Ages of LMC Star Clusters from Their Integrated Properties

Ages of LMC Star Clusters from their Integrated Properties

A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulﬁllment of the requirements for the degree of

Doctor of Philosophy

in the Department of Physics of the College of Arts and Sciences by

Randa Asa’d M.S University of Cincinnati

May, 11 2012

Committee Chairs: M. M. Hanson, Ph.D. and M. D. Sokoloﬀ, Ph.D Abstract

Star Clusters are the building blocks of galaxies. Determining their ages gives us information about the formation history of their hosting galaxies.

For far-away galaxies, star clusters are not resolved. Only their integrated properties can be observed. Both integrated photometry and integrated spectra have been used as age indicators of stellar clusters. The Large Magellanic Cloud (LMC) is a perfect galaxy to test these methods of age determination, because its clusters are close enough to see their individual stars, but also far enough away so that each cluster can be observed as a whole.

This work ﬁrst shows that the traditional methods of using the integrated broad-band photometry for age determination are highly inaccurate. This is attributed primarily to two things. First, the UBV integrated broad-band aging methods require matching a cluster with an expected model prediction of the cluster colors as a function of age. The biggest problem we ﬁnd is the stellar clusters in our sample do not typically lie on the model line based on their known age and extinction. That is to say, real cluster colors often do not match the model colors and can be found some distance from expected model values. A second issue, which has been previously documented in numerous studies, is the strong degeneracy between age and extinction in the UBV color-color plane. Certainly, providing more photometric bands will reduce degeneracy between age and reddening. Better yet, if extinction can be independently determined, we show that ages from methods based on integrated broad-band colors will more closely match those obtained from more accurate methods based on stellar photometry. But the underlying issue remains. Simple stellar population models often do not accurately represent the colors of real stellar clusters due to the incomplete and stochastic sampling of the stellar mass function in low and moderate mass stellar clusters.

On the other hand, integrated spectra provide better age predictions than broad-band photometry in the wavelength range 3626 6248 A when compared with high resolution computational models. I obtained the integrated spectra of 20 clusters that didn’t have integrated spectra in the optical range, or they have never been observed before. Using ths sample and 7 other clusters from the literature I show that the statistical Kolmogorov- Smirnov (KS) test can better ﬁnd the closest match between the observed spectrum and theoretical model than the traditional χ2. Finally, I present a new software routine that eﬃciently predicts the age of a star cluster given its optical integrated spectrum compared to spectra generated by computational models. . To my parents : Dorina and Samir Acknowledgements

I would like to acknowledge my advisors, Dr. Margaret Hanson and Dr. Mike Sokoloff. I have been lucky to have them as advisors and mentors. Dr. Margaret Hanson is a role model for me. She not only trusted me by giving me the opportunity to choose and shape my own research project, but also helped me improve both my teaching and leadership skills by encouraging me to attend workshops, classes and even conferences overseas. Dr. Sokoloff has been very patient with me from the first day when I told him that I don’t have the needed background knowledge for any research work. He simply replied: ”That’s why you are here; To learn!”. And indeed, ever since then he has been teaching and guiding me. My gratitude also goes to Dr. Andrea Ahumada, who although not physically present with me, was a great advisor for me. She was so patient and kind to answer tens of my questions about my project.

I would also like to thank all my professors in the physics department at University of Cincinnati, my professors at Jordan University of Science and Technology who taught me the basics of physics, as well as all my professors and teachers who taught me since the day I learned how to hold a pencil in my hand.

My words won’t be enough to express my gratitude to the great people I met in Cincinnati. They not only made the six years I spent here a joyful time, but also inspired and taught me a lot. They reshaped my personality in a good way.

I would also like to acknowledge my two sisters, my friends and relatives overseas who never stopped encouraging me throughout the years. I am thankful for every person who had a role in my life helping me reach this point. Last and not least I want to thank my dear parents who trusted me, allowed me to follow my dreams and never stopped believing in me.

For Chapter 2: Rolf Andreassen provided signiﬁcant assistance in creating the χ2 surface plots. We also acknowledge critical suggestions and guidance early on in this project from Rupali Chandar, Ata Sarajedini, Bogdan Popescu and in particular, Mark Hancock, who shared his χ2 minimization software with us. This material is based upon work supported by the Na- tional Science Foundation under Grant No. AST-0607497 and AST-1009550 to the University of Cincinnati, P.I., M. Hanson. R.S.A. was supported in part by NSF Grant No. PHY-0855860 to the University of Cincinnati, P.I., M. Sokoloﬀ.

For Chapter 4: I acknowledge Dr. Stephane Blondin who helped me learn IRAF, Dr. Mario Muray for the assistance with the ﬂux calibration, Dr. Nidia Morel helped establishing the collaboration of this work. Dr. San- tos, Dr. Fernandes, Claus Leitherer and Bogdan Popescu provided useful comments. I also acknowledge Dr. Sean Points for his assistance the staﬀ at CTIO and SOAR for their valuable help and guidance. This material is based upon work supported by the National Science Foundation under Grant No. AST-0607497 and AST-1009550 to the University of Cincinnati, P.I., M. Hanson. NOAO sponsored my travels to Blanco and SOAR viii Contents

List of Figures xi

List of Tables xvii

1 Introduction 1 1.1 The Large Magellanic Cloud (LMC) ...... 1 1.2 Ages and Colors of Stars ...... 3 1.3 Simple Stellar Populations ...... 3 1.4 Masses of clusters using MASSCLEAN ...... 4 1.5 Some attempts to determine accurate ages of star clusters ...... 5

2 Investigating aging methods of LMC star clusters using integrated colours 9 2.1 abstract ...... 9 2.2 Introduction ...... 10 2.3 The cluster sample ...... 12 2.3.1 Using MASSCLEAN to estimate cluster mass ...... 12 2.4 CMD age compared with diﬀerent studies of photometric age ...... 14 2.4.1 s-parameter age ...... 14 2.4.2 Hunter et al. photometric ages ...... 16 2.4.3 A χ2 minimization method ...... 19 2.5 The s-parameter age and Hunter age ...... 22 2.6 The χ2 minimization method ...... 23 2.6.1 The colours produced by the model ...... 26 2.6.2 Further investigations of the χ2 minimization method ...... 27 2.6.3 Restricting the extinction limit ...... 30

ix CONTENTS

2.6.4 The χ2 minimization surface plots ...... 31 2.6.5 χ2 minimization for lower metallicity ...... 35 2.7 Discussion ...... 35 2.8 Conclusion ...... 37

3 Integrated Spectra of Stellar Clusters 49 3.1 The Spectrum of a Star ...... 49 3.1.1 The Spectral Classes ...... 51 3.2 Ages of Star Clusters from their Integrated Spectra ...... 52 3.3 Observations ...... 58 3.3.1 Day Calibration images ...... 62 3.3.2 Night observations ...... 66 3.4 Data Reduction ...... 67

4 Ages of LMC star clusters from integrated spectra 73 4.1 Introduction ...... 73 4.2 The Data ...... 74 4.3 Integrated Spectra Models ...... 81 4.4 The Method ...... 84 4.5 More Integrated Spectra from the Literature ...... 97 4.6 Review of Previous Results on the Subsample of this Work ...... 119 4.7 Discussion ...... 119 4.8 Conclusion and future work ...... 119

5 Conclusion and Future Work 131 5.1 Introduction ...... 131 5.2 Introducing New Software: ASAD ...... 132 5.3 Future Work ...... 133

Bibliography 137

x List of Figures

1.1 The Large Magellanic Cloud galaxy ...... 2 1.2 The HR diagram ...... 3 1.3 Integrated colors for diﬀerent SSP models as a function of age for solar metallicity ...... 4 1.4 Star clusters follow a main sequence similar to the one of the stars. . . .6 1.5 S parameter ...... 7

2.1 The number of clusters in our sample for each log (age). Our sample has few age gaps, the biggest one is between log (age)= 8.2 and 8.6 yrs. . . 13 2.2 Estimating cluster mass...... 14 2.3 The number of clusters in our sample for each mass region listed in section 2.1...... 15 2.4 The s-parameter-derived age vs CMD-derived age. The two aging methods show a very good match, with a correlation coefficient of 0.95. . . . 16 2.5 Mass regions on the s-parameter age versus CMD age diagram. . . . . 17 2.6 Hunter et al. (2003) photometry-derived age vs CMD-derived age. . . . 18 2.7 Similar to Figure 6, but the mass regions are identified. For this sample the scatter about the line doesn’t appear to be a clear function of cluster mass...... 18 2.8 The modeled colour-colour diagram for different values of reddening. . . 20 2.9 The predicted photometric age using the χ2 minimization method versus the published CMD age...... 21 2.10 The mass ranges of the clusters using χ2 minimization aging methods versus the published CMD age...... 22 2.11 U-B vs B-V colours of the clusters in each subsample...... 23

xi LIST OF FIGURES

2.12 Comparing the model (SB99) U − B with the de-reddened published U − B for the 84 clusters sample...... 24 2.13 Comparing the model (SB99) U − B with the de-reddened published U − B for the 84 clusters sample...... 24 2.14 The same analyses as in Figure 12 is done for B − V for the 84 clusters sample...... 25 2.15 The same analyses as in Figure 12 is done for B − V for the 84 clusters sample...... 25 2.16 The difference in χ2 predicted and CMD age...... 26 2.17 The difference between the predicted and published ages...... 28 2.18 The sigma lines...... 28 2.19 The distribution of the difference between the predicted and published E(B − V )...... 29 2.20 The predicted photometric using χ2 minimization age versus the published CMD age with the error bars for the clusters with a predicted extinction higher than 0.35...... 30 2.21 The extinction predicted by the χ2 minimization method when we limit our extinction to 0.5 versus the extinction predicted when we allow extinctions up to 0.8...... 31 2.22 The predicted photometric age versus the published CMD age with the error bars using the known published extinction...... 32 2.23 NGC 1844 has one minimum value at the log (age/yr) = 8.36 with E(B− V ) = 0.02 (listed in Table 3)...... 33 2.24 For SL 549, on the other hand, there are two solutions, one at log (age/yr) = 9.32 with E(B − V ) = 0.008, and the other at log (age/yr) = 7.80 with E(B − V ) = 0.7...... 33 2.25 NGC 2231 shows a solution at log (age/yr) = 8.44 and E(B − V ) = 0.46 (listed in Table 3)...... 34 2.26 SL 791 has no clear distinct minimum...... 34 2.27 The predicted photometric age using the χ2 minimization method versus the published CMD age for the metallicity of 0.004...... 36 2.28 The mass ranges of the clusters using χ2 minimization aging methods versus the published CMD age for the metallicity of 0.004...... 36

xii LIST OF FIGURES

3.1 Balmer discontinuity at 3630 A ...... 50 3.2 The classes from main-sequence (dwarf) stars. Note the very strong eﬀect of the Balmer jump, at the early A stars...... 53 3.3 A sketch of the EW ...... 54 3.4 Lick/IDS indices ...... 56 3.5 The results of ...... 57 3.6 Telescope Sketch ...... 59 3.7 ANU telescope ...... 60 3.8 The components of a spectrograph ...... 60 3.9 Bias image ...... 63 3.10 Bias image ...... 63 3.11 Dark image ...... 64 3.12 Dark image ...... 64 3.13 Flat image ...... 65 3.14 Flat image ...... 65 3.15 A raw image of the spectrum of the cluster NGC2002 ...... 68 3.16 NeAr comparison lamp ...... 68 3.17 NeAr comparison lamp ...... 69

3.18 Hδ Balmer absorption ...... 70 3.19 Spectrum of a standard star before calibration with units of ADU versus pixel. Note tha the ’blue’ end of the detector is on the right side . . . . 71 3.20 Final calibrated spectrum units of ergs/cm/cm/s/A versus Angstroms. . 71

4.1 The region observed in each cluster ...... 75 4.2 The distribution of ages (log age/year) for the sample observed with the Blanco telescope represented by the red boxes and the clusters observed with SOAR telescope represented by the blue boxes ...... 79 4.3 The distribution of masses (refer to Chapter 2 for details about the deﬁ- nition of mass ranges) for the sample observed with the Blanco telescope represented by the red lines and the clusters observed with SOAR telescope represented by the blue lines ...... 80

xiii LIST OF FIGURES

4.4 The extinction-age space for the clusters observed with Blanco represented by the red diamonds and the clusters observed with SOAR telescope represented by the blue squares ...... 80 4.5 The clusters observed with Blanco...... 82 4.6 The clusters observed with SOAR...... 83 4.7 NGC1711 ...... 86 4.8 NGC1856 ...... 87 4.9 NGC1903 ...... 88 4.10 NGC1984 ...... 89 4.11 NGC2002 ...... 90 4.12 NGC2011 ...... 91 4.13 NGC2156 ...... 92 4.14 NGC2157 ...... 93 4.15 NGC2164 ...... 94 4.16 NGC2173 ...... 95 4.17 NGC1651 ...... 96 4.18 NGC1850 ...... 98 4.19 NGC1863 ...... 99 4.20 NGC1983 ...... 100 4.21 NGC1994 ...... 101 4.22 NGC2002 ...... 102 4.23 NGC2031 ...... 103 4.24 NGC2065 ...... 104 4.25 NGC2155 ...... 105 4.26 NGC2173 ...... 106 4.27 NGC2213 ...... 107 4.28 NGC2249 ...... 108 4.29 The correlation between our obtained ages and the literature CMD ages 109 4.30 The correlation between our obtained E(B-V) and the literature E(B-V) 110 4.31 NGC1839 ...... 112 4.32 NGC1870 ...... 113 4.33 NGC1894 ...... 114 4.34 SL237 ...... 115

xiv LIST OF FIGURES

4.35 NGC2136 ...... 116 4.36 NGC2172 ...... 117 4.37 SL234 ...... 118 4.38 The correlation between the ages obtained from integrated photometry and CMD ages for the current subsample. The correlation coefficient is 0.67 ...... 120 4.39 The mass ranges on the previous figure ...... 121 4.40 The correlation between the extinction obtained from integrated photometry and the extinction from literature for the current subsample . . 122 4.41 The correlation between the ages obtained from integrated spectra and CMD ages for the current subsample. The correlation coefficient is 0.78 123 4.42 The mass ranges on the previous figure ...... 124 4.43 The correlation between the extinction obtained from integrated spectra and the extinction from literature for the current subsample ...... 125 4.44 A reasonable match between the model and the observation using the χ2 method ...... 126 4.45 A reasonable match between the model and the observation using the χ2 method ...... 127 4.46 A poor match predicted by the χ2 method ...... 128 4.47 A poor match predicted by the χ2 method ...... 129

5.1 The clusters that have observed spectra in the visible range...... 134

xv LIST OF FIGURES

xvi List of Tables

2.1 The sample list ...... 39 2.2 Ages references ...... 43 2.3 χ2 Predicted age and uncertainty ...... 47

3.1 Fraunhover lines ...... 51

4.1 Blanco Run (February 2011) ...... 76 4.2 SOAR Run (December 2011) ...... 76 4.3 Targets Observed ...... 78 4.4 Our Results ...... 96 4.5 Data from the Literature ...... 111 4.6 Results ...... 112

xvii LIST OF TABLES

xviii Chapter 1

Introduction

The star formation history of a galaxy can be studied by tracking the age of its star clusters. Star clusters are the building blocks of the galaxies. They are large groups of stars that are formed together and are gravitationally bound. Knowing the ages of star clusters helps us understand the formation history of their host galaxies. Accurate determination of clusters’ ages gives us a better understanding of galaxies which in turn reveals more information about our universe.

1.1 The Large Magellanic Cloud (LMC)

The Large Magellanic Cloud (LMC) is a galaxy of our Local Group. The galaxies of the Local Group are our nearest neighbors in the universe. There are more than 40 (mostly small) galaxies in the Local Group including our Galaxy, the Large Magellanic Cloud (LMC), the Small Magellanic Cloud (SMC) and Andromeda (M31). These galaxies lie within a distance of 1.5 Mpc from our own galaxy Van den Bergh (2000). Figure 1.1 is an image of the Large Magellanic Cloud galaxy. The LMC can be seen with the naked eye in the southern hemisphere summer sky. This galaxy is a great laboratory for studying the star clusters. With its relatively close by distance of slightly less than 50 kiloparsecs (160,000 light years) it makes is possible for us to observe the individual constituent stars of its clusters. At the same time it is far away enough to enable us to observe the clusters as a whole single astronomical object. The distance to the LMC is virtually the same for all clusters and stars within it. Meaning clusters and stars can be directly compared without worrying about relative

1 1. INTRODUCTION

Figure 1.1: The Large Magellanic Cloud galaxy - NASA

distance diﬀerences, which greatly hamper similar studies within the Milky Way. The

LMC hosts hundreds of star clusters of various age, mass and metallicity, providing an enormously rich sample to constrain star and star cluster evolution and the star formation history of the LMC (Vuillemin, 1988, Sagar & Pandey, 1989, Olszewski et al.,

1991, Vallenari et al., 1994, 1998, Olsen, 1999, Piatti et al., 2003, Mackey & Gilmore,

2003, Harris & Zaritsky, 2009).

The wide variety of age estimation methods, available in the literature led us to this work.

For my dissertation, I will ﬁrst test how accurate the results of the most often used method (integrated photometry) is for a sample of 84 star clusters. After that I will present an alternative method (integrated spectroscopy), and show my age estimation results for 20 clusters of this sample.

2 1.2 Ages and Colors of Stars

1.2 Ages and Colors of Stars

The color of a star depends on its mass and age. For our study, we take the color- magnitude diagram (CMD) method of ﬁnding the age as the ”accurate” method of ﬁnding the age. This method looks at the individual stars in the cluster and plots them on the color magnitude diagram. This diagram is similar to the Hertzsprung - Russel (HR) diagram which is a plot of luminosity versus temperature.

Figure 1.2: The HR diagram - Source: diagram (2012)

When the cluster is very young, stars of all masses are present forming the main sequence, with more massive stars on the upper left side, and the less massive stars on the lower right side. More massive stars leave the main sequence first as they run out of Hydrogen fusion. On the HR diagram, the region where the stars leave the main sequence is called the turn off point. The location of the turn off point determines the age of the cluster.

1.3 Simple Stellar Populations

The most elementary model of star clusters is the Simple Stellar Population (SSP) . This model assumes all stars are born at the same time in a single burst of star formation of negligible time duration and all with the same initial chemical composition. The theoretical CMD from an SSP is called an isochrone from the Greek word meaning ”same age” (Salaris & Cassisi, 2005). For distant, unresolved stellar clusters, one may only be able to observe the integrated light properties than observing the individual stars within the cluster to build the CMD of each cluster.To interpret this integrated

3 1. INTRODUCTION light, it is important to obtain theoretical tools like the SSP that can predict the age and chemical composition of a population from its integrated magnitude and colors. In a diagram of magnitude versus log age, the overall property is a general fading of the total cluster magnitude for increasing age when the age is greater the 107 yr. This is mainly due to having less stars at older ages, as well as the overall general decrease of the He-burning luminosity for increasing age. It should be noted that the absolute values of the integrated magnitude of an unresolved SSP is not very useful without knowing the mass of the observed SSP (Salaris & Cassisi, 2005).

Figure 1.3: Integrated colors for diﬀerent SSP models as a function of age for solar metallicity - Source: Popescu & Hanson (2009)

1.4 Masses of clusters using MASSCLEAN

Cluster mass is typically derived based on the estimated cluster age and the observed luminosity of the cluster. However, to convert this to a mass requires an SSP model. One such SSP model is MASSive CLuster Evolution and ANalysis (MASSCLEAN) package (Popescu & Hanson, 2009). MASSCLEAN uses evolutionary tracks which give the evolution of stars for diﬀerent masses. For clusters with masses larger than 104

4 1.5 Some attempts to determine accurate ages of star clusters solar masses were directly generated by MASSCLEAN. For masses less than 104) solar masses, we scaled the result from MASSCLEAN for a cluster with mass = 106 solar masses. We did this is to avoid the magnitude fluctuations that occur for lower mass clusters . We modeled a high mass cluster to get expected luminosity with age. We then derived the cluster mass based on the age and luminosity of the observed cluster scaled to the luminosity of the modeled 106 mass cluster. As follows: The mass is proportional to the flux. V is proportional to (−2.5 log flux). To scale the magnitude of a mass of 103 solar masses:

V3 + 2.5logM3 = V6 + 2.5logM6

V3 − V6 = 2.5logM6 − 2.5logM3 6 3 V3 = V6 + 2.5log((10 )/(10 ))

1.5 Some attempts to determine accurate ages of star clusters

The earliest method used to identify ages of star clusters is the Color-Magnitude Dia- gram (CMD). This is done by observing the colors and magnitude of individual stars in the cluster and placing them on a Color-Magnitude Diagram, then fitting isochrones of different ages to identify the best fit to represent the cluster’s age. Investigating the star clusters in the LMC started in the early 1960s. (Hodge, 1960a,b,c,d, 1961) found that some LMC clusters are much younger than any of the globular clusters in our galaxy, which means that the formation history of the LMC is different than that of our own Galaxy (Harris & Zaritsky, 2009). One of the earliest, most famous works of using a CMD to obtain ages of star clusters is the work of Hodge (1983). He obtained the ages of 81 LMC clusters. The CMD method was not the only method of determining the ages in the 1980s, the other method was assigning ages by means of integrated colors. The need for a new method arose from the fact that for distant clusters individual stars cannot be observed. The entire cluster is seen as one object. In 1980, Searle, Wilkinson and Bagnuolo (SWB) Searle et al. (1980) showed that the star clusters follow a main sequence similar to the one of the stars (Figure 1.4).They found that the integrated photometry of populous star clusters may be arranged in

5 1. INTRODUCTION a one dimensional sequence based on integrated colors. Their work showed that the integrated colors (from a blue to red color) correlate with cluster ages. The color-age correlation of these studies shows that redder colors (more positive color) indicate an older cluster. A young cluster can contain stars of all masses, and the very massive, blue stars dominate the color of the entire cluster. As the cluster ages, the massive stars die. The color of the entire cluster as a whole becomes increasingly red, as the blue stars die and the redder, long living, low mass stars begin to dominate the clusters color. Inspired by this idea diﬀerent methods of determining the ages of star clusters from integrated photometry were established. van den Bergh (1981) compiled the integrated photometry for 147 LMC clusters. Elson & Fall (1985) plotted the (U-B) vs (B-V) for 33 LMC clusters, and ﬁtted a line, inspired by the line of SWB that passes through the data. They then divided the the line into 50 regions starting from the upper left corner reaching the lower right corner (Figure 1.5). They called the sequence of numbers of 1 to 50 the s parameter. A relation relating the s parameter with the age was given.

Figure 1.4: Star clusters follow a main sequence similar to the one of the stars. - Source: (Searle et al., 1980)

In the mean time, more CMD ages for single clusters were obtained by diﬀerent groups (Flower, 1984, Alcaino & Liller, 1987, Da Costa et al., 1987, Buonanno et al., 1988, Mould et al., 1989) and others. Using these new CMD ages Elson & Fall (1988) improved their s parameter age calibration. Sagar & Pandey (1989) created a database

6 1.5 Some attempts to determine accurate ages of star clusters

Figure 1.5: S parameter - Source: (Elson & Fall, 1985) with all CMD age obtained until 1989. Bica et al. (1992) enlarged the sample of LMC clusters with integrated photometry totaling 129 objects. (Girardi et al., 1995) expanded on this calibration by replacing the proposed sequence line of (Elson & Fall, 1985) with the direct outputs from simple stellar population (SSP) models introduced by (Bertelli et al., 1994). They used the published extinction for the clusters when available, and used a value of E(B − V ) of 0.07 for the clusters with no published extinction. Bica et al. (1996) compiled a catalog with the integrated photometry of 624 LMC clusters. Another approach was taken by (Pietrzynski & Udalski, 2000) using the Optical Gravitational Lensing Experiment (OGLE). They consistently determined ages for more than 600 clusters by creating their own CMDs and fitting Padova isochrones for Z = 0.008. This method can be applied to a large sample but it is not very accurate because this method requires high-resolution images in order to resolve individual stars and subtract the the interloper field population of stars. As the power of computers advanced in the late 1990s, many Simple Stellar Population models were established. These models vary in their details but agree, in principle, in their isochrones and evolutionary tracks. Few examples are (Leitherer et al., 1999, Hurley et al., 2000, Bruzual & Charlot, 2003, Vazquez & Leitherer, 2005) and (Maraston, 2005). These models were used in different ways to determine the ages of numerous stellar clusters in external galaxies like the LMC. (Hunter et al., 2003) derived ages by comparing their

7 1. INTRODUCTION photometric colors with the Starburst99 Leitherer99 evolutionary model with Z= 0.008 for ages up to 1 Gyr. For ages in the range from 1 to 10 Gyr, they used the UBV colours of Searle73 and the (Charlot & Bruzual, 1991) SSP models for the evolution of the V-band luminosity. Hunter et al. (2003) compared their cluster colors with models using UBV and BVR to get age. They used the extinction curve of (Cardelli et al.,

1989), RV = AV /E(B −V ) = 3.10 and assumed a value of E(B −V ) = 0.13 mag for all clusters. Another method using integrated colors and recently used by (Chandar et al., 2010) to derive ages for over 900 LMC clusters based on the Hunter et al. (2003) colours. The method matches the observed integrated colours to reddened model colors using a statistical minimization calculation. This serves to achieve the best possible match between observed and model colors and hence the best cluster age estimate based on integrated colours. Meanwhile, more CMD ages were obtained (Vallenari et al., 1994, 1998, Geisler et al., 1997, Olsen, 1999, Dirsch et al., 2000, Dieball et al., 2000, Mackey & Gilmore, 2003) and others. In chapter 2, I discuss the diﬀerent types of photometric ages and compare each one of them with the CMD ages. A weak correlation was found and motivated us to observe the spectra of these star clusters in order to get their ages by means of integrated spectra. Chapter 3 discusses the details of our observing runs, and the reduction of our spectra. In chapter 4 I present our result of obtaining ages by means of integrated spectra and conclude with future work on stellar cluster aging methods in chapter 5.

8 Chapter 2

Investigating aging methods of LMC star clusters using integrated colours

This chapter has been published in Randa Asa’d and M.M. Hanson, 2012, Monthly Notices of the Royal Astronomical Society, 419, 2116

2.1 abstract

We present an investigation of 84 star clusters in the Large Magellanic Cloud (LMC) galaxy, using different broad-band photometric, age-estimation methods. Because of its intermediate distance, the LMC is uniquely positioned to compare its clusters that have previously been aged using both resolved photometry (colour-magnitude diagrams, CMDs) of the constituent stars and unresolved methods (integrated, broad-band colour photometry). In our comparison between the published CMD ages to three similar, but different methods based on UBV integrated colours we find rather poor matches. We attribute this primarily to two things. First, the UBV integrated broad-band aging methods require matching a cluster with an expected model prediction of the cluster colours as a function of age. The biggest problem we find is the stellar clusters in our sample do not typically lie on the model line based on their known age and extinction. That is to say, real cluster colours often do not match the model colours and can be found some distance from expected model values. A second issue, which has been

9 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS previously documented in numerous studies, is the strong degeneracy between age and extinction in the UBV plane. Certainly, providing more photometric bands will reduce degeneracy between age and reddening. Better yet, if extinction can be independently determined, we show that ages from methods based on integrated colours will more closely match those obtained from CMD ages. But the underlying issue remains. Simple stellar population models often do not accurately represent the colours of real stellar clusters due to the incomplete and stochastic sampling of the stellar mass function in low and moderate mass stellar clusters.

2.2 Introduction

Knowing the characteristics of star clusters helps us understand the evolution and structure of the galaxies they populate. Determining the age of star clusters has been an important goal for astronomers studying other galaxies because it provides us with quantitative measures for the star formation history of a galaxy and can answer questions like: Was star formation constant? Did it have a burst due to a collision or other triggering event? What fraction of stars was formed in these clusters (Mighell et al., 1998, Rich et al., 2000, Piatti & Claria, 2001, Piatti et al., 2002)? A signiﬁcant obsta- cle in achieving this goal is the great distance of most extragalactic star clusters; the individual stars can not be viewed. We can only observe the integrated light coming from these clusters and this limits our ability to assign properties such as age to them. Broadly speaking, two of the most common ways to estimate the age of a star cluster is to obtain a colour-magnitude diagram (CMD) of the constituent stars in the cluster (Hodge 1983, Elson 1988, Geisler et al. 2003) or derive broad-band photometric ages based on the clusters integrated light (Girardi & Bica, 1993, de Grijs & Anders, 2006, Pandey et al., 2010). There are other methods such as modeling the clusters integrated spectra (Leonardi & Rose, 2003, Schiavon et al., 2004), or matching template integrated spectra of star clusters onto observed integrated spectra of the studied clusters (Ahumada et al., 2002, Santos et al., 2006) but they will not be investigated here. Depending on the age and photometric bands used, fairly accurate cluster ages can be derived when the full CMD of a stellar cluster is created, particularly if there is a well deﬁned giant branch. To derive integrated photometric ages, one depends on modeling the integrated light of all the stars and must make some assumptions about

10 2.2 Introduction the cluster properties to derive its age (Vallenari et al., 1998, Balbinot et al., 2010, Chandar et al., 2010). The Large Magellanic Cloud (LMC) galaxy is a logical object to base a new investigation of photometric ages because its clusters have been historically studied in integrated light. Yet, the LMC is nearby enough that a large number of clusters have been resolved into their constituent stars, allowing CMDs to be obtained and thus ages derived in that way. The LMC is the hybrid case where the two methods, near and far, meet. Moreover, it possesses an extensive system of rich stellar clusters with a wide range in age, structure, environment and mass (Vuillemin, 1988, Sagar & Pandey, 1989, Olszewski et al., 1991, Vallenari et al., 1994, 1998, Olsen, 1999, Piatti et al., 2003, Mackey & Gilmore, 2003, Harris & Zaritsky, 2009). The goal of this paper is not to estimate the ages of star clusters based on a specific integrated-colours method, but rather to compare these aging methods obtained from the literature with the published CMD ages. We do not present any new methods or data. The contribution of this work to the literature is a general investigation of how well different integrated-colour aging methods match the CMD ages. Despite some efforts (Yi et al., 2000, Hancock et al., 2008) there remains a serious need for more calibration clusters to test these heavily-used integrated-light methods (Conroy & Gunn, 2010). The CMD ages are taken as the calibrated age against which the integrated-colour ages are compared. By collecting a relatively large number of clusters with published CMD ages (84 clusters), we present new comparisons and discuss the findings. In section 2 we present our data sample with CMD ages taken from the literature and we estimate the mass for the star clusters in our sample. There are many developed methods that rely on integrated colours to determine cluster ages. We will briefly discuss three of these aging methods and compare them to the CMD ages. Section 3 compares the CMD age with historic s-parameter age (Elson & Fall, 1985). Section 4 compares the CMD age with the photometric ages found by Hunter et al. (2003). Section 5 compares the CMD age with the photometric ages found using a new χ2 minimization method recently used by Hancock et al. (2008) and Chandar et al. (2010). These three photometric methods for finding the age are similar but somewhat different in their technique and results. In section 6 we discuss our findings and outline our conclusions in section 7.

11 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

2.3 The cluster sample

We began with a search of the literature for LMC star clusters with ages derived from photometric CMDs. This was not an easy task, given that the different studies use different evolutionary models to derive their ages. We only considered clusters that had published CMD ages, but we also required a published uncertainty in their CMD age, as well as published UBV integrated colours. Very old clusters (log (age) > 9.5 yrs) were excluded because they pose significant complexities (broader variation in metal abundance and the complications of models for the late evolution of low mass stars). A final list of 84 clusters was compiled and is presented in Table 1. For convenience, we used the most common name type, NGC, in Table 1 for the cluster name. For the clusters without NGC names, we used [SL63] = (SL) (Shapley & Lindsay, 1963). Column 3 is the CMD log (age) obtained from the literature. Columns 4 and 5 represent the range in the log of the uncertainty in the age (sources mentioned in Table 2). Column 6 is the apparent magnitude, followed by the absolute magnitude in column 7. The distance modulus used for the LMC is 18.48 (Hunter et al., 2003). Column 8 has observed U − B followed by B − V in column 9. The sources of these colours are listed in column 10. Column 11 shows extinction, E(B − V ), with the references in column 12. Table 2 provides the references of all the ages found for our cluster sample. Here ages are given in linear years, the same as given in the references cited. Only ages with published uncertainties were included in this list. For our study and what was listed in Table 1, we typically chose the cluster age with the smallest uncertainties or the age from the most recent study (suggesting it used the most modern stellar evolutionary models). Our sample of clusters span a wide range of log (age) from 6.6 to 9.5 yrs. Figure 1 shows that we have few log (age) gaps in our sample, the biggest one being between log(age) = 8.2 and 8.6 yrs. More than 25% of the clusters are in the region of log (age) = 7.6, 7.7 and 7.8 yrs.

2.3.1 Using MASSCLEAN to estimate cluster mass

We used MASSCLEAN, the stellar cluster simulation package (Popescu & Hanson, 2009), to estimate cluster mass by computing the absolute magnitude (V) as a function

12 2.3 The cluster sample

Figure 2.1: The number of clusters in our sample for each log (age). Our sample has few age gaps, the biggest one is between log (age)= 8.2 and 8.6 yrs. - More than 25% of the clusters are in the region of log (age)= 7.6, 7.7 and 7.8 yrs of log (age) for a range of cluster masses (Figure 2). Using the distance modulus of 18.48 (Hunter et al., 2003), and the published extinction we derived the absolute magnitude for our clusters and then placed our clusters on that plot. This gives us an estimate of the cluster’s total mass. The legend in Figure 2 shows the mass of our 4 cluster sample in solar mass. The lines for clusters with masses larger than 10 M 4 were directly generated by MASSCLEAN. For masses less than 10 M , we scaled the 6 result from MASSCLEAN for a cluster with mass = 10 M . We did this is to avoid the magnitude ﬂuctuations that occur for lower mass clusters (Popescu & Hanson, 2010a,b). We rescaled the predicted V magnitude with age by adding the factor 2.5∗ log ((106) / cluster mass) to the MASSCLEAN output magnitude. Among the youngest clusters, their masses are rather small, while the oldest clusters are typically 10 or more times more massive. It is expected that as cluster mass decreases, variation in the observed integrated colours should increase, due to increased dominating eﬀects of stochastic variations within the cluster’s stellar mass distribution (Chiosi et al., 1988, Bruzual A., 2002, Yi, 2003, Cervino & Luridiana, 2004, 2006). For this reason, we divided Figure 2 into 5 regions in anticipation of looking for trends in our age results based on cluster mass. Category 1 has 5 clusters with masses from

13 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.2: Estimating cluster mass. - We used MASSCLEAN (Popescu & Hanson, 2009) to estimate cluster mass by computing the absolute magnitude (V) as a function of log (age) for a range of cluster masses.

4 1000 to 3,750 M . Category 2 has 24 clusters with mass from 3,750 to 10 M M .

Category 3 has 28 clusters with masses between 10,000 and 25,000 M . Category 4 has 22 clusters with masses between 25,000 and 100,000 M . Category 5 has 5 clusters with masses between 100,000 - 250,000 M . This is shown in Figure 3.

2.4 CMD age compared with diﬀerent studies of photometric age

2.4.1 s-parameter age

Elson & Fall (1985) expanded on the first integrated colour-colour stellar cluster classification introduced by Searle et al. (1980) (SWB), by using the more commonly available UBV two-colour system. Elson & Fall (1985) introduced a parameter, called s, which was found by fitting a sequential line through the clusters - similar to the age sequence found in colour by SWB - and splitting it into 51 intervals of equal length. The cluster location on this sequence correlates to the cluster age. They calibrated this s sequence with LMC stellar clusters with known CMD ages. Girardi et al. (1995) expanded on this calibration by replacing the proposed sequence line of Elson & Fall (1985) with

14 2.4 CMD age compared with diﬀerent studies of photometric age

Figure 2.3: The number of clusters in our sample for each mass region listed in section 2.1. - the direct outputs from simple stellar population (SSP) models introduced by Bertelli et al. (1994). They used the published extinction for the clusters when available, and used a value of E(B − V ) of 0.07 for the clusters with no published extinction. A list of 64 clusters with both CMD ages and s-parameter ages was given in Girardi et al. (1995) to calibrate this sequence. We compared our CMD ages with the s-parameter ages for those clusters in our sample that were listed in Girardi & Bertelli (1998). We were careful not to use any of the same 64 LMC clusters Girardi et al. (1995) used for their initial calibration of the s-parameter - log (age) relation. In Figure 4, we present 21 clusters taken from Girardi & Bertelli (1998), and compare their s-parameter derived age with that from our literature CMD values. There appears to be in excellent agreement, as the clusters lie very close to the 1:1 expected line, with a correlation coefficient of 0.95. Figure 5 shows the distribution of mass regions from the s-parameter study on this same age-age diagram of Figure 4. We do not see any mass-dependent effect in the strength of the match between s-parameter ages and CMD ages. There is 1 cluster in the mass region 1, the lowest cluster masses, 3 clusters in mass region 2 with a correlation coefficient of 0.99, 10 clusters in mass region 3 with a correlation coefficient of 0.91, 4 clusters in mass region 4 with a correlation coefficient of 0.98, and 2 clusters

15 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.4: The s-parameter-derived age vs CMD-derived age. The two aging methods show a very good match, with a correlation coeﬃcient of 0.95. - Extinction was previously constrained for most clusters in mass region 5 with a correlation coeﬃcient of 1. With our small sample, the s- parameter method appears no better at predicting the age of high mass clusters (the 4s and 5s) than the low mass clusters (the 1s and 2s).

2.4.2 Hunter et al. photometric ages

The second set of ages derived from integrated-colour come from the catalog of Hunter et al. (2003). The Hunter et al. (2003) ages where derived by comparing their photometric data with the Starburst99 (Leitherer et al., 1999) evolutionary model with Z= 0.008 for ages up to 1 Gyr. For ages in the range from 1 to 10 Gyr, they used the UBV colours of Searle et al. (1973) and the Charlot & Bruzual (1991) SSP models for the evolution of the V-band luminosity. Hunter et al. (2003) compared their cluster colours with models using UBV and BVR to get age. They used the extinction curve of Cardelli et al. (1989), RV = AV /E(B − V ) = 3.10 and assumed a value of E(B − V ) = 0.13 mag for all clusters. From our literature search of typical E(B − V ), as given in Table 1, this is a reasonable assumption. In Figure 6, we compare the CMD ages of our clusters with the ages determined by Hunter et al. (2003). In the same paper Hunter et al. (2003) showed that the

16 2.4 CMD age compared with diﬀerent studies of photometric age

Figure 2.5: Mass regions on the s-parameter age versus CMD age diagram. - Using the s-parameter to predict age is no better with high mass clusters (the 4s and 5s) than with the low mass clusters (the 1s and 2s). relation between CMD derived ages and their ages from integrated colours was not well correlated. They had only 10 star clusters to make such a comparison. In this paper we investigate this result in more detail with 33 clusters. Indeed, we also see a rather large scatter of the clusters away from the expected correlated line, with a correlation coefficient of just 0.34. There are only 2 clusters in the mass region 1 with a correlation coefficients of 1, 13 clusters in mass region 2 with a correlation coefficient of 0.72, 10 clusters in mass region 3 with a correlation coefficient of 0.32, and 3 clusters in mass region 4 with a correlation coefficient of -0.49. The agreement between CMD-derived ages and the Hunter et al. (2003) derived ages goes down as cluster mass increases, but we caution the final two high mass bins are not sufficiently populated to make this statement with any certainty. It was suggested by de Grijs & Anders (2006) that if one uses the Johnson-Cousins filter system even if based on the appropriate conversion equations, instead of the native Landolt KPNO system, one will obtain lower ages than expected at the young-age end of the age range covered by our LMC cluster sample, and vice versa. The systematic differences in LMC cluster ages between the Hunter et al. (2003) results and others may be caused by their conversions of the photometry to a different filter system. This

17 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.6: Hunter et al. (2003) photometry-derived age vs CMD-derived age. - We see a large scatter of the clusters away from the 1:1 line with a correlation coeﬃcient of 0.34.

Figure 2.7: Similar to Figure 6, but the mass regions are identified. For this sample the scatter about the line doesn’t appear to be a clear function of cluster mass. - There are only 2 clusters in the mass region 1 with a correlation coefficients of 1, 13 clusters in mass region 2 with a correlation coefficient of 0.72, 10 clusters in mass region 3 with a correlation coefficient of 0.32, and 3 clusters in mass region 4 with a correlation coefficient of -0.49. None of our CMD clusters from mass region 5 were included in the Hunter et al. (2003) study.

18 2.4 CMD age compared with diﬀerent studies of photometric age trend in the diﬀerence in age estimations is not clear in our Figure. However, this might go unnoticed due to the small number of clusters in this subsample.

2.4.3 A χ2 minimization method

Our ﬁnal comparison will investigate a more recently developed method, used by Chan- dar et al. (2010) to derive ages for over 900 LMC clusters based on the Hunter et al. (2003) colours. Also used by Hancock et al. (2008) to study Milky Way stellar clusters, the method matches the observed integrated colours to reddened model colours using a statistical minimization calculation. This serves to achieve the best possible match between observed and model colours and hence the best cluster age estimate based on integrated colours. Regrettably, the Chandar et al. (2010) study did not provide tab- ulated ages for their individual clusters for us to compare to the CMD ages we have. Luckily, we can readily reproduce their ages using their method. Moreover, in our previous investigations, we were limited to a subsample of our total number of CMD clusters where there was overlap with previous studies. For this comparison, we can use our whole sample of 84 clusters with CMD-derived ages, not just those clusters in common. The best-ﬁt values of age and extinction are those that minimize χ2 (Hancock et al., 2008, Chandar et al., 2010):

N X (colour)obs − (colour)mod χ2 = ( i i )2. (2.1) σ i=1 i

We deﬁne (colour)obsi as the observed colour and (colour)modi as the model colour.

The uncertainty of the observed colours is σi. We use σi = 0.019 for U-B and σi = 0.016 for B-V from Bica et al. (1996), where the photometry originates. Note that N=2 because we have 2 colour sets: U − B and B − V . It was shown by Hancock et al. (2008) that U −B was the most powerful for providing the most accurate predicted age of any of the colours. Combining U − B with B − V further improves the accuracy of the predicted age. We ﬁnd the minimum and maximum ages within a ∆χ2 to determine the uncertainty in the predicted age. We did the same thing to ﬁnd the uncertainty in the predicted extinction. We used the Starburst99 models (Leitherer et al. 1999) version 5.1.1, which include the Padova asymptotic giant branch (AGB) stellar model (Vazquez & Leitherer 2005). We adopt the single LMC metallicity of 0.008 also used byChandar et al. (2010). Just

19 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS as was used by Hancock et al. (2008), our SB99 model spectral energy distributions (SEDs) were generated assuming a Kroupa (2002) initial mass function (IMF) that favours high mass stars with exponents of 1.3 and 2.3 for the mass ranges from 0.1 to 0.5 M and 0.5 to 100 M , respectively. We have assumed instantaneous (a single 6 5 burst) star formation with total stellar mass of 10 M . We chose the step size of 10 years between ages of 106 and 107 years, 106 years between ages of 107 and 108 years and 107 years between ages of 108 and 109 years. Finally we reddened the model colours with values from E(B − V ) = 0.0 to 0.8 mag, in increments of 0.02 mag. Figure 8 shows the model output colour-colour relationship used for diﬀerent values of reddening. Figure 8 illustrates the well known and signiﬁcant degeneracy exhibited between stellar cluster age and extinction in such a diagram (Wise & Silva, 1996, Gordon et al., 1997, Lancon et al., 2001, Whitmore & Zhang, 2002).

Figure 2.8: The modeled colour-colour diagram for diﬀerent values of reddening. - The key shows the diﬀerent reddening values of E(B − V ) applied to the model colours.

While there is no observed extinction for LMC clusters beyond E(B − V ) = 0.23, we assumed no prior knowledge for the extinction limit in our study. We allowed the χ2 method to explore extinction values that covered the full colour range populated with observed clusters. We used the CCM extinction law Cardelli et al. (1989) where E(U − B) = 0.890687 E(B − V ). Figure 9 shows the age predicted using the χ2

20 2.4 CMD age compared with diﬀerent studies of photometric age minimization method versus the published CMD age. A list of all the output ages derived are given in Table 3 with errors. The uncertainties in predicted age from the χ2 minimization method are fairly large in some cases. The correlation coeﬃcient in Figure 9 is 0.53, an improvement over the Hunter et al. (2003) clusters, but not as well correlated as the Girardi & Bertelli (1998) clusters, where extinction was previously constrained.

Figure 2.9: The predicted photometric age using the χ2 minimization method versus the published CMD age. - The correlation coeﬃcient is 0.53

Figure 10 shows the mass regions of the clusters on the diagram of the predicted photometric age versus the published CMD age. It was our interest to know if our χ2 method would be more effective with higher mass clusters. There are 5 clusters in the low mass range 1. The correlation coefficient for this mass range is 0.99. There are 24 clusters in the mass range 2 with a correlation coefficient of 0.40. In the mass range 3 there are 28 clusters. The correlation coefficient for this mass range is 0.66. The 22 clusters in the mass range 4 have a correlation coefficient of 0.06. Finally we have 5 clusters in the mass range 5 with a correlation coefficient of -0.97. Our sample is statistically very small, but we do not see any evidence that the χ2 method works any better or worse based on the cluster’s mass over the mass range we have sampled.

21 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.10: The mass ranges of the clusters using χ2 minimization aging methods versus the published CMD age. - The χ2 minimization method seems to match equally well with CMD derived ages of high mass clusters (4s and 5s) as it does for the low mass clusters (1s and 2s).

2.5 The s-parameter age and Hunter age

As seen from the previous section, the correlation coeﬃcients are 0.95 and 0.34 for the s-parameter age and the Hunter age, respectively. To understand why the s-parameter ages shows such a high correlation compared to the Hunter ages it should be noted that Girardi et al. (1995) used the published extinction for each cluster while Hunter et al. (2003) used one value for the extinction for all the LMC clusters. We plot the U − B vs B − V colours of the clusters in each subsample in Figure 11. The s-parameter ages come from two sources: Girardi et al. (1995) and Girardi et al. (1998). Because the clusters in the Girardi et al. (1995) were used for the initial calibration of the s-parameter - log (ages) relation, we gave those clusters an open symbol in Figure 11. Recall that these clusters were not included in the calculation of the correlation coeﬃcient. Yet the value, 0.95, based on the Girardi et al. (1998) clusters was still impressibly high. Does this suggest this method is superior and all clusters should be aged using the s-parameter method? Not necessarily. Recall Girardi et al. (1995) knew the correct

22 2.6 The χ2 minimization method extinction before hand. Also as can be seen in Figure 11, most of the s-parameter clusters are found to lie very close to the model line, making it much easier to assign ages. On the other hand, the Hunter sample of clusters often lie relatively far from the model line, and single extinction was used for all clusters. This makes it much harder to assign an accurate age to these clusters, particularly if extinction is unusual. This may explain in part the reason for the large diﬀerence in correlation coeﬃcients of the two methods. If the extinction corrected colours of the sample clusters happen to lie close to the model SSP line, the age assignment is likely to be more accurate. The larger the scatter of the sample from the model line, the more challenging the age determination.

Figure 2.11: U-B vs B-V colours of the clusters in each subsample. - The s- parameter ages from the initial paper used to calibrate for the s-parameter are shown as an open circle.

2.6 The χ2 minimization method

To better understand the ages given by the χ2 method, we will ﬁrst examine the accuracy of the predicted model colours. In essence, we want to see if for a speciﬁc age, the model colours match the observed colours of clusters based on their CMD ages. This is a critical assumption being made in using the χ2 method.

23 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.12: Comparing the model (SB99) U − B with the de-reddened published U − B for the 84 clusters sample. - The correlation coeﬃcient is 0.88.

Figure 2.13: Comparing the model (SB99) U − B with the de-reddened published U − B for the 84 clusters sample. - Dispersion is not a clear function of mass.

24 2.6 The χ2 minimization method

Figure 2.14: The same analyses as in Figure 12 is done for B − V for the 84 clusters sample. - The correlation coeﬃcient is 0.85.

Figure 2.15: The same analyses as in Figure 12 is done for B − V for the 84 clusters sample. - Dispersion is not a clear function of mass.

25 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

2.6.1 The colours produced by the model

As mentioned in an earlier section, we used the Starburst99 model for our calculations. For every cluster age, the model predicts a specific pair of U − B and B − V colours. In Figure 12 we compare the observed, dereddened, U − B colour for each cluster in our sample of 84 versus the predicted model U − B colour based on the cluster CMD age. Several serious mismatches are revealed here, and they do not appear to be a strong effect of cluster mass over our mass range. We have made a similar comparison of the observed, dereddened B − V colours with the model predicted U − B colours in Figure 13. Even more serious mismatches are revealed here. The correlation coefficient is 0.88 and 0.85, respectively, for the two bands. An important premise of the χ2 minimization method is that the underlying cluster colour, once corrected for extinction, is properly predicted by the model. However, our Figures 12 & 13 show that in a rather significant fraction of real clusters, this is not the case. This demonstrates a serious problem with the χ2 minimization method. The predicted model colour may be correct for an average cluster of that age, but that model colour might not be the colour of a real cluster. We will take this one step further: all integrated colour aging methods are suspect if the SSP models they rely on for predicting the underlying colour do not always match those of the real, unreddened clusters.

Figure 2.16: The difference in χ2 predicted and CMD age. - The inner lines represent a factor of 3 difference in age, and the outer lines a factor of 10 difference in age.

26 2.6 The χ2 minimization method

The colours from SSP models were never intended to predict the colours of stellar clusters. Stellar population synthesis models were developed for interpreting the integrated light observed from entire galaxies of stars, not single star clusters (Leitherer et al., 1999, Bruzual & Charlot, 2003). In general, there is good agreement between observations of entire galaxies and these models. This is because galaxies have very large masses representing billions of stars, allowing them to be studied using the statistical assumptions essential to SSP codes. However, for most star clusters, this is 6 not the case. As cluster mass decreases below 10 M , and based on the cluster age and photometric bands used (Yi, 2003, Cervino & Luridiana, 2006, Popescu & Hanson, 2010a,b), the statistical ﬂuctuations in the integrated colour will begin to become sig- niﬁcant and continue to increase with lowering mass (Chiosi et al., 1988). Virtually all 6 4 clusters in the LMC are less massive than 10 M . Most clusters are even less than 10

M . We’ve searched again and again for evidence that the lower mass set of clusters in our sample of 84 CMD clusters showed greater error in their integrated colour ages without ﬁnding any. The sample size we have may be too small to clearly show such a trend if one exists.

2.6.2 Further investigations of the χ2 minimization method

In Figure 9, we showed the predicted ages of our 84 CMD clusters using the χ2 minimization method. There does appear to be a disturbing trend: more than half of the CMD clusters with relatively old ages (log(age) > 8.5 yrs), are predicted by χ2 minimization to be relatively young (log(age) < 8.5 yrs). We investigate this trend further in a new plot of the same data in Figure 14. The central dashed line shows identical age predictions between CMD and the χ2 minimization method. The dotted lines represent a factor of 3 difference in age, and the outer solid lines represent a factor of 10 difference in age. The lower panel provides a histogram of the same information, showing the distribution of the difference between the χ2 minimization method predicted and published ages. The inner and outer lines represent a factor of 3 and 10 change in age, respectively. It would appear there is a possible overabundance of clusters for which the CMD ages are older than the predicted χ2 integrated colour age. Why might the χ2 method tend to under-predict the age of older clusters? The answer might lie with the extinction derived using the χ2 minimization method. The top panel of Figure 15 shows just how off the predicted extinction values can be. The

27 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.17: The diﬀerence between the predicted and published ages. - The inner and outer lines represent a factor of 3 and 10 change in age, respectively

Figure 2.18: The sigma lines. - The inner lines represent a change of E(B − V ) = 0.2, and the outer lines represent a diﬀerence of 0.5.

28 2.6 The χ2 minimization method central dashed line indicates identical values for extinction between the observed and χ2 minimization method. The inner dotted lines represent a difference of 0.2 mag in extinction, and the outer solid lines represent a difference of 0.5 mag. The lower panel is a histogram showing the distribution of the difference between the predicted and published E(B − V ). The inner and outer lines represent a factor of 0.2 mag and 0.5 mag change, respectively. Its not that the published extinction and χ2 predicted extinction are so poorly matched, but there is a significant bias showing the χ2 method is over estimating the extinction in a significant number of clusters.

Figure 2.19: The distribution of the diﬀerence between the predicted and published E(B − V ). - The inner and outer lines represent a diﬀerence of E(B − V ) = 0.2 and 0.5, respectively.

Plotting the CMD age versus predicted age diagram for clusters with a predicted extinction higher that 0.35, we get Figure 16. The overestimated extinction on average leads to an underestimation of the age for those clusters.

29 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.20: The predicted photometric using χ2 minimization age versus the published CMD age with the error bars for the clusters with a predicted extinction higher than 0.35. - As expected, the model underestimates the age of these clusters.

2.6.3 Restricting the extinction limit

As Figure 8 shows, the predicted reddening from the χ2 minimization method can reach E(B − V ) values nearing 0.8, while the real observations limit the LMC extinction too much less than that. There is no observed extinction for our LMC cluster sample greater than E(B − V ) = 0.23 (Table 1). Might the χ2 minimization work better if we limit the searchable range in extinction, as was done in Chandar et al. (2010)? In Figure 17 we plot the extinction predicted by the χ2 minimization method when we limit our extinction to E(B − V ) < 0.5 versus the extinction predicted where we allow extinctions up to E(B − V ) < 0.8. Up to 0.5 the predicted extinction is the same, but for E(B − V ) > 0.5 diﬀerent solutions with a lower extinction are simply forced to be found. Finally, we test the results from the χ2 minimization method using the cluster extinction values found from the literature. This is shown in Figure 18. By using the published extinction, one gets a much better prediction for the age without any obvious age bias. The correlation coeﬃcient is 0.89, the best of all the correlations using χ2 minimization method, and approaching the match achieved by Girardi et al. (1995)

30 2.6 The χ2 minimization method

Figure 2.21: The extinction predicted by the χ2 minimization method when we limit our extinction to 0.5 versus the extinction predicted when we allow extinctions up to 0.8. - who also used the known extinction. This level of correlation is about as high as one would expect, given that the model predictions of the cluster colours do not correlate to real cluster colours any better than this, even when the cluster age and extinction is known (see Figures 12 & 13).

2.6.4 The χ2 minimization surface plots

To better understand the χ2 minimization method and its results, we created plots showing the χ2 values over a 2 − D surface plot of the entire extinction and age- range explored by the algorithm. This is shown for four clusters in Figures 19 & 20. Although unphysical, we considered an extinction range for this demonstration from E(B − V ) = −0.1 to 1. Because of the nature of the output, these plots were created using a different program than the one used in our previous χ2 minimization calculations, however, both are described by Eqn. 1. Small differences may appear in rounding off errors, meaning the results are similar, just not identical. A quick look at these Figures reveals the fact that there is a strong correlation between age and reddening (this was already clear in Figure 8). This age-extinction degeneracy using colours has been known for a long time. But also, some plots show multiple minima,

31 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.22: The predicted photometric age versus the published CMD age with the error bars using the known published extinction. - The correlation coeﬃcient is 0.89 each might be potentially ﬂagged as ‘solutions’. In the upper panel of Figure 19, we provide the solution set for NGC 1844. It has one minimum value at the age of Log(age) = 8.36 yr with E(B − V ) = 0.02. The CMD age for this cluster was found to be log(age) = 7.70 yr). In the lower panel of Figure 19 we show SL549 which shows two solutions, one at Log(age) = 9.3 yr with E(B − V ) = 0.008, and the other at Log(age)= 7.8 yr with E(B − V ) = 0.7. When the χ2 minimization calculation is allowed to run up to E(B − V ) = 0.8, both solutions are equally acceptable. For this cluster the predicted older value with lower reddening is very close to the published values of E(B − V ) = 0.04 and the Log(CMD age) of 9.3 yr. NGC 2231, in the upper panel of Figure 20 shows two solution of Log(age) = 8.44 yr and E(B − V ) = 0.46 (listed in Table 3) but it also has another solution found: Log(age) = 9.1 yr, with E(B − V ) = 0.05. This later solution, not the one found as the most likely by the χ2 minimization, is a more reasonable match to the CMD value (Log(CMD age) = 9.08 yr). Also the later value of E(B − V ) is more acceptable given that no E(B − V ) >0.35 were found in the literature for LMC clusters. Finally, the lower panel of Figure 20 shows the surface plot for SL 791. This does not show any clear minimum. An age of Log(age)=8.08 yr and E(B −V ) = 0.0 is predicted

32 2.6 The χ2 minimization method

Figure 2.23: NGC 1844 has one minimum value at the log (age/yr) = 8.36 with E(B − V ) = 0.02 (listed in Table 3). -

Figure 2.24: For SL 549, on the other hand, there are two solutions, one at log (age/yr) = 9.32 with E(B − V ) = 0.008, and the other at log (age/yr) = 7.80 with E(B − V ) = 0.7. - The one assigned and given in Table 3 is the ﬁrst one.)

33 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.25: NGC 2231 shows a solution at log (age/yr) = 8.44 and E(B − V ) = 0.46 (listed in Table 3). - However it also has a solution at log (age/yr) = 9.05, with E(B − V ) = 0.05, which is a closer match to the CMD age value.

Figure 2.26: SL 791 has no clear distinct minimum. - An age of log (age/yr) = 8.08 and E(B − V ) = 0.0 is listed in Table 3.

34 2.7 Discussion from the χ2 minimization method. Looking over these four plots, we see a trend. Blue clusters tend to be ﬁt to young, unreddened clusters reasonably consistent with their CMD age. However, intrinsically red clusters can yield two solutions, one indicating an intrinsically red and old cluster with little extinction and another indicating an intrinsically blue and young cluster, with greater extinction. This eﬀect is manifest in Figure 9 where half the older clusters were assigned too young of ages by the χ2 method. The χ2 minimization method should not be trusted as a means to a single solution. One should look at the full solution set, such as shown in our surface plots, to decide whether the assigned solution is the only solution or if it is one of several solutions or even a family of solutions. Of course, if the extinction is already known, then the χ2 minimization method might be better trusted (§5.3).

2.6.5 χ2 minimization for lower metallicity

In our analysis above we used the LMC metallicity of 0.008. Although this value is appropriate for clusters younger than 1 Gyr, it might not be for the older ones. Pandey et al. (2010) have done an extensive study comparing SSP models to the integrated photometry of LMC clusters and note the expected changes in colours due to lower metallicities. Some of our clusters are older than 1 Gyr , where metallicity is known to be significantly lower (Piatti et al., 2009). To ensure we are not seeing a metallicity effect, we consider a lower metallicity of 0.004 for the χ2 minimization analyses in this section. Figure 21 shows the predicted photometric age using the χ2 minimization method versus the published CMD age. The correlation coefficient is 0.52. Recall that the correlation coefficient for the metallicity of 0.008 is 0.53. Figure 22 shows the mass ranges of the clusters using χ2 minimization aging methods versus the published CMD age. The poor match between CMD age and age from integrated photometry can not be explained away as a change in metallicity with age. As the figures above, no mass trend is seen in Figure 22 either.

2.7 Discussion

From the analysis of these methods we see that the s-parameter age and the Hunter et al. (2003) age give more accurate age estimations for clusters with known extinction

35 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Figure 2.27: The predicted photometric age using the χ2 minimization method versus the published CMD age for the metallicity of 0.004. - The correlation coeﬃcient is 0.52

Figure 2.28: The mass ranges of the clusters using χ2 minimization aging methods versus the published CMD age for the metallicity of 0.004. -

36 2.8 Conclusion and that lie close to the model line. The further the cluster lies from the model line, the larger the uncertainty will be for an age estimate even if the extinction is knows. One might refer to these as ‘fair weather’ cluster age methods. The χ2 minimization method solves for both the age and the extinction simultaneously, making it potentially more powerful. The problem arises when this method is applied to extragalactic clusters with unknown extinctions. If the extinction of the LMC clusters were truly unknown, one would need a plot like Figure 8 to estimate the extinction limits over which the χ2 minimization method would need to be run. And as was shown, this can lead to a rather biased result due to the strong degeneracy between age and reddening (unknown metallicity only adds to this degeneracy). At times, this method will ﬁnd solutions of old, lightly reddened clusters to be young and more heavily reddened. As seen by comparing Figure 9 and Figure 18, if we can constrain the extinction using another, independent method, better ages are predicted. However, even that is not going to be any more accurate than the previous methods discussed (s-parameter and the aging methods used by Hunter et al. 2003). All of these methods are hindered by the fact that they rely on a ﬁt to a SSP model line that assumes it predicts the cluster colour accurately as a function of age. We’ve shown that this is not always the case.

2.8 Conclusion

We have scanned the literature to create a sample of 84 stellar clusters in the LMC that have reasonably modern, well constrained ages from a CMD analysis. We used this sample as a basis to investigate age determination methods using integrated colour photometry of those stellar clusters. We conclude the following:

1. The model predicted colours do not always match the observed cluster colours for a certain age. The single model line that was created assumes galaxy mass systems and doesn’t account for statistical ﬂuctuation expected in lower mass single stellar clusters.

2. Even if the model colours were correct for the clusters being modeled, there is a large degeneracy between age and extinction for clusters using UBV integrated- colours methods on a colour-colour plot. This is somewhat addressed if extinction can be constrained independently.

37 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

3. Perhaps due to our small statistical sample (84 clusters) we did not ﬁnd any trend indicating the integrated colour aging methods worked any better for the highest 5 3 mass systems (> 10 M ) over the lower mass systems (10 M ) in our sample.

4. The χ2 minimization method, while appearing superior in design, does not demon- stratively ﬁnd more accurate ages over previous methods using integrated colours when compared to CMD ages. This should be expected since it suﬀers from all the same inadequacies of all the integrated colours, aging method as given above.

5. Moreover, the χ2 minimization method appears susceptible to overestimating E(B − V ) in older, red stellar clusters, leading to younger estimated ages. Our χ2 solution surface plots show strong discontinuities, leading to missed solutions. Some clusters will show multiple or even ‘families’ of reasonable solutions. This is in part due to the degeneracy of an integrated colour aging method.

6. Using a lower value for the metallicity (0.004) in our older clusters was not seen to improve the χ2 minimization method.

Finally, implicit to our study was that we had consistent and accurate ages for 84 LMC clusters. This is simply not true. However, we have put together the largest sample presently available from the literature based on recent CMD analyses. A sizable sample of LMC star clusters with accurate ages based on CMD diagrams and obtained using a single, consistent evolutionary model, is sorrily needed to advance this field. Such a sample is needed to provide sufficient confidence in calibrating integrated broad- band and spectroscopic methods applied to distant extragalactic stellar clusters.

38 2.8 Conclusion source Elson(1991) Elson(1991) Elson(1991) Elson(1991) Hodge(1983) Elson+(1988) Maurer(1990) Maurer(1990) Persson(1983) Piatti+(2003I) Allesio+(2007) Kerber+(2007) Kerber+(2007) Kerber+(2007) Piatti+(2003II) Mould+(1986a) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) Alcaino+(1987) 0.1 0.1 0.1 0.2 0.1 0.2 0.2 0.1 0.09 0.16 0.12 0.13 0.12 0.09 0.15 0.27 0.12 0.25 0.18 0.21 0.15 0.18 0.06 0.04 0.14 0.065 E(B-V) Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Hunter Hunter Hunter Hunter Hunter Hunter Hunter Hunter Hunter source Continued on next page 0.71 0.12 0.76 0.16 0.60 0.61 0.22 0.18 0.34 0.27 0.21 0.77 0.15 0.69 0.25 0.45 -0.12 0.339 0.327 0.132 0.209 0.192 0.427 0.231 0.219 0.212 (B-V) 0.28 0.26 0.17 0.23 0.13 0.31 0.08 0.15 -0.37 -0.20 -0.51 -0.46 -0.23 -0.14 -0.27 -0.90 -0.02 -0.317 -0.105 -0.257 -0.330 -0.314 -0.080 -0.217 -0.456 -0.333 (U-B) The sample list -6.54 -7.61 -7.48 -8.08 -9.06 -6.479 -8.866 -9.002 -7.953 -6.952 -9.059 -7.028 -7.054 -6.015 -7.521 -6.772 -8.338 -9.468 -8.826 -9.257 -9.065 -6.287 -5.756 -7.034 -7.524 -5.8815 V (mag) Table 2.1: 9.85 9.70 9.57 9.88 9.73 12.28 10.11 12.25 12.80 10.93 11.90 11.18 12.93 12.08 11.31 9.874 12.91 11.57 11.762 12.046 11.796 10.917 10.274 12.751 11.020 11.390 v (mag) 7.6 7.7 9.4471 8.7075 Age(l) 9.47707 9.04134 9.11387 7.95418 7.25523 7.79927 7.68119 8.17602 7.61274 7.74029 9.30096 7.30096 7.69891 7.60202 8.04134 7.36168 8.07913 7.87501 8.77808 8.04134 7.55624 8.00856 7.2 7.3 7.4471 7.3979 9.07913 9.30096 8.84504 8.69891 6.99996 7.20407 8.46235 7.51846 7.99996 7.67207 9.25523 7.07913 7.47707 7.30096 7.69891 7.04134 7.77812 7.61274 8.60202 7.69891 7.47707 7.62321 Age(u) 7.4 7.5 Age 9.3979 7.7075 7.7634 9.30096 8.95418 8.95418 7.69891 7.23039 8.60202 7.68119 7.57974 8.09685 7.51846 9.27868 7.20407 7.60202 7.47707 7.90302 7.23039 7.95418 8.69891 7.90302 7.51846 7.85729 Name NGC1651 NGC1711 NGC1718 NGC1755 NGC1777 NGC1783 NGC1810 NGC1818 NGC1831 NGC1834 NGC1836 NGC1838 NGC1839 NGC1844 NGC1846 NGC1847 NGC1850 NGC1854 NGC1856 NGC1858 NGC1860 NGC1863 NGC1865 NGC1866 NGC1868 NGC1870

39 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS source Elson(1991) Elson(1991) Elson(1991) Elson(1991) Elson(1991) Hodge(1983) Hodge(1983) Dirsh+(2000) Elson+(1988) Maurer(1990) Maurer(1990) Maurer(1990) Maurer(1990) Maurer(1990) Persson(1983) Persson(1983) Persson(1983) Kerber+(2007) Kerber+(2007) Alcaino+(1987) Zaritski+(2004) Zaritski+(2004) Zaritski+(2004) Zaritski+(2004) Zaritski+(2004) Dieball+(2000II) Vallenari+(1998) 0.1 0.1 0.1 0.13 0.16 0.16 0.09 0.06 0.09 0.14 0.14 0.12 0.06 0.08 0.07 0.09 0.18 0.18 0.16 0.16 0.15 0.16 0.07 0.10 0.13 0.02 0.10 E(B-V) Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Hunter Hunter Hunter Hunter Hunter source Continued on next page 0.35 0.14 0.20 0.33 0.78 0.16 0.09 0.34 0.04 0.20 0.26 0.24 0.26 0.57 0.84 0.28 0.69 0.81 0.12 0.19 0.28 -0.16 0.322 0.134 0.275 0.012 -0.007 (B-V) 0.06 0.25 0.24 0.03 0.23 -0.25 -0.15 -0.20 -0.75 -0.69 -0.58 -0.71 -0.83 -0.07 -0.12 -0.10 -0.91 -0.49 -0.13 -0.07 -0.16 -0.14 -0.460 -0.813 -0.632 -0.679 -0.789 (U-B) -8.25 -7.41 -8.63 -7.41 -7.843 -7.863 -7.116 -6.516 -6.139 -7.966 -9.919 -8.918 -9.134 -8.752 -9.407 -8.148 -9.727 -7.929 -7.188 -7.798 -9.656 -6.806 -9.751 -7.602 -6.327 -5.833 -5.942 V (mag) 8.84 9.78 8.97 9.32 11.04 11.86 12.46 12.62 10.70 9.996 10.10 9.259 10.58 10.83 11.85 11.24 12.17 9.194 12.37 10.54 13.05 12.60 11.38 10.16 11.38 10.927 11.374 v (mag) 7.8 7.4 8.3 7.8 9.27 Age(l) 7.77812 7.99996 7.90302 7.69891 9.47707 6.95418 6.95418 6.90307 6.95418 6.84504 6.84504 7.95418 7.95418 6.77812 6.77812 7.07913 6.95418 8.95418 7.69891 9.49131 7.95418 7.95418 7 7.4 8.1 7.4 8.95 7.69891 7.60202 7.69891 7.47707 9.30096 6.84504 6.69891 6.81951 6.84504 6.69891 6.69891 7.69891 7.69891 6.30101 6.30101 6.90307 6.69891 8.69891 7.47707 9.27868 7.47707 7.47707 Age(u) 7.6 7.2 7.6 8.20 9.11 Age 9.3979 9.3979 7.74029 7.84504 7.81286 7.60202 6.90307 6.84504 6.86328 6.90307 6.77812 6.77812 7.84504 7.84504 6.60202 6.60202 6.99996 6.84504 8.84504 7.60202 7.77812 7.77812 Continued Name Table 2.1 – NGC1872 NGC1894 NGC1903 NGC1969 NGC1972 NGC1978 NGC1983 NGC1984 NGC1994 NGC2002 NGC2004 NGC2011 NGC2014 NGC2031 NGC2058 NGC2065 NGC2074 NGC2092 NGC2100 NGC2102 NGC2121 NGC2136 NGC2153 NGC2155 NGC2156 NGC2157 NGC2159

40 2.8 Conclusion source Elson(1991) Elson(1991) Elson(1991) Elson(1988) Elson+(1988) Elson+(1988) Elson+(1988) Persson(1983) Piatti+(2003I) Geisler+(2003) Geisler+(2003) Geisler+(2003) Geisler+(2003) Kerber+(2007) Kerber+(2007) Kerber+(2007) Piatti+(2003II) Alcaino+(1987) Alcaino+(1987) Zaritski+(2004) Zaritski+(2004) Zaritski+(2004) Vallenari+(1998) Vallenari+(1998) Vallenari+(1998) Vallenari+(1998) Vallenari+(1998) 0.2 0.1 0.1 0.2 0.1 0.2 0.2 0.03 0.15 0.09 0.10 0.01 0.15 0.15 0.17 0.18 0.16 0.16 0.16 0.06 0.15 0.15 0.06 0.07 0.04 0.07 0.045 E(B-V) Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Bica Hunter Hunter Hunter Hunter Hunter source Continued on next page 0.20 0.68 0.10 0.18 0.82 0.71 0.53 0.71 0.11 0.67 0.42 0.13 0.42 0.77 0.66 0.61 0.37 0.44 0.73 0.78 0.76 0.77 0.007 0.357 0.550 0.683 0.073 (B-V) 0.31 0.28 0.20 0.20 0.28 0.24 0.20 0.13 0.33 0.03 0.07 0.08 0.13 0.17 0.20 0.18 -0.14 -0.24 -0.16 -0.27 -0.34 -0.16 0.080 0.105 -0.377 -0.243 -0.467 (U-B) -6.94 -8.45 -7.04 -7.22 -7.86 -5.59 -6.06 -5.873 -5.795 -6.379 -6.571 -6.705 -6.484 -7.737 -6.878 -6.852 -5.475 -6.909 -4.926 -6.165 -5.875 -4.816 -7.427 -6.057 -4.994 -5.637 -5.1995 V (mag) 12.16 12.70 10.34 11.75 11.88 13.42 13.15 12.38 10.93 13.20 11.94 12.24 11.27 13.04 12.16 13.74 12.78 13.07 13.85 12.64 13.61 13.06 12.461 12.124 13.501 12.067 11.673 v (mag) 9.27 8.85 9.3979 9.3979 Age(l) 8.04134 7.90302 7.90302 9.34235 8.90302 9.11387 7.69891 9.11387 7.77812 7.83245 7.55624 9.20407 8.77808 7.75584 8.77808 8.77808 9.30096 8.30096 8.77808 8.77808 7.25523 9.04134 9.32216 8.95 8.79 7.4471 7.4313 7.69891 7.30096 7.60202 9.23039 9.14605 8.77808 8.69891 7.47707 9.04134 7.60202 7.25523 8.99996 8.47707 8.60202 8.60202 9.07913 7.99996 8.60202 8.60202 7.20407 8.84504 9.17602 9.04134 Age(u) 9.11 8.82 Age 7.4313 7.90302 7.69891 7.77812 9.32216 9.25523 8.84504 8.95418 7.60202 9.07913 7.69891 7.68119 9.11387 8.65317 7.62321 8.69891 8.69891 9.20407 8.17602 8.69891 8.69891 7.23039 8.95418 9.30096 9.20407 Continued SL218 SL234 SL237 SL244 SL268 SL304 SL349 SL353 SL359 SL385 SL387 SL444 SL495 SL505 SL549 SL555 Name Table 2.1 – NGC2160 NGC2162 NGC2164 NGC2172 NGC2173 NGC2193 NGC2209 NGC2213 NGC2214 NGC2231 NGC2249

41 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS source Elson(1988) Geisler+(2003) Geisler+(2003) Zaritski+(2004) 0.2 0.07 0.05 0.05 E(B-V) Bica Bica Bica Bica source 0.66 0.67 0.60 0.02 (B-V) 0.16 0.05 0.13 -0.17 (U-B) -5.65 -5.367 -5.305 -4.335 V (mag) 13.33 13.33 14.30 13.45 v (mag) Age(l) 9.25523 9.38014 9.25523 8.04134 9.07913 9.20407 9.07913 7.84504 Age(u) Age 9.17602 9.30096 9.17602 7.95418 Continued Ages are in logarithmic scale. Age(u) and Age(l) are the upper and lower limits of age respectively. SL556 SL674 SL678 SL791 Name Table 2.1 –

42 2.8 Conclusion 3 3 1 Continued on next page 2.5(7)2.1(7) -3.2(7) - 2(7) Nelson+(1983) Robertson(1974) 2.5(8) Elson(1991) 1.0(8) 0.5(8) 0.25(8) Piatti+(2003) Piatti+(2003) 1 1 1 1 3 3 1 1 1 1 1 1 1 Ages references 9(8) -2(7) 0.7(7) Mateo+(1985) Elson(1991) 7(8) - Flower+(1980) 7.5(8) - Flower(1984) 10(6) 15(6) Elson+(1988) 24(6)21(6) 10(6)25(6) 5(6) Alcaino+(1987) 6(6) Alcaino+(1987) Alcaino+(1987) 5.2(7)4.0(8) 2(7) 1.0(8)1.0(8) Elson+(1988) Piatti+(2003) 0.25(8) Piatti+(2003) 5.7(7) 2(7) Elson+(1988) 5.5(7) 4.2(7) Elson+(1988) 8.6(7) 0.5(7) Becker+(1983) 11.5(7) 5.6(7) Elson+(1988) Table 2.2: 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 Name Age Error Source Age Error Source Age Error Source NGC1651NGC1711 2(9)NGC1718 2.5(7) 0.8(9)NGC1755 2.5(9) 1(7)NGC1777 3.2(7) 0.5(9) Mould+(1986a)NGC1783 1.2(7) 9(8) 1.6(9) Elson(1991) NGC1810 Elson+(1988) 9(8)NGC1818 0.4(9) 2(8) Elson(1991) 5(7)NGC1831 1.7(7) 4(8) Elson+(1988) NGC1834 Elson+(1988) 4(7) 0.1(7) 4(8)NGC1836 4.8(7) Mould+(1989) 1.1(8)NGC1838 3.8(7) Hodge(1983) 1.5(7) Hodge(1983) 1.25(8)NGC1839 4.6(8) 1.0(7) Alcaino+(1987) 0.25(8)NGC1844 Hodge(1984) 3.3(7) Alcaino+(1987) NGC1846 5.1(7) - Piatti+(2003) 0.8(7)NGC1847 1.9(9) 0.4(7) 3(8) Alcaino+(1987) NGC1850 1.6(7) 0.1(9)NGC1854 Flower(1984) Hodge(1983) 5(8) 0.4(7) 4(7) Mackey+(2007)NGC1856 3(7) Buonanno+(1988)NGC1858 8.0(7) Hodge(1983) 1(7) 2.2(9) 5(8)NGC1860 1.7(7) 1(7) 3.0(7) 0.1(9)NGC1863 9.0(7) 0.6(7) Hodge(1983) 7(8)NGC1865 5.8(7) Mackey+(2007) 3.0(7) Hodge(1984) Hodge(1983) Alcaino+(1987) NGC1866 5.0(8) 1.7(7) Mateo(1988) Alcaino+(1987) NGC1868 1.0(8) 8(7) 73(6) Alcaino+(1987) NGC1870 3.3(7) Piatti+(2003) 20(6) 7.2(7) 3(7) 0.3(7) 3.0(7) Alcaino+(1987) Hodge(1983) Hodge(1983) Alcaino+(1987)

43 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS 1 1 1 Continued on next page 3 1 2(7) 0.7(6) Elson(1991) 1(8)1(8) - - Flower(1983) 4(8) Flower(1983) 2(8) Flower+(1983)3(7) 3.9(8)3(7) - - - Flower+(1975) Flower(1984) 4.0(7) Flower+(1975) 1.5(7) 4.0(7) Elson(1991) 1.5(7) Elson(1991) 10(6) - Westerlund(1961) 4.5(8) - Flower(1984) 2(9) - Olszewski(1984) 2.8(9) 0.5(9) Piatti+(2002) 3.2(6)2.2(6)2.4(6) - - - Westerlund(1961) 2.8(6) Westerlund(1961) 3.4(6) Westerlund(1961) - - Westerlund(1961) 2.3(6) Westerlund(1961) 4.8(6)2.8(6) Westerlund(1961) 7(6)2.7(7) Westerlund(1961) 1.6(7) 1.0(7) - Elson(1991) Roberson(1974) 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Continued Name Age Error Source Age Error Source Age Error Source Table 2.2 – NGC1872NGC1894 4(7)NGC1903 5.5(7) 1.5(7)NGC1969 0.5(7) 7(7)NGC1972 6.5(7) Dieball+(2000II) Elson(1991) NGC1978 4.0(7) 3(7) 1.5(7)NGC1983 2.5(9) 1.0(7) Dieball+(2000II) Vallenari+(1998) NGC1984 0.5(9) 8(6) Dieball+(2000II) NGC1994 7(6)NGC2002 Elson+(1988) 7.3(6) 1(6)NGC2004 1.6(7) 2(6) 0.7(6)NGC2011 0.7(7) 8(6) Hodge(1983) NGC2014 Hodge(1983) 6(6) Hodge(1983) NGC2031 1(6) Elson(1991) 6(6)NGC2058 1.6(8) 1(6)NGC2065 1(6) 0.3(8) 7(7) Hodge(1983) NGC2074 7(7) Hodge(1983) Dirsch+(2000) NGC2092 2(7) 4(6) Hodge(1983) NGC2100 2(7) 4(6)NGC2102 2(6) 1(7) Hodge(1983) NGC2121 2(6) 7(6) Hodge(1983) 0.2(7)NGC2136 7(8) Hodge(1983) NGC2153 2(6) 4(7) Hodge(1983) Hodge(1983) NGC2155 1.3(9) 2(8)NGC2156 2.5(9) 1(7) 0.4(9) Hodge(1983) NGC2157 0.6(9) 6(7) Hodge(1983) Geisler+(1997b) NGC2159 4(7) Hodge(1983) Elson+(1988) 3(7) 6(7) 1.5(7) 3(7) Hodge(1983) Elson(1991) Hodge(1983)

44 2.8 Conclusion 1 1 Continued on next page 3 5(7)5(7) -3(7) - Baird+(1974) - Hodge+(1973) Flower+(1975) 3(7) 4.0(7) 1.5(7) - Elson(1991) Flower+(1975) 5.5(8)5.5(8) 1.0(8) 1.0(8) Dieball+(2000I) 1.7(8) Dieball+(2000I) 3.0(8) Dieball+(2000II) 1.8(9)2.2(9) - 0.6(9)1.3(9) Da costa+(1987) 0.5(9) Mould+(1986) Da costa+(1987) 1.5(9) - Geisler(1987) 2.8(7)1.3(9) - 0.2(9) Walker(1979) Robertson(1974) 4.0(7) 5.6(8) 1.5(7) - Elson(1991) Flower(1984) 2 2 2 2 2 1 1 1 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 Continued SL218SL234 5.0(7)SL237 4.8(7)SL244 1.0(7) 27(6)SL268 2.0(7) Piatti+(2003) 1.3(9)SL304 Alcaino+(1987) 9(6) 4.5(8)SL349 0.3(9) 4.2(7)SL353 1.5(8) Alcaino+(1987) Geisler+(2003) SL359 1.5(7) 5(8) Vallenari+(1998) SL385 5(8) Alcaino+(1987) 1.6(9) 1(8)SL387 1.5(8) 1(8)SL444 0.4(9) Vallenari+(1998) SL495 0.5(8) 5(8) Vallenari+(1998) Geisler+(2003) SL505 5(8) Vallenari+(1998) 1.7(7) 1(8)SL549 1(8)SL555 0.1(7) 9(8) Vallenari+(1998) 2.0(9) 1.6(9) Hodge(1983) Piatti+(2003) 2(8) 0.5(9) 0.5(9) Geisler+(2003) Geisler+(2003) Geisler+(2003) Name Age Error Source Age Error Source Age Error Source Table 2.2 – NGC2160NGC2162 8(7)NGC2164 1.3(9)NGC2172 3(7) 0.4(9) 5(7)NGC2173 6(7) Geisler+(1997b) NGC2193 2.1(9) 3(7) Hodge(1983) NGC2209 1.8(9) 2(7) 0.4(9)NGC2213 0.4(9) 7(8) Hodge(1983) NGC2214 Elson+(1988) 9(8) Hodge(1983) NGC2231 Elson+(1988) 1(8) 4(7)NGC2249 1.2(9) 4(8) 6.6(8) 1(7) Hodge+(1983) 0.1(9) Elson+(1988) 0.4(8) 1.2(9) Hodge(1983) Hodge(1983) 0.2(9) Elson+1988 Dottori+(1987) 8(8) - Hardy+(1980)

45 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS 5(7) - Baird(1974) 3 3 1 Geneva 3 P adova, 2 , Continued (1983) SL556SL674 1.5(9)SL678 2.0(9)SL791 0.3(9) 1.5(9) 0.4(9) 0.3(9) 9(7) Elson(1988) Geisler+(2003) Geisler+(2003) 2(7) 2(9) Hodge(1983) - Mateo+(1986) Name Age Error Source Age Error Source Age Error Source Table 2.2 – Hodge 1

46 2.8 Conclusion

Table 2.3: χ2 Predicted age and uncertainty

Name Age Age(u) Age(l) Name Age Age(u) Age(l) NGC1651 7.90304 9.07182 9.10374 NGC2074 6.69015 6.70753 6.71596 NGC1711 7.61273 7.69015 7.78528 NGC2092 6.53144 6.54403 6.59102 NGC1718 7.74814 7.84505 9.26945 NGC2100 6.57974 6.63343 6.66271 NGC1755 7.93445 8.25522 8.32217 NGC2102 6.6812 6.69893 6.71596 NGC1777 7.87501 7.98672 8.36167 NGC2121 7.53143 7.61273 9.60308 NGC1783 8.2787 9.03337 9.05302 NGC2136 7.83246 7.91376 8.30098 NGC1810 6.71596 6.97768 7.17604 NGC2153 6.79235 7.41493 7.51847 NGC1818 6.77811 7.30098 7.43132 NGC2155 7.57973 7.67205 9.50509 NGC1831 8.56815 8.67204 8.76337 NGC2156 8.41492 8.4471 8.49131 NGC1834 6.77811 7.30098 7.43132 NGC2157 7.98672 8.36167 8.41492 NGC1836 7.79929 7.90304 8.2304 NGC2159 7.81286 7.89758 8.25522 NGC1838 7.6232 7.72423 7.79234 NGC2160 8.25522 8.39789 8.4471 NGC1839 7.85121 7.94934 8.20407 NGC2162 8.34237 9.00426 9.05302 NGC1844 7.99117 8.36167 8.4471 NGC2164 7.95419 8.07913 8.14608 NGC1846 7.85121 7.94443 9.18463 NGC2172 7.99995 8.34237 8.41492 NGC1847 7.5051 7.61273 7.69015 NGC2173 7.68119 7.74814 9.60308 NGC1850 7.7781 7.84505 7.98222 NGC2193 7.71595 7.79929 9.26711 NGC1854 7.59102 7.69015 7.75582 NGC2209 8.39789 8.47707 8.96373 NGC1856 7.65316 7.74031 7.81949 NGC2213 7.90304 9.07182 9.10374 NGC1858 6.6812 6.69893 6.71596 NGC2214 7.86327 7.95419 8.11389 NGC1860 7.74031 7.81949 7.90843 NGC2231 7.89204 8.20407 9.0863 NGC1863 6.74032 7.20407 7.34238 NGC2249 8.56815 8.69014 8.81286 NGC1865 7.46235 7.56815 7.65316 SL218 7.66271 7.75582 7.83246 NGC1866 8.4471 8.50509 8.602 SL234 7.74031 7.80613 7.84505 NGC1868 8.43131 8.50509 8.83245 SL237 7.47707 7.54402 7.66271 NGC1870 7.49131 7.60201 7.68119 SL244 6.79235 7.5051 7.60201 NGC1872 8.43131 8.49131 8.57973 SL268 8.43131 8.91376 8.99994 NGC1894 6.69893 6.87502 6.96844 SL304 6.79235 7.47707 7.59102 NGC1903 7.84505 7.96843 8.2304 SL349 7.76338 7.8388 7.95419 NGC1969 7.99995 8.34237 8.43131 SL353 7.54402 7.63342 7.73234 NGC1972 7.56815 7.67205 7.74031 SL359 7.5051 7.6232 7.69892 NGC1978 7.69015 7.75582 9.42969 SL385 8.43131 8.49131 8.55625 NGC1983 6.62321 6.65317 6.6812 SL387 8.2787 8.41492 8.47707 NGC1984 6.6812 6.69893 6.71596 SL444 7.49131 7.60201 7.68119 NGC1994 6.69015 6.70753 6.72423 SL495 7.46235 7.57973 7.65316 NGC2002 6.63343 6.66271 6.69015 SL505 7.49131 7.55625 7.68119 NGC2004 6.69893 6.71596 6.959 SL549 7.61273 9.35019 9.39087 NGC2011 6.69893 6.71596 6.99559 SL555 7.53143 7.6434 9.3673 NGC2014 6.51847 6.56816 6.57974 SL556 7.73234 7.82602 7.90304 NGC2031 8.32217 8.41492 8.49131 SL674 6.79235 7.53143 7.6232 Continued on next page

47 2. INVESTIGATING AGING METHODS OF LMC STAR CLUSTERS USING INTEGRATED COLOURS

Table 2.3 – Continued Name Age Age(u) Age(l) Name Age Age(u) Age(l) NGC2058 7.96374 8.32217 8.43131 SL678 7.7781 7.86918 7.96374 NGC2065 7.97767 8.32217 8.43131 SL791 7.99995 8.04134 8.07913

Ages are in logarithmic scale. Age(u) and Age(l) are the upper and lower limits of age respectively.

48 Chapter 3

Integrated Spectra of Stellar Clusters

In the previous chapter we revealed the weak correlations between different integrated photometric methods for finding the ages of star clusters compared to the CMD methods. This problem led us to explore a different age method estimation, namely the method of the integrated spectra. This chapter discusses the integrated spectra of star clusters in some details. These will be used in the next chapter with our known CMD ages, to determine the confidence of such methods.

3.1 The Spectrum of a Star

If we were to look at the spectrum of an isolated star atmosphere, we would see an emission spectrum, where atoms emit photons as they move from higher energy levels (reached by collisions) to lower levels. The actual observed spectrum of a star is that of the core seen through its atmosphere, or in other words, the spectrum of the atmosphere with the core in the background. This produces a spectrum in the shape of a blackbody with several absorption lines; the lines absorbed by the electrons to jump to higher energy levels. In addition to the absorption lines, there is an ”absorbed continuum”. This continuum is the range of energies that ionize the atoms. For Hydrogen, the visible continuum is short-ward of 3646A. Figure 3.1 shows Balmer discontinuity.

49 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.1: Balmer discontinuity at 3630 A - ref: Jacoby et al. (1984).

50 3.1 The Spectrum of a Star

3.1.1 The Spectral Classes

Stars follow a spectral classification given by the letters: O, B, A, F, G, K and M. These classes are related to the temperature of the star. O stars are the hottest and M stars are the coolest. Each one of these letters have a sub-classification that runs from 0 to 9. Our sun is a G star. Stars on the cooler side of the sun are called ’late type’ and stars on the hotter side are called ’early type’. Within a single spectral class, earlier stars are the hotter stars with lower numbers. Later stars are cooler, showing the larger numbers within a spectral class. B0 stars are ’earlier’ than B4 stars, but B9 stars are the most ’late” B stars. The appearance of stellar spectra is dominated by a few strong lines that change slowly over the spectral classes. (Salaris & Cassisi, 2005). Fraunhover lines are absorption lines that were first observed in the spectrum of the sun, They are described in the table below (Summarized form:lines (1997)): (Only Identification discussed is this work are listed)

Table 3.1: Fraunhover lines

Line Wavelength Line Wavelength Identiﬁcation A 7590A D 5890A Sodium B 6870A G 4310A CH molecule C 6560A H 3970A Calcium E 5270A K 3930A Calcium F 4860A

The O stars are made of mostly highly ionized Silicon, Nitrogen, etc. The deﬁning characteristic is the ionized Helium. For B stars, the deﬁning characteristic is neutral Helium and no ionized Helium. Lower stages of ionized Silicon and Nitrogen are present. In this type of stars, Balmer lines strengthen. For A stars, Balmer lines peak at A0 and lines from singly ionized Calcium and metals appear. For F stars, Balmer and ionized metal lines weaken, while lines from neutral metals strengthen. For G stars, Blamer lines continue to weaken and ionized Calcium lines peak in intensity. Lines of neutral metals continue to strengthen. In K stars many lines due to neutral metals and

51 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS molecular bands (TiO) start to appear. and for M stars TiO bands dominate. M stars are the coolest and have the most complex spectrum due to the large number of spectral lines produced by the molecules. TiO (Titanium Oxide) dominates the spectrum. In the coolest stars, the background continuum can only be seen as emission lines, because of the strong absorption lines. At M8 there is nearly nothing to be seen in the blue violet. Figures 3.2 shows the evolution of different spectral lines through the different classes. A useful tool in determining the age from integrated spectra is the equivalent width (EW). If a box of an area equal to the area of a spectral feature is drawn, the width of that box is defined to be the EW. Figure 3.3 shows a sketch of the EW.

3.2 Ages of Star Clusters from their Integrated Spectra

The details of the relation between the age of the LMC clusters and their integrated spectra has been studied for more than two decades. Bica & Alloin (1986a) investigated the equivalent width (EW) of the spectral lines in the range 3780 - 7690 A for 63 star clusters (15 in the LMC) with known reddening as a function of age and metallicity. Their spectra had a low resolution of 11 A to avoid perceived problems due to the velocity dispersion, due to the motion of individual stars within one cluster. The main conclusion of their work is that the lines of Hα to Hδ show similar age dependence 8 peaking at around 4x10 yr. The EW(Hα) of a given age is always smaller than the three next Balmer lines because the underlying continuum is dominated by late type stars which do not contribute to the line absorption. It is the continuum distribution diﬀerences and not the Balmer lines equivalent widths that distinguish between young populations and old metal poor ones in galaxies. A list of the the EW for the diﬀerent spectral lines as function of age is given in Bica & Alloin (1986b). Near-infrared spectral properties of stars clusters were investigated by Bica & Alloin (1987) in the range 6300-9700A with a resolution of 12.5A. The sample included 11 clusters from the LMC. It was also investigated in Bica et al. (1990) for the range 5600 -10000 A for 28 LMC clusters with a resolution of 14 A. We are mainly interested in the optical range so the details of these investigations will not be discussed here.

52 3.2 Ages of Star Clusters from their Integrated Spectra

Figure 3.2: The classes from main-sequence (dwarf) stars. Note the very strong eﬀect of the Balmer jump, at the early A stars. - scanned from Kaler (1997).

53 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.3: A sketch of the EW -

The near-ultraviolet range was studied by Bica et al. (1994) for a sample of 37 Galactic and Magellanic Cloud clusters in the range of 3100-4200 A with a resolution of 15 A. Their work showed that old clusters have systematically larger equivalent widths and younger clusters have diluted equivalent widths. The shorter the wavelength the stronger the dilution. They explain that the dilution is due to the presence of hot main sequence stars which contribute to the underlying continuum but not the features. They also show that the Balmer jump is an excellent age indicator for ages younger than 50 Myr when Balmer absorption line age indicator fails. Santos et al. (1995) used a sample of blue-violet (3600 - 5800 A) spectra of 97 blue Magellanic Clouds clusters (83 in the LMC) with a resolution of 16 A to create a library of spectral templates for different cluster ages. They divided their spectra into different types: LMC clusters with absorption line spectra and emission line spectra. Within the absorption line clusters, they noted whether there was a supergiant of different temperature dominating the spectrum or not. For the emission line spectra the mass loss from massive stars effects the integrated spectra. More templates were created by Piatti et al. (2002) from a library of 47 Galactic open clusters in the range 3600 - 7400A with a resolution of 14 A. A powerful equation was derived by Santos & Piatti (2004) to relate the equivalent width of specific spectral features and clusters age. It gives a good estimation of the age, but it is not meant to be an ultimate reference. The authors themselves used it in Santos et al. (2006) just as a first step in determining the age of their clusters. This equation was derived from spectra with a resolution of 10 - 15 A. Whether a better relation can be derived using spectra with higher resolution is still to be investigated.

54 3.2 Ages of Star Clusters from their Integrated Spectra

Numerous studies have used this equation and the templates created to estimate the ages of star clusters in the Small and Large Magellanic Clouds Piatti et al. (2005), Santos et al. (2006), Palma et al. (2008), Talavera et al. (2010) In addition to the method of the templates and the EW mentioned, there are other ways to obtain ages of star clusters from integrated spectra. A widely-used method is using the Lick/IDS indices. The list of references introducing this method is long, but the work of Worthey & Ottaviani (1997) will be taken as an example here. Spectra of stars were observed in the period 1972 - 1984 using the red-sensitive IDS spectrograph on the 3m Shane telescope at Lick observatory. The range observed is 4000 - 6000 A with a resolution of 8-10A. Figure 3.4 explains the concept behind the Lick/IDS indices. This work showed that Hβ is the most age sensitive index, followed by HγF then HδF ,HγA and HδA. Where F and A are the narrower and wider regions in Figure 3.4 respectively. Beasley et al. (2002) observed 24 LMC clusters with the FLAIR spectrograph at the UK Schmidt telescope. The unique approach of their study is that the cluster was observed fully at once without having to scan it with a slit. The wavelength range observed is 4000 - 5000 A with a resolution of 0.2 A. They plotted the metallicity- sensitive indices (Fe , Mgb, Mg2) versus age-sensitive indices ( Hβ,HγF ,HδF ) for each cluster on a grid of the Simple Stellar Population (SSP) models. Ages and metallicity were obtained by interpolating the model grid to get the best age and metallicity match. The results were then compared to the CMD ages. Their conclusion was that for the majority of the LMC clusters the SSP - models predicted ages that are consistent with the CMD ages. However, age estimates of the old globular clusters work only when assuming older ages when interpreting the data, because the oldest isochrones of the SSP models overlap younger isochrones due to modeling of mass loss on the RGB. Leonardi & Rose (2003) observed 28 LMC clusters (and 3 SMC + 4 Galactic clusters) with the 1.5m telescope at CTIO in the range (3500 - 4700) A with a resolution of 3.2A. The slit was trailed through each cluster to get the integrated spectra. They defined three indices by taking the ratio of the counts in the bottom of two neighboring spectral absorption lines. The first spectral index (Hδ / λ4045) is calculated by taking the ratio of the residual central intensity in Hδ relative to that of Fe I (λ4045). The second index is the Ca II index, formed from the ratio of the Ca II (H + H) to that of Ca II K. The third index is the Balmer discontinuity (BD) index. It is defined as the

55 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.4: Lick/IDS indices - source: Worthey & Ottaviani (1997).

56 3.2 Ages of Star Clusters from their Integrated Spectra ratio of the average ﬂux in the range 3700 - 3825A to that in the range 3525 - 3600A. Figure 3.5 shows the results of this work.

Figure 3.5: The results of - Leonardi & Rose (2003).

Wolf et al. (2007) used the database of Santos et al. (2002) at spectral resolutions from 6 to 23 A to obtain the ages of star clusters from their integrated spectra using 4 different methods. The first method uses the full spectrum, fitting both the line strengths and the continuum shape. The second method, the continuum-normalized (CN) uses only the information contained in the lines, losing important continuum information. A benefit of this second method is that is no adverse affected by inaccurate flux calibration in the data or continuum shape errors in the models. The third method

57 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

fits the continuum shape of the spectrum. The fourth method uses line index fits that focuses only on specific spectral lines that are known to be sensitive to metallicity or age. Comparing the fitting methods, they found a tighter correlation between ages derived from the full spectrum and continuum fits than from the full spectrum and CN spectrum fits for clusters younger than 1 Gyr. This suggests that these derived ages are more strongly driven by the continuum shape than by the spectral lines. Because the derived ages of young clusters are so strongly influenced by the continua and they have seen signs of problems in the models matching the cluster continua, they conclude that the best method for deriving accurate ages for globular clusters, especially when simultaneously determining metallicity, is fitting models to their continuum-normalized spectra. Koleva et al. (2008) as well as Cid Fernandes & Gonzlez Delgado (2010) confirm that, in general, the full spectrum fitting is a reliable method to derive the parameters of the stellar population. Our goal is to check if the integrated spectra can predict the ages of the star clusters better than the integrated photometry for the sample of 84 with CMD ages from literature. The sections below discusses details about the setup of our observations.

3.3 Observations

As stated in chapter 1, the Large Magellanic Cloud galaxy can only be observed from the southern hemisphere. We have observed our clusters using the Australian National University (ANU) 2.3m telescope at Siding Spring Observatory in Australia, the Blanco 4m telescope on Cerro Tololo, N. Chile, and the 4.1m Southern Astrophysical Research (SOAR) telescope on Cerro Pachon, N. Chile. The numbers associated with the names of the telescopes represent the aperture of the telescope in meters, that is the diameter of the primary mirror which collects the light. The larger the aperture the more light can be captured and hence the better the quality of the image or spectrum obtained. The essential components of these telescopes are shown in figure 3.6 where the in- coming light from the observed object is collected on the primary concave mirror and focused on the secondary mirror then reflected to the instrument used (e.g: spectrograph) before the final image or spectrum is captured with the CCD camera and saved

58 3.3 Observations on the computer. Figure 3.7 is a pictures of the ANU 2.3m telescopes in Australia. Here the telescope is in its stationary position with the primary mirror closed.

Figure 3.6: Telescope Sketch - The essential components of a telescope (sketch made by Randa Asa’d)

Different instruments can be mounted on a telescope depending on the goal of the telescope observation. Our goal was to get the spectra of star clusters, so we used the optical spectrographs. We used the Wide Field Spectrograph (WiFeS) Dopita et al. (2007) with the ANU 2.3 m telescope, the typical Ritchey-Chretien (RC) spectrograph with the Blanco 4m telescope and the Goodman spectrograph on SOAR telescope. The details of the observing run with the ANU 2.3m telescope will not be discussed here. The results of that run will not be included in this study due to the major difference in data reduction methods and analysis which might create inhomogeneities in our sample. The spectra obtained from the 2.3m telescope will not be included in the present analysis. Astronomical spectroscopy is a very diverse field because of the wide range of appli- cations each requiring different types of techniques Wagner (1992). This work is done using long-slit spectroscopy. Figure 3.8 shows the components of a spectrograph. The different components of the spectrograph can be adjusted depending on the

59 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.7: ANU telescope - A pictures of the ANU 2.3m telescopes in Australia (Picture taken by Randa Asa’d)

Figure 3.8: The components of a spectrograph - source: Spectrograph (2004).

60 3.3 Observations targets to be observed. The slit width is chosen depending on the resolution needed, but it also affects the amount of light hitting the spectrograph. The width of the spectral lines is the projection of your slit width. For a wide slit, the lines will be very ”fat” and the resolution lower. For a small slit, the lines will be ”thin”, and the spectral resolution higher, but there will be more light lost, increasing integration time at the telescope. For this project, because the objects are not very bright we are using a medium-width slit to take more light with relatively short integration times. The slit width we used from our Blanco telescope run was 3”. That gives a resolution of about 14 A and thus fully avoids problems due to velocity dispersion as mentioned in section 3.3. Spectra are defined by two main factors: resolution and dispersion. Resolution is due to the slit width used, and dispersion (Angstrom/pix or Angtrom/arcsecond) is due to the grating used as will be discussed below Massey & Hanson (2010). Before dispersal, the rays passing through the slit must be parallel as they come from the star. This parallelism is produced in the spectrograph by a mirror called the collimator Gray et al. (2009). The grating then functions as a disperser. A variety of gratings are available for each spectrograph. Different gratings have different numbers of grooves per mm. The more grooves a grating has per mm the higher the dispersion. Gratings also differ in their blaze wavelength. The blaze wavelength is the wavelength at which the grating has the highest efficiency. Depending on the wavelength range to be observed, one strives to choose the grating with the most appropriate blaze wavelength. In our run with the Blanco telescope, we used the KPGL2 grating with 316 l/mm. For our SOAR run, we aimed for better resolution so we used the 600 l/mm grating with the 1.03” long slit to produce a resolution of about 3.51A. The angle at which the grating is mounted needs to be carefully chosen. The grating equation ( mλ = σ (sin i + sinθ) with i = angle of incidence, θ = angle of diffraction and σ = the separation of grating elements) is used to find the best set up for the grating. Here m is the order of the pattern. For the dispersed light a camera mirror must be used to focus all the individual rays of the same color to the same point. The final beam is then sent to the final detector (CCD camera). The output voltage from a given pixel is converted to a digital number and is typically discussed from then on as either counts or ADUs (analog-to-digital units). The

61 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS amount of voltage needed (i.e., the number of collected electrons or received photons) to produce 1 ADU is termed the gain of the device (Howell, 2006). Another important element of the spectrograph is the ﬁlter. According to to the previous equation, if one wants to observe a certain wavelength range at a constant d, i and θ (Massey & Hanson, 2010):

m1λ1 = σ(sin i + sinθ ) m2λ2 = σ(sin i + sin θ ) if m1 is the ﬁrst order (m1 =1) and m2 is the second order (m2 = 2), then:

λ2 =0.5λ1

This means that if one would like to observe in the range 6000-8000 A of the first order, for example, a range of 3000-4000 A of the second order will be projected onto the detector as well. To eliminate this effect order-blocking filters must be used. In this example a filter that blocks light of wavelength shorter than 600 nm is needed. The filter can be red or blue depending on the wavelength range blocked by the filter. We used the BG38 filter with the sensitivity in the region 3500 - 7500 A for our Blanco run. For the SOAR run we did not need a filter.

3.3.1 Day Calibration images

Before observing the scientific objects, one needs to take calibration images. These images are: the bias image,the dark image, the flat image and the arc image. The bias image (also called zero image) is the image taken with the shutter of the telescope closed, so that no light is coming in with a total exposure time of 0.0 seconds. This image is needed for calibrating the readout noise. The readout noise is produced by the extra unwanted electrons created when photoelectrons are moving across the pixels for readout. Another source for the readout noise is the conversion of the analog signal to the digital number. Using the average of 10 bias images helps removing this readout noise by subtracting the offset from the scientific image (Howell, 2006). Figure 3.9 shows a 2 dimensional image of one of the bias images taken on night 3 with the Blanco telescope in February 2011. A projection of the central vertical line taken through the 2D image is shown in Figure 3.10. Note that there is a fluctuation around zero. This additional signal comes from the readout noise. The noise can be

62 3.3 Observations reduced by adding many exposures. Subtracting the average of all the zero images from all science images will eliminate this oﬀset.

Figure 3.9: Bias image - 2-dimentional

Figure 3.10: Bias image - 1-dimentional

Dark images are images taken with the shutter closed and for an exposure time equal to the exposure time of the scientiﬁc object. Dark images are used to correct for the dark currents that form due to the agitation of electrons in any material at temperatures above absolute zero or possible light leaks in the system. If any light (noise) is seen in a dark image after the bias is subtracted from it, the dark correction should be applied. This is done by subtracting each scientiﬁc image by the average dark image of the same exposure time. Figure 3.11 is the 2D average dark image for 4 images of an exposure time of 30 minutes. Figure 3.12 is the projection of the central vertical line of Figure 3.11. It is clearly seen that there is a dark current that we need to correct for.

63 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.11: Dark image - 2-dimentional

Figure 3.12: Dark image - 1-dimentional

64 3.3 Observations

No dark images were needed for our SOAR run because the light leak is so low, there is no significant counts above the bias. The flat fielding image is the image taken with the shutter open, with the telescope pointing to a brightly lit screen inside the dome. These images are taken to calibrate for pixel−pixel variation, as different pixels respond differently to the received light. Dividing the scientific image by the average flat field image, removes the pixel−pixel variation. Figure 3.13 is the 2D average flat field image for 10 images and Figure 3.14 is the projection of the central vertical line of Figure 3.13. The strong sensitivity near the center is due to an optimal blazing of the grating.

Figure 3.13: Flat image - 2-dimentional

Figure 3.14: Flat image - 1-dimentional

The arc (or lamp) images are taken of speciﬁc emission lamps of known chemi-

65 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS cal composition and hence known spectrum. These images are used to calibrate the wavelength of the scientiﬁc images. When using the telescope to take these calibration images, an additional mirror is used to obtain the light from the lamp or the quartz lamp rather than the light coming from the telescope main mirror.

3.3.2 Night observations

Observer’s tasks while observing at night can vary from one telescope to another. An observer at the ANU 2.3 m telescope for example, is responsible for focusing the telescope and for finding and using a guide star to guide the telescope while observing the target. As objects appear to be moving across the sky with time, a guiding star is needed to keep the telescope pointing at the same object for the whole exposure time. An observer at the Blanco 4 m telescope or SOAR telescope, on the other hand, doesn’t have to worry about these tasks, as the night assistant takes care of setting up the guiding. Before observing the actual scientific targets, spectra of spectrophotometric standard stars that have known flux characteristics are obtained to calibrate the flux of the scientific targets. Due to their large size on the sky, stellar clusters are observed by scanning the long−slit across the cluster to cover it all and to get a truly integrated representation of all the stellar light from the cluster. Two elements that need to be taken into consideration while observing are the seeing and the airmass. Seeing describes blurring of the objects as seen with the telescope due to the Earth’s atmosphere. Temperature variations create changes in the optical refracting index of the layers of the atmosphere, causing refraction of the light rays and decreasing the quality of the seeing. Seeing is a measurement of the diameter of a point source in units of arcseconds. Airmass measures the path length that the light from an object travels through the Earth’s atmosphere. At sea level, the airmass of an object at zenith (directly overhead)is defined as 1. For small azimuthal angles, the airmass is equal to the secant of the azimuthal angle.

66 3.4 Data Reduction

3.4 Data Reduction

Data reduction is the process that transforms the two-dimensional image taken by the CCD camera of the telescope to a plot of flux versus wavelength. For our data, we used the Image Reduction and Analysis Facility (IRAF) software package in a number of steps. The first step is to trim the image to the illuminated region of the detector. After that comes the calibration steps mentioned above: bias, dark and flat field calibrations. Once that is done the image is converted into a one-dimensional image by integrating the flux along vertical lines of the two-dimensional image. This spectrum has, in addition to the actual spectrum of the scientific object, a spectrum of the sky background. This needs to be removed by identifying and extracting a region of background on the detector, integrating the flux and subtracting it from the object’s spectrum. The clusters observed and the regions we chose for our observed clusters are shown in the next chapter. Figure 3.15 is a raw 2D image of the spectrum of the cluster NGC2002 observed with the SOAR telescope before the data reduction. The horizontal line are the lines of the integrated spectra, the weak vertical lines are bad pixels on the detector. The previous calibration step leaves us with a one-dimension spectrum in units of ADU (analog to digital unit) counts versus the pixel number on the detector. In order to change these units to scientifically useful units we need one more set of calibration images. As mentioned above, the wavelength calibration is done using comparison gas lamps made of chemical elements of known spectral features like NeAr or NeHeAr. These calibration images are taken with the same telescope and spectrograph settings as the ones used for the actual observing. Figure 3.16 is the 2D NeAr lamp image and Figure 3.17 is the 1D extracted form of Figure 3.16. The wavelength of the known spectral lines of the lamp are identified manually then the software (IRAF) is set to use the calibrated lamp information as a reference to calibrate the scientific objects observed for the wavelength. Once the calibration is done one can check that it was done correctly by making sure that the Balmer lines lie at the correct wavelength expected. Balmer lines are the spectral lines in the optical

67 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

Figure 3.15: A raw image of the spectrum of the cluster NGC2002 - The horizontal line are the lines of the integrated spectra. The weak vertical lines are bad pixels on the detector

Figure 3.16: NeAr comparison lamp - 2-dimentional

68 3.4 Data Reduction

Figure 3.17: NeAr comparison lamp - 1-dimentional

69 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS range corresponding to the transition of the electron in the Hydrogen atom from the second energy level to the higher energy levels requiring photons of wavelengths 410nm,

434nm, 486nm and 656 nm. These lines are called Hδ ,Hγ,Hβ and Hα respectively.

Figure 3.18 shows an example of the Hδ absorption at the correct wavelength.

Figure 3.18: Hδ Balmer absorption - At 410nm

The last calibration step is done using the well known calibrated spectrum of an observed spectrophotometric standard star. We used EGGR21 as our standard star. This is a white dwarf star. Figure 3.19 shows the spectrum of this star and Figure 3.20 shows the ﬁnal image of the ﬂux-wavelength calibrated spectrum of one of our observed clusters: NGC 1983.

70 3.4 Data Reduction

Figure 3.19: Spectrum of a standard star before calibration with units of ADU versus pixel. Note tha the ’blue’ end of the detector is on the right side - EGGR 21

Figure 3.20: Final calibrated spectrum units of ergs/cm/cm/s/A versus Angstroms. - NGC 1983

71 3. INTEGRATED SPECTRA OF STELLAR CLUSTERS

72 Chapter 4

Ages of LMC star clusters from integrated spectra

This chapter will be submitted for publication

4.1 Introduction

The formation history of a galaxy can be understood by knowing the ages of its star clusters. The Large Magellanic Cloud (LMC) galaxy is a good place to test different age determination methods of star clusters because it is close enough to resolve its clusters, but far enough away so that the whole cluster can be observed as one object. Although the color-magnitude diagram (CMD) method of obtaining the ages is not absolute due to the different isochrones (Geveva or Padova) used by different groups, it is in general considered the most accurate method (Leonardi & Rose, 2003, Wolf et al., 2007). For this reason we are using a sample of clusters that have CMD ages in the literature to test the accuracy of other methods used to age the cluster. In chapter 2, the relation between the CMD age of 84 resolved LMC clusters and their age as determined by integrated photometry was examined and found to be poorly corelated (Asa’d & Hanson, 2012). The goal of this chapter is to test if the integrated spectra of star clusters can better predict the cluster’s age. The integrated spectra of a star cluster have been used in many ways to obtain the age. One way is examining specific spectral features and getting the age based on the strength of these features (Worthey & Ottaviani, 1997, Beasley et al., 2002). An-

73 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA other way is using ratios of different spectral features (Leonardi & Rose, 2003). A third method is fitting the full spectrum to computational models (Koleva et al., 2008, Cid Fernandes & Gonzlez Delgado, 2010). The method used in this chapter is the method of fitting the full spectrum to computational models. This is unique because our integrated spectra cover a larger range than that analyzed previously in the literature and it uses a higher resolution than previous spectral studies (Bica & Alloin, 1986a, 1987, Bica et al., 1990, 1994, Santos et al., 1995, Piatti et al., 2002, 2005, Santos et al., 2006, Palma et al., 2008, Talavera et al., 2010). We chose this particular method to avoid the problem of bad pixels that might be present at important spectral features. It also enables us to use the information in all spectral lines in the range as well as the continuum to fit for both age and reddening at the same time (Bica & Alloin, 1986a, 1987, Bica et al., 1990, 1994, Santos et al., 1995, Piatti et al., 2002, 2005, Santos et al., 2006, Palma et al., 2008, Talavera et al., 2010).

4.2 The Data

The data used in this study were obtained in two observing runs: 6 nights in February 2011 with the RC spectrograph on the 4m Blanco telescope on Cerro Tololo (Chile), and 4 nights in December 2011 with the Goodman spectrograph on the SOAR telescope on Cerro Pachon (Chile). Our plan was to observe the full sample of 84 clusters given in Asa’d & Hanson (2012) but we only obtained the spectra for a total of 20 clusters due to weather conditions during both runs and instrumental problems with the RC spectrograph on Blanco. We obtained the integrated spectra by scanning the cluster with the slit starting on the southern edge. The slit is aligned east-west. The non- sidereal guiding rate in RA is 0”/hr. The non-sidereal rate in ”/hr for each cluster in Dec is a function of the cluster’s angular diameter and exposure time. The main challenge is to decide what to call the ”edges” of each cluster. Figure 4.1 shows the region included in each cluster observed with SOAR. Tables 1 and 2 give more information about each target and the time and speed of the scanning with the slit range. Table 1 shows the Blanco clusters and Table 2 shows the SOAR targets. For the clusters observed with the Blanco 4m telescope the images were not saved due to the nature of the software used and hence they are not available.

74 4.2 The Data

Figure 4.1: The region observed in each cluster - SOAR run. (North is to right)

75 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

One challenge we faced was that we were not seeing the position of the slit on the actual clusters in real time at the telescope. Further, the ﬁnding charts available had only low spatial resolution. That is why the edges of the cluster are not so perfectly aligned with the slit. We provide images of the clusters observed with the SOAR telescope with higher resolution in the online material of this paper.

Table 4.1: Blanco Run (February 2011)

Name Exp. ID starting Dec Ending Dec Exp. Time Speed NGC1983 3039 -68:59:12 -68:58:55 50 min 0.001”/sec NGC1984 3043 -69:08:16 -69:07:50 50 min 0.002 ”/sec NGC1984 3046 -69:08:16 -69:07:50 25 min 0.0015 ”/sec NGC1984 3047 -69:08:16 -69:07:50 5 min 0.0015 ”/sec NGC1856 3051 -69:07:54 -69:07:30 15 min 0.0014 ”/sec NGC2173 3055 -72:58:55 -72:58:26 30 min 0.017 ”/sec NGC2011 4051 -67:31:23 -67:31:07 60 min 0.001”/sec NGC2011 4052 -67:31:23 -67:31:07 60 min 0.001 ”/sec NGC2164 4056 -68:31:15 -68:30:40 30 min 0.019 ”/sec NGC2164 4057 -68:31:15 -68:30:40 30 min 0.019 ”/sec NGC2002 5053 -66:53:13 -66:52:50 60 min 0.007 ”/sec NGC2002 5054 -66:53:13 -66:52:50 60 min 0.007 ”/sec NGC2157 5058 -69:12:07 -69:11:28 45 min 0.007 ”/sec NGC2157 5059 -69:12:07 -69:11:28 45 min 0.007 ”/sec NGC2173 5063 -72:58:55 -72:58:26 45 min 0.015 ”/sec NGC2173 5064 -72:58:55 -72:58:26 45 min 0.015 ”/sec NGC1711 6089 -69:59:20 -69:58:48 45 min 0.013 ”/sec NGC1711 6090 -69:59:20 -69:58:48 45 min 0.012 ”/sec NGC2156 6094 -68:27:55 -68:27:20 45 min 0.014 ”/sec NGC2156 6095 -68:27:55 -68:27:20 45 min 0.014 ”/sec NGC1903 6099 -69:20:31 -69:20:00 45 min 0.012 ”/sec

Table 4.2: SOAR Run (December 2011)

Name Exp. ID Diameter Diameter Exp. Time Speed NGC1994 1082 18” 0.0050◦ 20 min 54”/hr NGC1994 1104 18” 0.0050◦ 30 min 36”/hr NGC1994 1110 18” 0.0050◦ 30 min 36”/hr NGC2002 2101 32” 0.0089◦ 10 min 96”/hr Continued on next page

76 4.2 The Data

Table 4.2 – Continued Name Exp. ID Diameter Diameter Exp. Time Speed NGC2002 2104 32” 0.0089◦ 20 min 48”/hr NGC2173 2112 32” 0.0089◦ 30 min 64”/hr NGC2173 2116 32” 0.0089◦ 30 min 64”/hr NGC2249 2128 38.7” 0.0107◦ 40 min 58”/hr NGC1850 2140 56” 0.0156◦ 30 min 112”/hr NGC2213 2143 24” 0.0066◦ 30 min 48”/hr NGC2213 2147 24” 0.0066◦ 30 min 48”/hr NGC1983 2155 19” 0.0053◦ 15 min 76”/hr NGC1863 3131 20” 0.0056◦ 30 min 40”/hr NGC2031 3140 50” 0.0138◦ 30 min 100”/hr NGC2065 3143 42” 0.0117◦ 20 min 84”/hr NGC1651 3149 62” 0.0172◦ 30 min 124”/hr NGC1651 3156 62” 0.0172◦ 30 min 124”/hr NGC2155 3167 42” 0.0117◦ 40 min 63”/hr NGC2155 3173 42” 0.0117◦ 40 min 63”/hr NGC2155 3179 42” 0.0117◦ 40 min 63”/hr

77 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA Ref. Dirsch et al. (2000) Kerber et al. (2007) Kerber et al. (2007) Kerber et al. (2007) Meurer et al. (1990) Meurer et al. (1990) Meurer et al. (1990) Meurer et al. (1990) Mould et al. (1986a) Persson et al. (1983) Persson et al. (1983) Persson et al. (1983) Persson et al. (1983) Persson et al. (1983) Persson et al. (1983) Mould et al. (1986b) Vallenari et al. (1998) Da Costa et al. (1985) Alcaino & Liller (1987) Alcaino & Liller (1987) 0.1 0.1 0.2 0.16 0.21 0.16 0.14 0.08 0.10 0.09 0.18 0.09 0.14 0.12 0.09 0.18 0.02 0.14 0.09 0.01 E(B-V) Ref. Elson (1991) Elson (1991) Elson (1991) Jones (1987) Hodge (1984) Hodge (1983) Hodge (1983) Hodge (1983) Hodge (1983) Hodge (1983) Hodge (1983) Hodge (1983) Hodge (1983) Dirsch et al. (2000) Elson & Fall (1988) Mould et al. (1986a) Mould et al. (1986b) Vallenari et al. (1998) Da Costa et al. (1985) Alcaino & Liller (1987) Targets Observed 7.4 7.6 7.7 7.2 8.2 9.4 7.90 7.85 6.85 6.78 7.78 9.30 7.60 7.76 6.90 6.86 7.85 9.32 8.95 8.82 Age 4 4 2 2 1 3 4 4 4 4 3 3 2 3 4 3 4 5 4 4 Table 4.3: Mass 14 14 14 14 14 14 14 14 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 Resolution Run SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 SOAR2011 Blanco2011 Blanco2011 Blanco2011 Blanco2011 Blanco2011 Blanco2011 Blanco2011 Blanco2011 Name 1 NGC1711 2 NGC1856 3 NGC1903 4 NGC1984 5 NGC2011 6 NGC2156 7 NGC2157 8 NGC2164 9 NGC1651 10 NGC1850 11 NGC1863 12 NGC1983 13 NGC1994 14 NGC2002 15 NGC2031 16 NGC2065 17 NGC2155 18 NGC2173 19 NGC2213 20 NGC2249

78 4.2 The Data

It was our goal to cover a wide range of ages, masses and extensions. Figures 4.2, 4.3 and 4.4 show the statistics of our observed sample.

3 Number of Clusters

0 5 6 7 8 9 10 11 Age Range

Figure 4.2: The distribution of ages (log age/year) for the sample observed with the Blanco telescope represented by the red boxes and the clusters observed with SOAR telescope represented by the blue boxes - See the Tables 1 and 2 for more details

For the Blanco run the slit width was 3” but for the SOAR run we used the 1.3” slit. The aperture extracted for each cluster is shown in Appendix 1. The wavelength calibration was done using HeNeAr lamps for the Blanco run and the HgAr lamp in the SOAR run. The wavelength calibration for the data observed with Blanco was straight forward, but it was tricky for the SOAR data because there was an instrumental defect causing the camera angle to change during the night from one pointing to another. The calibration lamp with the closest camera angle was used for each science object. Luckily, the precision of the wavelength is not critical, it just has to match the model for the well known features. The wavelength was ﬁnally corrected for the radial velocity by shifting the spectrum to match the main Balmer lines of the model used. For the Blanco run, EG21 and CD32 were used as the standard photometric stars to calibrate the ﬂux. A couple of exposures were taken of EG21 at the beginning before observing the targets, and few exposures of CD32 were taken at the end of the

79 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

3 Number of Clusters

0 0 1 2 3 4 5 6 Mass Range

Figure 4.3: The distribution of masses (refer to Chapter 2 for details about the deﬁnition of mass ranges) for the sample observed with the Blanco telescope represented by the red lines and the clusters observed with SOAR telescope represented by the blue lines - See Tables 1 and 2 for more details

0.2

0.15

0.1 Reddening

0.05

0 5 6 7 8 9 10 11 Log (Age/yr)

Figure 4.4: The extinction-age space for the clusters observed with Blanco represented by the red diamonds and the clusters observed with SOAR telescope represented by the blue squares - See Tables 1 and 2 for more details

80 4.3 Integrated Spectra Models night. The SOAR flux calibration, on the other hand, was more challenging due to the limited number of exposures taken of standard photometric stars (in many cases one per night). A shorter wavelength range of some of our clusters were observed by (Leonardi & Rose, 2003). Dr. Jim Rose kindly shared the spectra with us to check our final flux-calibrated spectra against theirs for the available range. There is a good agreement between our clusters and theirs.

Once the calibration was done, we combined the spectra of the clusters that were observed more than once (see tables 1 and 2). The three exposures of NGC1984 were combined together, the same thing was done for the two exposures of NGC2011, NGC2164, NGC2002 and NGC2156. Exposure 5055 of NGC2157 and exposure 6096 of NGC1711 were not as good as the other spectra of the same clusters (low S/N), so we didn’t use them. For NGC2173 we only used the exposure 3055. For the clusters we observed with SOAR, we omit the exposures 1082, 1104, 2101 and 4148. The last step was to delete some ”artificial” features that might be due to bad pixels. We removed the features around 5523.5 A and 6512.5 A. We also removed the feature around 5071 A that was present in all clusters except for NGC1983, NGC1984 and NGC2011. For the clusters observed with SOAR, artificial features between 5560 A and 5590 A were removed, few clusters were fixed for artificial features around 5265A. NGC2031 was also fixed between 3730-3760 A. NGC2002 didn’t require any fixing. For NGC2155 more lines were ”fixed”. The range observed with the Blanco run is 3503 - 7244 A with a resolution of 14 A. A better resolution was obtained for the SOAR data, we observed the range 3625 - 6232 A with a resolution of 3.6 A. For consistent analysis we will be using the range of 3626 - 6230 A for all clusters. The flux was normalized at λ = 5870A so that it can easily be compared with the model. We are not concerned about the absolute, only the relative flux of our clusters for this study. Figures 4.5 and 4.6 show the spectra of clusters observed with Blanco and SOAR.

4.3 Integrated Spectra Models

As mentioned in section 1, integrated spectra can be used in diﬀerent ways to obtain the age of the clusters. We are interested in the method of comparing models of the full

81 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

NGC2173 NGC2164 NGC2157 20 NGC2156 NGC2011 NGC2002 NGC1983 NGC1903 NGC1856 NGC1711 15

10 Normalized Flux

0 3500 4000 4500 5000 5500 6000 6500 7000 Wavelength (A)

Figure 4.5: The clusters observed with Blanco. - The spectra are shifted on the vertical axis for clarity.

82 4.3 Integrated Spectra Models

25 NGC2249 NGC2213 NGC2173 NGC2155 NGC2065 NGC2031 20 NGC2002 NGC1994 NGC1983 NGC1863 NGC1850 NGC1651 15

10 Normalized Flux

0 3500 4000 4500 5000 5500 6000 6500 7000 Wavelength (A)

Figure 4.6: The clusters observed with SOAR. - The spectra are shifted on the vertical axis for clarity.

83 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA spectrum to the integrated spectra to solve for age and reddening simultaneously. There are two types of integrated spectra models. The first one is the theoretical computed spectra as will be discussed below. The second one is the templates (Bica et al., 1990, Santos et al., 1995, Piatti et al., 2002) that were created from real observations of clusters with known properties. In this work, we focus on the method of obtaining the predicted ages from a modern theoretical model that has a high resolution of 0.3A. Due to observational limitation the templates have a resolution of just 12-14A. The theoretical models also provide a larger variety of ages and reddening to compare against the clusters spectra. The theoretical integrated spectra models are created by assuming a certain number of stars formed at the same time in a cluster with different masses. As the cluster ages, its stars evolve according to their initial masses. The evolution of the integrated spectrum reflects the overall changes occurring to the entire system of stars (the cluster) as a function of time. Therefore the shape of the integrated spectrum is an indicator of the age of the cluster. A large number of models that produce synthetic spectra for a wide range of ages are available (Leitherer et al., 1999, Vazdekis, 1999, Bruzual & Charlot, 2003, Cervino & Luridiana, 2006, Kotulla et al., 2009, GonzálezDelgado et al., 2005) . We chose the GonzálezDelgado et al. (2005) model because of its high resolution (0.3 A). This model assumes Salpeter (1955) initial mass function (IMF) with cut-off masses of 0.1 -120 solar masses. The library used in the calculations is the Padova asymptotic giant branch (AGB) stellar model for Z= 0.008.

4.4 The Method

Our goal is to obtain the best match between the observed spectrum (corrected for a range of reddening values) and the model (for the range of ages available). It is shown by (Bica & Alloin, 1986a) that the metallicity features of young open clusters is relatively weak in the visible range, so we do not vary metallicity in our analysis. We investigated diﬀerent methods. We started with the method of looking for the combination of age and reddening that minimizes the sum:

6230 X (OF )λ − (MF )λ χ2 = ( )2. (4.1) (OF )5870A λ=3626A

84 4.4 The Method where OF is the observed flux and MF is the model flux. The observed flux is reddening corrected. This is done by applying the Cardelli et al. (1989) (CCM) extinction law in the optical range. We use the range of reddening from 0.0 to 0.5, in steps of 0.01. We then normalize the flux at λ = 5870A where no critical spectral features are present. It is well known that the age and reddening of a cluster are not physically correlated, but they both effect the shape of the spectrum. The model flux is obtained by first smoothing the model resolution to match the observed spectra. The model is then normalized at λ = 5870A. It is clear now why we chose to divide by (OF )5870A in the equation of χ2 above. It was suggested by Cid Fernandes & Gonzlez Delgado (2010) to divide by each individual (OF )λ:

6230 X (OF )λ − (MF )λ χ2 = ( )2. (4.2) (OF )λ λ=3626A to give more weight to the absorption lines. Such a method is useful for shorter wavelength ranges. For longer wavelength ranges, with long ”tails” (redward of 5000 A), this method will give more weight to the longer wavelengths because they have less flux, thus being divided by smaller numbers. We choose to give all bins a uniform weight in the calculation of the χ2. The combination of reddening-corrected observed spectrum and model spectrum (representing log ages from 6.60 to 10.25 in steps of 0.05) is taken as the reddening and age of the cluster. We look for the fit that minimizes the sum (model - observed)2 for bin by bin in λ. Although this method is a reasonable one to use, we noticed that for our high resolution spectra, a few wavelength points that mismatch the flux range (bad pixels, or any other observational imperfections) can lead to highly inaccurate results. Examples are given in the conclusion section of this chapter (Figures 4.46 and 4.47). That motivated us to take another approach, the Kolmogorov-Smirnov (KS) test, used by Burke et al. (2010) to compare spectra of stars with models. Figures from 4.7 to 4.28 show the residuals obtained from using this method. The numerical results are given in table 2.

85 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.7: NGC1711 - The most upper spectrum is the model spectrum of log age 7.550, the spectrum below is the observed spectrum corrected for E(B-V) = 0.09. These two spectra were chosen as the best match by the KS statistics as shown in the center of the ﬁgure. The bottom of the ﬁgure shows the residuals of the above model spectrum and observed spectrum. The spectra are normalized at 5870A and shifted on the vertical axis for clarity.

86 4.4 The Method

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.8: NGC1856 - Same as ﬁgure 4.7 for log age = 8.450 and E(B-V) = 0.12.

87 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.9: NGC1903 - Same as ﬁgure 4.7 for log age = 7.850 and E(B-V) = 0.17.

88 4.4 The Method

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.10: NGC1984 - Same as ﬁgure 4.7 for log age = 6.650 and E(B-V) = 0.28.

89 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.11: NGC2002 - Same as ﬁgure 4.7 for log age = 6.700 and E(B-V) = 0.21.

90 4.4 The Method

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.12: NGC2011 - Same as ﬁgure 4.7 for log age = 6.650 and E(B-V) = 0.26.

91 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.13: NGC2156 - Same as ﬁgure 4.7 for log age = 8.000 and E(B-V) = 0.03.

92 4.4 The Method

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.14: NGC2157 - Same as ﬁgure 4.7 for log age = 7.850 and E(B-V) = 0.16.

93 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.15: NGC2164 - Same as ﬁgure 4.7 for log age = 7.900 and E(B-V) = 0.01.

94 4.4 The Method

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.16: NGC2173 - Same as ﬁgure 4.7 for log age = 9.950 and E(B-V) = 0.01.

95 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.17: NGC1651 - Same as ﬁgure 4.7 for log age = 8.900 and E(B-V) = 0.26.

Table 4.4: Our Results

Name Run Age E(B-V) NGC1651 SOAR 8.900 0.26 NGC1850 SOAR 7.750 0.11 NGC1863 SOAR 7.450 0.10 NGC1983 SOAR 6.650 0.08 NGC1994 SOAR 6.650 0.20 NGC2002 SOAR 7.000 0.49 NGC2031 SOAR 8.250 0.00 NGC2065 SOAR 7.950 0.15 NGC2155 SOAR 9.200 0.00 NGC2173 SOAR 9.350 0.00 NGC2213 SOAR 6.800 0.48 NGC2249 SOAR 8.400 0.12 NGC1711 Blanco 7.550 0.09 Continued on next page

96 4.5 More Integrated Spectra from the Literature

Table 4.4 – Continued Name Run Age E(B-V) NGC1856 Blanco 8.450 0.12 NGC1903 Blanco 7.850 0.17 NGC1983 Blanco 6.650 0.25 NGC1984 Blanco 6.650 0.28 NGC2002 Blanco 6.700 0.21 NGC2011 Blanco 6.650 0.26 NGC2156 Blanco 8.000 0.03 NGC2157 Blanco 7.850 0.16 NGC2164 Blanco 7.900 0.01 NGC2173 Blanco 9.950 0.01

Figure 4.29 shows the correlation between our ages and the literature CMD ages. A general good agreement is noticed, except few outliers. The error bars associated with the ages determined from integrated spectra are just representing the age gap between the models used (log age/year = 0.05). The clusters NGC1983, NGC2002 and NGC 2173 were observed in both runs. The SOAR run predicted a better age for these clusters. For the fitting shown in the figure and the calculation of the correlation coefficient we only used the SOAR results for these clusters. Figure 4.30 shows the correlation between our E(B-V) and the literature E(B-V) ages

4.5 More Integrated Spectra from the Literature

For better statistical results we include clusters that have integrated spectra in the needed range from the literature. Four integrated spectra of clusters from Santos et al. (2006) were kindly provided by Dr. Santos, and three integrated spectra of clusters from (Palma et al., 2008) were kindly provided by Palma. The details of this sample is given in Table 4. In order to be consistent with our own data we are using the same wavelength range and wavelength bin size of 3 A. The data was provided in bins of 2 A so we used the IRAF tasks ”dispcor” and ”listpix” to produce the ASCII ﬁles of wavelength and ﬂux, with wavelength bins of 3 A.

97 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.18: NGC1850 - Same as ﬁgure 4.7 for log age = 7.750 and E(B-V) = 0.11.

98 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.19: NGC1863 - Same as ﬁgure 4.7 for log age = 7.450 and E(B-V) = 0.10.

99 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.20: NGC1983 - Same as ﬁgure 4.7 for log age = 6.650 and E(B-V) = 0.08.

100 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.21: NGC1994 - Same as ﬁgure 4.7 for log age = 6.650 and E(B-V) = 0.20.

101 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.22: NGC2002 - Same as ﬁgure 4.7 for log age = 7.000 and E(B-V) = 0.49.

102 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.23: NGC2031 - Same as ﬁgure 4.7 for log age = 8.250 and E(B-V) = 0.00.

103 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.24: NGC2065 - Same as ﬁgure 4.7 for log age = 7.950 and E(B-V) = 0.15.

104 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.25: NGC2155 - Same as ﬁgure 4.7 for log age = 9.200 and E(B-V) = 0.00.

105 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.26: NGC2173 - Same as ﬁgure 4.7 for log age = 9.350 and E(B-V) = 0.00.

106 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.27: NGC2213 - Same as ﬁgure 4.7 for log age = 6.800 and E(B-V) = 0.48.

107 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.28: NGC2249 - Same as ﬁgure 4.7 for log age = 8.400 and E(B-V) = 0.12.

108 4.5 More Integrated Spectra from the Literature

10 SOAR Blanco 1:1 9.5 fit line

8.5

7.5

Predicted KS log (age/yr) 7

6.5

6 6 6.5 7 7.5 8 8.5 9 9.5 10 CMD log (age/yr)

Figure 4.29: The correlation between our obtained ages and the literature CMD ages - The correlation coeﬃcient is 0.80. NGC2213 is an outlier. Note the bad spectrum obtained for this cluster making the age determination almost impossible

109 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

0.5

0.4

0.3

0.2 Predicted KS E(B-V)

0.1

SOAR Blanco 0 1:1 0 0.1 0.2 0.3 0.4 0.5 Literature E(B-V)

Figure 4.30: The correlation between our obtained E(B-V) and the literature E(B-V) - NGC2213 and NGC2002 are outliers

110 4.5 More Integrated Spectra from the Literature Ref. Dieball et al. (2000) Persson et al. (1983) Persson et al. (1983) Alcaino & Liller (1987) Alcaino & Liller (1987) Alcaino & Liller (1987) Alcaino & Liller (1987) 0.1 0.1 0.27 0.14 0.17 0.15 0.10 E(B-V) Ref. Hodge (1983) Hodge (1983) Dieball et al. (2000) Alcaino & Liller (1987) Alcaino & Liller (1987) Alcaino & Liller (1987) Alcaino & Liller (1987) 7.52 7.86 7.74 7.43 7.68 7.60 7.43 Age Data from the Literature 2 3 3 2 2 3 2 Mass Table 4.5: 14 14 14 14 17 17 17 Resolution Run Palma et al. (2008) Palma et al. (2008) Palma et al. (2008) Santos et al. (2006) Santos et al. (2006) Santos et al. (2006) Santos et al. (2006) Name 4 SL237 5 SL234 1 NGC1839 2 NGC1870 3 NGC1894 6 NGC2136 7 NGC2172

111 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Figures 4.31 to 4.37 shows the residuals when comparing the observed spectra with the model (as described in the section above).

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.31: NGC1839 - Same as ﬁgure 4.7 for log age = 8.050 and E(B-V) = 0.04.

The table below shows the results of ages and reddening obtained with this method.

Table 4.6: Results

Name Source Age E(B-V) NGC1839 Santos06 8.050 0.04 NGC1870 Santos06 7.800 0.06 NGC1894 Santos06 7.850 0.26 SL237 Santos06 6.900 0.26 NGC2136 Palma08 7.900 0.13 NGC2172 Palma08 7.550 0.12 SL234 Palma08 7.800 0.04

112 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.32: NGC1870 - Same as ﬁgure 4.7 for log age = 7.800 and E(B-V) = 0.06.

113 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.33: NGC1894 - Same as ﬁgure 4.7 for log age = 7.850 and E(B-V) = 0.26.

114 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.34: SL237 - Same as ﬁgure 4.7 for log age = 6.900 and E(B-V) = 0.26.

115 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.35: NGC2136 - Same as ﬁgure 4.7 for log age = 7.900 and E(B-V) = 0.13.

116 4.5 More Integrated Spectra from the Literature

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.36: NGC2172 - Same as ﬁgure 4.7 for log age = 7.550 and E(B-V) = 0.12.

117 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Normalized Flux 5

3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.37: SL234 - Same as ﬁgure 4.7 for log age = 7.800 and E(B-V) = 0.04.

118 4.6 Review of Previous Results on the Subsample of this Work

4.6 Review of Previous Results on the Subsample of this Work

In Paper 1 (Asa’d & Hanson, 2012), we showed a weak correlation between the ages obtained using integrated photometry versus CMD ages for a sample of 84 star clusters. Our goal in this new work is to examine if integrated spectra can better predict the age of clusters. Out of that sample we only have the observed integrated spectra of 27 clusters. For a fair comparison between the method using integrated photometry and the method using integrated spectra we first briefly show the correlation discussed in paper 1 for this particular subsample of 27 clusters in figures 4.38, 4.39 and 4.40.

4.7 Discussion

Figures 4.41, 4.42 and 4.43 show the results obtained form the integrated spectra of the entire subsample used in this study.

4.8 Conclusion and future work

We summarize the conclusion of the work in the following points: 1) We obtain the integrated spectra of 20 clusters that didn’t have integrated spectra in the optical range, or that have never been observed. 2) We obtain high resolution images of the clusters observed. These images are not used in this study but they are made available to be used for other studies. 3) We show that using integrated spectra with full spectrum ﬁtting is a better age estimator that the integrated photometry method. 4)With just a couple of exceptions, this method also doesn’t predict unphysical E(B-V) that goes beyond 0.3. 5) We show that the KS statistics is a better calculation to be used when comparing observed spectra to model spectra. 6) We also argue that the computational models can predict the ages of the clusters better than the templates, until the templates are updated and expanded.

119 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

10 data fit line unity line 9.5

8.5 log (age/yr)

2 8 r

7.5

Predicted 7

6.5

6 6 6.5 7 7.5 8 8.5 9 9.5 10 CMD log (age/yr)

Figure 4.38: The correlation between the ages obtained from integrated photometry and CMD ages for the current subsample. The correlation coeﬃcient is 0.67 - See Asa’d & Hanson (2012) for a discussion of the analysis

120 4.8 Conclusion and future work

10 unity line

9.5

4 4 9

4 8.5 3 4 4 23

log (age/yr) 4

2 8 23 2 r 42 4 5 4 4 3 7.5 2

Predicted 7 3 1223 3 6.5

6 6 6.5 7 7.5 8 8.5 9 9.5 10 CMD log(age/yr)

Figure 4.39: The mass ranges on the previous ﬁgure - See Asa’d & Hanson (2012)

121 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

0.8 data unity line 0.7

0.6

0.5

0.4

0.3 Predicted E(B-V)

0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Published E(B-V)

Figure 4.40: The correlation between the extinction obtained from integrated photometry and the extinction from literature for the current subsample - See Asa’d & Hanson (2012)

122 4.8 Conclusion and future work

10 Our Palma06 Santos06 9.5 1:1 fit line

8.5

7.5

Predicted KS log (age/yr) 7

6.5

6 6 6.5 7 7.5 8 8.5 9 9.5 10 CMD log (age/yr)

Figure 4.41: The correlation between the ages obtained from integrated spectra and CMD ages for the current subsample. The correlation coefficient is 0.78 - Different colors on the graph represent different sources of integrated spectra

123 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

10 1:1

9.5 5 4 9 4

8.5 4 4 4 2 8 33 43 43 2 4 2 3 4 2 7.5 3

Predicted KS log (age/yr) 7 3 2 4 123 6.5

6 6 6.5 7 7.5 8 8.5 9 9.5 10 CMD log(age/yr)

Figure 4.42: The mass ranges on the previous ﬁgure - Mass doesn’t seem to be the reason for the bad age estimation of NGC2213

124 4.8 Conclusion and future work

0.5

0.4

0.3

0.2 Predicted KS E(B-V)

0.1

Our Palma06 Santos06 0 1:1 0 0.1 0.2 0.3 0.4 0.5 Literature E(B-V)

Figure 4.43: The correlation between the extinction obtained from integrated spectra and the extinction from literature for the current subsample - NGC2213 and NGC2002 are outliers.

125 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

Figures 4.44 and 4.45 show reasonable matches between the model and the observation using the χ2 method. Figures 4.46 and 4.47 , on the other hand, show poor matches predicted by this method.

2.6 Age=8.10 E(B-V)=0.00 2.4

2.2

1.8

1.6

1.4 Normalized Flux 1.2

0.8

0.6 3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.44: A reasonable match between the model and the observation using the χ2 method - NGC1863

We are currently developing automated software that can analyze observed integrated spectra and match it with recent modeled predicted spectra to obtain the age and reddening automatically. The software will allow the user to choose the appropriate extinction law and other parameters as needed to be used for any galactic or extra galactic star cluster.

126 4.8 Conclusion and future work

2.4 Age=8.30 E(B-V)=0.00 2.2

1.8

1.6

1.4

Normalized Flux 1.2

0.8

0.6 3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.45: A reasonable match between the model and the observation using the χ2 method - NGC2065

127 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

4 Age=9.05 E(B-V)=0.00 3.5

2.5

1.5 Normalized Flux

0.5

0 3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.46: A poor match predicted by the χ2 method - NGC1850

128 4.8 Conclusion and future work

4 Age=6.85 E(B-V)=0.29 3.5

2.5

1.5 Normalized Flux

0.5

0 3500 4000 4500 5000 5500 6000 Wavelength (A)

Figure 4.47: A poor match predicted by the χ2 method - NGC2031

129 4. AGES OF LMC STAR CLUSTERS FROM INTEGRATED SPECTRA

130 Chapter 5

Conclusion and Future Work

5.1 Introduction

Because star clusters are the building blocks of the galaxies, they are the best tools for studying the formation history of these galaxies. When the ages of star clusters are well know, they can reveal the big picture of the diﬀerent phases in the history of the hosting galaxy. This is why obtaining accurate ages of stellar clusters is critical.

There are diﬀerent methods of determining the ages of stellar clusters. The one that is considered to be the most accurate is the method of the color-magnitude diagram (CMD) in which the constituent stars of the cluster are studied. For far away galaxies, however, one cannot observe the individual stars, that is why aging methods based on integrated properties of clusters are important. Both integrated photometry (color) and integrated spectra have been used for age determination.

The Large Magellanic Cloud (LMC) is a perfect galaxy for testing the accuracy of the methods that use the integrated properties for determining the age, because it close enough to resolve its stars in the star clusters, and hence more than 100 of its clusters have CMD ages in the literature. In the mean time, the LMC is far enough that its clusters can be observed as a whole to obtain their integrated properties. I started this study by collecting a sample of stellar clusters from the literature that has CMD ages with errors, E(B − V ), observed U − B and observed B − V . The ﬁnal sample included 84 clusters.

131 5. CONCLUSION AND FUTURE WORK

In Chapter 2, I revealed a poor correlation between the ages obtained from integrated photometry and the established CMD ages. I showed that there are severe problems in using that method. The most severe problem is the strong degeneracy between extinction and age, which often leads to catastrophic failures particularly if a χ2 minimization method is employed.

An alternative solution is using the integrated spectra of these clusters in the visible range as age indicators. Because such spectra for most our clusters had never been observed before, so I obtained the spectra of 20 clusters through multiple telescope observing runs. A description of the instruments and telescopes used and the method of reducing these data is provided in Chapter 3.

In Chapter 4, I showed that the integrated spectra provides a better prediction of the age by performing a KS test that compares the observed spectrum to a high resolution model spectrum provided by Gonz´alezDelgado et al. (2005). Although many studies show that integrated spectra are good age indicators (San- tos et al., 1995, Piatti et al., 2002, 2005, Santos et al., 2006, Palma et al., 2008, Talavera et al., 2010, Beasley et al., 2002, Wolf et al., 2007, Koleva et al., 2008, Cid Fernandes & Gonzlez Delgado, 2010), very few user-friendly tools are available to easily obtain ages of clusters instantaneously from their integrated spectra. This was the main motivation of this chapter. Here, I am presenting a software package that estimates the age and extinction of star clusters based on their integrated spectra.

5.2 Introducing New Software: ASAD

This chapter introduces a new tool to be used as an Analyzer of Spectra for Age Determination (ASAD). This tool was developed in collaboration with A. M. Asa’d. It was my intention to make our program user-friendly. The only required input is the integrated spectrum of the cluster. The basic idea of ASAD is to compare the observed integrated spectra of star clusters with the computed spectral models of Gonz´alezDel- gado et al. (2005). I chose this particular model because of its high resolution. More

132 5.3 Future Work spectral libraries will be available in future versions of ASAD. The algorithm used by ASAD is the one introduced in chapter 4, a Kolmogorov-Smirnov (KS) test. As for now ASAD was used to reproduced all the results of chapter 4. More functions will be added to ASAD in the future. Earlier this year Ben´ıtez-Llambay et al. (2012) introduced an algorithm called Fast Integrated Spectra Analyzer (FISA) that predicts the age and reddening of small angular diameter open clusters from their integrated spectra in the range 3600-7400 A by comparing them to the currently available template spectrum libraries. Although the scientific goals of FISA and ASAD are similar, as they both aim to predict the age and reddening of star clusters from their integrated spectra, there are major differences in the method used to achieve this goal. First, we use computational theoretical models for determining the ages rather than the templates. Our motivation for doing so is the high resolution of the model used GonzálezDelgado et al. (2005), as well as the larger variety of options of ages provided by the model. The model of GonzálezDelgado et al. (2005) consists of 74 options for the age, while there are only 27 templates available. The second difference is that we are using Cardelli et al. (1989) (CCM) extinction law rather than the Seaton law Seaton (1979) used by FISA. We are allowing for a range of E(B-V) between 0 and 0.5, while FISA covers the range −0.2 to 0.2. Finally ASAD uses the KS test rather than the χ2 method used by FISA.

5.3 Future Work

One ultimate goal is to obtain optical spectra for the full list of 84 clusters to compare the ages obtained from new integrated spectra with their known CMD ages. Figure 5.1 shows the clusters that were observed (analyzed in chapter 4) and the clusters that still need to be studied. Note that the clusters studied span a wide range of age and reddening. The availability of ASAD software will make it easier for us to investigate the integrated spectra in order to obtain more accurate age determinations for stellar clusters. Using ASAD and the libraries of integrated spectra available in the literature we will determine: What wavelength range can be best used to accurately determine the ages of star clusters (IR, optical or UV)? We will then expand ASAD to not only use the method of full spectrum ﬁtting to determine the age and reddening of stellar clusters, but also to examine speciﬁc spectral features to get the age based

133 5. CONCLUSION AND FUTURE WORK

0.3 Done To Do

0.25

0.2

0.15 Reddening

0.1

0.05

0 6.5 7 7.5 8 8.5 9 9.5 Log (Age/yr)

Figure 5.1: The clusters that have observed spectra in the visible range. - Our goal is to obtain the spectra of the other clusters too

134 5.3 Future Work on the strength of these features (Worthey & Ottaviani, 1997, Beasley et al., 2002). In addition, I will explore the use of ratios of different spectral features (Leonardi & Rose, 2003) for better age estimations. Metallicity and mass will be set as variables in my future investigations as well, as this is known to have a significant affect on aging methods Popescu & Hanson (2010a), Beasley et al. (2002).

135 5. CONCLUSION AND FUTURE WORK

136 Bibliography

Ahumada, A. V., Claria, J. J., Bica, E., & Dutra, C. M. 2002, Astronomy and Astro- physics, 393, 855 10

Alcaino, G., & Liller, W. 1987, The Astronomical Journal, 94, 372 6, 78, 111

Asa’d, R. S., & Hanson, M. M. 2012, Monthly Notices of the Royal Astronomical Society, 419, 2116 73, 74, 119, 120, 121, 122

Balbinot, E., Santiago, B. X., Kerber, L. O., Barbuy, B., & Dias, B. M. S. 2010, Monthly Notices of the Royal Astronomical Society 11

Beasley, M. A., Hoyle, F., & Sharples, R. M. 2002, Monthly Notices of the Royal Astronomical Society, 336, 168 55, 73, 132, 135

Ben´ıtez-Llambay, A., Clari´a,J. J., & Piatti, A. E. 2012, , 124, 173 133

Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., & Nasi, E. 1994, Astronomy and Astrophysics Supplement Series, 106, 275 7, 15

Bica, E., & Alloin, D. 1986a, Astronomy and Astrophysics, 162, 21 52, 74, 84

—. 1986b, Astronomy and Astrophysics Supplement Series, 66, 171 52

—. 1987, Astronomy and Astrophysics, 186, 49 52, 74

Bica, E., Alloin, D., & Schmitt, H. R. 1994, Astronomy and Astrophysics, 283, 805 54, 74

Bica, E., Claria, J. J., & Dottori, H. 1992, The Astronomical Journal, 103, 1859 7

Bica, E., Claria, J. J., Dottori, H., Santos, J. F. C., J., & Piatti, A. E. 1996, The Astrophysical Journal Supplement Series, 102, 57 7, 19

137 BIBLIOGRAPHY

Bica, E., Santos, J. F. C., & Alloin, D. 1990, Astronomy and Astrophysics, 235, 103 52, 74, 84

Bruzual, G., & Charlot, S. 2003, Monthly Notices of the Royal Astronomical Society, 344, 1000 7, 27, 84

Bruzual A., G. 2002, in , 616 13

Buonanno, R., Corsi, C. E., & Fusi-Pecci, F. 1988, in , 635 6

Burke, D. L., Axelrod, T., Blondin, S., et al. 2010, , 720, 811 85

Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, The Astrophysical Journal, 345, 245 8, 16, 20, 85, 133

Cervino, M., & Luridiana, V. 2004, Astronomy and Astrophysics, 413, 145 13

—. 2006, Astronomy and Astrophysics, 451, 475 13, 27, 84

Chandar, R., Fall, S. M., & Whitmore, B. C. 2010, The Astrophysical Journal, 711, 1263 8, 11, 19, 30

Charlot, S., & Bruzual, A. G. 1991, The Astrophysical Journal, 367, 126 8, 16

Chiosi, C., Bertelli, G., & Bressan, A. 1988, Astronomy and Astrophysics, 196, 84 13, 27

Cid Fernandes, R., & Gonzlez Delgado, R. M. 2010, Monthly Notices of the Royal Astronomical Society, 403, 780 58, 74, 85, 132

Conroy, C., & Gunn, J. E. 2010, The Astrophysical Journal, 712, 833 11

Da Costa, G. S., King, C. R., & Mould, J. R. 1987, The Astrophysical Journal, 321, 735 6

Da Costa, G. S., Mould, J. R., & Crawford, M. D. 1985, , 297, 582 78 de Grijs, R., & Anders, P. 2006, Monthly Notices of the Royal Astronomical Society, 0, 295 10, 17 diagram, H. 2012, http://www.mscd.edu/physics/astro/activities/hrdiagram.htm 3

138 BIBLIOGRAPHY

Dieball, A., Grebel, E. K., & Theis, C. 2000, Astronomy and Astrophysics, 358, 144 8, 111

Dirsch, B., Richtler, T., Gieren, W. P., & Hilker, M. 2000, Astronomy and Astrophysics, 360, 133 8, 78

Dopita, M., Hart, J., McGregor, P., et al. 2007, Astrophysics and Space Science, 310, 255 59

Elson, R. A., & Fall, S. M. 1988, The Astronomical Journal, 96, 1383 6, 78

Elson, R. A. W. 1991, The Astrophysical Journal Supplement Series, 76, 185 78

Elson, R. A. W., & Fall, S. M. 1985, The Astrophysical Journal, 299, 211 6, 7, 11, 14

Flower, P. J. 1984, The Astrophysical Journal, 278, 582 6

Geisler, D., Bica, E., Dottori, H., et al. 1997, The Astronomical Journal, 114, 1920 8

Girardi, L., & Bertelli, G. 1998, Monthly Notices of the Royal Astronomical Society, 300, 533 15, 21

Girardi, L., & Bica, E. 1993, Astronomy and Astrophysics, 274, 279 10

Girardi, L., Chiosi, C., Bertelli, G., & Bressan, A. 1995, Astronomy and Astrophysics, 298, 87 7, 14, 15, 30

Gonz´alezDelgado, R. M., Cervi˜no,M., Martins, L. P., Leitherer, C., & Hauschildt, P. H. 2005, , 357, 945 84, 132, 133

Gordon, K. D., Calzetti, D., & Witt, A. N. 1997, The Astrophysical Journal, 487, 625 20

Gray, R. O., Corbally, C. J., & Burgasser, A. 2009, Stellar Spectral Classiﬁcation, Princeton series in astrophysics (Princeton, N.J. ; Woodstock: Princeton University Press) 61

Hancock, M., Smith, B. J., Giroux, M. L., & Struck, C. 2008, Monthly Notices of the Royal Astronomical Society, 389, 1470 11, 19, 20

Harris, J., & Zaritsky, D. 2009, The Astronomical Journal, 138, 1243 2, 5, 11

139 BIBLIOGRAPHY

Hodge, P. W. 1960a, The Astrophysical Journal, 131, 351 5

—. 1960b, The Astrophysical Journal, 132, 341 5

—. 1960c, The Astrophysical Journal, 132, 346 5

—. 1960d, The Astrophysical Journal, 132, 351 5

—. 1961, The Astrophysical Journal, 134, 226 5

—. 1983, The Astrophysical Journal, 264, 470 5, 78, 111

—. 1984, Publications of the Astronomical Society of the Paciﬁc, 96, 947 78

Howell, S. B. 2006, Handbook of CCD Astronomy, 2nd edn., Cambridge observing handbooks for research astronomers (Cambridge: Cambridge University Press) 62

Hunter, D. A., Elmegreen, B. G., Dupuy, T. J., & Mortonson, M. 2003, The Astro- nomical Journal, 126, 1836 xi, 7, 8, 11, 12, 13, 16, 17, 18, 19, 21, 22

Hurley, J. R., Pols, O. R., & Tout, C. A. 2000, Monthly Notices of the Royal Astro- nomical Society, 315, 543 7

Jacoby, G. H., Hunter, D. A., & Christian, C. A. 1984, , 56, 257 50

Jones, J. H. 1987, , 94, 345 78

Kaler, J. B. 1997, Stars and Their Spectra: An Introduction to the Spectralsequence, 1st edn. (Cambridge, U.K. ; New York: Cambridge University Press) 53

Kerber, L. O., Santiago, B. X., & Brocato, E. 2007, Astronomy and Astrophysics, 462, 139 78

Koleva, M., Prugniel, P., Ocvirk, P., Le Borgne, D., & Soubiran, C. 2008, Monthly Notices of the Royal Astronomical Society, 385, 1998 58, 74, 132

Kotulla, R., Fritze, U., Weilbacher, P., & Anders, P. 2009, , 396, 462 84

Kroupa, P. 2002, Science, 295, 82 20

Lancon, A., Goldader, J. D., Leitherer, C., & Delgado, R. M. G. 2001, The Astrophys- ical Journal, 552, 150 20

140 BIBLIOGRAPHY

Leitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, The Astrophysical Journal Supplement Series, 123, 3 7, 16, 27, 84

Leonardi, A. J., & Rose, J. A. 2003, The Astronomical Journal, 126, 1811 10, 55, 57, 73, 74, 81, 135 lines. 1997, ”Fraunhover lines.” A Dictionary of Astronomy. 1997. Encyclopedia.com. 2 Jan. 2012, http://www.encyclopedia.com 51

Mackey, A. D., & Gilmore, G. F. 2003, Monthly Notices of the Royal Astronomical Society, 338, 85 2, 8, 11

Maraston, C. 2005, Monthly Notices of the Royal Astronomical Society, 362, 799 7

Massey, P., & Hanson, M. M. 2010, arXiv:1010.5270 61, 62

Meurer, G. R., Freeman, K. C., & Cacciari, C. 1990, The Astronomical Journal, 99, 1124 78

Mighell, K. J., Sarajedini, A., & French, R. S. 1998, The Astronomical Journal, 116, 2395 10

Mould, J., Kristian, J., Nemec, J., Jensen, J., & Aaronson, M. 1989, The Astrophysical Journal, 339, 84 6

Mould, J. R., Da Costa, G. S., & Crawford, M. D. 1986a, The Astrophysical Journal, 304, 265 78

Mould, J. R., Da Costa, G. S., & Wieland, F. P. 1986b, The Astrophysical Journal, 309, 39 78

Olsen, K. A. G. 1999, The Astronomical Journal, 117, 2244 2, 8, 11

Olszewski, E. W., Schommer, R. A., Suntzeﬀ, N. B., & Harris, H. C. 1991, The Astro- nomical Journal, 101, 515 2, 11

Palma, T., Ahumada, A., Claria, J., & Bica, E. 2008, Astronomische Nachrichten, 329, 392 55, 74, 97, 111, 132

Pandey, A. K., Sandhu, T. S., Sagar, R., & Battinelli, P. 2010, Monthly Notices of the Royal Astronomical Society, 403, 1491 10, 35

141 BIBLIOGRAPHY

Persson, S. E., Aaronson, M., Cohen, J. G., Frogel, J. A., & Matthews, K. 1983, The Astrophysical Journal, 266, 105 78, 111

Piatti, A. E., & Claria, J. J. 2001, VizieR Online Data Catalog, 337, 90453 10

Piatti, A. E., Geisler, D., Bica, E., & Claria, J. J. 2003, Monthly Notices of the Royal Astronomical Society, 343, 851 2, 11

Piatti, A. E., Geisler, D., Sarajedini, A., & Gallart, C. 2009, Astronomy and Astro- physics, 501, 585 35

Piatti, A. E., Santos, J. F. C., Clari, J. J., et al. 2005, Astronomy and Astrophysics, 440, 111 55, 74, 132

Piatti, A. E., Sarajedini, A., Geisler, D., Bica, E., & Claria, J. J. 2002, Monthly Notices of the Royal Astronomical Society, 329, 556 10, 54, 74, 84, 132

Pietrzynski, G., & Udalski, A. 2000, Acta Astronomica, 50, 337 7

Popescu, B., & Hanson, M. M. 2009, The Astronomical Journal, 138, 1724 4, 12, 14

—. 2010a, The Astrophysical Journal, 713, L21 13, 27, 135

—. 2010b, The Astrophysical Journal, 724, 296 13, 27

Rich, R. M., Shara, M., Fall, S. M., & Zurek, D. 2000, The Astronomical Journal, 119, 197 10

Sagar, R., & Pandey, A. K. 1989, Astronomy and Astrophysics Supplement Series, 79, 407 2, 6, 11

Salaris, M., & Cassisi, S. 2005, Evolution of Stars and Stellar Populations (Chichester, England ; Hoboken, NJ: Wiley) 3, 4, 51

Salpeter, E. E. 1955, , 121, 161 84

Santos, J., Alloin, D., Bica, E., & Bonatto, C. J. 2002, in , 727 57

Santos, J. F. C., Bica, E., Claria, J. J., et al. 1995, Monthly Notices of the Royal Astronomical Society, 276, 1155 54, 74, 84, 132

142 BIBLIOGRAPHY

Santos, J. F. C., Claria, J. J., Ahumada, A. V., et al. 2006, Astronomy and Astro- physics, 448, 1023 10, 54, 55, 74, 97, 111, 132

Santos, J. F. C., & Piatti, A. E. 2004, Astronomy and Astrophysics, 428, 79 54

Schiavon, R. P., Caldwell, N., & Rose, J. A. 2004, The Astronomical Journal, 127, 1513 10

Searle, L., Sargent, W. L. W., & Bagnuolo, W. G. 1973, The Astrophysical Journal, 179, 427 16

Searle, L., Wilkinson, A., & Bagnuolo, W. G. 1980, The Astrophysical Journal, 239, 803 5, 6, 14

Seaton, M. J. 1979, , 187, 73P 133

Shapley, H., & Lindsay, E. M. 1963, Irish Astronomical Journal, 6, 74 12

Spectrograph. 2004, http://outreach.atnf.csiro.au/education/senior/astrophysics/spectrographs.html 60

Talavera, M., Ahumada, A., Santos, J., et al. 2010, Astronomische Nachrichten, 331, 323 55, 74, 132

Vallenari, A., Aparicio, A., Fagotto, F., et al. 1994, Astronomy and Astrophysics, 284, 447 2, 8, 11

Vallenari, A., Bettoni, D., & Chiosi, C. 1998, Astronomy and Astrophysics, 331, 506 2, 8, 11, 78 van den Bergh, S. 1981, Astronomy and Astrophysics Supplement Series, 46, 79 6

Van den Bergh, S. 2000, The Galaxies of the Local Group, Cambridge astrophysics series No. 35 (Cambridge, U.K. ; New York: Cambridge University Press) 1

Vazdekis, A. 1999, , 513, 224 84

Vazquez, G. A., & Leitherer, C. 2005, The Astrophysical Journal, 621, 695 7

Vuillemin, A. 1988, Astronomy and Astrophysics Supplement Series, 72, 249 2, 11

143 BIBLIOGRAPHY

Wagner, R. M. 1992, in , 160 59

Whitmore, B. C., & Zhang, Q. 2002, The Astronomical Journal, 124, 1418 20

Wise, M. W., & Silva, D. R. 1996, The Astrophysical Journal, 461, 155 20

Wolf, M. J., Drory, N., Gebhardt, K., & Hill, G. J. 2007, The Astrophysical Journal, 655, 179 57, 73, 132

Worthey, G., & Ottaviani, D. L. 1997, The Astrophysical Journal Supplement Series, 111, 377 55, 56, 73, 135

Yi, S., Brown, T. M., Heap, S., et al. 2000, The Astrophysical Journal, 533, 670 11

Yi, S. K. 2003, The Astrophysical Journal, 582, 202 13, 27

144