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Abstract

We use asad2, the new version of asad (Analyzer of Spectra for Age Determination), to obtain the age and reddening of 27 Large Magellanic Cloud (LMC) clusters from full fitting of integrated spectra using different statistical methods [χ2 and Kolmogorov–Smirnov (KS) test] and a set of stellar population models including GALAXEV and MILES. We show that our results are in good agreement with the colour–magnitude diagram (CMD) ages for both models, and that metallicity does not affect the age determination for the full spectrum fitting method regardless of the model used for ages with log (age/year) < 9. We discuss the results obtained by the two statistical results for both GALAXEV and MILES versus three factors: age, signal-to-noise ratio and resolution (full width at half maximum). The predicted reddening values when using the χ2 minimization method are within the range found in the literature for resolved clusters (i.e. <0.35); however the KS test can predict E(B − V) higher values. The sharp spectrum transition originated at ages around the supergiants contribution, at either side of the AGB peak around log (age/year) 9.0 and log (age/year) 7.8 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 spanning a wide range of ages. asad2 is a user-friendly program available for download on the Web and can be immediately used at http://randaasad.wordpress.com/asad-package/.

methods: observational, techniques: spectroscopic, Magellanic Clouds, galaxies: star clusters: general

1 INTRODUCTION

Accurate ages of star clusters provide critical information about the formation history of the host galaxy and particularly its assembly time-scales. Our goal in this work is to present the results, and offer a user-friendly program which can provide the parameters of the stellar clusters automatically from their integrated spectra. Such a program can be used in large surveys in which the stellar clusters’ integrated spectra are obtained, so that important parameters (age and reddening) can be quickly extracted in order to obtain scientific information about the host galaxy.

The Large Magellanic Cloud (LMC) is close enough so that its stellar clusters can be resolved to derive accurate ages, and yet far enough to obtain the integrated spectra of these clusters. This makes the LMC stellar clusters ideal for testing the integrated spectra methods of obtaining the ages.

Although there are different ways to derive the age, we use the method of the full integrated spectrum fitting. This way we exploit the full information contained in the integrated cluster light, which is the only way to study stellar cluster systems in distant galaxies. Despite the well-known age–metallicity degeneracy, Bica & Alloin (1986) and Benítez-Llambay, Clariá & Piatti (2012) have shown that metallicity does not play a significant role in the optical range when applying spectral aging methods, hence we apply the method of Ahumada et al. (2002) and Palma et al. (2008) of solving for age and reddening as most of our clusters are young [log (age/year) < 9]. In Asa'd (2014), we introduced the Analyzer of Spectra for Age Determination (asad) package, which can solve for age and reddening of stellar clusters simultaneously assuming constant metallicity. This has been performed by a χ2 minimization between the observed optical integrated spectra of the clusters and the synthetic model spectra to find the best match. In this work we introduce asad2, the updated version of asad, with enhanced features. We use a fixed LMC metallicity Z = 0.008 in this work. In Section 2 we briefly describe the data. We summarize the features of asad presented in Asa'd (2014) and introduce the new statistical method of asad2 in Section 3. The new version of our program provides a more extensive set of model libraries for matching, including GALAXEV models (discussed in Section 4.1) and MILES models (discussed in Section 4.2) followed by analysis of error estimates. Reddening predictions are discussed in Section 5. In Section 6 we discuss the results obtained for four of our clusters. A summary is given in Section 7.

2 THE DATA

The data set used in this work is the one presented in Asa'd, Hanson & Ahumada (2013). 20 LMC clusters were obtained in two observing runs in 2011 with the RC spectrograph on the 4-m Blanco telescope and with the Goodman spectrograph on the Southern Astrophysical Research Telescope (SOAR). We obtained integrated spectra by scanning the cluster with the slit starting on the southern edge, with the slit aligned eastwest. To expand our sample, we used seven additional LMC stellar clusters from the literature: four clusters from Santos et al. (2006) and three from Palma et al. (2008). These spectra were kindly provided by the authors. Table 1 shows the targets observed with a summary of the literature age and reddening.

Table 1.
Open in new tab

Targets observed.

Name Run/sourceResolution (Å)S/NAge1ReferenceE(B − V)2Reference
NGC 1711Blanco2011141187.40Elson (1991)0.16Persson et al. (1983)
NGC 1856Blanco201114677.90Hodge (1984)0.21Kerber, Santiago & Brocato (2007)
NGC 1903Blanco201114287.85Vallenari, Bettoni & Chiosi (1998)0.16Vallenari et al. (1998)
NGC 1984Blanco201114546.85Hodge (1983)0.14Meurer, Freeman & Cacciari (1990)
NGC 2011Blanco201114466.78Hodge (1983)0.08Meurer et al. (1990)
NGC 2156Blanco201114497.78Hodge (1983)0.1Persson et al. (1983)
NGC 2157Blanco201114797.60Elson (1991)0.10Persson et al. (1983)
NGC 2164Blanco201114987.70Hodge (1983)0.1Persson et al. (1983)
NGC 1651SOAR20113.649.30Mould, Da Costa & Crawford (1986)0.09Mould et al. (1986)
NGC 1850SOAR20113.6227.60Hodge (1983)0.18Alcaino & Liller (1987)
NGC 1863SOAR20113.6217.76Alcaino & Liller (1987)0.2Alcaino & Liller (1987)
NGC 1983SOAR20113.6166.90Hodge (1983)0.09Meurer et al. (1990)
NGC 1994SOAR20113.6496.86Hodge (1983)0.14Meurer et al. (1990)
NGC 2002SOAR20113.6187.20Elson (1991)0.12Persson et al. (1983)
NGC 2031SOAR20113.698.20Dirsch et al. (2000)0.09Dirsch et al. (2000)
NGC 2065SOAR20113.6337.85Hodge (1983)0.18Persson et al. (1983)
NGC 2155SOAR20113.6109.40Elson & Fall (1988)0.02Kerber et al. (2007)
NGC 2173SOAR20113.679.32Mould et al. (1986)0.14Mould et al. (1986)
NGC 2213SOAR20113.678.95Da Costa, Mould & Crawford (1985)0.09Da Costa et al. (1985)
NGC 2249SOAR20113.678.82Elson & Fall (1988)0.01Kerber et al. (2007)
NGC 1839Santos et al. (2006)14–7.52Alcaino & Liller (1987)0.27Alcaino & Liller (1987)
NGC 1870Santos et al. (2006)14–7.86Alcaino & Liller (1987)0.14Alcaino & Liller (1987)
NGC 1894Santos et al. (2006)14–7.74Dieball, Grebel & Theis (2000)0.1Dieball et al. (2000)
SL237Santos et al. (2006)14–7.43Alcaino & Liller (1987)0.17Alcaino & Liller (1987)
NGC 2136Palma et al. (2008)17–7.60Hodge (1983)0.10Persson et al. (1983)
NGC 2172Palma et al. (2008)17–7.78Hodge (1983)0.1Persson et al. (1983)
SL234Palma et al. (2008)17–7.68Alcaino & Liller (1987)0.15Alcaino & Liller (1987)
Name Run/sourceResolution (Å)S/NAge1ReferenceE(B − V)2Reference
NGC 1711Blanco2011141187.40Elson (1991)0.16Persson et al. (1983)
NGC 1856Blanco201114677.90Hodge (1984)0.21Kerber, Santiago & Brocato (2007)
NGC 1903Blanco201114287.85Vallenari, Bettoni & Chiosi (1998)0.16Vallenari et al. (1998)
NGC 1984Blanco201114546.85Hodge (1983)0.14Meurer, Freeman & Cacciari (1990)
NGC 2011Blanco201114466.78Hodge (1983)0.08Meurer et al. (1990)
NGC 2156Blanco201114497.78Hodge (1983)0.1Persson et al. (1983)
NGC 2157Blanco201114797.60Elson (1991)0.10Persson et al. (1983)
NGC 2164Blanco201114987.70Hodge (1983)0.1Persson et al. (1983)
NGC 1651SOAR20113.649.30Mould, Da Costa & Crawford (1986)0.09Mould et al. (1986)
NGC 1850SOAR20113.6227.60Hodge (1983)0.18Alcaino & Liller (1987)
NGC 1863SOAR20113.6217.76Alcaino & Liller (1987)0.2Alcaino & Liller (1987)
NGC 1983SOAR20113.6166.90Hodge (1983)0.09Meurer et al. (1990)
NGC 1994SOAR20113.6496.86Hodge (1983)0.14Meurer et al. (1990)
NGC 2002SOAR20113.6187.20Elson (1991)0.12Persson et al. (1983)
NGC 2031SOAR20113.698.20Dirsch et al. (2000)0.09Dirsch et al. (2000)
NGC 2065SOAR20113.6337.85Hodge (1983)0.18Persson et al. (1983)
NGC 2155SOAR20113.6109.40Elson & Fall (1988)0.02Kerber et al. (2007)
NGC 2173SOAR20113.679.32Mould et al. (1986)0.14Mould et al. (1986)
NGC 2213SOAR20113.678.95Da Costa, Mould & Crawford (1985)0.09Da Costa et al. (1985)
NGC 2249SOAR20113.678.82Elson & Fall (1988)0.01Kerber et al. (2007)
NGC 1839Santos et al. (2006)14–7.52Alcaino & Liller (1987)0.27Alcaino & Liller (1987)
NGC 1870Santos et al. (2006)14–7.86Alcaino & Liller (1987)0.14Alcaino & Liller (1987)
NGC 1894Santos et al. (2006)14–7.74Dieball, Grebel & Theis (2000)0.1Dieball et al. (2000)
SL237Santos et al. (2006)14–7.43Alcaino & Liller (1987)0.17Alcaino & Liller (1987)
NGC 2136Palma et al. (2008)17–7.60Hodge (1983)0.10Persson et al. (1983)
NGC 2172Palma et al. (2008)17–7.78Hodge (1983)0.1Persson et al. (1983)
SL234Palma et al. (2008)17–7.68Alcaino & Liller (1987)0.15Alcaino & Liller (1987)

Notes.1These are the CMD ages obtained from the literature. The unit is log(age/year).

2These are the E(B − V) obtained from the literature.

Table 1.
Open in new tab

Targets observed.

Name Run/sourceResolution (Å)S/NAge1ReferenceE(B − V)2Reference
NGC 1711Blanco2011141187.40Elson (1991)0.16Persson et al. (1983)
NGC 1856Blanco201114677.90Hodge (1984)0.21Kerber, Santiago & Brocato (2007)
NGC 1903Blanco201114287.85Vallenari, Bettoni & Chiosi (1998)0.16Vallenari et al. (1998)
NGC 1984Blanco201114546.85Hodge (1983)0.14Meurer, Freeman & Cacciari (1990)
NGC 2011Blanco201114466.78Hodge (1983)0.08Meurer et al. (1990)
NGC 2156Blanco201114497.78Hodge (1983)0.1Persson et al. (1983)
NGC 2157Blanco201114797.60Elson (1991)0.10Persson et al. (1983)
NGC 2164Blanco201114987.70Hodge (1983)0.1Persson et al. (1983)
NGC 1651SOAR20113.649.30Mould, Da Costa & Crawford (1986)0.09Mould et al. (1986)
NGC 1850SOAR20113.6227.60Hodge (1983)0.18Alcaino & Liller (1987)
NGC 1863SOAR20113.6217.76Alcaino & Liller (1987)0.2Alcaino & Liller (1987)
NGC 1983SOAR20113.6166.90Hodge (1983)0.09Meurer et al. (1990)
NGC 1994SOAR20113.6496.86Hodge (1983)0.14Meurer et al. (1990)
NGC 2002SOAR20113.6187.20Elson (1991)0.12Persson et al. (1983)
NGC 2031SOAR20113.698.20Dirsch et al. (2000)0.09Dirsch et al. (2000)
NGC 2065SOAR20113.6337.85Hodge (1983)0.18Persson et al. (1983)
NGC 2155SOAR20113.6109.40Elson & Fall (1988)0.02Kerber et al. (2007)
NGC 2173SOAR20113.679.32Mould et al. (1986)0.14Mould et al. (1986)
NGC 2213SOAR20113.678.95Da Costa, Mould & Crawford (1985)0.09Da Costa et al. (1985)
NGC 2249SOAR20113.678.82Elson & Fall (1988)0.01Kerber et al. (2007)
NGC 1839Santos et al. (2006)14–7.52Alcaino & Liller (1987)0.27Alcaino & Liller (1987)
NGC 1870Santos et al. (2006)14–7.86Alcaino & Liller (1987)0.14Alcaino & Liller (1987)
NGC 1894Santos et al. (2006)14–7.74Dieball, Grebel & Theis (2000)0.1Dieball et al. (2000)
SL237Santos et al. (2006)14–7.43Alcaino & Liller (1987)0.17Alcaino & Liller (1987)
NGC 2136Palma et al. (2008)17–7.60Hodge (1983)0.10Persson et al. (1983)
NGC 2172Palma et al. (2008)17–7.78Hodge (1983)0.1Persson et al. (1983)
SL234Palma et al. (2008)17–7.68Alcaino & Liller (1987)0.15Alcaino & Liller (1987)
Name Run/sourceResolution (Å)S/NAge1ReferenceE(B − V)2Reference
NGC 1711Blanco2011141187.40Elson (1991)0.16Persson et al. (1983)
NGC 1856Blanco201114677.90Hodge (1984)0.21Kerber, Santiago & Brocato (2007)
NGC 1903Blanco201114287.85Vallenari, Bettoni & Chiosi (1998)0.16Vallenari et al. (1998)
NGC 1984Blanco201114546.85Hodge (1983)0.14Meurer, Freeman & Cacciari (1990)
NGC 2011Blanco201114466.78Hodge (1983)0.08Meurer et al. (1990)
NGC 2156Blanco201114497.78Hodge (1983)0.1Persson et al. (1983)
NGC 2157Blanco201114797.60Elson (1991)0.10Persson et al. (1983)
NGC 2164Blanco201114987.70Hodge (1983)0.1Persson et al. (1983)
NGC 1651SOAR20113.649.30Mould, Da Costa & Crawford (1986)0.09Mould et al. (1986)
NGC 1850SOAR20113.6227.60Hodge (1983)0.18Alcaino & Liller (1987)
NGC 1863SOAR20113.6217.76Alcaino & Liller (1987)0.2Alcaino & Liller (1987)
NGC 1983SOAR20113.6166.90Hodge (1983)0.09Meurer et al. (1990)
NGC 1994SOAR20113.6496.86Hodge (1983)0.14Meurer et al. (1990)
NGC 2002SOAR20113.6187.20Elson (1991)0.12Persson et al. (1983)
NGC 2031SOAR20113.698.20Dirsch et al. (2000)0.09Dirsch et al. (2000)
NGC 2065SOAR20113.6337.85Hodge (1983)0.18Persson et al. (1983)
NGC 2155SOAR20113.6109.40Elson & Fall (1988)0.02Kerber et al. (2007)
NGC 2173SOAR20113.679.32Mould et al. (1986)0.14Mould et al. (1986)
NGC 2213SOAR20113.678.95Da Costa, Mould & Crawford (1985)0.09Da Costa et al. (1985)
NGC 2249SOAR20113.678.82Elson & Fall (1988)0.01Kerber et al. (2007)
NGC 1839Santos et al. (2006)14–7.52Alcaino & Liller (1987)0.27Alcaino & Liller (1987)
NGC 1870Santos et al. (2006)14–7.86Alcaino & Liller (1987)0.14Alcaino & Liller (1987)
NGC 1894Santos et al. (2006)14–7.74Dieball, Grebel & Theis (2000)0.1Dieball et al. (2000)
SL237Santos et al. (2006)14–7.43Alcaino & Liller (1987)0.17Alcaino & Liller (1987)
NGC 2136Palma et al. (2008)17–7.60Hodge (1983)0.10Persson et al. (1983)
NGC 2172Palma et al. (2008)17–7.78Hodge (1983)0.1Persson et al. (1983)
SL234Palma et al. (2008)17–7.68Alcaino & Liller (1987)0.15Alcaino & Liller (1987)

Notes.1These are the CMD ages obtained from the literature. The unit is log(age/year).

2These are the E(B − V) obtained from the literature.

3 ASAD FULL SPECTRUM FITTING TOOL

In its first version, asad (Asa'd 2014) outputs the age and reddening of stellar clusters of known metallicity from their integrated spectra. It performs a χ2 minimization by comparing the observed integrated spectra to the spectral models of Gonzalez Delgado et al. (2005). In this section we will use the same spectral models of Gonzalez Delgado et al. (2005) but investigate the method used by Burke et al. (2010) to measure the goodness of fit between observed and model spectra, namely the Kolmogorov–Smirnov (KS) test. This test selects the maximum of the absolute value of the difference between the cumulative observed spectrum and the cumulative model spectrum each normalized to unity over the range of wavelengths included in the fit.1 We used the same input parameters as the ones in Asa'd et al. (2013), a wavelength range of 3626–6230 Å, and a step size of 3 Å normalized at 5870 Å. The Cardelli, Clayton & Mathis (1989) extinction law was used with reddening values between 0.00 and 0.50 in steps of 0.01. Column 2 in Tables 2 and 3 shows the results for the best age and reddening value obtained. Column 3 lists the percentage error. It is noticed that although no values of E(B − V) higher than 0.35 were found in the literature for the LMC clusters, the KS test predicts E(B − V) values as high as 0.49. An investigation of the surface plot of NGC 2002, the cluster with the highest model E(B − V), is shown in Fig. 1. It shows that for NGC 2002 many solutions for the age/reddening combination are possible (i.e. dark red regions) based on the KS test. The possible solutions lay in a narrow region of log (age/year) between 6.7 and 7, with a wide region in reddening extending from 0.26 up to 0.49. Note that there is a significant decrease of the reddening estimate below log (age/year) of 7. This is likely because it corresponds to the peak of the Red Supergiants contributions, which redden the resulting stellar populations spectra. When the reddening limit allowed in asad2 is expanded to 0.8, the predicted E(B − V) gets as high as 0.61 for this cluster. However, we know virtually all clusters in the LMC have line-of-sight extinction values well below this. The reddening and age are seen as highly correlated using the KS matching algorithm. This does not happen to the same level when using the χ2 minimization method as shown in Fig. 2. Fig. 3 shows the correlation between the ages obtained using the KS method and the CMD ages. The correlation coefficient is 0.78. The red dashed line is the fit line. For NGC 2213 although the CMD log (age/year) is 8.95, the KS method gives a prediction of 6.8. A closer look at the reddening predicted for this cluster shows a high value of 0.48. For this cluster the age/reddening degeneracy was not resolved properly with the KS method; this might be due to the bad signal-to-noise ratio (S/N). We show in Section 4.3 that the difference in age predictions by the KS test versus the χ2 minimization method varies for S/N < 60 and it is minimum for S/N > 60.

The surface plot of NGC 2002 predicted by Gonzalez Delgado et al. (2005) model with the KS test. The dark red regions represent the best match. Four solutions for the age/reddening combination are possible. The possible solutions lay in a narrow region of log (Age/year) that is between 6.7 and 7, but a wide region of reddening extending from 0.26 up to 0.49.
Figure 1.

The surface plot of NGC 2002 predicted by Gonzalez Delgado et al. (2005) model with the KS test. The dark red regions represent the best match. Four solutions for the age/reddening combination are possible. The possible solutions lay in a narrow region of log (Age/year) that is between 6.7 and 7, but a wide region of reddening extending from 0.26 up to 0.49.

Open in new tabDownload slide
The surface plot of NGC 2002 using Gonzalez Delgado et al. (2005) model with the χ2 minimization method. Only one solution for the age/reddening combination is strongly preferred.
Figure 2.

The surface plot of NGC 2002 using Gonzalez Delgado et al. (2005) model with the χ2 minimization method. Only one solution for the age/reddening combination is strongly preferred.

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The correlation between the ages obtained using the KS method and the CMD ages. The correlation coefficient is 0.78. The red dashed line is the fit line. See the text for a discussion about the outlier. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.
Figure 3.

The correlation between the ages obtained using the KS method and the CMD ages. The correlation coefficient is 0.78. The red dashed line is the fit line. See the text for a discussion about the outlier. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.

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Table 2.
Open in new tab

Age predicted by different model libraries using different statistical methods.

NameAge1ErrorAge2ErrorAge3ErrorAge4ErrorAge5Error
(%)(%)(%)(%)(%)
NGC 16518.90608.96548.81689.05448.7572
NGC 17117.55417.63707.5851––––
NGC 18398.052398.112898.11289––––
NGC 18507.75417.70267.7645––––
NGC 18568.452558.412248.361888.543378.45255
NGC 18637.45517.51447.4650––––
NGC 18707.80137.8607.81118.00387.852
NGC 18947.85297.81177.8117––––
NGC 19037.8508.161047.8628.11828.15100
NGC 19836.65446.74316.4664––––
NGC 19846.65376.90126.4065––––
NGC 19946.65387.00386.6440––––
NGC 20027.00376.82587.0037––––
NGC 20116.65266.94456.4652––––
NGC 20318.25128.36458.1698.34388.2615
NGC 20657.95268.211297.96298.201248.15100
NGC 21367.901008.162637.91104––––
NGC 21559.20379.992899.164210.14019.2037
NGC 21568.00667.96518.01708.04828.0482
NGC 21577.85787.86827.8162––––
NGC 21647.90587.86457.9162––––
NGC 21727.55417.65267.60347.85177.780
NGC 21739.3579.41239.23199.55709.357
NGC 22136.80999.16626.80999.15587.7893
NGC 22498.40628.61388.31698.70248.3467
SL2347.80327.81357.8135––––
SL2376.90706.90707.2632––––
NameAge1ErrorAge2ErrorAge3ErrorAge4ErrorAge5Error
(%)(%)(%)(%)(%)
NGC 16518.90608.96548.81689.05448.7572
NGC 17117.55417.63707.5851––––
NGC 18398.052398.112898.11289––––
NGC 18507.75417.70267.7645––––
NGC 18568.452558.412248.361888.543378.45255
NGC 18637.45517.51447.4650––––
NGC 18707.80137.8607.81118.00387.852
NGC 18947.85297.81177.8117––––
NGC 19037.8508.161047.8628.11828.15100
NGC 19836.65446.74316.4664––––
NGC 19846.65376.90126.4065––––
NGC 19946.65387.00386.6440––––
NGC 20027.00376.82587.0037––––
NGC 20116.65266.94456.4652––––
NGC 20318.25128.36458.1698.34388.2615
NGC 20657.95268.211297.96298.201248.15100
NGC 21367.901008.162637.91104––––
NGC 21559.20379.992899.164210.14019.2037
NGC 21568.00667.96518.01708.04828.0482
NGC 21577.85787.86827.8162––––
NGC 21647.90587.86457.9162––––
NGC 21727.55417.65267.60347.85177.780
NGC 21739.3579.41239.23199.55709.357
NGC 22136.80999.16626.80999.15587.7893
NGC 22498.40628.61388.31698.70248.3467
SL2347.80327.81357.8135––––
SL2376.90706.90707.2632––––

Note. – 1Predicted by Gonzalez Delgado et al. (2005) using the KS test.

2Predicted by GALAXEV using the χ2 minimization method.

3Predicted by GALAXEV using the KS test.

4Predicted by MILES using the χ2 minimization method for clusters with CMD age equal to or greater than log (Age/year) 7.78.

5Predicted by MILES using the KS test for clusters with CMD age equal to or greater than log (Age/year) 7.78.

Table 2.
Open in new tab

Age predicted by different model libraries using different statistical methods.

NameAge1ErrorAge2ErrorAge3ErrorAge4ErrorAge5Error
(%)(%)(%)(%)(%)
NGC 16518.90608.96548.81689.05448.7572
NGC 17117.55417.63707.5851––––
NGC 18398.052398.112898.11289––––
NGC 18507.75417.70267.7645––––
NGC 18568.452558.412248.361888.543378.45255
NGC 18637.45517.51447.4650––––
NGC 18707.80137.8607.81118.00387.852
NGC 18947.85297.81177.8117––––
NGC 19037.8508.161047.8628.11828.15100
NGC 19836.65446.74316.4664––––
NGC 19846.65376.90126.4065––––
NGC 19946.65387.00386.6440––––
NGC 20027.00376.82587.0037––––
NGC 20116.65266.94456.4652––––
NGC 20318.25128.36458.1698.34388.2615
NGC 20657.95268.211297.96298.201248.15100
NGC 21367.901008.162637.91104––––
NGC 21559.20379.992899.164210.14019.2037
NGC 21568.00667.96518.01708.04828.0482
NGC 21577.85787.86827.8162––––
NGC 21647.90587.86457.9162––––
NGC 21727.55417.65267.60347.85177.780
NGC 21739.3579.41239.23199.55709.357
NGC 22136.80999.16626.80999.15587.7893
NGC 22498.40628.61388.31698.70248.3467
SL2347.80327.81357.8135––––
SL2376.90706.90707.2632––––
NameAge1ErrorAge2ErrorAge3ErrorAge4ErrorAge5Error
(%)(%)(%)(%)(%)
NGC 16518.90608.96548.81689.05448.7572
NGC 17117.55417.63707.5851––––
NGC 18398.052398.112898.11289––––
NGC 18507.75417.70267.7645––––
NGC 18568.452558.412248.361888.543378.45255
NGC 18637.45517.51447.4650––––
NGC 18707.80137.8607.81118.00387.852
NGC 18947.85297.81177.8117––––
NGC 19037.8508.161047.8628.11828.15100
NGC 19836.65446.74316.4664––––
NGC 19846.65376.90126.4065––––
NGC 19946.65387.00386.6440––––
NGC 20027.00376.82587.0037––––
NGC 20116.65266.94456.4652––––
NGC 20318.25128.36458.1698.34388.2615
NGC 20657.95268.211297.96298.201248.15100
NGC 21367.901008.162637.91104––––
NGC 21559.20379.992899.164210.14019.2037
NGC 21568.00667.96518.01708.04828.0482
NGC 21577.85787.86827.8162––––
NGC 21647.90587.86457.9162––––
NGC 21727.55417.65267.60347.85177.780
NGC 21739.3579.41239.23199.55709.357
NGC 22136.80999.16626.80999.15587.7893
NGC 22498.40628.61388.31698.70248.3467
SL2347.80327.81357.8135––––
SL2376.90706.90707.2632––––

Note. – 1Predicted by Gonzalez Delgado et al. (2005) using the KS test.

2Predicted by GALAXEV using the χ2 minimization method.

3Predicted by GALAXEV using the KS test.

4Predicted by MILES using the χ2 minimization method for clusters with CMD age equal to or greater than log (Age/year) 7.78.

5Predicted by MILES using the KS test for clusters with CMD age equal to or greater than log (Age/year) 7.78.

Table 3.
Open in new tab

Reddening predicted by different model libraries using different statistical methods.

NameE(B − V)1ErrorE(B − V)2ErrorE(B − V)3ErrorE(B − V)4ErrorE(B − V)5Error
(%)(%)(%)(%)(%)
NGC 16510.261890.00−1000.292220.00−1000.37311
NGC 17110.09−440.02−880.05−69––––
NGC 18390.04−850.00−1000.01−96––––
NGC 18500.11−390.06−670.08−56––––
NGC 18560.12−430.12−430.15−290.10−520.13−38
NGC 18630.10−500.05−750.06−70––––
NGC 18700.06−570.02−860.03−790.01−930.04−71
NGC 18940.261600.251500.24140––––
NGC 19030.1760.06−630.15−60.06−630.06−63
NGC 19830.08−110.00−1000.22144––––
NGC 19840.281000.00−1000.42200––––
NGC 19940.20430.05−640.2579––––
NGC 20020.493080.261170.47292––––
NGC 20110.262250.00−1000.40400––––
NGC 20310.00−1000.00−1000.04−560.00−1000.01−89
NGC 20650.15−170.04−780.13−280.04−780.06−67
NGC 21360.13300.05−500.1110––––
NGC 21550.00−1000.00−1000.00−1000.00−1000.01−50
NGC 21560.03−700.00−1000.02−800.00−1000.03−70
NGC 21570.16600.14400.1550––––
NGC 21640.01−900.00−1000.00−100––––
NGC 21720.12200.04−600.07−300.05−500.05−50
NGC 21730.00−1000.00−1000.00−1000.00−1000.00−100
NGC 22130.484330.00−1000.494440.00−1000.47422
NGC 22490.1211000.00−1000.1615000.00−1000.141300
SL2340.04−730.01−930.01−93––––
SL2370.26530.23350.34100––––
NameE(B − V)1ErrorE(B − V)2ErrorE(B − V)3ErrorE(B − V)4ErrorE(B − V)5Error
(%)(%)(%)(%)(%)
NGC 16510.261890.00−1000.292220.00−1000.37311
NGC 17110.09−440.02−880.05−69––––
NGC 18390.04−850.00−1000.01−96––––
NGC 18500.11−390.06−670.08−56––––
NGC 18560.12−430.12−430.15−290.10−520.13−38
NGC 18630.10−500.05−750.06−70––––
NGC 18700.06−570.02−860.03−790.01−930.04−71
NGC 18940.261600.251500.24140––––
NGC 19030.1760.06−630.15−60.06−630.06−63
NGC 19830.08−110.00−1000.22144––––
NGC 19840.281000.00−1000.42200––––
NGC 19940.20430.05−640.2579––––
NGC 20020.493080.261170.47292––––
NGC 20110.262250.00−1000.40400––––
NGC 20310.00−1000.00−1000.04−560.00−1000.01−89
NGC 20650.15−170.04−780.13−280.04−780.06−67
NGC 21360.13300.05−500.1110––––
NGC 21550.00−1000.00−1000.00−1000.00−1000.01−50
NGC 21560.03−700.00−1000.02−800.00−1000.03−70
NGC 21570.16600.14400.1550––––
NGC 21640.01−900.00−1000.00−100––––
NGC 21720.12200.04−600.07−300.05−500.05−50
NGC 21730.00−1000.00−1000.00−1000.00−1000.00−100
NGC 22130.484330.00−1000.494440.00−1000.47422
NGC 22490.1211000.00−1000.1615000.00−1000.141300
SL2340.04−730.01−930.01−93––––
SL2370.26530.23350.34100––––

Note. – 1Predicted by Gonzalez Delgado et al. (2005) using the KS test.

2Predicted by GALAXEV using the χ2 minimization method.

3Predicted by GALAXEV using the KS test.

4Predicted by MILES using the χ2 minimization method for clusters with CMD age equal to or greater than log (Age/year) 7.78.

5Predicted by MILES using the KS test for clusters with CMD age equal to or greater than log (Age/year) 7.78.

Table 3.
Open in new tab

Reddening predicted by different model libraries using different statistical methods.

NameE(B − V)1ErrorE(B − V)2ErrorE(B − V)3ErrorE(B − V)4ErrorE(B − V)5Error
(%)(%)(%)(%)(%)
NGC 16510.261890.00−1000.292220.00−1000.37311
NGC 17110.09−440.02−880.05−69––––
NGC 18390.04−850.00−1000.01−96––––
NGC 18500.11−390.06−670.08−56––––
NGC 18560.12−430.12−430.15−290.10−520.13−38
NGC 18630.10−500.05−750.06−70––––
NGC 18700.06−570.02−860.03−790.01−930.04−71
NGC 18940.261600.251500.24140––––
NGC 19030.1760.06−630.15−60.06−630.06−63
NGC 19830.08−110.00−1000.22144––––
NGC 19840.281000.00−1000.42200––––
NGC 19940.20430.05−640.2579––––
NGC 20020.493080.261170.47292––––
NGC 20110.262250.00−1000.40400––––
NGC 20310.00−1000.00−1000.04−560.00−1000.01−89
NGC 20650.15−170.04−780.13−280.04−780.06−67
NGC 21360.13300.05−500.1110––––
NGC 21550.00−1000.00−1000.00−1000.00−1000.01−50
NGC 21560.03−700.00−1000.02−800.00−1000.03−70
NGC 21570.16600.14400.1550––––
NGC 21640.01−900.00−1000.00−100––––
NGC 21720.12200.04−600.07−300.05−500.05−50
NGC 21730.00−1000.00−1000.00−1000.00−1000.00−100
NGC 22130.484330.00−1000.494440.00−1000.47422
NGC 22490.1211000.00−1000.1615000.00−1000.141300
SL2340.04−730.01−930.01−93––––
SL2370.26530.23350.34100––––
NameE(B − V)1ErrorE(B − V)2ErrorE(B − V)3ErrorE(B − V)4ErrorE(B − V)5Error
(%)(%)(%)(%)(%)
NGC 16510.261890.00−1000.292220.00−1000.37311
NGC 17110.09−440.02−880.05−69––––
NGC 18390.04−850.00−1000.01−96––––
NGC 18500.11−390.06−670.08−56––––
NGC 18560.12−430.12−430.15−290.10−520.13−38
NGC 18630.10−500.05−750.06−70––––
NGC 18700.06−570.02−860.03−790.01−930.04−71
NGC 18940.261600.251500.24140––––
NGC 19030.1760.06−630.15−60.06−630.06−63
NGC 19830.08−110.00−1000.22144––––
NGC 19840.281000.00−1000.42200––––
NGC 19940.20430.05−640.2579––––
NGC 20020.493080.261170.47292––––
NGC 20110.262250.00−1000.40400––––
NGC 20310.00−1000.00−1000.04−560.00−1000.01−89
NGC 20650.15−170.04−780.13−280.04−780.06−67
NGC 21360.13300.05−500.1110––––
NGC 21550.00−1000.00−1000.00−1000.00−1000.01−50
NGC 21560.03−700.00−1000.02−800.00−1000.03−70
NGC 21570.16600.14400.1550––––
NGC 21640.01−900.00−1000.00−100––––
NGC 21720.12200.04−600.07−300.05−500.05−50
NGC 21730.00−1000.00−1000.00−1000.00−1000.00−100
NGC 22130.484330.00−1000.494440.00−1000.47422
NGC 22490.1211000.00−1000.1615000.00−1000.141300
SL2340.04−730.01−930.01−93––––
SL2370.26530.23350.34100––––

Note. – 1Predicted by Gonzalez Delgado et al. (2005) using the KS test.

2Predicted by GALAXEV using the χ2 minimization method.

3Predicted by GALAXEV using the KS test.

4Predicted by MILES using the χ2 minimization method for clusters with CMD age equal to or greater than log (Age/year) 7.78.

5Predicted by MILES using the KS test for clusters with CMD age equal to or greater than log (Age/year) 7.78.

4 STELLAR POPULATIONS MODEL LIBRARIES

The two new models added to asad2 are GALAXEV (Bruzual & Charlot 2003) and MILES (Vazdekis et al. 2010) as recently updated in Vazdekis et al. (2015).

4.1 GALAXEV

We use the optical range of the GALAXEV (Bruzual & Charlot 2003) models, which contain the spectral evolution of stellar populations at a resolution of 3 Å (full width at half maximum, FWHM). We chose the spectral models derived using the Padova (1994) (Bertelli et al. 1994) evolutionary tracks and the Salpeter (1955) IMF with lower mass cut-off 0.1 solar mass and upper mass cut-off of 100 solar mass.

The ages are converted into log (age/year) and rounded to two decimal points.2

We used fixed metallicity Z = 0.008.3 The results obtained using the χ2 minimization method and the percentage errors are listed in Columns 4 and 5 of Tables 2 and 3. Fig. 4 shows the correlation between the ages obtained using GALAXEV by the χ2 minimization method versus the CMD ages. The correlation coefficient is 0.93. Fig. 5 shows the correlation between the ages obtained using GALAXEV with the χ2 minimization method versus the ages obtained using the model of Gonzalez Delgado et al. (2005). The correlation coefficient is 0.96. The difference in the predicted log (age/year) by the two models for 50 per cent of the clusters is less than 0.05. We expect the deviating clusters at around log (age/year) 6.7 and 8.1 to correspond to differences in the treatment of these models of the Red Supergiants phase, and the onset of the AGB, respectively.

The correlation between the ages obtained using GALAXEV with the χ2 minimization method versus the CMD ages. The correlation coefficient is 0.93. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.
Figure 4.

The correlation between the ages obtained using GALAXEV with the χ2 minimization method versus the CMD ages. The correlation coefficient is 0.93. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.

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The correlation between the ages obtained using GALAXEV with the χ2 minimization method versus the ages obtained using the model of Gonzalez Delgado et al. (2005). The correlation coefficient is 0.96. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.
Figure 5.

The correlation between the ages obtained using GALAXEV with the χ2 minimization method versus the ages obtained using the model of Gonzalez Delgado et al. (2005). The correlation coefficient is 0.96. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.

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The results obtained using the KS method with the GALAXEV model and the percentage errors are listed in Columns 6 and 7 of Tables 2 and 3. Fig. 6 shows the correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method. The correlation coefficient is 0.81.

The correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method with GALAXEV model. The correlation coefficient is 0.81. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.
Figure 6.

The correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method with GALAXEV model. The correlation coefficient is 0.81. The red dashed line is the fit line. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5.

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The outlier is NGC 2213; when removed from the calculations the correlation coefficient is 0.94. For this cluster, the χ2 minimization method predicts an old age with zero reddening, while the KS test predicts a young age with a high reddening. Comparing the predicted ages with the CMD age, we find that the χ2 minimization method predicts a more accurate result for this cluster.

To test the effect of metallicity on our method, we used the different metallicities provided by this model to compare the ages obtained by each metallicity. Fig. 7 shows the age prediction using different combinations of metallicity as indicated in the key. The blue stars show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.0004. The red circles show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.004. The green squares show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.008 and so on. The dashed lines represent the upper and lower limits of the range of ages within log (age/year) 0.5. 369 values out of 405 lie within that range, that is 91 per cent. Few outliers are noted for the young clusters. Most outliers are for the older clusters [log (age/year) > 9] where the age/metallicity degeneracy is noticeable. For the oldest ages [log (age/year) > 9.5] most points are outliers which means that our technique is not very suitable for these old clusters. Our method is applicable to the young [(age/year) < 9] clusters but not appropriate as the age/metallicity degeneracy becomes too relevant, preventing us to assume a metallicity.

Age prediction using different combinations of metallicity as indicated in the key. See the text for more details.
Figure 7.

Age prediction using different combinations of metallicity as indicated in the key. See the text for more details.

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4.2 MILES

MILES website allows choosing the preferred model configuration. Any configuration desired can be easily imported into asad2. We chose the models that employ the Girardi et al. (2000) theoretical isochrones (Padova00) and Salpeter (1955) IMF converted to the observational plane on the basis of extensive stellar photometric libraries and the MILES stellar spectral library. A particularly important peculiarity of the MILES spectra for this work is its excellent flux-calibration quality and good parameter coverage. asad2 first groups models with the same metallicity together, and then extracts the flux and stores it for the corresponding wavelength: one flux column for each age.4

The ages are converted into log (age/year) and rounded to two decimal points. Note that the ages provided by the model start at log (age/year) 7.78, which is relatively large compared to the other models. Another option is to start with 7.4 when using the model version based on BaSTI isochrones. We chose the Padova library for uniformity (with the other models used in asad2). The ages increase in step size of roughly 0.05.5 The results and the percentage errors are listed in Columns 8 and 9 of Tables 2 and 3 for the χ2 minimization method.

Fig. 8 shows the correlation between the ages obtained using MILES with the χ2 minimization method versus the CMD ages. We excluded the clusters with a CMD age younger than log (age/year) 7.78 (12 clusters of our sample). The correlation coefficient is 0.92. Fig. 9 shows the correlation between the ages obtained using MILES versus the ages obtained using the model of Gonzalez Delgado et al. (2005). The outlier is NGC 2172. Gonzalez Delgado et al. (2005) predict a log (age/year) 6.8 while MILES predicts a log (age/year) 7.85. MILES prediction is closer to the CMD age of this cluster [log (age/year) = 7.78]. Fig. 10 shows that there is another close possible solution around log (age/year) 7.5. The outlier in Fig. 9 shows that MILES chooses the older option among the two possible ones, which causes the two models to disagree for this particular cluster. Fig. 11 shows the correlation between the ages obtained using MILES versus the ages obtained using GALAXEV. The correlation coefficient is 0.99 when excluding the young clusters.

The correlation between the ages obtained using MILES with the χ2 minimization method versus the CMD ages when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.
Figure 8.

The correlation between the ages obtained using MILES with the χ2 minimization method versus the CMD ages when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.

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The correlation between the ages obtained using MILES with the χ2 minimization method versus the ages obtained using the model of Gonzalez Delgado et al. (2005) when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.
Figure 9.

The correlation between the ages obtained using MILES with the χ2 minimization method versus the ages obtained using the model of Gonzalez Delgado et al. (2005) when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.

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The surface plot of NGC 2172 predicted by Gonzalez Delgado et al. (2005) model with the χ2 minimization method. A second possible solution is noticed around log (age/year) 7.5.
Figure 10.

The surface plot of NGC 2172 predicted by Gonzalez Delgado et al. (2005) model with the χ2 minimization method. A second possible solution is noticed around log (age/year) 7.5.

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The correlation between the ages obtained using MILES versus the ages obtained using GALAXEV when using the χ2 minimization method when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.
Figure 11.

The correlation between the ages obtained using MILES versus the ages obtained using GALAXEV when using the χ2 minimization method when excluding the clusters younger than log (age/year) of 7.78. The green dotted line is the fit line.

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It is worth mentioning here that the spectral resolution of the model is greater than that of the clusters. We used a resolution of 3 Å for the model to make it similar to the resolution used with the previous models (to make the comparison consistent). To test our results, we did the fits again using the resolution of the model that matches the data [3.6 Å for SOAR data and 14 Å for Blanco data as described in Asa'd (2014)]; the results are almost identical as shown in Fig. 12. The outlier is NGC 1856 observed with Blanco.

The results obtained using a fixed resolution for the model higher than that of the data, compared to the results obtained when matching the resolution of the model to that of the data.
Figure 12.

The results obtained using a fixed resolution for the model higher than that of the data, compared to the results obtained when matching the resolution of the model to that of the data.

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The results obtained with MILES using the KS test and the percentage errors are listed in Columns 10 and 11 of Tables 2 and 3. Fig. 13 shows the correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method. The correlation coefficient is 0.80. NGC 2213 is an outlier. When compared with the CMD ages the χ2 minimization method gives a better prediction.

The correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method for MILES model. The correlation coefficient is 0.80. The red dashed line is the fit line.
Figure 13.

The correlation between the ages obtained using the KS test versus the ages obtained using the χ2 minimization method for MILES model. The correlation coefficient is 0.80. The red dashed line is the fit line.

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As we did with GALAXEV, we use the different metallicities of MILES to compare the ages obtained by each metallicity. Fig. 14 shows the age prediction using different combinations of metallicity as indicated in the key of the figure.

Age prediction using different combinations of metallicity for the MILES model as indicated in the key. See the text for more details.
Figure 14.

Age prediction using different combinations of metallicity for the MILES model as indicated in the key. See the text for more details.

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The blue stars show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.0004. The red circles show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.004. The green squares show log (age/year) obtained using metallicity Z = 0.0001 versus log (age/year) obtained using metallicity Z = 0.008 and so on. The dashed lines represent the upper and lower limits of the range of ages within 0.5 log (Age/year). 261 values out of 270 lie within that range, that is 96.7 per cent. We conclude that metallicity does not strongly affect the age determination for this method for log (age/year) < 9.5.

Fig. 15 shows the average absolute values of the difference in log (age/year) obtained using the different metallicities of both GALAXEV and MILES. The figure shows three main ranges. For young cluster [log (Age/year) < 7.4] the average age difference is less than 0.1. For intermediate ages [7.4 < log (Age/year) < 8.8] the average difference is around 0.2. Finally for ages > 8.8 the average difference is > 0.35. Except for two outliers, the average difference in log (Age/year) obtained by different metallicities with MILES is less than that seen for GALAXEV.

The average absolute value of the difference in log (age/year) obtained using the different metallicities of both GALAXEV and MILES.
Figure 15.

The average absolute value of the difference in log (age/year) obtained using the different metallicities of both GALAXEV and MILES.

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4.3 Dependence on age, S/N and resolution

To better understand the difference in the results obtained by the two statistical results for both GALAXEV and MILES, we investigate the dependence of this difference on three factors: age, S/N and resolution.

Fig. 16 shows the absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus CMD log (age/year). The least difference is seen for intermediate ages 7 < log (age/year) < 8.5.

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus CMD log (age/year).
Figure 16.

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus CMD log (age/year).

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Fig. 17 shows the absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus S/N. The difference varies for S/N < 60 and it is minimum for S/N > 60.

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) for versus S/N.
Figure 17.

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) for versus S/N.

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Fig. 18 shows the average absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus resolution element in angstroms (FWHM) available. For GALAXEV the difference decreases as the resolution increases. For MILES the difference is the same for the two resolutions 14 Å (FWHM) and 17 Å (FWHM).

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus resolution (FWHM) available.
Figure 18.

The absolute values of the difference in log (age/year) obtained using the two statistical methods (KS method–χ2 minimization method) versus resolution (FWHM) available.

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The correlation between the reddening obtained using the χ2 minimization method with both GALAXEV and MILES models versus the literature values. Note that only clusters older than log (age/year) 7.78 were included for MILES.
Figure 19.

The correlation between the reddening obtained using the χ2 minimization method with both GALAXEV and MILES models versus the literature values. Note that only clusters older than log (age/year) 7.78 were included for MILES.

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4.4 Error analysis

It is noted from the age values of Table 2 that the ages predicted by the two models (GALAXEV and MILES) when using either the χ2 minimization method or the KS test are mostly within a range of log (age/year) 0.5. As a means to estimate the uncertainty in our aging method, we have derived the relative error for each stellar cluster in our sample using the equation:
(1)

Here AgeCMD is the CMD age from the literature in years, and Agepredicted is the age obtained in this work in years. These values are presented for each cluster in Table 2. There are few age predictions with percentage error greater than 100 per cent. For GALAXEV age predictions, there are three clusters that have percentage error greater than 100 per cent regardless of the statistical method used, and three clusters for which the percentage error is greater than 100 per cent for the age predicted by the χ2 minimization method, while the age predicted by the KS test is closer to the correct value. Overall asad2 can predict good age estimates for unresolved clusters.

5 REDDENING

The main goal of the paper is to analyse the age determination for different models using different statistical methods. Although age and reddening are not physically related, the shape of the integrated spectrum for a cluster depends on both age and reddening. It is noted from Table 3 that the predicted reddening values when using the χ2 minimization method are within the range found in the literature for resolved clusters (i.e. < 0.35); however the KS test can predict E(B − V) values as high as 0.49 when constraining the upper limit to 0.5. Greater values are obtained when increasing the upper limit (see Section 2 for a discussion on NGC 2002). Determining the reddening is not easy for unresolved clusters. In this section we analyse the reddening predictions obtained by asad2 using the χ2 minimization method as shown in Fig. 19. The percentage error for the reddening determination is listed in Table 3. We used the equation:
(2)
where E(B − V)Lit. refers to the literature value and E(B − V)pred. refers to the predicted value in this work.

To understand the correlation between the reddening prediction as a function of age, we plot in Fig. 20 the difference in reddening values (our predicted values–literature values) versus the CMD age. For MILES we excluded the clusters with CMD age younger than log (age/year) 7.78. Both Figs 19 and 20 show that our method underestimates the values of the reddening except for four intermediate-age clusters. NGC 2002 has a CMD log (age/year) 7.20 and a literature reddening 0.12 while GALAXEV predicts a log (age/year) 6.82 with a reddening of 0.26. SL237 has a CMD log (age/year) 7.43 with a literature reddening 0.17 while GALAXEV predicts a log (age/year) 6.90 with a reddening 0.23. For such young age regime the rapidly varying spectrum shape as a result of the supergiants’ contributions around log (age/year) 7.0 is scattering both the age and reddening estimates. This effect should be better seen in the red part of the spectrum. We examined this by obtaining the age estimates when using the blue part of our spectrum (3626–4700 Å) and the red part of the spectrum (4700–6230 Å) separately. Fig. 21 shows the clusters that have a difference in the age prediction between the two spectral ranges larger than 0.5 as a function of CMD age. The clusters showing the largest age difference are located around the supergiants contribution, at either side of the AGB peak around log (age/year) 9.0 and around log (age/year) 7.8. We can conclude that the sharp spectrum transition originated at these ages is limiting our ability to provide values in agreement with the CMD estimates and as a result the reddening determination is not accurate.

The difference in reddening values (our predicted values–literature values) versus the CMD age. For MILES we excluded the clusters with CMD age younger than log (age/year) 7.78.
Figure 20.

The difference in reddening values (our predicted values–literature values) versus the CMD age. For MILES we excluded the clusters with CMD age younger than log (age/year) 7.78.

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The clusters that have a difference in the age prediction between the two spectral ranges larger than 0.5 as a function of CMD age. For MILES we excluded the clusters with CMD age younger than log (age/year) 7.78.
Figure 21.

The clusters that have a difference in the age prediction between the two spectral ranges larger than 0.5 as a function of CMD age. For MILES we excluded the clusters with CMD age younger than log (age/year) 7.78.

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6 DISCUSSION ON SPECIFIC CLUSTERS

In this section we discuss the details of four specific clusters of different ages, ranging from CMD log (age/year) 6.86 to 9.32. The full images are available as supplementary online material with this paper.

6.1 NGC 1994

NGC 1994 is a young cluster with a CMD log (age/year) 6.86. Fig. 22 shows the plots obtained by asad2 for this cluster. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test. The curves show the match between the dereddened observed integrated spectrum of NGC 1994 and the best GALAXEV model. We notice an offset between 4100 and 4300 Å for both statistical methods. The surface plots represent the inverse of all the possible solution for age–reddening combination. We notice that the results of GALAXEV show a range of possible solutions for the reddening [with log (age/year) of 7] when using the χ2 minimization method, and a range of close solutions between reddening of 0.23 and 0.30 and log (age/year) 6.5 and 6.7. As discussed in the previous section, we do not show the results from the MILES models as they cannot predict such young ages.

Results for NGC 1994. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.
Figure 22.

Results for NGC 1994. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.

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6.2 NGC 2002

NGC 2002 has a CMD log (age/year) 7.20. Fig. 23 shows the plots obtained by asad2 for this cluster. GALAXEV cannot produce a perfect spectral match because of the shape of the continuum of the observed spectrum. NGC 2002 has an even greater flux offset between model and observed spectrum than NGC 1994 because it has a worse S/N. The surface plots of GALAXEV show a range of possible solutions; the χ2 minimization solution is not unique (global minimum). Again, we do not show the results from the MILES models as they cannot predict such young ages.

Results for NGC 2002. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.
Figure 23.

Results for NGC 2002. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.

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6.3 NGC 2249

NGC 2249 has a CMD log (age/year) 8.82. Fig. 24 shows the plots obtained by asad2 for this cluster. The χ2 minimization method predicts ages closer to the CMD value. The KS method predicts younger ages with greater reddening.

Results for NGC 2249. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.
Figure 24.

Results for NGC 2249. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.

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6.4 NGC 2173

NGC 2173 has a CMD log (age/year) 9.32. Fig. 25 shows the plots obtained by asad2 for this cluster. The spectra show good match. The surface plots show that the solutions are unique (only one dark red region) but not precise (the dark red region has an extended area.).

Results for NGC 2173. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.
Figure 25.

Results for NGC 2173. The left column shows the results of the χ2 minimization method and the right column shows the results of the KS test.

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7 SUMMARY

In this paper we presented asad2 which is the updated version of asad (Asa'd 2014). We used it to conclude the following points.

  1. Unlike the χ2 minimization method, the KS method can predict reddening values higher than the values accepted for the LMC clusters. For one of the clusters in the sample, it also fails to break the age/reddening degeneracy.

  2. Metallicity does not strongly affect the age determination for the full spectrum filling method regardless of the model used for log (age/year) < 9. We are developing our method for older clusters, where the age/metallicity degeneracy is significant. For young cluster [log (Age/year) < 7.4] the average age difference when comparing the age prediction of different metallicities is less than 0.1. For intermediate ages [7.4 < log (Age/year) < 8.8] the average difference is around 0.2 and for ages > 8.8 the average difference is > 0.35. In general, the average difference in log (Age/year) obtained by different metallicities with MILES is less than that seen for GALAXEV.

  3. There is a strong correlation between the ages predicted by Delgado model and GALAXEV. The difference in the predicted log (age/year) by the two models for 50 per cent of the clusters is less than 0.05.

  4. There is a good agreement between the ages predicted by MILES and GALAXEV for ages greater than log (age/year) of 7.78, but because MILES does not have predictions for younger ages the estimated young ages do not match those of GALAXEV.

  5. When comparing the results obtained with MILES models using a fixed resolution higher than that of the data to those obtained when matching the MILES resolution to the data resolution, we notice that the results are almost identical.

  6. When comparing the age prediction difference of |(KS method–χ2 minimization method)| versus CMD log (age/year), the least difference is seen for intermediate ages 7 < log (age/year) < 8.5.

  7. When comparing the age prediction difference of |(KS method–χ2 minimization method)| versus S/N, the difference varies for S/N < 60 and it is minimum for S/N > 60.

  8. When comparing the age prediction difference of |(KS method–χ2 minimization method)| versus resolution (FWHM), for GALAXEV the difference decreases as the resolution increases. For MILES the difference is the same for the two resolutions 14 Å (FWHM) and 17 Å (FWHM).

  9. The sharp spectrum transition originated at supergiant and AGB ages is limiting our ability to provide values in agreement with the CMD estimates and as a result the reddening determination is not accurate.

We thank Adnan Shahpurwala who carefully ran the Windows version of asad2 and compared the results. His availability to always help is highly appreciated. We thank the anonymous referee for providing constructive comments for improving the content of this paper. We also thank Dr. Santos and Dr. Palma for allowing us to use their integrated spectra for seven clusters. This material is based upon work supported in part by the FRG14-2-05 Grant P.I., R. Asa'd from American University of Sharjah. We also acknowledge support from grant AYA2013-48226-C3-1-P from the Spanish Ministry of Economy and Competitiveness (MINECO).

1

asad2 allows the user to choose the statistical method preferred (χ2 minimization method or the KS test method).

2

The ages provided by the model are not perfectly uniform in the step size. They start at log (age/year) 5.10, and increase in step of 0.05 up to 6.00, then increase in steps of 0.02 up to 7.48 and then vary slightly in the step size up to 10.10. The spectral fluxes between log (age/year) 5.1 and 6.2 are identical so asad2 skips the ages less than log (age/year) 6.2.

3

Represented by m52 in the model library.

4

In the MILES model, the flux values are divided into separate files based on the model's metallicity, age, and IMF slope. The values of the metallicity, age, and IMF slope are encoded in the name of each file.

5

For the LMC clusters we used the fixed metallicity Z = 0.008 (represented by [M/H] = −0.4 in the model library).

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