes fainterthan the MSTOP.For the LMC clusters analyzed herein, we adopt metal-licities as summarized in Table 1. The metallicity measure-ments are largely from high-resolution spectroscopic obser-vations of these clusters, with the exception of NGC 1466.NGC 1466 has a photometric metallicity derived from RRLyrae observations, and at present lacks spectroscopic mea-surements except for a handful of individual stars. Column2 notes the metallicities from the cited references in col-umn 3, which are provided in the metallicity scale noted incolumn 4. In order to adopt a consistent metallicity scalethroughout this work, these [Fe/H] measurements are con-verted to the CG97 (Carretta & Gratton 1997) metallicityscale, with the result provided in the final column of Ta-ble 1; use of the CG97 metallicity scale provides consistencywith the Mar´ın-Franch et al. (2009) study. The errors in thetransformed metallicities include an assumed 0.2 dex mea-surement uncertainty as well as the propagated uncertaintiesof the transformation equations (Carretta & Gratton 1997;Carretta et al. 2009).
To determine relative ages for the LMC clusters, we fol-low closely the procedure developed by Mar´ın-Franch et al.(2009) for their study of Galactic globular cluster relativeages. By measuring differences in the MSTOP apparentmagnitude with respect to reference clusters, anchoring theapparent magnitudes to a distance scale, and comparing toexpectations from theory, we determine precise relative agesfor the LMC clusters. The details of our methodology areare outlined below. Throughout this process, we adopt theCG97 metallicity scale as discussed in Section 2; the CG97scale is also used in Mar´ın-Franch et al. (2009).A mean ridge line (MRL) is derived to representthe fiducial line for each cluster. As in Mar´ın-Franchet al. (2009), we determine mean ridge lines for theF606W − F814W, F814W CMD because the sub-giantbranch is more vertical and the results are improved with re-spect to using F606W as the magnitude. However, in the restof the analysis, the F606W − F814W, F606W CMD is usedto derive the MSTOP in F606W magnitude (Mar´ın-Franchet al. 2009). To determine the MRL, we use a moving bin inmagnitude with a size of 0.5 mag and steps of 0.02 magni-tude. The MRL location is determined from the average ofeach bin, rejecting 3- σ outliers to determine a MRL. We re-peat this MRL-derivation process, shifting the bin locationseach time, to lessen dependence of the result on the bin cen-ters. Over five iterations, the derived MRLs are combined; asmoothed radial basis function is used to represent the finalfiducial line.The magnitude of the MSTOP is found by taking thebluest point of a spline fit locally to the MRL in the MSTOPregion. The MSTOP location is re-determined ten times,each time offsetting the MRL bins by 0.01 mag; the adoptedMSTOP magnitude for the cluster is calculated as the meanof these ten determinations of the bluest point of the spline.Through this process, we determine apparent magnitudes inF606W of the MSTOP for the six LMC clusters, providedin the fourth column of Table 2.Because this is a relative analysis, the MSTOPs ofthe LMC clusters need to be compared to referenceMSTOP locations. Two particular regions along the fidu-cial lines were designated by Mar´ın-Franch et al. (2009)to be minimally affected by age; specifically, on the mainsequence (M MSTOP, F606W +3 (cid:54) m (cid:54) M MSTOP, F606W +1.5)and on the red giant branch (M
MSTOP, F606W -2.5 (cid:54) m (cid:54) M MSTOP, F606W -1.5). Because these RGB and MS regionsare largely unaffected by age, a comparison of MSTOP mag-nitude between the reference and MRL gives an indicationof the relative age of two clusters. The MRL of these twolocations are used to “shift” the entire MRL of a referencecluster in color and magnitude to match the same regions ineach LMC cluster. In doing so, any differences in line of sightreddening between the clusters are automatically accountedfor, making the age determinations free of assumptions ofdistance or reddening. By using the GGC clusters as refer-ence clusters, we thus determine the differences in MSTOPmagnitudes with respect to the LMC clusters.We use the same GGC reference clusters as Marin-Franch et al. (2009) across the following metallicity ranges:NGC 6981 (–1.3 (cid:54) [Fe/H] < –1.1), NGC 6681 (–1.5 (cid:54) [Fe/H] < –1.3), NGC 6101 (–1.8 (cid:54) [Fe/H] < –1.5), and NGC 4590 c (cid:13) , 1– ?? Wagner-Kaiser et al.
Table 1.
Assumed metallicities for our target LMC clusters
Cluster [Fe/H] ref
Reference Original Scale [Fe/H] CG NGC 1466 -1.9* Walker (1992b) ZW84 -1.70 ± ± ± ± ± ± ∗ Measurement only given to one decimal precision by Walker (1992b). The propagation of error fromthe conversion of the measurement from the ZW84 scale to the CG97 scale leads to what a generousuncertainty in metallicity. (–2.3 (cid:54) [Fe/H] < –1.8). We use a least squares approach tominimize offsets between the MRL of the reference clustersand the LMC clusters in the intervals defined by Mar´ın-Franch et al. (2009) and described above. The result of thisprocess is demonstrated in Figure 2, where each LMC clus-ter (black dotted lines) is compared to the relevant GGCreference (blue solid lines). The fiducials of the GGC refer-ence clusters are shifted to match the LMC clusters in theregions of the CMD discussed above; these regions are alsohighlighted in Figure 2. The MSTOP for the LMC (green)and reference Galactic cluster (maroon) are also indicated inthe plot. While the fiducials for the LMC clusters are largelyconsistent with their GGC reference cluster counterpart, wenote that there is a slight mismatch between the NGC 1841and NGC 4590 fiducials on the upper red giant branch. Thisdoes not appear to be driven by our approach but may bedue to differing metallicities or [ α /Fe] abundances betweenthe two clusters.As in Mar´ın-Franch et al. (2009), shifts among the setof GGC reference clusters are determined by matching MRLfor the reference clusters in adjacent metallicity ranges. Theabsolute MSTOP magnitude in F606W for NGC 6752 of3.87 ± (cid:54) –1.5, we find a minimal mean offset ofthe MSTOP magnitudes of 0.01 ± α /Fe] comparable to the enhancementseen in the Galactic globular clusters (Mucciarelli, Origlia &Ferraro 2010). The grid in Figure 3 is generated assumingan α -enhanced model ([ α /Fe] = 0.2). The grid of Dotteret al. (2008) DSED isochrones are used to derive MSTOPin the same iterative process as described above - fitting a spline locally to the MSTOP and determining the bluestpoint. This facilitates a comparison between the calibratedMSTOP magnitudes from the observed clusters to the the-oretical models to determine ages. We interpolate betweenthe models to determine ages for the six LMC clusters, pre-sented in Table 2.The relative ages we derive are consistent with the LMCclusters having similar properties to the old, inner haloMilky Way clusters. However, we note that the metallici-ties of the LMC clusters are not fully agreed upon in theliterature; if our adopted metallicities are inaccurate thenour conclusions on the relative ages of these clusters mayneed re-examination. We estimate a change of 0.1 dex inmetallicity leads to a change of up to ≈ ± (cid:54) –1.5),the mean age is 12.0 ± ± c (cid:13) , 1– ?? elative ages and distances for LMC GCs Figure 2.
A comparison of the LMC fiducial sequences (dotted black lines) to the shifted reference Galactic cluster fiducials (solid bluelines, see Table 2). The intervals upon which the least-squares match is performed are indicated by the thick regions for each fiducial.The location of the LMC MSTOP is indicated by the open green circle and by the maroon triangle for the Galactic reference clusterMSTOP location.
Table 2.
Relative ages for our LMC cluster sample
Cluster [Fe/H] CG a Ref. Cluster b m F606W, MSTOP M F606W, MSTOP
Relative Age (Gyr) Absolute Age (Gyr)
NGC 1466 -1.70 NGC 6101 22.62 ± ± +0 . − . +1 . − . NGC 1841 -2.02 NGC 4590 22.61 ± ± +0 . − . +1 . − . NGC 2210 -1.45 NGC 6681 22.34 ± ± +1 . − . +1 . − . NGC 2257 -1.71 NGC 6101 22.32 ± ± +1 . − . +1 . − . Hodge11 -1.76 NGC 6101 22.56 ± ± +0 . − . +1 . − . Reticulum -1.57 NGC 6101 22.31 ± ± +0 . − . +2 . − . a From Table 1. b As in Mar´ın-Franch et al. (2009). to also be very similar to those in our Galaxy (Mackey& Gilmore 2004a; Mar´ın-Franch et al. 2009). Terzan 8 isthe one cluster in the Sagittarius dwarf galaxy that is moremetal-poor than -1.5 on the CG97 scale. Mar´ın-Franch et al.(2009) find the age of this cluster to be within 0.5 +/- 0.5Gyr of the mean value we quote above. However, this trenddoes not necessarily seem to be consistent in the Small Mag-ellanic Cloud (SMC). While NGC 121 is the only “old”cluster in the SMC, the majority of recent work suggestsit is younger than the oldest Galactic clusters despite hav- ing similar metallicity; estimates put the age in the rangeof 10.5 to 11.8 Gyr, depending on study and model choice(Glatt et al. 2008; Dolphin et al. 2001; Mighell, Sarajedini &French 1998). However, NGC 121 has not been measured onthe same relative age scale we use herein and a direct com-parison is incomplete in this respect. Although the MWG,LMC, and Sagittarius appear to have closely synchronousinitial metal-poor GC formation, the example of the SMCindicates that this may not be universal.The ages derived here are relative ages, not absolute c (cid:13) , 1–, 1–
NGC 1466 -1.70 NGC 6101 22.62 ± ± +0 . − . +1 . − . NGC 1841 -2.02 NGC 4590 22.61 ± ± +0 . − . +1 . − . NGC 2210 -1.45 NGC 6681 22.34 ± ± +1 . − . +1 . − . NGC 2257 -1.71 NGC 6101 22.32 ± ± +1 . − . +1 . − . Hodge11 -1.76 NGC 6101 22.56 ± ± +0 . − . +1 . − . Reticulum -1.57 NGC 6101 22.31 ± ± +0 . − . +2 . − . a From Table 1. b As in Mar´ın-Franch et al. (2009). to also be very similar to those in our Galaxy (Mackey& Gilmore 2004a; Mar´ın-Franch et al. 2009). Terzan 8 isthe one cluster in the Sagittarius dwarf galaxy that is moremetal-poor than -1.5 on the CG97 scale. Mar´ın-Franch et al.(2009) find the age of this cluster to be within 0.5 +/- 0.5Gyr of the mean value we quote above. However, this trenddoes not necessarily seem to be consistent in the Small Mag-ellanic Cloud (SMC). While NGC 121 is the only “old”cluster in the SMC, the majority of recent work suggestsit is younger than the oldest Galactic clusters despite hav- ing similar metallicity; estimates put the age in the rangeof 10.5 to 11.8 Gyr, depending on study and model choice(Glatt et al. 2008; Dolphin et al. 2001; Mighell, Sarajedini &French 1998). However, NGC 121 has not been measured onthe same relative age scale we use herein and a direct com-parison is incomplete in this respect. Although the MWG,LMC, and Sagittarius appear to have closely synchronousinitial metal-poor GC formation, the example of the SMCindicates that this may not be universal.The ages derived here are relative ages, not absolute c (cid:13) , 1–, 1– ?? Wagner-Kaiser et al.
Figure 3.
The magnitude of the MSTOP of the LMC clus-ters (green circles) according to their assumed metallicities. TheMSTOP determined for Galactic globular clusters from Mar´ın-Franch et al. (2009) are plotted as blue triangles. The solid linesdelineate the MSTOP from the theoretical models (Dotter et al.2008) from 6 Gyr (upper right) to 15 Gyr (lower left) at 0.5Gyr intervals, alternating solid and dashed lines for clarity. TheGalactic reference clusters are indicated by the colored squares.The theoretical grid assumes [ α /Fe] = 0.2. ages. To compare ages directly with previous studies, a ref-erence absolute age must be adopted. From the absolute agesof O’Malley, Gilligan & Chaboyer (2017), we use the meanabsolute age of the GGC reference clusters to calibrate ourLMC relative ages to absolute ages. Specifically, O’Malley,Gilligan & Chaboyer (2017) found ages of 12.4 ± ± ± ± Table 3.
GGC HB Calibration Clusters
Cluster [Fe/H] CG E(B–V) Distance Modulus
NGC 5272 -1.32 ± ± ± ± ± ± halo; likely in-situ clusters). Although there is not sufficientevidence here to make a strong conclusion, it is certainlyof interest to pursue in future work in order to better un-derstand the formation history of the LMC and its globularcluster system. To obtain distance estimates from observations of the hor-izontal branch (HB), fiducials of the HBs are created forthe LMC clusters and compared to several reference GGCclusters. We initially estimate the cluster HB fiducial by eyeand fit a cubic spline to the points. To iterate on this andobtain a better estimate, the HB is binned in intervals ofcolor of 0.04 along the initial spline, overlapping by 0.01. Ineach color bin, using stars within a 3- σ range of the initialspline, we determine the average magnitude of the HB inthat bin. These results are used to redetermine the HB witha cubic spline, as seen by the solid blue line in Figure 5 foreach LMC cluster, where the included HB stars are indi-cated (cyan points). We note that while blue straggler starsor field stars may contaminate the included HB stars, theirlow frequency is unlikely to skew the estimated HB fiducials.This process is repeated for six GGC reference clustersto serve as comparisons to the HB fiducials of the LMCclusters. These Galactic clusters are chosen to (i) have lowreddening, (ii) have a populated HB, (iii) have availablephotometry in the same HST filters from Sarajedini et al.(2007). Using the same method described above, we deriveHB fiducials for two moderately metal-rich Galactic clusters(NGC 5272, NGC 6584), two intermediate metallicity clus-ters (NGC 5024, NGC 6809), and two metal-poor clusters(NGC 4590, NGC 6341). We adopt the foreground redden-ings and distance moduli from the Harris (2010) catalogue for these reference clusters; these values are listed in Ta-ble 3. We note that Harris (2010) derive their distancesfrom the assumption that M V (HB) = 0.16 [Fe/H] + 0.84and their E(B–V) from an average of several measurements;we assume a reddening law of R V =3.1 (Cardelli, Clayton& Mathis 1989). Additionally, the Harris (2010) cataloguemetallicities are on the C09 scale; for consistency (as in Sec-tion 2) we convert these to the CG97 scale, and these valuesare listed in Table 3.In order to obtain distance measurements, we assume c (cid:13) , 1– ?? elative ages and distances for LMC GCs Figure 4.
The age-metallicity relation for the Galactic globular clusters and the LMC clusters, compared. The leftmost panel showsages from VandenBerg et al. (2013) (red squares), the middle panel shows ages from Dotter et al. (2010) (cyan diamonds), and the agesfrom Mar´ın-Franch et al. (2009) (blue triangles). Our results may be compared directly to Mar´ın-Franch et al. (2009), and qualitativelywith VandenBerg et al. (2013) and Dotter et al. (2010), who employ different methods and age calibrations.
Figure 5.
Fiducial horizontal branches for the six LMC clusters in our sample. In each panel, the HST photometry is plotted in black,the included stars are the larger cyan points, and the fiducial spline (see text for details) is indicated by the solid blue line. The clustername and number of stars (N*) included in the fit are indicated in the lower left of each panel. reddenings for the LMC clusters from Walker (1992, 1993),as indicated in Table 4. While an assumption of redden-ing is necessary to derive distances, the accuracy of theadopted reddening values could plausibly affect our distanceestimates. However, the reddening estimates we adopt arefound to differ on average from the foreground reddening es- timates of Schlegel, Finkbeiner & Davis (1998) and Schlafly& Finkbeiner (2011) by ∼ c (cid:13) , 1– ?? Wagner-Kaiser et al.
Figure 6.
Fiducial horizontal branches for the reference Galactic globular clusters in our sample. In each panel, the HST photometry isplotted in black, the included stars are the larger cyan points, and the fiducial spline (see text for details) is indicated by the solid blueline. The cluster name and number of stars (N*) included in the fit are indicated in the lower left of each panel.
GGC distances from Table 3, determines the distance foreach LMC cluster. Each LMC cluster has its distance de-rived with respect to two reference GGC cluster fiducials, asindicated in the fourth column of Table 4. The final columnof this table provides the average of those two distances.The cited uncertainties on the derived distances in Ta-ble 4 incorporate the scatter (standard deviation in magni-tude) and number of stars used to derive each LMC fiducial,the scatter and number of stars for the GGC fiducials, andthe errors from the least-squares fitting between the GGCand LMC fiducials. Through this process, we obtain an average distance of18.59 ± µ = 18.49 ± c (cid:13) , 1– ?? elative ages and distances for LMC GCs Table 4.
Distance Estimates: ZAHB
Cluster [Fe/H] CG a Assumed E(B–V) b E(B–V) c Reference HBs µ ZAHB
NGC 1466 -1.70 0.09 0.07 NGC 5024, NGC6809 18.67 ± ± ± ± ± ± a As in Table 1. b Absorptions adopted from Walker (1992, 1993), assuming R V =3.1. c Absorptions from Schlegel, Finkbeiner & Davis (1998) for comparison, assuming R V =3.1. Figure 7.
In each panel, the HST photometry is plotted in black. The shiftedHB fiducials of the reference clusters are indicated by thedashed blue and magenta lines. The solid cyan line indicates the fiducial of the LMC cluster.
As the most well-understood phase of stellar evolution, fit-ting of main-sequence stars offers an opportunity to pro-vide excellent distance measurements. Using parallaxes andhighly precise HST photometry of local subdwarfs from GO-11704 (Chaboyer et al. 2017), we leverage the accuratelymeasured subdwarf absolute magnitudes and the clean mainsequences of the six LMC clusters to determine distances.Details of the four subdwarfs in the metallicity range of theLMC clusters are presented in Table 5. The magnitudes andcolors of these stars are adjusted for their individual redden-ing, noted in Column 5.In order to compare the observed main sequences of the LMC clusters to the photometry for the local subwarfs, it isnecessary to adjust the colors of the latter to account for thevarious metallicities of the clusters and the subdwarfs. First,the metallicities of the individual stars are adjusted for theirunique [ α /Fe] abundances using the following relation fromSalaris, Chieffi & Straniero (1993) and Dotter et al. (2010).[ M/H ] = [
F e/H ] + log(0 . × [ α/Fe ] + 0 . < M F W < − F814W c (cid:13) , 1–, 1–
F e/H ] + log(0 . × [ α/Fe ] + 0 . < M F W < − F814W c (cid:13) , 1–, 1– ?? Wagner-Kaiser et al. color of the subdwarf to the reference metallicity of each ofthe clusters. The reference metallicity of each LMC clus-ter is also corrected as in Equation 1 for an assumed α -enhancement of [ α /Fe] = 0.2.Assuming a reddening for each LMC cluster (Walker1992a, 1993, see Table 6), a main sequence fiducial is fit witha power law for cluster stars between an absolute F606Wmagnitude of 4.5 and 7 in overlapping magnitude bins of 0.1mag. The fiducials are shown in the panels of Figure 8 asred curves for each cluster. The fiducial is shifted via leastsquares to minimize the offsets of the HST parallax starsfrom the fiducial line in magnitude. The resulting distancemoduli are given in the final column of Table 6, with thequoted error representing the uncertainty in the fiducial fit.We find an average distance modulus to the LMC of18.40 ± ± ± σ but discrepant. This is likely due to different underlying as-sumptions, as discussed further at the end of this section.From the HB and subdwarf distances, we derive an averagedistance to the LMC of 18.52 ± ± . D is the distance to any location on the diskplane; for our case, this is the distance to each cluster. Weassume the LMC disk to be inclined to the plane of thesky by the angle i around an axis at position angle θ . θ is measured counterclockwise from the west; to align withusual astronomical convention, Θ is defined the position an-gle from the north (Θ = θ - 90). These values are adoptedfrom van der Marel & Cioni (2001); we note that Grocholskiet al. (2007) explored a variety of geometries from other pastwork, finding differences in the resulting distance of (cid:46) i and Θ. The right ascension and declina-tion are referred to respectively by α and δ in the equationsbelow. D/D = cos i/ [cos i cos ρ − sin i sin ρ sin ( φ − θ )] (2)To calculate the distance to the LMC center (D above),it is necessary to calculate ρ and sin ( φ − θ ). The former iscalculated as in equation 3, below:cos ρ = cos δ cos δ cos ( α − α ) + sin δ sin δ (3)Via a typical trigonometric expansion, sin ( φ − θ ) may be determined as sin ( φ − θ ) = sin ( φ ) cos ( θ ) - cos ( φ ) sin ( θ ).These components are detailed in equations 4 and 5:sin ρ cos φ = − cos δ sin ( α − α ) (4)sin ρ sin φ = sin δ cos δ − cos δ sin δ cos α − α (5)Through these equations, we determine an average,error-weighted distance modulus to the LMC center of D = 18.20 ± ± σ from the mean D distance to the LMC center, leading toseveral possibilities. One interpretation of these results sug-gests that NGC 1841 may not be a member of the LMC diskor may have been pulled out of the LMC disk (Grocholskiet al. 2007). Another view is that an uncertain estimate ofthe reddening could be affecting the distance measurement;if the reddening of NGC 1841 is doubled from E(B–V) =0.18, it is brought into agreement with the LMC mean dis-tance. Regardless of the reason(s) for the discrepancy, weremove NGC 1841 as an anomaly and continue determiningthe distance to the LMC center.Leaving out the extreme outlier of NGC 1841, the error-weighted mean is 18.41 ± ± to the center of the LMCis also comparable to, though marginally shorter than, re-cent determinations of the LMC distance of 18.49 ± ± ± ± ± ± c (cid:13) , 1– ?? elative ages and distances for LMC GCs Table 5.
Properties of the Reference Subdwarfs used for Cluster Distance Measurements ID Π (mas) F606W F814W E(B-V) [Fe/H] [ α /Fe] HIP46120 14.49 ± ± ± ± ± ± ± ± ± ± ± ± Figure 8.
Subdwarf fitting to the main sequences of the LMC clusters. The photometry is shown in black. A fiducial, in red, is fit tothe de-reddened cluster photometry. The subdwarfs, shown in cyan, are offset in magnitude to minimize the standard deviation to thefiducial, resulting in an estimate of the cluster distance.
Table 6.
Distance Estimates: Subdwarf Fitting
Cluster Assumed ValuesName E(B-V) a [Fe/H] b µ D (kpc) µ D (kpc) NGC 1466 0.09 -1.7 18.66 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a E(B-V) adopted from Walker (1992a, 1993) b From Table 1.c (cid:13) , 1– ?? Wagner-Kaiser et al.
Figure 9.
Distances derived from the horizontal branch analy-sis are compared to the subdwarf distances (blue triangles) andsubdwarf distances adjusted for the LMC geometry (red squares).The y-axis is calculated by subtracting the subdwarf derived dis-tances from the horizontal branch distance estimates. The outly-ing point is NGC 1841. While there is an offset between the twoapproaches, it appears to be zero-point related and does not varywith distance.
In this paper, we have used new deep homogeneous photom-etry for six ancient globular clusters in the Large MagellanicCloud to measure the epoch of metal-poor globular clusterformation relative to that in the Milky Way, and calculatea new distance estimate to the LMC. Our main results are:(i) By utilising the same methodology as employed byMF09, we have calculated reddening and distance indepen-dent relative ages for our six targets with a mean precisionof 8.4%, and down to 6% for individual clusters. The LMCsample is coeval with the metal-poor inner halo GalacticGCs measured by MF09 to within 0.2 ± ± ± ∼ ± ± ± ± ACKNOWLEDGMENTS
We thank an anonymous referee whose comments and sug-gestions were very helpful. D.M. is grateful for supportfrom an Australian Research Council Future Fellowship(FT160100206). D.G. gratefully acknowledges support fromthe Chilean BASAL Centro de Excelencia en Astrof´ısica yTecnolog´ıas Afines (CATA) grant PFB-06/2007.
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