Ages of LMC Star Clusters using ASAD$_2$

0.77 MB·

by  Randa S. Asa'd

Ages of LMC Star Clusters using ASAD
2
Randa S. Asa’d
6 American University of Sharjah, Physics Department, P.O.Box 26666, Sharjah, UAE
1
[email protected]
0
2

n Alexandre Vazdekis
a
J Instituto de Astrofsica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain; Departamento de
8 Astrofsica, Universidad de La Laguna, E-38205 Tenerife, Spain
2

Sami Zeinelabdin
]
A
American University of Sharjah, P. O. Box 26666, Sharjah, UAE
G
.
h
p
-
o ABSTRACT
r
t We use ASAD , the new version of ASAD (Analyzer of Spectra for Age Determination), to
s 2
a obtain the age and reddening of 27 LMC clusters from full fitting of integrated spectra using
[ different statistical methods (χ2 and K-S test) and a set of stellar population models including

GALAXEV and MILES. We show that our results are in good agreement with the CMD ages
1
v for both models, and that metallicity does notaffect the age determination for the full spectrum
9 fitting method regardless of the model used for ages with log (age/year) < 9. We discuss the
6 results obtained by the two statistical results for both GALAXEV and MILES versus three
6
factors: age, S/N and resolution (FWHM).
7
The predicted reddening values when using the χ2 minimization method are within the range
0
. found in the literature for resolved clusters (i.e: < 0.35), however the K-S test can predict
1
E(B−V)highervalues. The sharpspectrumtransitionoriginatedatagesaroundthe supergiants
0
6 contribution, at either side of the AGB peak around log (age/year) 9.0 and log (age/year) 7.8
1 are limiting our ability to provide values in agreement with the CMD estimates and as a result
: the reddening determination is not accurate. We provide the detailed results of four clusters
v
i spanning a wide range of ages. ASAD2 is a user-friendly program available for download on the
X
Web and can be immediately used at http://randaasad.wordpress.com/asad−package/.
r
a
1. Introduction reddening)canbequicklyextractedinordertoob-
tain scientific information about the host galaxy.
Accurateagesofstarclustersprovidecriticalin-
The Large Magellanic Cloud is close enough so
formationabout the formationhistory of the host
that its stellar clusters can be resolved to derive
galaxy and particularly its assembly timescales.
accurate ages, yet far enough to obtain the in-
Our goal in this work is to present the results
tegrated spectra of these clusters. This makes
of, and, offer a user-friendly program which can
the LMC stellar clusters ideal for testing the inte-
provide the parameters of the stellar clusters au-
grated spectra methods of obtaining the ages.
tomatically from their integrated spectra. Such
Although there are different ways to derive the
a program can be used with large surveys in
age, we use the method of the full integrated
which the stellar clusters’ integrated spectra are
spectrum fitting. This way we exploit the full
obtained, so that important parameters (age and
1
information contained in the integrated cluster
light, which is the only way to study stellar clus-
ter systems in distant galaxies. Despite the well 3. ASAD Full Spectrum Fitting Tool
known age-metallicity degeneracy, Bica & Alloin
In its first version, ASAD (Asa’d 2014) out-
(1986) and Ben´ıtez-Llambay et al. (2012) have
puts the age and reddening of stellar clusters
shown that metallicity does not play a signifi-
of known metallicity from their integrated spec-
cantroleinthe opticalrangewhenapplyingspec-
tra. It performs a χ2 minimization by compar-
tral aging methods, hence we apply the method
ing the observed integrated spectra to the spec-
of Ahumada et al. (2002); Palma et al. (2008) of
tral models of Gonzalez Delgado et al. (2005). In
solving for age and reddening as most of our clus-
this section we will use the same spectral models
ters are young (log (age/year) < 9). In Asa’d
of Gonzalez Delgado et al. (2005) but investigate
(2014), we introduced the Analyzer of Spectra
themethodusedbyBurke et al.(2010)tomeasure
for Age Determination(ASAD) package,that can
the goodness of fit between observed and model
solve for age and reddening of stellar clusters si-
spectra, namely the Kolmogorov−Smirnov (K-S)
multaneously assuming constant metallicity. This
has been performed by a χ2 minimization be- test. This test selects the maximum of the abso-
lute value of the difference between the cumula-
tween the observed optical integrated spectra of
tive observedspectrumand the cumulative model
the clusters and the synthetic model spectra to
spectrum eachnormalizedto unity overthe range
find the best match. In this work we introduce
of wavelengths included in the fit1. We used the
ASAD , the updated version of ASAD, with en-
2
same input parameters as the ones in Asa’d et al.
hanced features. We use a fixed LMC metallicity
(2013), a wavelength range of 3626 − 6230 ˚A,
Z=0.008 in this work. In section 2 we briefly de-
and a step size of 3˚A normalized at 5870˚A. The
scribe the data. We summarize the features of
Cardelli et al.(1989)extinctionlawwasusedwith
ASAD presented in Asa’d (2014) and introduce
reddening values between 0.00 and 0.50 in steps
the newstatisticalmethodofASAD insection3.
2
of 0.01. Column 2 in Tables 2 and 3 show the
The new version of our program provides a more
results for the best age and reddening value ob-
extensive set of model libraries for matching, in-
tained. Column 3 lists the percentage error. It is
cluding GALAXEV models (discussed in Section
noticedthatalthoughnovaluesofE(B−V)higher
4.1)andMILES models (discussedin Section 4.2)
than0.35werefoundintheliteraturefortheLMC
followedbyanalysisoferrorestimates. Reddening
clusters, the K-S test predicts E(B−V) values as
predictions are discussed in section 5. In section
high as 0.49. An investigation of the surface plot
6 we discuss the results obtained for four of our
of NGC2002, the cluster with the highest model
clusters. A summary is given in Section 7.
E(B−V), is shown in Figure 1. It shows that for
NGC2002 many solutions for the age/reddening
2. The Data
combination are possible (i.e. dark red regions)
The data set used in this work is the one pre- based on the K-S test. The possible solutions lay
sented in Asa’d et al. (2013). Twenty LMC clus- in a narrow region of log (age/year) between 6.7
ters were obtained in two observing runs in 2011 and 7, with a wide region in reddening extending
with the RC spectrograph on the 4 m Blanco from 0.26 up to 0.49. Note that there is a signifi-
telescope and with the Goodman spectrograph cant decrease of the reddening estimate below log
on the SOAR. We obtained integrated spectra by (age/year) of 7. This is likely because it corre-
scanning the cluster with the slit starting on the sponds to the peak ofthe Red Supergiantscontri-
southern edge, with the slit aligned eastwest. To butions,whichreddentheresultingstellarpopula-
expandoursample,weusedsevenadditionalLMC tionsspectra. Whenthereddeninglimitallowedin
stellar clusters from the literature: Four clusters ASAD isexpandedto0.8,the predictedE(B−V)
2
from Santos et al. (2006) and three clusters from gets as high as 0.61 for this cluster. However, we
Palma et al. (2008). These spectra were kindly knowvirtuallyallclustersintheLMChavelineof
provided by the authors. Table 1 shows the tar-
gets observed with a summary of the literature 1ASAD2 allows the user to choose the statistical method
age and reddening. preferred(χ2minimizationmethodortheK-Stestmethod)
2
Table 1
Targets Observed
Name Run/Source Resolution(˚A) S/N Age1 Reference E(B-V)2 Reference
NGC1711 Blanco2011 14 118 7.40 Elson(1991) 0.16 Perssonetal.(1983)
NGC1856 Blanco2011 14 67 7.90 Hodge(1984) 0.21 Kerberetal.(2007)
NGC1903 Blanco2011 14 28 7.85 Vallenarietal.(1998) 0.16 Vallenarietal.(1998)
NGC1984 Blanco2011 14 54 6.85 Hodge(1983) 0.14 Meureretal.(1990)
NGC2011 Blanco2011 14 46 6.78 Hodge(1983) 0.08 Meureretal.(1990)
NGC2156 Blanco2011 14 49 7.78 Hodge(1983) 0.1 Perssonetal.(1983)
NGC2157 Blanco2011 14 79 7.60 Elson(1991) 0.10 Perssonetal.(1983)
NGC2164 Blanco2011 14 98 7.70 Hodge(1983) 0.1 Perssonetal.(1983)
NGC1651 SOAR2011 3.6 4 9.30 Mouldetal.(1986) 0.09 Mouldetal.(1986)
NGC1850 SOAR2011 3.6 22 7.60 Hodge(1983) 0.18 Alcaino&Liller(1987)
NGC1863 SOAR2011 3.6 21 7.76 Alcaino&Liller(1987) 0.2 Alcaino&Liller(1987)
NGC1983 SOAR2011 3.6 16 6.90 Hodge(1983) 0.09 Meureretal.(1990)
NGC1994 SOAR2011 3.6 49 6.86 Hodge(1983) 0.14 Meureretal.(1990)
NGC2002 SOAR2011 3.6 18 7.20 Elson(1991) 0.12 Perssonetal.(1983)
NGC2031 SOAR2011 3.6 9 8.20 Dirschetal.(2000) 0.09 Dirschetal.(2000)
NGC2065 SOAR2011 3.6 33 7.85 Hodge(1983) 0.18 Perssonetal.(1983)
NGC2155 SOAR2011 3.6 10 9.40 Elson&Fall(1988) 0.02 Kerberetal.(2007)
NGC2173 SOAR2011 3.6 7 9.32 Mouldetal.(1986) 0.14 Mouldetal.(1986)
NGC2213 SOAR2011 3.6 7 8.95 DaCostaetal.(1985) 0.09 DaCostaetal.(1985)
NGC2249 SOAR2011 3.6 7 8.82 Elson&Fall(1988) 0.01 Kerberetal.(2007)
NGC1839 Santosetal.(2006) 14 - 7.52 Alcaino&Liller(1987) 0.27 Alcaino&Liller(1987)
NGC1870 Santosetal.(2006) 14 - 7.86 Alcaino&Liller(1987) 0.14 Alcaino&Liller(1987)
NGC1894 Santosetal.(2006) 14 - 7.74 Dieballetal.(2000) 0.1 Dieballetal.(2000)
SL237 Santosetal.(2006) 14 - 7.43 Alcaino&Liller(1987) 0.17 Alcaino&Liller(1987)
NGC2136 Palmaetal.(2008) 17 - 7.60 Hodge(1983) 0.10 Perssonetal.(1983)
NGC2172 Palmaetal.(2008) 17 - 7.78 Hodge(1983) 0.1 Perssonetal.(1983)
SL234 Palmaetal.(2008) 17 - 7.68 Alcaino&Liller(1987) 0.15 Alcaino&Liller(1987)
1ThesearetheCMDagesobtainedfromtheliterature. Theunitislog(age/yr)
2ThesearetheE(B-V)obtainedfromtheliterature.
3
sight extinction values well below this. The red-
dening and age are seen as highly correlated us-
ing the K-S matching algorithm. This does not
happen to the same level when using the χ2 min-
[ NGC2002 with z=0.008 ]
imization method as shown in Figure 2. Figure 3 0.5
56
shows the correlation between the ages obtained
0.4 48
using the K-S method and the CMD ages. The
cilsoogrtrh(eaelgafieti/toynleinacero).eiffisFco8ir.e9nN5t,GitshCe02.K2718-3.STmalhteehthoroueddghgdiatvsheheseadCpMlirneDe- E (B-V)00..32 234420st Statistic
diction of 6.8. A closer look at the reddening pre- Te
16
dicted for this cluster shows a high value of 0.48. 0.1
8
Forthisclustertheage/reddeningdegeneracywas
not resolved properly with the K-S method, this 0.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 0
log(Age/Year)
mightbe due to the badS/N.We showin Section
4.3 that the difference in age predictions by the
K-S test versus the χ2 minimization method vary Fig. 1.— The surface plot of NGC2002 predicted
for S/N < 60 and it is minimum for S/N > 60. byGonzalez Delgado et al.(2005) modelwith the
K-S test. The dark red regions represent the best
4. Stellar Populations Model Libraries match. Foursolutionsforthe age/reddeningcom-
bination are possible. The possible solutions lay
The two new models added to ASAD2 are in a narrow region of log (Age/year) that is be-
GALAXEV(Bruzual & Charlot2003)andMILES tween 6.7 and 7, but a wide region of reddening
(Vazdekis et al. 2010) as recently updated in extending from 0.26 up to 0.49.
Vazdekis et al. (2015)
4.1. GALAXEV
We use the optical range of the GALAXEV
(Bruzual & Charlot 2003) models which con-
tain the spectral evolution of stellar populations
at a resolution of 3˚A (FWHM). We chose the
spectral models derived using the Padova 1994 0.5 [ NGC2002 with z=0.008 ] 0.084
(Bertelli et al. 1994) evolutionary tracks and the
0.072
Salpeter (1955) IMF with lower mass cutoff 0.1 0.4
solar mass and upper mass cutoff of 100 solar 0.060c
maTssh.e ages are convertedinto log (age/year)and E (B-V)00..32 00..003468st Statisti
rounded to two decimal points2. Te
0.024
We used fixed metallicity Z = 0.0083. The re- 0.1
0.012
sults obtained using the χ2 minimization method
and the percentage errors are listed in columns 0.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 0.000
log(Age/Year)
4 and 5 of Tables 2 and 3. Figure 4 shows
2Theages providedbythemodel arenotperfectlyuniform Fig. 2.— The surface plot of NGC2002 using
in the step size. They start at log (age/year) 5.10, and Gonzalez Delgado et al.(2005)modelwiththe χ2
increase in step of 0.05 up to 6.00 then increase in steps
minimization method. Only one solution for the
of 0.02 up to 7.48 then vary slightly in the step size up
to 10.10. The spectral fluxes between log (age/year) 5.1 age/reddening combination is strongly preferred
and6.2areidenticalsoASAD2skipstheageslessthanlog
(age/year) 6.2.
3representedbym52inthemodellibrary
4
Table 2
Age predicted by different model libraries using different statistical methods
Name Age1 Error Age2 Error Age3 Error Age4 Error Age5 Error
NGC1651 8.90 60% 8.96 54% 8.81 68% 9.05 44% 8.75 72%
NGC1711 7.55 41% 7.63 70% 7.58 51% - - - -
NGC1839 8.05 239% 8.11 289% 8.11 289% - - - -
NGC1850 7.75 41% 7.70 26% 7.76 45% - - - -
NGC1856 8.45 255% 8.41 224% 8.36 188% 8.54 337% 8.45 255%
NGC1863 7.45 51% 7.51 44% 7.46 50% - - - -
NGC1870 7.80 13% 7.86 0% 7.81 11% 8.00 38% 7.85 2%
NGC1894 7.85 29% 7.81 17% 7.81 17% - - - -
NGC1903 7.85 0% 8.16 104% 7.86 2% 8.11 82% 8.15 100%
NGC1983 6.65 44% 6.74 31% 6.46 64% - - - -
NGC1984 6.65 37% 6.90 12% 6.40 65% - - - -
NGC1994 6.65 38% 7.00 38% 6.64 40% - - - -
NGC2002 7.00 37% 6.82 58% 7.00 37% - - - -
NGC2011 6.65 26% 6.94 45% 6.46 52% - - - -
NGC2031 8.25 12% 8.36 45% 8.16 9% 8.34 38% 8.26 15%
NGC2065 7.95 26% 8.21 129% 7.96 29% 8.20 124% 8.15 100%
NGC2136 7.90 100% 8.16 263% 7.91 104% - - - -
NGC2155 9.20 37% 9.99 289% 9.16 42% 10.1 401% 9.20 37%
NGC2156 8.00 66% 7.96 51% 8.01 70% 8.04 82% 8.04 82%
NGC2157 7.85 78% 7.86 82% 7.81 62% - - - -
NGC2164 7.90 58% 7.86 45% 7.91 62% - - - -
NGC2172 7.55 41% 7.65 26% 7.60 34% 7.85 17% 7.78 0%
NGC2173 9.35 7% 9.41 23% 9.23 19% 9.55 70% 9.35 7%
NGC2213 6.80 99% 9.16 62% 6.80 99% 9.15 58% 7.78 93%
NGC2249 8.40 62% 8.61 38% 8.31 69% 8.70 24% 8.34 67%
SL234 7.80 32% 7.81 35% 7.81 35% - - - -
SL237 6.90 70% 6.90 70% 7.26 32% - - - -
Note.—1 PredictedbyGonzalezDelgadoetal.(2005)usingK-Stest
2 PredictedbyGALAXEVusingtheχ2 minimizationmethod
3 PredictedbyGALAXEVusingtheK-Stest
4 Predictedby MILES usingthe χ2 minimizationmethodfor clusterswith CMD age equal to or greater
thanlog(Age/year)7.78
5PredictedbyMILESusingtheK-StestforclusterswithCMDageequaltoorgreaterthanlog(Age/year)
7.78
5
Table 3
Reddening predicted by different model libraries using different statistical methods
Name E(B−V)1 Error E(B−V)2 Error E(B−V)3 Error E(B−V)4 Error E(B−V)5 Error
NGC1651 0.26 189% 0.00 -100% 0.29 222% 0.00 -100% 0.37 311%
NGC1711 0.09 -44% 0.02 -88% 0.05 -69% - - - -
NGC1839 0.04 -85% 0.00 -100% 0.01 -96% - - - -
NGC1850 0.11 -39% 0.06 -67% 0.08 -56% - - - -
NGC1856 0.12 -43% 0.12 -43% 0.15 -29% 0.10 -52% 0.13 -38%
NGC1863 0.10 -50% 0.05 -75% 0.06 -70% - - - -
NGC1870 0.06 -57% 0.02 -86% 0.03 -79% 0.01 -93% 0.04 -71%
NGC1894 0.26 160% 0.25 150% 0.24 140% - - - -
NGC1903 0.17 6% 0.06 -63% 0.15 -6% 0.06 -63% 0.06 -63%
NGC1983 0.08 -11% 0.00 -100% 0.22 144% - - - -
NGC1984 0.28 100% 0.00 -100% 0.42 200% - - - -
NGC1994 0.20 43% 0.05 -64% 0.25 79% - - - -
NGC2002 0.49 308% 0.26 117% 0.47 292% - - - -
NGC2011 0.26 225% 0.00 -100% 0.40 400% - - - -
NGC2031 0.00 -100% 0.00 -100% 0.04 -56% 0.00 -100% 0.01 -89%
NGC2065 0.15 -17% 0.04 -78% 0.13 -28% 0.04 -78% 0.06 -67%
NGC2136 0.13 30% 0.05 -50% 0.11 10% - - - -
NGC2155 0.00 -100% 0.00 -100% 0.00 -100% 0.00 -100% 0.01 -50%
NGC2156 0.03 -70% 0.00 -100% 0.02 -80% 0.00 -100 0.03 -70%
NGC2157 0.16 60% 0.14 40% 0.15 50% - - - -
NGC2164 0.01 -90% 0.00 -100% 0.00 -100% - - - -
NGC2172 0.12 20% 0.04 -60% 0.07 -30% 0.05 -50% 0.05 -50%
NGC2173 0.00 -100% 0.00 -100% 0.00 -100% 0.00 -100% 0.00 -100%
NGC2213 0.48 433% 0.00 -100% 0.49 444% 0.00 -100% 0.47 422%
NGC2249 0.12 1100% 0.00 -100% 0.16 1500% 0.00 -100% 0.14 1300%
SL234 0.04 -73% 0.01 -93% 0.01 -93% - - - -
SL237 0.26 53% 0.23 35% 0.34 100% - - - -
Note.—1 PredictedbyGonzalezDelgadoetal.(2005)usingK-Stest
2 PredictedbyGALAXEVusingtheχ2 minimizationmethod
3 PredictedbyGALAXEVusingtheK-Stest
4 PredictedbyMILESusingtheχ2 minimizationmethodforclusterswithCMDageequaltoorgreaterthanlog(Age/year)7.78
5 PredictedbyMILESusingtheK-StestforclusterswithCMDageequaltoorgreaterthanlog(Age/year)7.78
6
the correlation between the ages obtained using
GALAXEV using the χ2 minimization method
versus the CMD ages. The correlation coefficient 10
is0.93. Figure5showsthecorrelationbetweenthe
9.5
ages obtained using GALAXEV with the χ2 min-
imization method versus the ages obtained using ) 9
r
the model of Gonzalez Delgado et al. (2005). The ea
correlation coefficient is 0.96. The difference in /y 8.5
e
thepredictedlog(age/year)bythetwomodelsfor (ag 8
50%oftheclustersislessthan0.05. Weexpectthe
g
o
deviatingclustersataroundlog(age/year)6.7and l 7.5

8.1 to correspond to differences in the treatment D
M
C 7
ofthesemodelsoftheRedSupergiantsphase,and
the onset of the AGB, respectively. 6.5
The results obtained using the K-S method
6
with the GALAXEV model and the percentage 6 6.5 7 7.5 8 8.5 9 9.5 10
KS method log (age/year)
errors are listed in columns 6 and 7 of Tables 2
and3. Figure6showsthecorrelationbetweenthe
Fig. 3.— The correlation between the ages ob-
ages obtained using the K-S test versus the ages
tained using the K-S method and the CMD ages.
obtained using the χ2 minimization method. The
Thecorrelationcoefficientis0.78. Thereddashed
correlation coefficient is 0.81.
line is the fit line. See the text for a discussion
The outlier is NGC2213, when removed from about the outlier. The dashed lines represent the
the calculations the correlation coefficient is 0.94. upper and lower limit of the range of ages within
For this cluster, the χ2 minimization method pre- log (age/year)0.5.
dictsanoldagewithzeroreddening,whiletheK-S
test predicts a young age with a high reddening.
Comparingthe predictedageswiththe CMDage,
wefind thatthe χ2 minimizationmethodpredicts
a more accurate result for this cluster.
10
To test the effect of metallicity on our method,
9.5
we used the different metallicities provided by
)
r
this model, to compare the ages obtained by each a 9
e
y
metallicity. Figure 7 shows the age prediction /
ge 8.5
using different combinations of metallicity as in- a
(
dicated in the key. The blue stars show log g 8
o
l
(age/year) obtained using metallicity Z= 0.0001 V 7.5
E
versus log (age/year) obtained using metallicity X
A
L 7
Z= 0.0004. The red circles show log (age/year) A
G
obtained using metallicity Z= 0.0001 versus log 6.5
(age/year) obtained using metallicity Z= 0.004.
6
6 6.5 7 7.5 8 8.5 9 9.5 10
The green squares show log (age/year) obtained CMD log (age/year)
using metallicity Z= 0.0001 versus log (age/year)
Fig. 4.— The correlation between the ages ob-
obtained using metallicity Z= 0.008 and so on.
tainedusingGALAXEVwiththeχ2minimization
The dashed lines represent the upper and lower
methodversustheCMDages. Thecorrelationco-
limit of the range of ages within log (age/year)
efficientis 0.93. The reddashedline isthe fitline.
0.5. 369 values out of 405 lie within that range,
The dashed lines represent the upper and lower
that is 91%. Few outliers are noted for the young
limit of the range of ages within log (age/year)
clusters. Most outliers are for the older clusters
0.5.
(log(age/year)>9)wheretheage/metallicityde-
generacy is noticeable. For the oldest ages (log
7
(age/year) > 9.5) most points are outliers which
mean that our technique is not very suitable for
10 theseoldclusters. Ourmethodisapplicabletothe
young (age/year) < 9) clusters but not appropri-
9.5
) ateastheage/metallicitydegeneracybecomestoo
r
ea 9 relevant, preventing us to assume a metallicity.
y
/
ge 8.5
a 4.2. MILES
(
g 8
lo MILES website allows choosing the preferred
EV 7.5 model configuration. Any configuration desired
X
ALA 7 canbeeasilyimportedintoASAD2. Wechosethe
G modelsthatemploytheGirardi et al.(2000)theo-
6.5
retical isochrones(Padova00)and Salpeter (1955)
6 6 6.5 7 7.5 8 8.5 9 9.5 10 IMF converted to the observational plane on the
Previous Model log (age/year)
basisofextensivestellarphotometriclibrariesand
Fig. 5.— The correlation between the ages ob- the MILES stellar spectral library. A particu-
tained using GALAXEV with the χ2 minimiza- larly important peculiarity of the MILES spectra
tion method versus the ages obtained using the for this work is its excellent flux-calibration qual-
modelofGonzalez Delgado et al.(2005). Thecor- ity and good parameters coverage. ASAD first
2
relation coefficient is 0.96. The red dashed line is groupsmodelswiththe samemetallicitytogether,
the fit line. The dashed lines represent the up- then extracts the flux and stores it for the cor-
per andlowerlimit ofthe rangeofageswithin log responding wavelength, one flux column for each
(age/year)0.5. age4.
The ages are convertedinto log (age/year)and
rounded to two decimal points. Note that the
agesprovidedbythemodelstartatlog(age/year)
7.78, which is relatively large compared to the
other models. Another option is to start with
10
7.4whenusingthe modelversionbasedonBaSTI
) 9.5 isochrones. We chose the Padova library for uni-
r
a formity (with the other models used in ASAD ).
ye 9 2
/ The ages increase in step size of roughly 0.055.
e
ag 8.5 The results and the percentage errors are listed
(

og 8 in columns 8 and 9 of Tables 2 and 3 for the χ2
l
minimization method.
od 7.5
h
t Figure8showsthecorrelationbetweentheages
me 7 obtained using MILES with the the χ2 minimiza-
S
K 6.5 tion method versus the CMD ages. We excluded
the clusters with a CMD age younger than log
6
6 6.5 7 7.5 8 8.5 9 9.5 10
χ2 minimization method log (age/year) (age/year) 7.78 (12 clusters of our sample). The
correlation coefficient is 0.92. Figure 9 shows
Fig. 6.— The correlation between the ages ob-
the correlation between the ages obtained using
tained using the K-S test versus the ages ob-
MILES versus the ages obtained using the model
tained using the χ2 minimization method with
of Gonzalez Delgado et al. (2005). The outlier is
GALAXEV model. The correlation coefficient is
0.81. The red dashed line is the fit line. The 4Inthe MILESmodel, theflux values aredivided intosep-
dashed lines represent the upper and lower limit arate files based on the model’s metallicity, age, and IMF
of the range of ages within log (age/year)0.5. slope. The values of the metallicity, age, and IMF slope
areencodedinthenameofeachfile
5For the LMC clusters we used the fixed metallicity Z =
0.008(represented by[M/H]=-0.4inthemodellibrary)
8
NGC2172. Gonzalez Delgado et al. (2005) pre-
dicts a log (age/year) 6.8 while MILES predict a
log (age/year) 7.85. MILES prediction is closer
to the CMD age of this cluster (log (age/year) =
10
7.78). Figure 10 shows that there is another close z=z=00.0.0000011 a anndd z =z=00.0.000044
z=0.0001 and z=0.008
possible solution around log (age/year) 7.5. The 9.5 z=0.0001 and z=0.02
z=0.0001 and z=0.05
outlierinFigures9showsthatMILESchoosesthe z=0.0004 and z=0.004
z=0.0004 and z=0.008
9 z=0.0004 and z=0.02
older option among the two possible ones, which z=0.0004 and z=0.05
) z=0.004 and z=0.008
ccthalueusstaeegrte.hseFotiwbgutoarmienoe1dd1elsushstoionwgdsiMstahgIeLrecEeoSrforverletarhtsiiuossnpatbhreteticwauegleaenrs ge/year 8. 58 zzzz====z=0000....00000.0000044882 aaaaannnnnddddd zzzzz=====000001.....00000:125255
a Upper Limit
obtained using GALAXEV. The correlation coef- ( Lower Limit
g 7.5
ficient is 0.99 when excluding the young clusters. o
L
It is worth mentioning here that the spectral 7
resolutionofthe modelis greaterthan that of the
6.5
clusters. Weusedaresolutionof3˚Aforthemodel
to make it similar to the resolution used with the 6
6 6.5 7 7.5 8 8.5 9 9.5 10
previous models (to make the comparison consis- Log (age/year)
tent). Totestourresults,wedidthefits againus-
ing the resolution of the model that matches the Fig. 7.— Age prediction using different combina-
data (3.6˚A for SOAR data and 14˚A for Blanco tionsofmetallicityasindicatedinthekey. Seethe
data asdescribedinAsa’d(2014)), the resultsare text for more details.
almost identical as shown in Figure 12. The out-
lier is NGC1856 observed with Blanco.
TheresultsobtainedwithMILESusingtheK-S
testandthepercentageerrorsarelistedincolumns
10 and 11 of Tables 2 and 3. Figure 13 shows the
correlation between the ages obtained using the
K-S test versus the ages obtained using the χ2
minimization method. The correlation coefficient 10
is 0.80. NGC2213 is an outlier. When compared 9.5
with the CMD ages the χ2 minimization method )
r 9
gives a better prediction. ea
y
As we did with GALAXEV, we use the differ- e/ 8.5
g
a
entmetallicitiesofMILEStocomparetheagesob- ( 8
g
tainedbyeachmetallicity. Figure14showstheage o
l 7.5
prediction using different combinations of metal- S
E
L
licity as indicated the in key of the figure. I 7
M
Thebluestarsshowlog(age/year)obtainedus- 6.5
ingmetallicityZ=0.0001versuslog(age/year)ob-
6
tained using metallicity Z= 0.0004. The red cir- 6 6.5 7 7.5 8 8.5 9 9.5 10
CMD log (age/year)
cles show log (age/year) obtained using metallic-
Fig. 8.— The correlation between the ages ob-
ityZ=0.0001versuslog(age/year)obtainedusing
tained using MILES with the χ2 minimization
metallicity Z= 0.004. The green squares show log
method versus the CMD ages when excluding the
(age/year) obtained using metallicity Z= 0.0001
clusters younger than log (age/year) of 7.78. The
versus log (age/year) obtained using metallicity
green dotted line is the fit line.
Z= 0.008 and so on. The dashed lines represent
the upper and lower limit of the range of ages
within 0.5 log (Age/year). 261 values out of 270
lie within that range, that is 96.7%. We conclude
9
10 10
9.5 9.5
) )
r 9 r 9
a a
e e
y y
e/ 8.5 e/ 8.5
g g
a a
( 8 ( 8
g g
o o
l 7.5 l 7.5
S S
E E
L L
I 7 I 7
M M
6.5 6.5
6 6
6 6.5 7 7.5 8 8.5 9 9.5 10 6 6.5 7 7.5 8 8.5 9 9.5 10
Gonzalez-Delgado log (age/year) GALAXEV log (age/year)
Fig. 9.— The correlation between the ages ob- Fig. 11.— The correlation between the ages ob-
tainedusingMILESwiththe theχ2 minimization tained using MILES versus the ages obtained us-
method versus the ages obtained using the model ing GALAXEV when using the χ2 minimization
of Gonzalez Delgado et al. (2005) when excluding method whenexcluding the clustersyoungerthan
the clusters younger than log (age/year) of 7.78. log (age/year) of 7.78. The green dotted line is
The green dotted line is the fit line. the fit line.
10
[ NGC2172 with z=0.008 ] )
0.5 r
a
0.096 ye
0.4 0.080 age/ 9.5
(
E (B-V)00..32 00..004684st Statistic tion log 9
0.032Te lu 8.5
o
s
0.1 e
0.016 l R 8
a
0.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 0.000 ctu
log(Age/Year) A
7.5
7.5 8 8.5 9 9.5 10
Resolution 3A log (age/year)
Fig. 10.—ThesurfaceplotofNGC2172predicted Fig. 12.—Theresultsobtainedusingafixedreso-
byGonzalez Delgado et al.(2005) modelwith the lution for the model higher than that of the data,
χ2 minimization method. A second possible solu- compared to the results obtained when matching
tion is noticed around log (age/year)7.5 the resolution of the model to that of the data.
10