The Chemistry and Properties of Stars in Ngc 362

THE CHEMISTRY AND PROPERTIES OF STARS IN NGC 362

A thesis submitted to the University of Manchester for the degree of Master of Science in the Faculty of Engineering and Physical Sciences

November 2014

By Lucas Ben Assayag School of Physics and Astronomy Contents

Abstract 8

Declaration 9

Acknowledgments 12

Conventions and Abbreviations 13

1 Introduction 14 1.1 Motivation ...... 14 1.2 Deﬁnitions ...... 14 1.2.1 Abundance ...... 14 1.2.2 Stellar populations ...... 15 1.3 The chemical evolution of the Universe ...... 16 1.3.1 Formation of the ﬁrst stars ...... 17 1.3.2 Low-mass stellar evolution ...... 17 1.3.3 High-mass stellar evolution ...... 19 1.4 Globular Clusters ...... 20 1.4.1 Overview ...... 20 1.4.2 Abundance studies ...... 21 1.5 NGC 362 ...... 25 1.5.1 The second parameter problem ...... 26 1.5.2 Previous studies ...... 28

2 1.6 Overview of this thesis ...... 30

2 Data Processing 31 2.1 Equivalent Width ...... 38 2.2 Equivalent Width measurement ...... 39 2.3 MOOG Software ...... 41 2.4 Results ...... 45

3 Other elements 50 3.1 Results ...... 50 3.2 Sodium ...... 54 3.3 Silicon ...... 55 3.4 Calcium ...... 57 3.5 Titanium ...... 58 3.6 α elements ...... 60 3.7 Conclusions ...... 61

4 Error estimation 62 4.1 Statistical abundance uncertainties ...... 62 4.2 Abundance uncertainty to model atmosphere parameters ...... 67

5 Discussion 69 5.1 Radial dependences of abundances ...... 69 5.1.1 Iron abundance ...... 70 5.1.2 Sodium abundance ...... 74 5.1.3 Silicon abundance ...... 75 5.1.4 Calcium abundance ...... 76 5.1.5 Titanium abundance ...... 77 5.1.6 α-element abundance ...... 78 5.2 Comparison of stellar parameters ...... 81 5.3 Comparison with the literature ...... 86

3 5.3.1 Comparison of the iron abundances ...... 87 5.3.2 Comparison of the sodium abundances ...... 88 5.3.3 Comparison of the silicon abundances ...... 89 5.3.4 Comparison of the calcium abundances ...... 91 5.3.5 Comparison of the titanium abundances ...... 92 5.4 Enrichment history of NGC 362 ...... 94

6 Conclusion 96

4 List of Tables

1.1 Iron abundance studies of NGC 362 ...... 25 1.2 Abundance studies of NGC 362 ...... 28

2.1 Log of FLAMES observations for NGC 362 ...... 33 2.2 Line List ...... 34 2.3 List of Galactic Stars ...... 40 2.4 Derived atmospheric parameters ...... 45 2.5 Metallicity studies of NGC 362 ...... 48

3.1 Derived abundances ...... 51 3.2 Comparison between studies of NGC 362 ...... 54 3.3 Star-by-star comparison between this study and Carretta et al. (2013) 54

4.1 Statistical uncertainties ...... 63 4.2 Abundance sensitivity to model atmosphere parameters ...... 68

5.1 Comparison between spectroscopic and photometric eﬀective temperatures ...... 81

5 List of Figures

1.1 Comparison of spectra between stars having diﬀerent metallicity . . . 16 1.2 HR Diagram of a Sun-like star ...... 18 1.3 Example of Na-O anticorrelatoin in diﬀerent clusters ...... 22 1.4 Colour magnitude diagram of the double main sequence in ω Centauri 24 1.5 Colour-magnitude diagrams for NGC 288 and NGC 362 ...... 26

2.1 Hertzsprung–Russell Diagram of NGC 362 ...... 32 2.2 Image of NGC 362 ...... 33 2.3 Equivalent Width ...... 38 2.4 Interface of the ﬁrst program ...... 39 2.5 Continuum setting ...... 41 2.6 Example of a deblending ...... 42 2.7 Graphical determination of the model atmosphere with MOOG . . . 43

2.8 [Fe/H] vs Teﬀ ...... 49

3.1 [Na/Fe] vs [Fe/H] ...... 55 3.2 [Si/Fe] vs [Fe/H] ...... 57 3.3 [Ca/Fe] vs [Fe/H] ...... 58 3.4 [Ti/Fe] vs [Fe/H] ...... 59 3.5 [α/Fe] vs [Fe/H] ...... 60

5.1 Histogram of the distribution of the distance from the centre of the cluster...... 70 5.2 [Fe/H] vs Distance from the centre of NGC 362 ...... 71

6 5.3 [Fe/H] vs log g ...... 73 5.4 [Na/Fe] vs Distance from the centre of NGC 362 ...... 74 5.5 [Si/Fe] vs Distance from the centre of NGC 362 ...... 75 5.6 [Ca/Fe] vs Distance from the centre of NGC 362 ...... 76 5.7 [Ti/Fe] vs Distance from the centre of NGC 362 ...... 77 5.8 [α/Fe] vs Distance from the centre of NGC 362 ...... 78 5.9 [α/H] vs Distance from the centre of NGC 362 ...... 79 5.10 [Ti/H] vs Distance from the centre of NGC 362 ...... 80

5.11 Teﬀspec – Teﬀphot vs Distance from the centre of NGC 362 ...... 85

5.12 Teﬀspec and Teﬀphot vs Distance from the centre of NGC 362 ...... 85

5.13 Comparison of [Fe/H] vs Teﬀ ...... 87 5.14 Comparison of [Na/Fe] vs [Fe/H] ...... 88 5.15 Comparison of [Si/Fe] vs [Fe/H] ...... 89 5.16 (Si) vs [Fe/H] ...... 90 5.17 Comparison of [Ca/Fe] vs [Fe/H] ...... 91 5.18 (Ca) vs [Fe/H] ...... 92 5.19 Comparison of [Ti/Fe] vs [Fe/H] ...... 93 5.20 Theoretical yields for the chemical enrichment due to Type II SN explosions ...... 95

7 Abstract

Abundance studies in Galactic globular clusters increase knowledge of the chemical enrichment of the Universe and the formation of stars or galaxies. This thesis presents chemical abundances for iron, calcium, silicon and titanium in 56 stars in the Galactic globular cluster NGC 362 from spectra obtained with FLAMES, the multi-object spectrograph at the Very Large Telescope. The abundances were derived using equivalent width measurements. This study covered wavelengths from 6300 to 6900 A.˚ The average iron abundance derived is [Fe/H] = –1.26 ± 0.03 dex, consistent with previous studies. An unexpected scatter was found, explained by the presence of blended stars and the decision to determine each atmospheric parameter (Teff , log(g), vt and [Fe/H]) independently of photometric measurements. It might be better to fix one of them for future studies. The average sodium, silicon and calcium abundances are also in agreement with the literature. We determined [Na/Fe] = 0.11 ± 0.18 dex, [Si/Fe] = 0.25 ± 0.13 dex and [Ca/Fe] = 0.38 ± 0.06 dex. The titanium abundance determined in this thesis is higher by ∼ 0.40 dex than previous studies, due to effects caused by the proximity of the 6562 AH˚ α line. The measured abundance for this study is [Ti/Fe] = 0.56 ± 0.20 dex. The enhancement of the α elements (Si, Ca and Ti) suggests an enrichment from Type II Supernovae (SNe) and minimal contributions from Type Ia SNe.

8 Declaration

No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualiﬁcation of this or any other university or other institution of learning.

9 Copyright

i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the Intellectual Property) and any reproductions of copyright works in the thesis, for example graphs and tables (Reproductions), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual- prop- erty.pdf), in any relevant Thesis restriction declarations deposited in the University Library, The University Librarys regulations (see http://www.manchester.ac.uk/library/

10 aboutus/regulations) and in The University’s policy on presentation of Theses.

11 Acknowledgments

First I would like to thank my supervisors Dr. Iain McDonald and Prof. Albert Zijlstra. Iain, I cannot believe how much you have done for me throughout the year! You are an incredible supervisor. Albert, thank you for the wise advice you gave me. I would also like to thank the students of the East Wing, especially Skandar, Mike and Chris for their warm welcome and for making this year abroad a very nice experience. This thesis would have never been written without the support I got from my family. Papa, Maman, Ugo and Andy, you have always believed in me and I am very grateful for that. My thanks also go out to all my friends that remained in France, it was so good to see you during the holidays to release the pressure. Thanks for the good laughs you gave me with our discussions. Finally, I wish to thank my girlfriend Salom´efor her love and support. You cannot imagine how helpful it was to be able to talk to you everyday.

12 Conventions and Abbreviations

The conventional abbreviations for SI units and astronomical quantities are used. The following abbreviations have been used in this thesis: ACS — Advanced Camera for Surveys AGB — Asymptotic Giant Branch Dec — Declination EW — Equivalent Width FLAMES — Fibre Large Array Multi Element Spectrograph HB — Horizontal Branch HR(D) — Hertzsprung-Russell (Diagram) HST — Hubble Space Telescope ISM — Interstellar Medium LTE — Local Thermodynamic Equilibrium MEDUSA — Multi-Object Spectroscopy mode NGC — New General Catalogue of Nebulae and Clusters of Stars RA — Right Ascension RGB — Red Giant Branch S/N — Signal-to-noise (ratio) SN(e) — Supernova(e) UT — Unit Telescope UVES — Ultraviolet and Visual Echelle Spectrograph VLT — Very Large Telescope

13 Chapter 1

Introduction

1.1 Motivation

Metal-poor stars record the history of the Universe. They are the oldest observable stars and they make up Milky Way globular clusters. If we have access to the primordial composition of the clusters, we may improve our knowledge about their formation and their evolution. By determining the chemical abundance of their most recent generation of stars, we can have a better understanding of the origin of the elements and the chemical enrichment of the Universe.

1.2 Deﬁnitions

The purpose of this section is to give relevant deﬁnitions which will help understanding the other parts.

1.2.1 Abundance

The abundance of an element can be found in two forms in the literature: the ‘’ notation and the ‘square-bracket’ notation. In the ‘’ notation, the abundance of an element is expressed relative to 1012 hydrogen atoms. Therefore, given an element A:

14 CHAPTER 1. INTRODUCTION 15

log10 (A) = log10(NA/NH ) + 12, where NA is the number of atoms of the element A. In the ‘square-bracket’ notation, the abundance is expressed relative to that of the Sun. For two elements A and B, we then have:

[A/B] = log10(NA/NB)star − log10(NA/NB) . If we select iron as element A and hydrogen as element B, the equation is:

[F e/H] = log10(NF e/NH )star − log10(NF e/NH ) . The quantity [Fe/H] is often used as an easily observed substitute for the metallicity1.

1.2.2 Stellar populations

The historical definition of the three different stellar populations is linked to the metallicity. Population I stars are young, metal-rich stars that can be found in the disk of our Galaxy. For instance, the Sun is a Population I star. Population II stars are old, metal-poor stars, mainly found in the ‘halo’ of galaxies, dwarf spheroidal galaxies and globular clusters. Population III stars refers to hypothetical metal-free stars that would be the first generation of stars. They would have formed from the primordial gas constituted of hydrogen, helium and traces of lithium. These definitions are now outdated, though still in general use, but it has been realized since that a wide range of stellar ages and metallicities are present in the cosmos. Beers & Christlieb (2005) propose a nomenclature for stars of different metallicities. Particularly, they define metal-poor stars as stars having a metallicity less than –1.0. If [Fe/H] < –2.0 the star is called very metal-poor. This continues until [Fe/H] < –5.0 and the hyper-metal-poor stars2. These stars are studied because they are the oldest stars observed and they record the heavy element abundances produced in the first generation of stars, so if we can measure their chemical abundance and compare it with predictions from stellar evolution we will have a better understanding of the formation and evolution of previous generations of stars. The

1It must be noted that the evolution of iron may have been diﬀerent from the evolution of other metals, resulting in iron-poor-stars not necessarily lacking in other metals. 2These hyper-metal poor stars reveal substantial enhancement of C, N and O (Tumlinson 2007). CHAPTER 1. INTRODUCTION 16 most metal-poor star which has so far been observed has a metallicity of –5.6 (Frebel et al. 2005).

1.3 The chemical evolution of the Universe

This project is about measuring the chemical abundance of stars. To be able to understand the distribution of elements that will be obtained, we need to understand how the elements formed and how the Universe has been enriched. If we look at the mass fraction of the metals (i.e. elements from Li to U) in our Galaxy, we see that it evolved from ∼ 2 × 10−9 (after the Big Bang nucleosynthesis, only Li and Be are found) to ∼ 0.02 today (Frebel & Norris 2013). If we look at stars of diﬀerent metallicities we can have a quick overview of the chemical evolution of stars (e.g. Figure 1.1).

Figure 1.1: Comparison of spectra between stars having different metallicity (Aoki et al. 2006): the top spectrum belongs to the Sun ([Fe/H] = 0); the medium spectrum belongs to a very metal-poor star ([Fe/H] = –3.2); the bottom spectrum belongs to the most metal-poor star observed ([Fe/H] = –5.6). Note that the most metal-poor one has only one detectable absorption line in comparison to the multiplicity of absorption lines we can find in the spectrum of the Sun. This shows how different population of stars have been enriched. CHAPTER 1. INTRODUCTION 17

1.3.1 Formation of the ﬁrst stars

The first elements created were the lightest ones: hydrogen, helium and lithium. They were formed during the Big Bang nucleosynthesis (or primordial nucleosynthesis) that occurred a few seconds after the Big Bang. 7Be was also formed during that stage, but it fully decayed due to its instability before the first stars formed. The Big Bang theory predicts that the primordial gas clouds contained 75% of H, 25 % of He and ∼ 2 × 10−9 of Li (by mass; Frebel & Norris 2013). As stars form from the gravitational collapse of clouds of gas, the first generation of stars (population III stars) must have the same composition as the primordial gas clouds. The relative instability of nuclei with atomic masses 5–8 prevented the formation of heavier elements through the primordial nucleosynthesis. These elements are synthesised in the core of stars thanks to nuclear fusion. This process, called stellar nucleosynthesis, is related to the stellar evolution. Mass loss from stars returns nuclear-processed material to the interstellar medium (ISM) where it can form metal- rich stars. This mass loss is determined by stellar evolution, which is described for a solar mass star in the next Section.

1.3.2 Low-mass stellar evolution

From the beginning of its life, up to the main-sequence turn-off point, the Sun- like star burns hydrogen in its core to form helium via the proton-proton chain and releases energy (Iben 1967). When hydrogen is exhausted in the core of the star, the equilibrium between the outward pressure (which resulted from the energy release) and gravity is broken. This leads to a contraction of the core (turn off point) from where the star moves onto the Red Giant Branch (RGB) where hydrogen burns in an envelope (to form helium) around an inert helium core (see Figure 1.2). As the envelope expands and cools it becomes convective. The products of hydrogen fusion are brought to the surface during this stage called first dredge-up. But this phenomenon alone cannot explain the inhomogeneities found in carbon CHAPTER 1. INTRODUCTION 18

Figure 1.2: HR Diagram of a Sun-like star. The stars presented in this thesis are slightly lighter, but their evolution is qualitatively the same as Sun-like stars. This picture was taken from http://nothingnerdy.wikispaces.com/file/view/ stellar_evolution_on_HR.png. abundances for RGB stars in metal-poor clusters. Indeed, Bell et al. (1979) found that the carbon abundance was a decreasing function of the luminosity in M92. Suntzeﬀ (1981) conﬁrmed this trend for M3 and M13. It implies that some other form of mixing occurs within RGB stars, called deep mixing or extra-mixing. Ther- mohaline mixing (Angelou et al. 2010) and rotational-induced mixing (Charbonnel & Lagarde 2010) are currently favoured but the process is not fully understood yet. The Sun-like stellar evolution continues as the helium formed in the envelope accumulates at the core, and the core heats because of gravity (constriction). When the temperature reaches approximatively 108K, helium burning can start. Helium then transforms into carbon. This reaction is called the triple-alpha process because it requires three helium atoms to form one atom of carbon. Oxygen can also be formed if four alpha particles fuse. As the star goes down to the horizontal branch (HB), helium keeps forming carbon in the core whereas hydrogen keeps forming helium in the envelope (Iben 1974). When the helium core is exhausted the core contracts and the star enters the Asymptotic Giant Branch (AGB). This is where the abundance of a star changes the most (if it is massive enough). The core is CHAPTER 1. INTRODUCTION 19 formed by carbon and oxygen, surrounded by a helium burning and a hydrogen burning envelope (Iben & Renzini 1983). If the star is not massive enough (Mstar <

8Msun) the core cannot burn and form heavier elements. Another mixing known as third dredge-up occurs during the AGB stage of a low-mass star: as the helium burning shell is highly thermally unstable (due to the fusion rate being strongly dependent on the temperature) it undergoes thermal pulses every 104 – 105 years, which allow elements from the intershell region (between the hydrogen and helium burning shells) to mix into the outer envelope. Products of He burning appear near the stellar surface. The outer envelope gets ejected through stellar winds, driven by radial pulsations of the stars mantle on yearly timescales. The C-O core and the envelope separate. The ejected envelope is ionised by the revealed stellar core and becomes a Planetary Nebula. The C-O core is inert and fusion no longer provides energy: the remnant radiates the leftover energy and cools, ending its life as a white dwarf.

1.3.3 High-mass stellar evolution

In the case of a massive star, successive steps of exhaustion and contraction occur, stopping with an iron-group core (Fe,Co,Ni), surrounded by lighter elements up to the external envelope made of hydrogen. Elements up to nickel (Z=28) can be formed thanks to the alpha process. However, the iron-group core cannot form heavier elements because the further reactions are endothermic (they require net energy to occur). The elements formed during the lifetime of the high-mass star will be returned to the ISM through supernova explosions. Heavier elements are formed thanks to neutron capture processes, mainly the s-process and the r-process (Burbidge et al. 1957, Cameron 1957). The s-process is a slow neutron capture process (it takes 100 to 105 years to capture neutrons). The s-process contains three components:

• the ‘main’ s-process which produces elements from Sr up to Pb during the AGB phase of low and intermediate mass stars. CHAPTER 1. INTRODUCTION 20

• the ‘weak’ s-process which produces elements from Fe up to Sr between the helium burning core and the carbon burning shell in massive stars.

• the ‘strong’ s-process which produces Pb and Bi.

As the reaction is very slow, the new nucleus will β-decay if it is unstable and form a heavier element (it wins a proton and loses a neutron). The s-process can build elements up to bismuth, but heavier elements are unstable and they only form thanks to the r-process. The r-process is a very quick (rapid) process that occurs when massive stars die as supernovae. It only takes a fraction of second to capture multiple neutrons hence the new nuclei do not β-decay immediately which enables the formation of unstable atoms up to uranium. These heavier elements will then enter the ISM through stellar winds (for s-process elements) or as supernova remnants. All the elements built during the lifetime of a star will enrich the ISM and then allow the next generations of stars to be more metal-rich, as we see with our Sun.

1.4 Globular Clusters

1.4.1 Overview

Galactic globular clusters are compact aggregations of many thousands of stars (104– 107). They are mainly found in the Galactic halo and contain very old (population II) stars. The stars within a globular cluster have approximately the same age, therefore they make useful places to test theories of stellar evolution. The first observation of a globular cluster was made by Abraham Ihle in 1665, of M22 in Sagittarius (Monaco et al. 2004). Ihle referred to it as a nebula. In 1677, Edmond Halley discovered Omega Centauri (NGC 5139). He also discovered M13 (Halley 1714). The first to use the term ‘globular cluster’ was Herschel in his second catalogue of 1000 deep sky objects (Herschel 1789). At that time 70 globular clusters were known. Nowadays we know about 157 clusters (Harris 2010). The metallicities of globular clusters CHAPTER 1. INTRODUCTION 21 range from [Fe/H] = –2.37 to –0.10. One of the first applications of globular clusters was the determination of the Galactic Center (Shapley 1918). He discovered that the Sun was not located in the Galactic Center, in opposition with what was believed until then, but quite far from it. Globular clusters have been well studied since then because they provide information about the earliest times of the Universe.

1.4.2 Abundance studies

There are two commonly used ways to derive the chemical abundance of stars from their spectra: the equivalent width measurement and the spectral synthesis. The equivalent width method consists in measuring the area of a spectral absorption line by fitting a Gaussian (or Voigt) profile. Spectral synthesis consists in generating a spectrum via solving the equations of radiation transfer through a model of the star’s atmosphere. The user tries to match the generated spectrum with the observed one. Usually astronomers use the equivalent width measurement, but sometimes the shape of the spectrum is too complex (e.g. CN contamination between Al lines, Johnson et al. 2008) and spectral synthesis is required. Curve of growth methods are used to derive the abundance of an element from equivalent width measurements. It was first believed that all the stars in a same globular cluster would have the same abundance. However, studies of abundances within globular clusters have shown many peculiarities (Cohen 1978, Smith 1987, Suntzeff 1993): most of them show that there is a star-to-star variation in some particular elements (light elements) within clusters, the most famous one being the Na-O anticorrelation (see Figure 1.3). One of the first detections of star-to-star variation was made by Cohen in 1978. She derived the abundance of 20 elements in five red giants in M13 and three in M3. The results showed Na and Ca abundance differences between stars of the same cluster. Norris et al. (1981) detected Al inhomogeneity among 69 giant stars in NGC 6752. They also observed CN-weak and CN-strong stars, and proposed to CHAPTER 1. INTRODUCTION 22

Figure 1.3: An example from Ivans et al. (2001) of Na-O anticorrelation in different clusters (M3, M4, M5, M10, M13, M71). We can clearly see that when [Na/Fe] increases [O/Fe] decreases. split the cluster in two groups of stars. Those stars would have different origins, they could have been different population of stars, but they could also have formed at the same time from a different part of the same gas cloud. Drake et al. (1992) measured abundances for Fe, Ca, Na, Al and O in M4, a cluster known for its CN bimodality (it contains CN-weak and CN-strong stars). They studied four giant stars, two CN-strong and two CN-weak. They found an anticorrelation between Na and O but also between Al and O: the CN-strong stars are rich in Na and Al whereas the CN-weak stars are rich in O. They found no variations between Fe and Ca abundances. Two scenarios can have been put forward to explain this anticorrelation: (Denis- senkov et al. (1998) proposed a combination of the two scenarios): the first is a primordial scenario, in which the difference may come from the enrichment of the gas cloud by a previous generation of stars (mass loss from a medium-mass AGB star or massive supernovae). The anticorrelation would exist throughout the star’s life. In the second scenario, the difference comes from the deep mixing that occurs during the RGB stage, allowing the star to produce more Na thanks to proton CHAPTER 1. INTRODUCTION 23 capture reaction. This is called the evolutionary scenario. Gratton et al. (2001) obtained the chemical composition of 14 dwarfs and 12 red giants in NGC 6397 and NGC 6752. They were the first to find an Na-O anticorrelation among main sequence stars. This observation refuted the assumption that Na-O anticorrelation was only due to deep mixing. Indeed, main sequence stars should not go through mixing because that would increase the availability of hydrogen in the core, lengthening the star’s main-sequence lifetime beyond what is observed. Thus they try to explain the Na-O anticorrelation by mass loss during the AGB phase of previous stars that would have changed the primordial composition of a second generation of stars. They also make a second hypothesis, related to this one, claiming that the death of a previous star as a planetary nebula would have enriched the interstellar gas from which new stars are formed. In both cases, the presence of multiple generations of stars is identified. Carretta et al. (2004) found the same results for a different cluster: 47 Tuc (NGC 104), giving more support to the premise. More recently, Carretta et al. (2009) studied 202 red giants in 17 globular clusters. This study revealed that the Na-O anticorrelation occurred in all clusters. We may generalize and say that the Na-O anticorrelation is found in all the globular clusters (no exception has been found so far). The Na-O anticorrelation is not the only chemical peculiarity in globular clusters. Shetrone (1996) studied red giants in M13 and halo field stars and found that the abundances of Mg and Al were anticorrelated. Gratton et al. (2001) confirmed this anticorrelation. However, it does not seem to be present in all clusters. The same question about its origin arose, and the same scenarios were presented. The presence of multiple populations of stars was a logical consequence of these abundance variations, but there was still no observation of that phenomenon. It was finally observed (mainly thanks to the progress made in the resolution and the precision of photometric measurements), as Bedin et al. (2004) discovered ‘the ”double main sequence” of ω Centauri’ (see Figure 1.4). CHAPTER 1. INTRODUCTION 24

Figure 1.4: Colour Magnitude Diagram of the double main sequence in ω Centauri from the work of Bedin et al. (2004). We can see the two diﬀerent sequences from the red and blue dots, which correspond to the stars followed in Bedin’s study.

The ACS (Advanced Camera for Surveys), aboard the Hubble Space Telescope (HST), results proved that the ‘blue main sequence’ was actually more metal-rich than the ‘red main sequence’ and that the ‘red main sequence’ was the one with the most stars. This colour difference is the opposite of what the models of stellar evolution expect. In order to explain this ‘blue main sequence’, Bedin et al. proposed an enhanced value of the He abundance. Norris (2004) calculated the enhancement: ∆Y ∼ 0.15, where Y is the abundance of He. The origin of this enhancement is not clear at the moment. It could be the mass loss by the first generation of AGB medium-mass stars. An accurate measurement of helium abundance would clarify the problem. But it is not an easy task because cool stars do not have strong He lines. Hot stars cannot be used either because the spectrum is affected by diffusion. Dupree & Avrett (2013) used a transition in He i in the near-infrared (at 1.08 µm) for two red giant stars in ω Centauri. Using a semi-empirical model, they obtained Y = 0.39-0.44 and Y= CHAPTER 1. INTRODUCTION 25

0.22 for the two stars, deducing an enhancement of ∆Y ≥ 0.17 for one star (which also has enhanced aluminium and magnesium). This result can give a quantitative approach concerning the enrichment in clusters but it must be noted that ω Centauri has an exceptionally high helium enhancement. Valcarce et al. (2014) found that ∆Y is typically ≤ 0.01 in M4. ω Centauri is not the only cluster where multiple main sequences and other abundance variations have been found. Piotto et al. (2007) discovered a triple main sequence in NGC 2808 based on the ACS on HST. Milone et al. (2012) also found a double main sequence in NGC 6397.

1.5 NGC 362

NGC 362 is a globular cluster located in the constellation Tucana. It was discovered by James Dunlop on August 1, 1826. Diﬀerent attempts have been made to determine this cluster’s age. Dotter et al. (2010) used isochrone ﬁtting from the ACS data and found that it was 11.50 ± 0.50 Gyr. More recently, VandenBerg et al. (2013) derived the age of 55 globular clusters using ACS public photometry. They showed that the age of NGC 362 is 10.75 ± 0.25 Gyr. The metallicity of NGC 362 has been derived by multiple authors. A summary of their results is given in Table 1.1.

Table 1.1: Iron abundance studies of NGC 362

Author [Fe/H]

Pilachowski et. al (1983) –0.9 Gratton (1987b) –1.2 Caldwell & Dickens (1988) –1.05 ± 0.10 Shetrone & Keane (2000) –1.33 ± 0.01 Kraft & Ivans (2003) –1.31 ± 0.03 Sz´ekely et al. (2007) –1.16 ± 0.25 Harris (2010) –1.26 Carretta et al. (2013) –1.171 ± 0.009 CHAPTER 1. INTRODUCTION 26

1.5.1 The second parameter problem

NGC 362 is a well studied cluster, mainly because it forms a ‘second parameter pair’ (maybe the most famous one) with another globular cluster: NGC 288. That means NGC 288 has a blue horizontal branch in the colour-magnitude diagram whereas NGC 362 has a red one (see Figure 1.5), despite their relatively close metallicity: [Fe/H] = –1.39 ± 0.01 dex and [Fe/H] = –1.33 ± 0.01 dex respectively for NGC 288 and NGC 362 (Shetrone & Keane 2000; more recent studies have been performed but Shetrone & Keane derived metallicities for both clusters).

Figure 1.5: Colour-magnitude diagrams for NGC 288 (left) and NGC 362 (right), taken from the ESO MAD Science Demonstration Proposal. Note the concentration of stars on the left side of the HB (blue HB) for NGC 288 and on the right side of the HB (red HB) for NGC 362.

It has been understood, since Sandage & Wallerstein (1960), that variations in the chemical composition of clusters lead to different horizontal branch stars: they are mainly on the red side in metal-rich globular clusters and on the blue side in metal-poor clusters. However, Faulkner (1966) found an exception: M13 (NGC 6205), considered as a metal-rich cluster, appears to have a blue horizontal CHAPTER 1. INTRODUCTION 27 branch. This was proof that metallicity could not explain alone the morphology of the horizontal branch and it was the first allusion to the complex ‘second parameter problem’. Sandage & Wildey (1967) clearly stated that problem: ‘at least one other parameter besides the metal abundance controls the distribution of stars along the horizontal branch’. Many scenarios have been proposed over the past 50 years, but the problem remains only partially solved. The first hypotheses are found in the literature of the late 1960’s. The helium abundance seems to have been the first candidate (Faulkner 1966). Rood & Iben (1968) suggested that the age could be the second parameter. Simoda & Iben (1970) mentioned the abundances of the CNO elements (ZCNO). Other propositions have been made since then, such as stellar rotation (Freeman & Norris 1981), mass loss (Shetrone & Keane 2000, Catelan 2000) and helium mixing (Catelan 2000). These explanations were accepted and challenged (e.g Pilachowski et al. (1983) showed that ZCNO could not be the second parameter because of the Na-O anticorrelation). Even if the age of the cluster seems to be accepted as a parameter, it does not solve the whole problem. More recently, Gratton et al. (2010) stated that the main reason why this is still an open problem is the existence of more than one ‘second parameter’. They recognised that the age is the second parameter and suggested variations of the abundance of helium to be the third parameter. Dotter et al. (2010), following the propositions of Freeman & Norris (1981) and Fusi Pecci & Bellazzini (1997), suggested that two parameters must be taken into account: one ‘global’ parameter which is different among different clusters such as the cluster’s age, and another ‘non-global’ parameter which varies within a globular cluster such as the internal pollution. CHAPTER 1. INTRODUCTION 28

1.5.2 Previous studies

NGC 362 has been studied for more than 30 years. Previous works have been summarised in Table 1.2.

Table 1.2: Abundance studies of NGC 362

Element PSWa(1983) Gb(1987b) SKc(2000) WCd(2010) CAGe(2013) [Fe/H] –0.87 ± 0.2 –1.18 ± 0.04 –1.33 ± 0.01 –1.21 ± 0.09 –1.17 ± 0.05 [O/Fe] 0.36 ± 0.4 0.04 ± 0.13 0.89 ± 0.18 [Na/Fe] 0.36 ± 0.3 –0.08 ± 0.01 0.04 ± 0.15 0.11 ± 0.25 [Mg/Fe] 0.28 0.36 ± 0.05 0.33 ± 0.04 [Al/Fe] 0.31 ± 0.12 0.24 ± 0.19 [Si/Fe] 0.09 ± 0.07 0.36 ± 0.05 0.26 ± 0.04 [Ca/Fe] 0.65 ± 0.3 0.21 ± 0.12 0.18 ± 0.02 0.34 ± 0.02 [Sc/Fe] 0.07 ± 0.2 –0.09 ± 0.07 –0.07 ± 0.04 [Ti/Fe] 0.30 ± 0.3 0.30 ± 0.09 0.30 ± 0.05 0.16 ± 0.03 [V/Fe] 0.15 ± 0.2 0.19 ± 0.06 –0.04 ± 0.01 –0.05 ± 0.03 [Cr/Fe] –0.25 ± 0.4 –0.03 ± 0.04 [Ni/Fe] –0.15 ± 0.3 –0.12 ± 0.19 –0.07 ± 0.03 –0.09 ± 0.04 [Cu/Fe] –0.20 –0.50 ± 0.12 [Y/Fe] 0.30 ± 0.12 0.07 ± 0.11 [Zr/Fe] 0.34 ± 0.12 0.50 ± 0.12 [Ba/Fe] –0.30 ± 0.4 –0.17 ± 0.23 0.28 ± 0.13 0.56 ± 0.30 0.18 ± 0.21 [La/Fe] 0.30 ± 0.3 0.36 ± 0.12 0.36 ± 0.12 0.33 ± 0.09 [Eu/Fe] 0.57 ± 0.06 0.78 ± 0.05 0.70 ± 0.07 Stars 3 1 12 13 92

a Pilachowski et al. (1983) b Gratton (1987b) c Shetrone & Keane (2000) d Worley & Cottrell (2010) e Carretta et al. (2013)

One of the first abundance studies of NGC 362 was carried out by Pilachowski et al. (1983). They studied three stars in this cluster and the abundance of 14 elements from oxygen to lanthanum. Although their sample was restricted, they detected the Na-O anticorrelation (their Table 7D): even though they found that the average [O/H] and [Na/H] values are the same, we can see that when the oxygen to hydrogen ratio decreases the sodium to hydrogen ratio increases. They detected an overabundance of alpha-elements and also an overabundance of oxygen, confirming CHAPTER 1. INTRODUCTION 29 that NGC 362 is composed of oxygen-rich stars. This sample also allows compar- isons with later studies such as Gratton (1987a, 1987b). His study contains eight clusters including NGC 362. He obtains the abundance of ten elements from oxygen to barium of one star in NGC 362 (I-23). He finds that his results concerning the clusters they had in common do not correspond to Pilachowski’s ones: he derives metallicities 0.30 dex lower. Gratton proposes substituting Pilachowski’s results with his results because of the use of more accurate detector technology (photo- graphic spectrographs versus CCD cameras). Unfortunately the comparison with this study will be very inaccurate because it is only composed of one star. A wider study has been carried out by Shetrone & Keane (2000) who tried to compare red giants between NGC 362 and NGC 288. They published abundances of 13 elements in 12 giant stars (their Table 4). They found an Na-O anticorrelation (like Pilachowski et al. 1983), but also an Al-O anticorrelation. The comparison with Pilachowski’s results reveals differences of 0.4 dex in abundances. They also argue that the difference comes from the method of observation (specifically the ‘difficulty of working with image tube spectra recorded on glass plates’). The comparison with Gratton’s results also reveals differences of about 0.1 dex in abundances. As the resolution and signal-to-noise ratio are higher for their sample, their measurements should be more accurate. Worley & Cottrell (2010) determined the abundance of heavy elements of 13 giant stars in NGC 362. They compared barium, lanthanum and europium with previous studies (e.g Pilachowski et al. (1983), Gratton 1987b, Shetrone & Keane 2000). They also derived the abundances of strontium, yttrium, zirconium and neodymium (their Table 15). Their abundance of barium was not very accurate due to sensitivity to microturbulence. The difference with all previous studies is therefore quite significant. The lanthanum abundance was only available in Pilachowski’s study. The values correspond although Pilachowski studied more metal-rich stars. The europium abundance was only available in the study by Shetrone & Keane. The europium abundance is 0.2 dex higher in Worley’s study than Shetrone’s one, CHAPTER 1. INTRODUCTION 30 stated to be due to the lack of hyperfine correction in Worley’s study. Recently, Carretta et al. (2013) measured the abundance of 21 elements for 92 red giant stars. They confirmed the observations of Shetrone & Keane (2000) and found that the abundance of neutron capture elements (heavy elements) is constant throughout the study, proving that these elements come from a previous generation of stars. They considered two generation of stars. They derived abundances using a different method than this study, which in the end was more accurate (it will be discussed in Section 5.3). The results obtained by Carretta’s study will serve as an important comparison to this study because they used more precise instruments than the previous studies. Indeed, multi-object spectrographs saves a lot of time, as they can point up to 130 stars at a time (FLAMES). New telescopes, such as the 8.2m telescope used by Carretta and this study, also save substantial time: it would take at least four times as long to observe a star with a 4m telescope. Fifteen years ago multi-object telescopes did not exist, astrophysicists would have to point each star at a time. It would have taken at least four month’s worth of telescope time to do the observations that Carretta did, which is impossible to ask for.

1.6 Overview of this thesis

This research project aims to determine the fundamental parameters of stars and abundances of their elements from medium-resolution spectroscopy using FLAMES, one of the VLT spectrographs. Chapter 2 describes the software and methods used to obtain the iron abundance of the stars. Chapter 3 details the results for all the elements and compares them with previous studies. Chapter 4 presents how the error calculations were carried out and also reveals the impact of a change in stars’ parameters on the abundance ratios. In Chapter 5 the results from the previous chapters are discussed. Chapter 6 summarises the conclusions of this work. Chapter 2

Data Processing

This study contained 120 HB, AGB and RGB stars, observed with the Fibre Large Array Multi Element Spectrograph (FLAMES) and the Ultraviolet and Visual Echelle Spectrograph (UVES). FLAMES and UVES are intermediate and high-resolution, multi-objects, fibre-fed spectrographs mounted on the Nasmyth A and Nasmyth B (respectively) foci of the VLT Unit Telescope 2 (UT2). The Hertzsprung–Russell Diagram of NGC 362 is shown in Figure 2.1. S/N varied between stars because of brightness differences. It ranged from 16 to 243 and the average value was ∼112. Stars were selected from the photometrically derived Hertzsprung–Russell diagram presented in Boyer et al. (2009). AGB stars were specifically targeted but comprise a relatively small proportion of the sample. Spare MEDUSA / UVES fibres were used on the most luminous giant stars (MEDUSA is the multi-object spectroscopy mode on UVES). The HR13, HR14A and HR15 gratings were used during the observations. High resolution (R ∼ 20 000) was necessary to be able to deblend the spectral lines when needed. The total observation time was approximately 5.4 hours. The log of the observations is given in Table 2.1.

• Observations in the HR13 grating (6100–6400A)˚ contained most of the lines (35 out of 79 Fe lines and six out of 10 lines from the other elements: Na, Si, Ca and Ti).

31 CHAPTER 2. DATA PROCESSING 32

Figure 2.1: Hertzsprung–Russell Diagram of NGC 362. The 56 stars for which abundances were derived in this study are plotted in blue.

• Observations in the HR14A grating (6380–6600A)˚ contained 34 Fe lines, one Ca line and two Ti lines.

• Observations in the HR15 grating (6600–6950A)˚ and contained 10 Fe lines and one Si line.

An image of NGC 362 is given in Figure 2.2. The field of view is 37x25’. For comparison, FLAMES has a 25’ field of view in diameter. The pixel size in this picture (1.4”) is similar to the MEDUSA fibre diameter (1.2”), therefore this picture highlights the blending in the centre of the cluster (which will be discussed in Section 5.2) as it can be the stars are overlapping. CHAPTER 2. DATA PROCESSING 33

Table 2.1: Log of FLAMES observations for NGC 362

Date UT Exposure (sec) Grating Airmass

2011-10-30 01:45:57 1200 HR15 1.488 2011-10-30 02:06:51 1200 HR15 1.468 2011-10-30 02:27:44 1200 HR15 1.454 2011-10-30 04:13:39 1420 HR14A 1.464 2011-10-30 04:38:12 1420 HR14A 1.486 2011-10-30 05:02:45 1420 HR14A 1.516 2011-12-21 00:49:40 2000 HR13 1.464 2011-12-21 01:30:37 2000 HR13 1.505

Figure 2.2: Image of NGC 362. This picture was taken from http://www.verschatse.cl/clusters/ngc362/details.htm. CHAPTER 2. DATA PROCESSING 34

The line list was adapted from Johnson & Pilachowski (2010) and reproduced in Table 2.2. The third column gives the excitation potential (E.P.) and the fourth column gives the weighted oscillator strength for the lines of the selected elements.

Table 2.2: Line List

Ion Wavelength E.P. log(gf) (A)˚ (eV) (dex)

Fe I 6120.25 0.92 –5.860 Fe I 6151.62 2.18 –3.309 Fe I 6157.73 4.08 –1.170 Fe I 6159.37 4.61 –1.840 Fe I 6165.36 4.14 –1.474 Fe I 6173.34 2.22 –2.820 Fe I 6180.20 2.72 –2.726 Fe I 6187.40 2.83 –3.988 Fe I 6187.99 3.94 –1.570 Fe I 6200.31 2.61 –2.317 Fe I 6207.23 4.99 –1.989 Fe I 6213.43 2.22 –2.532 Fe I 6219.28 2.20 –2.333 Fe I 6226.74 3.88 –2.050 Fe I 6229.23 2.85 –2.805 Fe I 6232.64 3.65 –1.103 Fe I 6240.65 2.22 –3.250 Fe I 6246.32 3.60 –0.643 Fe I 6252.56 2.40 –1.717 Fe I 6265.13 2.18 –2.460 Fe I 6270.23 2.86 –2.544 Fe I 6290.54 2.59 –4.300 CHAPTER 2. DATA PROCESSING 35

Table 2.2 – Continued

Ion Wavelength E.P. log(gf) (A)˚ (eV) (dex)

Fe I 6290.97 4.73 –0.504 Fe I 6297.79 2.22 –2.670 Fe I 6301.50 3.65 –0.588 Fe I 6302.49 3.69 –1.083 Fe I 6330.85 4.73 –1.200 Fe I 6335.33 2.20 –2.237 Fe I 6336.82 3.69 –0.696 Fe I 6355.03 2.85 –2.340 Fe I 6380.74 4.19 –1.326 Fe I 6385.72 4.73 –1.850 Fe I 6392.54 2.28 –3.940 Fe I 6393.60 2.43 –1.562 Fe I 6400.00 3.60 –0.470 Fe I 6400.32 0.92 –4.178 Fe I 6408.02 3.69 –1.128 Fe I 6411.65 3.65 –0.755 Fe I 6412.20 2.45 –5.063 Fe I 6419.64 3.94 –2.580 Fe I 6419.95 4.73 –0.280 Fe I 6430.85 2.18 –1.886 Fe I 6436.41 4.19 –2.410 Fe I 6469.19 4.83 –0.260 Fe I 6475.62 2.56 –2.832 Fe I 6481.87 2.28 –2.934 Fe I 6483.94 1.49 –5.638 CHAPTER 2. DATA PROCESSING 36

Table 2.2 – Continued

Ion Wavelength E.P. log(gf) (A)˚ (eV) (dex)

Fe I 6494.50 4.73 –1.176 Fe I 6494.98 2.40 –1.313 Fe I 6495.74 4.83 –1.060 Fe I 6496.47 4.79 –0.650 Fe I 6498.94 0.96 –4.489 Fe I 6518.37 2.83 –2.620 Fe I 6533.93 4.56 –1.380 Fe I 6546.24 2.76 –1.556 Fe I 6551.68 0.99 –5.970 Fe I 6556.79 4.80 –1.638 Fe I 6569.21 4.73 –0.350 Fe I 6574.23 0.99 –4.923 Fe I 6581.21 1.49 –4.789 Fe I 6592.91 2.73 –1.603 Fe I 6593.87 2.43 –2.342 Fe I 6597.56 4.79 –1.040 Fe I 6609.11 2.56 –2.632 Fe I 6646.93 2.61 –3.990 Fe I 6677.98 2.69 –1.418 Fe I 6703.57 2.76 –3.160 Fe I 6705.10 4.61 –1.392 Fe I 6750.15 2.42 –2.621 Fe I 6810.26 4.61 –0.986 Fe I 6858.15 4.61 –0.930 Fe I 6861.94 2.42 –3.890 CHAPTER 2. DATA PROCESSING 37

Table 2.2 – Continued

Ion Wavelength E.P. log(gf) (A)˚ (eV) (dex)

Fe I 6916.68 4.15 –1.450 Fe II 6149.26 3.89 –2.711 Fe II 6238.39 3.89 –2.434 Fe II 6247.56 3.89 –2.315 Fe II 6416.92 3.89 –2.447 Fe II 6432.68 2.89 –3.587 Fe II 6456.38 3.90 –2.155 Na I 6154.23 2.10 –1.560 Na I 6160.75 2.10 –1.210 Si I 6155.13 5.62 –0.774 Si I 6721.85 5.86 –1.016 Ca I 6161.30 2.52 –1.246 Ca I 6169.04 2.52 –0.837 Ca I 6169.56 2.53 –0.628 Ca I 6455.60 2.52 –1.557 Ti I 6554.23 1.44 –1.150 Ti I 6556.07 1.46 –1.060 CHAPTER 2. DATA PROCESSING 38

2.1 Equivalent Width

The equivalent width, W , characterizes the strength of a spectral line. It is defined as a rectangle included between the continuum (being taken as unity) and the zero intensity level, having the same area as the line profile (e.g. Figure 2.3). It is expressed in the same units as the abscissa (wavelength or frequency), in this work in Angströms.The˚ equivalent width can be calculated via the equation:

Z λ2 I − I W = 0 λ dλ (2.1) λ1 I0

where I0 is the continuum intensity and Iλ is the line intensity at the wavelength λ. This equation reveals that the continuum intensity must be determined very accurately, especially for weak lines, because it will greatly aﬀect W. The equivalent width will be positive for an absorption line and negative for an emission line. We are only concerned in this work with absorption lines.

Figure 2.3: Illustration of the equivalent width by Dyson & Williams (1997). The abscissa is expressed in frequency here. Iν is the intensity of the line at the frequency ν. CHAPTER 2. DATA PROCESSING 39

2.2 Equivalent Width measurement

The abundances have been derived by comparing the equivalent widths of individual spectral lines to stellar atmosphere models. Two programmes have been used. The first program is an updated version of the software used by Johnson et al. (2008). This FORTRAN program goes through the input line list and stellar spectrum and allows the user to measure individual equivalent widths (EWs) by fitting a Gaussian profile — or multiple Gaussian profiles if deblending is needed (Figure 2.6) — to the given absorption lines (see Figure 2.4). A second spectrum can be used as a guide to uncatalogued spectral lines. We used the high resolution Arcturus spectrum (Hinkle et al. 2000).

Figure 2.4: Interface of the first program. The black spectrum is the spectrum of the star being analysed; the blue spectrum is the reference star: Arcturus (Hinkle et al. 2000); the purple curve is the Gaussian fit matching the star spectrum; the green line is the continuum. Elements are shown to help identification in case of blending.

Some preliminary setup is required before proceeding with the EW measurement. The first step is to remove the Doppler shift in the spectrum. NGC 362 has a significant heliocentric radial velocity, vr = 223.5 km/s (Harris 2010). Consequently, it introduces a Doppler shift of around 5A.˚ As the exact shift differs from star to CHAPTER 2. DATA PROCESSING 40 star, the target spectrum is cross-correlated with the Arcturus spectrum to remove this shift. This process also allows identification of Galactic stars which are not part of NGC 362: these stars have a different radial velocity and need a different shift to match the Arcturus spectrum1. Seven Galactic stars were identified this way and are reported in Table 2.3. Radial velocities were not measured directly for these stars as the visual shift in the spectrum was obvious.

Table 2.3: List of Galactic Stars

Star RA (J2000) DEC (J2000)

671 01:03:52.87 –70:55:17.0 665 01:03:50.65 –70:55:35.0 683 01:04:07.06 –70:50:59.0 185 01:03:04.77 –70:54:49.0 645 01:03:40.76 –70:49:11.0 689 01:04:10.30 –70:52:14.0 448 01:03:19.50 –70:56:03.0

Once this is done the continuum has to be defined. Continuum placement can substantially affect the EW derived for weak lines, but strong lines are relatively unaffected. A major challenge is the determination of where it should be set. This involves deciding whether small-scale variations in the data are treated as noise or spectral features. The first idea was to set the continuum level locally, evenly sepa- rating the white noise. Indeed, the white noise has a random distribution therefore it should be equally distributed around the continuum level. But the dissociation between the noise and the weak spectral features was not evident. After a lengthy period of trial and error, and detailed discussions with C. I. Johnson, it was de- cided that the majority of weak spectral features were unresolved lines, and that the continuum should be placed on top of these (Figure 2.5).

1Contamination from the SMC can be ruled out due to the diﬀerence in distance between NGC 362 and the SMC. NGC 362 is 8.6 kpc from Earth while the SMC is about 60 kpc, seven times farther. The mean luminosity of the stars in this study is 70, meaning that a star in the SMC would have to be ∼ 3500 L in order to mimic a 70 L star. Only a very few, short-lived post-AGB can attain this luminosity at the temperature of the stars we have examined. A star in the SMC MT 4 would also have a lower surface gravity since g ∼ L . CHAPTER 2. DATA PROCESSING 41

Figure 2.5: Continuum setting - note that the peak with a > 1 intensity value is a cosmic ray and is consequently ignored.

After these adjustments are made it is possible to measure the individual equivalent widths for iron lines. The software scans the spectrum and fits either a simple Gaussian profile (see Figure 2.4) or up to five Gaussian profiles if the lines are blended (see Figure 2.6). It was not possible to measure the equivalent widths accurately for all the stars because some of the warmer stars (Teff > 5200K) were too faint to obtain a high signal-to-noise spectrum. Table 2.4 lists the 56 stars for which iron abundances were eventually obtained.

2.3 MOOG Software

The chemical abundance of the selected elements was determined using the abfind driver in the 2010 version of MOOG (Sneden 1973). MOOG simultaneously derives the atmospheric parameters for the star. The model atmosphere is different for each star and contains four parameters: the effective temperature (Teff ), the surface gravity (given as log(g)), the metallicity ([Fe/H]) and the microturbulence velocity

(vt). Local Thermodynamic Equilibrium (LTE) model atmospheres were taken from the α-enhanced ATLAS9 grid of non-overshoot models (Castelli & Kurucz 2003). The MOOG interface is shown in Figure 2.7 below. It displays three plots to help CHAPTER 2. DATA PROCESSING 42

Figure 2.6: Example of a deblending. The iron and calcium lines are very close together and have almost the same intensity, it is therefore required to deblend them in order to measure the equivalent width of the iron line accurately.

fix the parameters by iteration. These plots are related to Fe I, the other elements will be displayed later. The first plot is log() against the excitation potential (E.P.), where is the abundance of that element relative to log(H)=12 as described in Section 1.2. The second plot is log() against the reduced equivalent width, log(EW/λ). The last plot is log() against the wavelength. Since the abundance is a single, fixed value for each star, it should not vary with any of these physical quantities. Therefore the red lines representing the trend should be flat for all three plots and match the blue lines representing the mean abundance value. The first plot is influenced by the effective temperature and the second one by the microturbulence velocity. The last plot cannot be fixed by the atmospheric parameters but is indicative of the accuracy of the EW measurements, it may not always be flat but the slope should not be greater than ∼0.30. An increase in the temperature will cause a decrease in the slope of the blue curve of the first plot (the second plot will have the same behaviour if the velocity is increased). These parameters have an impact on the iron abundance therefore the solution must be found by iteration. Once the microturbulence velocity and the effective temperature are fixed so the CHAPTER 2. DATA PROCESSING 43

Figure 2.7: Graphical determination of the model atmosphere with MOOG. This graphical window shows three plots: the ﬁrst is log() against the excitation potential. The second one is log() against the reduced equivalent width. The last plot is log() against the wavelength. The red curves represent the trend and the blue lines represent the mean value. In this example the eﬀective temperature and the microturbulence velocity should be lowered. This manual procedure was performed for each of the stars in this study. CHAPTER 2. DATA PROCESSING 44

first two plots are flat, the surface gravity can be determined. It has an impact on the Fe II abundance which can be displayed on a additional plot. Fe I and Fe II should have the same abundance as these are just ionization states of the same element. Thus log(g) will be fixed so the Fe I and Fe II abundances match. As it also has a weak impact on the first two plots, it requires small changes to the previous values of Teff and vt. The metallicity value of the model atmosphere is then chosen to match the value obtained by MOOG. Sometimes outliers have to be removed, but there should never be more than five per star. Once the curves are flat and the abundances matched the atmospheric parameters values can be kept and the other elements can be displayed. The ideal analysis would contain lines covering the entire range of excitation potential and reduced equivalent width so that the errors on the determination of the effective temperature and the microturbulence velocity would be minimal. Unfortunately it was not possible to measure lines with a wide range of excitation potentials for all stars, hence we can expect these stars to have larger uncertainties in their atmospheric parameters, particularly in their effective temperature. CHAPTER 2. DATA PROCESSING 45

2.4 Results

Table 2.4 summarises the model atmosphere parameters derived for all the stars in the study. We have used the value log10 (F e) = 7.52 for the Sun (Sneden et al. 1991). Coordinates of the stars are given, representing the positions on which the ﬁbres were placed.

Table 2.4: Derived atmospheric parameters

Star Coordinates Teﬀ log(g) [Fe/H] vt RA (J2000) DEC (J2000) (K) (dex) (dex) (km s−1)

384 01:03:16.12 –70:51:22.0 4575 1.60 –1.18 1.55 490 01:03:21.87 –70:51:27.0 4825 1.55 –1.13 1.60 417 01:03:18.19 –70:50:35.0 4975 1.60 –1.17 1.70 200 01:03:05.86 –70:51:16.0 4850 1.70 –1.01 1.35 273 01:03:10.03 –70:50:22.0 4700 1.00 –1.35 1.75 254 01:03:08.93 –70:51:04.0 4900 2.10 –1.34 1.20 232 01:03:07.59 –70:55:50.0 5125 1.80 –1.25 1.83 319 01:03:12.38 –70:51:39.0 5250 1.80 –1.36 1.50 013 01:02:21.25 –70:51:22.0 5050 1.60 –1.26 1.82 045 01:02:39.01 –70:53:23.0 4925 2.30 –1.26 1.68 161 01:03:03.14 –70:47:38.0 5400 2.50 –1.26 2.15 685 01:04:08.55 –70:52:52.0 5475 2.55 –1.26 2.12 049 01:02:39.79 –70:53:03.0 5325 2.05 –1.20 1.89 168 01:03:03.39 –70:46:55.0 5575 2.00 –1.31 2.10 002 01:02:07.51 –70:52:19.0 5350 2.20 –1.26 2.20 646 01:03:40.84 –70:51:51.0 5200 2.20 –1.28 1.45 694 01:04:22.22 –70:50:32.0 5250 1.95 –1.25 1.57 687 01:04:09.67 –70:54:13.0 5275 2.00 –1.23 1.56 217 01:03:06.89 –70:49:59.0 5350 2.00 –1.31 2.32 CHAPTER 2. DATA PROCESSING 46

Table 2.4 – Continued

Star Coordinates Teﬀ log(g) [Fe/H] vt RA (J2000) DEC (J2000) (K) (dex) (dex) (km s−1)

684 01:04:07.47 –70:48:45.0 5375 2.05 –1.27 1.62 664 01:03:50.55 –70:49:22.0 5375 2.45 –1.28 2.07 320 01:03:12.49 –70:50:08.0 5100 1.30 –1.57 1.25 286 01:03:10.58 –70:51:30.0 4950 1.00 –1.68 1.87 237 01:03:07.76 –70:50:37.0 5325 1.90 –1.61 1.15 602 01:03:32.18 –70:48:40.0 5025 1.70 –1.45 1.90 315 01:03:12.06 –70:52:52.0 5200 1.70 –1.18 1.67 467 01:03:20.51 –70:51:44.0 5050 1.10 –1.61 1.76 565 01:03:27.16 –70:51:19.0 5550 2.60 –1.40 2.39 564 01:03:26.97 –70:53:15.0 5175 2.25 –1.50 2.04 670 01:03:52.62 –70:52:18.0 5000 1.20 –1.55 1.76 607 01:03:32.81 –70:52:43.0 5225 1.50 –1.41 2.13 005 01:02:10.73 –70 53 34.0 5175 1.40 –1.53 2.67 601 01:03:32.00 –70:51:16.0 5025 2.60 –0.80 1.30 686 01:04:08.58 –70:48:57.0 4900 2.20 –1.05 1.60 603 01:03:32.24 –70:53:35.0 5075 2.65 –0.98 1.61 172 01:03:03.71 –70:56:21.0 5000 2.30 –1.22 1.89 662 01:03:47.62 –70:55:03.0 5100 2.55 –1.08 1.51 522 01:03:23.87 –70:48:52.0 5100 2.30 –0.92 1.39 260 01:03:09.16 –70:47:30.0 5050 2.40 –1.01 1.45 597 01:03:31.14 –70:50:16.0 5125 2.40 –1.16 1.86 067 01:02:48.59 –70:47:28.0 5075 2.60 –1.09 1.65 426 01:03:18.78 –70:49:33.0 4925 2.15 –1.26 1.60 022 01:02:27.16 –70:47:18.0 5175 1.80 –1.40 2.12 590 01:03:30.17 –70:46:28.0 5575 2.10 –1.06 2.12 CHAPTER 2. DATA PROCESSING 47

Table 2.4 – Continued

Star Coordinates Teﬀ log(g) [Fe/H] vt RA (J2000) DEC (J2000) (K) (dex) (dex) (km s−1)

040 01:02:37.69 –70:47:59.0 5550 2.80 –1.08 2.20 385 01:03:16.15 –70:53:03.0 5225 1.80 –1.59 2.30 195 01:03:05.56 –70:46:59.0 5475 2.40 –1.09 1.80 625 01:03:35.95 –70:51:26.0 5275 2.25 –1.42 1.73 651 01:03:42.79 –70:47:57.0 5550 2.35 –1.10 1.97 074 01:02:51.05 –70:46:41.0 5550 2.20 –1.17 1.99 044 01:02:38.86 –70:50:33.0 5525 2.00 –1.26 1.70 312 01:03:11.97 –70:49:29.0 5400 2.10 –1.45 1.85 430 01:03:18.88 –70:55:22.0 5500 2.20 –1.32 1.77 637 01:03:37.96 –70:49:31.0 5725 3.20 –1.12 1.60 108 01:02:58.26 –70:55:51.0 5750 3.00 –1.09 1.88 692 01:04:18.71 –70:49:39.0 5250 2.90 –0.86 1.60

Our stars are warmer than the stars targeted in previous studies of NGC 362.

Teff ranges from 4575 to 5750 K with the majority of stars being between 5000 and 5500 K. These higher temperatures are a result of the observing strategy, with this sample containing a higher proportion of HB and RGB stars than the previous studies. We have obtained a mean metallicity [Fe/H] = –1.26 ± 0.03 dex (see Chapter 4 for error calculations). This Fe abundance matches perfectly the one given by the updated version of Harris catalogue (2010). It is 0.09 dex lower than Carretta et al. (2013) and Székely et al. (2007) and slightly higher than Kraft & Ivans (2003) and Shetrone & Keane (2000). These authors did not specify which solar abundance they chose for iron. This might introduce small differences in the results, but it is CHAPTER 2. DATA PROCESSING 48 not expected to produce differences larger than 0.05 dex. These studies have been recapitulated in the Table 2.5. Our determination of the metallicity of NGC 362 is also very close to that of NGC 288: [Fe/H]= –1.32 (Harris 2010). The iron abundance is plotted against the effective temperature in Figure 2.8. No trend seem to appear from this figure, as the correlation coefficient is 0.04. Most of the stars have a metallicity very close to –1.26 however a minority of stars have either a very high (e.g. –0.8) or a very low (e.g. –1.6) metallicity. Observations of globular clusters have all shown very little [Fe/H] spread (the exception being ω Centauri). This unexpected scatter may be due to measurement uncertainties or low signal-to-noise ratio. The real metallicity of those stars is expected to be somewhere between –1.15 and –1.30, as determined in previous studies.

Table 2.5: Metallicity studies of NGC 362

Author Derived [Fe/H] Number of Stars

This work –1.26 ± 0.03 56 Carretta et al. (2013) –1.171 ± 0.009 92 Harris (2010) –1.26 a Sz´ekely et al. (2007) –1.16 ± 0.25 45 Kraft & Ivans (2003) –1.31 ± 0.03 9 Shetrone & Keane (2000) –1.33 ± 0.01 12

a Harris’ result is a compilation from previous literature sources and should not be considered as a new determination in itself CHAPTER 2. DATA PROCESSING 49

Figure 2.8: [Fe/H] against the eﬀective temperature. The error bars have been added based on the calculations made in Chapter 4.1. The spread is visible although many stars remain close to –1.26. Chapter 3

Other elements

The abundances of proton-capture (sodium) and α-capture (silicon, calcium, titanium) elements were determined in addition to the iron abundance. The same method was applied. Equivalent widths were measured using the line list given in Table 2.2. As the atmospheric parameters had already been determined, all that remained was to run MOOG and display the values.

3.1 Results

[Na/Fe] and [Si/Fe] could be determined for 55 out of the 56 stars in this study. [Ca/Fe] was determined for all 56 of the stars. [Ti/Fe] could only be determined for 41 stars, since the Ti lines were often within the line wings of the 6562 AH˚ α line and the S/N was too low.

MOOG returns abundances as log10 (x)star, where x represents the elements Na, Si, Ca or Ti. The notation [x/Fe] was used to compare abundances and was obtained via the standard relation:

[x/F e] = [x/H] − [F e/H] (3.1)

The values log10 (x)sun were taken from Lodders (2003): log10 (Na) = 6.30, log10 (Si) =

7.54, log10 (Ca) = 6.34 and log10 (T i) = 4.92.

50 CHAPTER 3. OTHER ELEMENTS 51

The results are shown in Table 3.1.

Table 3.1: Derived abundances

Star [Fe/H] [Na/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]

384 –1.18 –0.24 0.14 0.41 0.28 490 –1.13 –0.33 0.07 0.30 0.22 417 –1.17 0.15 0.15 0.18 200 –1.01 –0.14 0.01 0.36 0.13 273 –1.35 0.08 0.28 0.40 0.48 254 –1.34 –0.17 0.25 0.45 0.52 232 –1.25 0.01 0.25 0.46 0.75 319 –1.36 0.13 0.39 0.48 013 –1.26 –0.09 0.22 0.44 0.70 045 –1.26 0.05 0.28 0.43 0.52 161 –1.26 0.06 0.33 0.28 0.92 685 –1.26 –0.36 0.51 0.36 0.71 049 –1.20 –0.22 0.19 0.31 168 –1.31 0.20 0.09 0.36 002 –1.26 0.12 0.17 0.39 0.58 646 –1.28 0.11 0.32 0.40 0.70 694 –1.25 0.17 0.10 0.30 0.74 687 –1.23 –0.04 0.11 0.34 0.91 217 –1.31 0.31 0.51 0.52 0.87 684 –1.27 0.06 0.39 0.26 0.37 664 –1.28 0.45 0.39 0.31 0.48 320 –1.57 0.60 0.53 0.54 286 –1.68 0.14 0.49 0.55 237 –1.61 0.38 0.59 0.45 602 –1.45 0.49 0.24 0.48 0.35 CHAPTER 3. OTHER ELEMENTS 52

Table 3.1 – Continued

Star [Fe/H] [Na/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]

315 –1.18 0.06 0.08 0.41 0.50 467 –1.61 0.17 0.51 0.56 0.64 565 –1.40 0.43 0.38 0.59 1.13 564 –1.50 0.30 0.61 0.47 0.56 670 –1.55 0.12 0.53 0.56 607 –1.41 0.42 0.38 0.46 0.81 005 –1.53 0.21 0.57 0.48 601 –0.80 0.21 0.22 0.41 0.23 686 –1.05 0.49 0.22 0.51 603 –0.98 0.13 0.05 0.25 0.10 172 –1.22 –0.16 0.03 0.43 0.14 662 –1.08 0.48 0.16 0.44 522 –0.92 –0.22 –0.12 0.29 0.36 260 –1.01 0.22 0 0.29 597 –1.16 –0.10 0.34 0.59 0.51 067 –1.09 –0.34 0.13 0.48 0.23 426 –1.26 0.14 0.36 0.41 0.32 022 –1.40 0.07 0.51 0.32 0.97 590 –1.06 –0.22 0.24 0.29 0.96 040 –1.08 –0.06 0.07 0.07 0.54 385 –1.59 0.69 0.57 0.36 195 –1.09 –0.21 0.13 0.18 0.25 625 –1.42 –0.11 0.32 0.35 1.22 651 –1.10 0.11 0.11 0.39 0.47 074 –1.17 0.24 0.01 0.31 044 –1.26 0.23 0.15 0.32 0.48 CHAPTER 3. OTHER ELEMENTS 53

Table 3.1 – Continued

Star [Fe/H] [Na/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]

312 –1.45 –0.33 0.20 0.41 0.70 430 –1.32 0.28 0.16 0.19 637 –1.12 0.04 0.21 0.89 108 –1.09 0.19 0.13 0.28 692 –0.86 0.46 0.15 0.45 0.30

Table 3.2 summarises the mean abundances of this study and previous ones. It must be noted that these previous studies did not specify which solar abundances they used. Therefore some small variations between studies are expected, but it should not exceed 0.05 dex. This study has four stars in common with Carretta et al. (2013). A star- by-star comparison for these four stars is given in Table 3.3. I derived a very high metallicity for stars 522 and 692 compared to Carretta et al. (2013). The atmospheric parameters are also quite different between the two studies for those stars. As previously mentioned in Section 2.4, it is expected that their metallicity should be between –1.15 and –1.30. The derivation from Carretta et al. (2013) may be more accurate for these stars. The results are reasonably close between the two studies if we only consider the stars 662 and 686, the difference in abundances being <0.1 dex. The atmospheric parameters are also quite similar as the difference in Teff is around 50 K, and the difference in log(g) is between 0.10 and 0.20 dex.

Star 686 exhibits non negligible differences in vt, but the difference in abundances remains roughly the same, Carretta’s ones being lower by about 0.10 dex, which is the difference found between the iron abundance of the two studies overall. CHAPTER 3. OTHER ELEMENTS 54

Table 3.2: Comparison between studies of NGC 362

Author [Fe/H] [Na/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe] This work –1.260 ± 0.025 0.11 ± 0.18 0.25 ± 0.13 0.38 ± 0.06 0.56 ± 0.20 CAGa(2013) –1.171 ± 0.009 0.11 ± 0.25 0.26 ± 0.04 0.34 ± 0.02 0.16 ± 0.03 SKb(2000) –1.33 ± 0.01 0.04 ± 0.15 0.36 ± 0.05 0.18 ± 0.02 0.30 ± 0.05 Gc(1987) –1.18 ± 0.04 –0.08 ± 0.01 0.09 ± 0.07 0.21 ± 0.12 0.30 ± 0.09 PSWd(1983) –0.87 ± 0.2 0.36 ± 0.3 0.65 ± 0.03 0.3 ± 0.3

a Carretta et al. (2013) b Shetrone & Keane (2000) c Gratton (1987b) d Pilachowski et al. (1983)

Table 3.3: Star-by-star comparison between this study and Carretta et al. (2013)

Star Teﬀ log(g) vt [Fe/H] [Na/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe] 522a 5100 2.30 1.39 –0.92 –0.22 –0.12 0.29 0.36 522b 5022 2.53 1.88 –1.128 0.21 0.30 0.33 0.16 662a 5100 2.55 1.51 –1.08 0.48 0.16 0.44 662b 5069 2.62 1.51 –1.177 0.40 0.26 0.34 686a 4900 2.20 1.60 –1.05 0.49 0.22 0.51 686b 4952 2.39 1.20 –1.199 0.63 0.33 0.35 0.22 692a 5250 2.90 1.60 –0.86 0.46 0.15 0.45 0.30 692b 5043 2.56 1.06 –1.142 0.48 0.26 0.37 0.15

a This work b Carretta et al. (2013)

3.2 Sodium

The sodium abundance was derived using two lines at 6154.63 and 6160.75 A.˚ The average value is 0.11 ± 0.16 dex. It is the same value as the one determined by Carretta et al. (2013), it is 0.07 dex higher than Shetrone & Keane (2000), 0.19 dex higher than Gratton (1987) and 0.25 dex lower than Pilachowski et al. (1983). It is still contained within the uncertainties of Carretta et al. (2013), Shetrone & Keane (2000) and Pilachowski et al. (1983). Overall it is in very good agreement with the previous studies. Figure 3.1 shows the relation between sodium and iron abundance. It reveals a large star-to-star variation with abundances ranging from –0.36 to 0.69 dex. This spread in the sodium abundance, and more generally in light-element abundance, is CHAPTER 3. OTHER ELEMENTS 55 common within globular clusters (Kraft 1994, Gratton et al. 2004). It is found at all metallicities but may be emphasized by the spread in iron abundance found in Chapter 2. The correlation coeﬃcient between [Na/Fe] and [Fe/H] is 0.28, meaning that there is no correlation between the two ratios. The stars targeted in this study are Na poor, compared to NGC 288: the sodium abundance derived in this study is 0.18 dex lower than the abundance derived by Carretta et al. (2009) for NGC 288, 0.04 dex lower than Hsyu et al. (2014) and 0.09 dex lower than Shetrone & Keane (2000). This is in agreement with the observations of Shetrone & Keane.

Figure 3.1: [Na/Fe] against [Fe/H].

3.3 Silicon

The silicon abundance was derived using two lines at 6155.13 and 6721.85 A.˚ The average value is 0.25 ± 0.09 dex. It is 0.01 dex higher than the one determined CHAPTER 3. OTHER ELEMENTS 56 by Carretta et al. (2013), 0.11 dex lower than Shetrone & Keane (2000) and 0.16 dex higher than Gratton (1987). It is in very good agreement with Carretta et al. (2013) and it is contained within the uncertainties of Shetrone & Keane (2000). Figure 3.2 displays the silicon abundance, plotted against the iron abundance. It shows a spread in Si abundance — ranging from –0.12 to 0.61 dex — possibly a consequence of the spread revealed in iron abundance. It brings to light an anticorrelation between Si and Fe. This anticorrelation was not noticed by Carretta et al. (2013). The slope of the anticorrelation is quite noticeable, the correspond- ing gradient is –0.70 ± 0.08. This result seems reliable based on the correlation coeﬃcient, 0.75, but it can also be a consequence of the scatter in metallicity (this anticorrelation will be further discussed in Section 5.3.3). The silicon abundance determined in this study is lower than the one derived in previous NGC 288 studies. Carretta et al. (2009) found [Si/Fe] = 0.37 ±0.03 dex and Shetrone & Keane (2000) found [Si/Fe] = 0.43 dex. The higher silicon abundance of NGC 288 was also observed by Shetrone & Keane. CHAPTER 3. OTHER ELEMENTS 57

Figure 3.2: [Si/Fe] against [Fe/H]. A linear ﬁt is plotted in blue.

3.4 Calcium

The calcium abundance was derived using four lines at 6161.30, 6169.04, 6169.56 and 6455.60 A.˚ The average value is 0.38 ± 0.07 dex. It is 0.04 dex higher than the one determined by Carretta et al. (2013), 0.20 dex higher than Shetrone & Keane (2000), 0.17 dex higher than Gratton (1987) and 0.27 dex lower than Pilachowski et al. (1983). It is in good agreement with Carretta et al. (2013). The behaviour of [Ca/Fe] with metallicity is shown in Figure 3.3. It illustrates the same trend as [Si/Fe], with a less pronounced slope and a smaller range, from 0.07 to 0.59 dex. The correlation coeﬃcient is 0.44, meaning that the trend is dubious. [Ca/Fe] was measured by Shetrone & Keane (2000) in NGC 288. They derived [Ca/Fe] = 0.28 dex. It is 0.10 dex lower than the [Ca/Fe] ratio determined in this study. This is diﬀerent from the observations of Shetrone & Keane, who derived [Ca/Fe] = 0.18 for NGC 362. CHAPTER 3. OTHER ELEMENTS 58

Figure 3.3: [Ca/Fe] against [Fe/H].

3.5 Titanium

The titanium abundance was derived using three lines at 6395.47, 6554.23 and 6556.07 A.˚ The average value is 0.56 ± 0.12 dex. It is 0.40 dex higher than the one determined by Carretta et al. (2013), 0.26 dex higher than Shetrone & Keane (2000), Gratton (1987) and Pilachowski et al. (1983). The value presented here is not contained within the uncertainties of these previous studies. The very high titanium abundance obtained in this study may be due to the proximity of the lines with the 6562 AH˚ α line, causing strong blending between the titanium lines as well as an uncertainty in the continuum placement. The 6395.47 A˚ line was weak, therefore very sensitive to the continuum placement. [Ti/Fe] was plotted against [Fe/H] in Figure 3.4. A very large spread can be observed, much more signiﬁcant than the spread observed in Carretta et al. (2013). [Ti/Fe] ranges from 0.10 to 1.20 dex. The large scatter cannot be explained only by the spread in iron abundance, a large part must be caused by the measurement CHAPTER 3. OTHER ELEMENTS 59 uncertainty. It is expected that Carretta et al.’s values are more realistic. Shetrone & Keane (2000) determined [Ti/Fe] = 0.27 for NGC 288. The ratio in this study is 0.29 dex higher, whereas Carretta’s ratio is 0.11 lower. Shetrone & Keane had found that the [Ti/Fe] ratio was slightly higher, by 0.03 dex, in NGC 362 than in NGC 288.

Figure 3.4: [Ti/Fe] against [Fe/H]. CHAPTER 3. OTHER ELEMENTS 60

3.6 α elements

In order to reduce the scatter in the data, the combined behaviour of the α elements can be studied. The α-element abundance should show a smaller spread as it is calculated as: [Si/Fe] + [Ca/Fe] + [Ti/Fe] [α/Fe] = . (3.2) 3

Figure 3.5 shows [α/Fe] versus [Fe/H]. There is still a large scatter, with values ranging from 0.15 to 0.70 dex, but it is almost halved compared to the spread observed in [Ti/Fe]. The trend is very similar to [Si/Fe] vs [Fe/H], with a strong anticorrelation. The related gradient is –0.56 ± 0.09, and the correlation coeﬃcient is 0.68, meaning that the trend is likely to be real.

Figure 3.5: [α/Fe] against [Fe/H]. A linear ﬁt is plotted in blue. CHAPTER 3. OTHER ELEMENTS 61

3.7 Conclusions

The mean abundance of three out of the four elements considered in this Chapter (Na, Si, Ca) is in very good agreement with the previous studies performed on the same cluster. The titanium abundance is much higher than the results from the literature. It is safer to use the measurements from the most recent study of the literature: Carretta et al. (2013). Overall all these elements reveal an anticorrelation with the iron abundance, and a large scatter. However due to low correlation coeﬃcients, these phenomena are probably due to the spread in iron abundance for Na, Ca and Ti. The anticorrelation is likely to be real for the silicon and the α elements abundance, based on higher correlation coeﬃcient. As these slopes were not observed by Carretta et al. for silicon, calcium or titanium, they are more likely to be due to the spread in metallicity observed in Chapter 2 (Carretta’s results seem more trustworthy based on the smaller range of metallicities they derived). Chapter 4

Error estimation

4.1 Statistical abundance uncertainties

The standard error for the selected elements, SE, has been estimated using the formula assuming a normal distribution:

√ SE = σ/ N (4.1) where σ is the standard deviation and N is the number of lines measured for the given element. The uncertainties are given in Table 4.1. The mean statistical uncertainties for this study are 0.03, 0.07, 0.16, 0.09, 0.07 and 0.12 dex for Fe i, Fe ii, Na, Si, Ca and Ti respectively. Na reveals larger uncertainties but this is expected as it is also noticed in previous studies such as Carretta et al. (2013).

62 CHAPTER 4. ERROR ESTIMATION 63 N √ σ/ (Ti) NN √ σ/ (Ca) NN √ σ/ (Si) NN √ σ/ (Na) NN Table 4.1: Statistical uncertainties √ σ/ ) ii (Fe NN √ σ/ ) i (Fe N 384490 43417 52 0.02200 37 0.02273 35 5 0.02254 40 5 0.02 0.07232 35 6 0.02 0.07319 33 4 2 0.03 0.07013 26 4 2 0.02 0.04 0.06045 35 4 2 0.03 0.08 0.08161 2 30 4 2 0.02 0.09 0.04685 2 27 5 2 0.04 0.02 0.04 0.08049 2 30 5 2 0.08 0.03 0.05 4 0.04168 2 28 5 2 0.06 0.03 0.01 4 0.05 1 24 4 0.04 2 0.06 0.03 0.28 4 0.11 2 4 0.07 2 2 0.03 0.22 4 0.04 2 4 0.06 2 0.04 2 0.35 0.06 0.08 2 5 0.06 1 0.11 4 0.15 4 0.09 0.28 2 2 0.04 2 4 0.09 1 0.05 0.27 2 0.13 0.10 3 0.09 0.05 2 2 2 0.21 4 2 2 0.02 2 0.06 0.10 0.04 1 0.01 0.01 0.01 4 0.08 2 1 4 4 0.08 0.16 0.08 0.09 2 4 4 2 1 0.06 0.09 0.05 0.17 Star CHAPTER 4. ERROR ESTIMATION 64 N √ σ/ (Ti) NN √ σ/ (Ca) NN √ σ/ (Si) NN √ σ/ (Na) Table 4.1 – Continued NN √ σ/ ) ii (Fe NN √ σ/ ) i (Fe N 002646 33694 29 0.03687 36 0.03217 34 5 0.02684 23 5 0.03 0.04664 28 6 0.03 0.09320 30 4 1 0.03 0.05286 31 5 2 0.02 0.07237 20 4 2 0.02 0.13 0.04602 23 5 2 0.02 0.28 0.08315 2 2 38 3 2 0.02 0.43 0.09467 2 35 5 0.08 2 0.30 0.02 0.28 0.06565 2 32 4 2 0.01 0.02 4 0.10 4 0.11564 2 23 4 2 0.16 0.03 0.25 4 0.15 2 0.04 27 3 0.08 2 0.01 0.03 0.06 4 0.12 2 6 0.07 2 0.04 2 2 0.03 0.10 3 0.05 2 5 0.13 2 0.03 1 0.28 3 0.12 0.05 0.12 2 4 0.12 2 0.03 1 0.11 4 0.04 2 0.04 2 0.12 2 0.37 4 0.07 2 0.06 2 0.13 2 0.08 3 0.26 2 0.07 2 0.06 2 0.26 3 0.13 1 0.20 0.16 0.08 4 0.36 2 0.10 4 2 0.03 0.10 0.06 0.04 2 4 4 2 4 0.13 0.07 0.08 0.06 0.03 2 2 1 0.07 0.06 Star CHAPTER 4. ERROR ESTIMATION 65 N √ σ/ (Ti) NN √ σ/ (Ca) NN √ σ/ (Si) NN √ σ/ (Na) Table 4.1 – Continued NN √ σ/ ) ii (Fe NN √ σ/ ) i (Fe N 670607 24005 23 0.02601 17 0.02686 43 4 0.02603 40 4 0.03 0.04172 39 3 0.03 0.09662 35 5 2 0.03 0.05522 33 4 2 0.02 0.16 0.07260 43 5 2 0.02 0.17 0.11597 33 4 2 0.02 0.49 0.10067 2 41 3 2 0.03 0.01 0.06426 2 31 5 2 0.13 0.02 0.12 0.03022 2 39 5 2 0.01 0.02 0.09 4 0.08590 4 2 28 4 2 0.03 0.02 0.18 4 0.10 2 30 5 0.03 2 0.04 0.08 0.02 0.14 4 0.09 2 5 0.07 2 0.07 2 0.02 2 0.11 4 0.10 2 4 0.07 2 0.21 0.23 4 0.05 0.16 2 0.13 4 0.08 2 0.01 2 0.08 4 0.07 2 0.02 2 0.25 0.11 4 0.09 0.04 2 0.08 2 0.01 2 0.09 4 2 0.08 2 0.01 2 0.08 3 0.16 2 0.03 0.03 0.16 4 0.14 2 0.09 0.08 2 3 2 0.09 0.11 3 0.08 0.10 0.10 2 3 0.03 2 3 0.12 0.01 2 0.08 0.14 2 0.15 2 0.08 0.13 Star CHAPTER 4. ERROR ESTIMATION 66 N √ σ/ (Ti) NN √ σ/ (Ca) NN √ σ/ (Si) NN √ σ/ (Na) Table 4.1 – Continued NN √ σ/ ) ii (Fe NN √ σ/ ) i (Fe N 040385 31195 30 0.04625 35 0.02651 30 4 0.02074 27 4 0.02 0.04044 25 4 0.03 0.07312 28 4 2 0.03 0.05430 27 3 1 0.02 0.13 0.04637 26 5 1 0.03 0.02108 1 25 4 2 0.03 0.07692 39 6 2 0.04 0.17 0.06 2 33 4 2 0.03 0.35 0.10 2 2 6 0.05 2 0.03 3 0.27 0.09 2 5 0.03 1 0.08 4 0.20 0.06 2 0.09 4 2 0.18 4 3 0.09 2 0.09 0.10 2 0.03 4 0.07 0.02 0.05 2 0.02 3 0.17 2 2 0.10 2 1 2 0.36 4 0.07 0.12 0.13 1 0.01 0.10 2 2 0.09 4 4 2 0.15 0.16 1 0.06 0.04 0.16 3 3 1 4 0.09 0.10 0.08 2 2 0.02 0.16 Star CHAPTER 4. ERROR ESTIMATION 67

4.2 Abundance uncertainty to model atmosphere

parameters

The four stars shared with Carretta et al. (2013) shown in Table 3.3 were used to estimate the internal errors in the atmospheric parameters. The average diﬀerence in the model atmosphere parameters between the two studies was taken as the estimated internal errors: Teﬀ = ± 100 K, log g = ± 0.20 dex, [Fe/H] = ± 0.20 dex

−1 and vt = ± 0.35 km s . The sensitivity was determined by changing one parameter at a time while the others remained constant, avoiding additional errors due to the inter-dependencies among the parameters.

The abundance uncertainty due to the atmospheric parameters, σmodatm, was calculated using the formula:

σ2 = σ2 + σ2 + σ2 + σ2 (4.2) modatm Teff log(g) [F e/H] vt

where σTeff , σlog(g), σ[F e/H] and σvt represent the change in derived abundance caused by changing the eﬀective temperature, surface gravity, metallicity and microturbulence velocity of the stellar atmosphere model by the above amounts. The total error was obtained by adding in quadrature the errors due to the model atmosphere parameters, σatm, and the observational errors, σobs, calculated in Section 4.1:

2 2 2 σtot = σatm + σobs (4.3)

As the uncertainties for all the selected elements were similar for the four stars plus a few randomly picked warmer stars, the average uncertainties were considered and are shown in Table 4.2. Considering both statistical and model atmosphere errors, the results for each element are still below 0.20 dex which allows us to perform accurate abundance analysis. MOOG displays the abundance ratios as [x/H] (where x is Fe, Na, Si, Ca, Ti), therefore no additional errors in [Na/Fe], [Si/Fe], [Ca/Fe] and [Ti/Fe] due to the CHAPTER 4. ERROR ESTIMATION 68

Table 4.2: Abundance sensitivity to model atmosphere parameters

Abundances Teff log(g) [Fe/H] vt σatm σtot ± 100 K ± 0.20 dex ± 0.20 dex ± 0.35 km s−1 (dex) (dex) [Fe/H]i ± 0.11 ± 0.00 ∓ 0.01 ∓ 0.13 0.17 0.17 [Fe/H]ii ∓ 0.06 ± 0.10 ± 0.05 ∓ 0.06 0.14 0.16 [Na/Fe] ± 0.06 ∓ 0.01 ± 0.00 ∓ 0.01 0.06 0.17 [Si/Fe] ± 0.01 ± 0.01 ± 0.01 ∓ 0.02 0.03 0.09 [Ca/Fe] ± 0.08 ∓ 0.01 ∓ 0.01 ∓ 0.10 0.13 0.15 [Ti/Fe] ± 0.12 ± 0.00 ∓ 0.01 ∓ 0.02 0.12 0.17 dependence with Fe are expected. The effective temperature has an impact on Fe i, Fe ii, Na, Ca and Ti. Only silicon is not greatly affected. Overall, Si is relatively insensitive to the perturbations of the atmospheric parameters. Therefore, it is the most accurate of the alpha elements. The surface gravity and metallicity changes are only effective on the ionised state of iron. This is expected because Fe ii, and more generally singly ionised transition metals, are more dependent on electron pressure which is affected by the surface gravity and the metallicity. The microturbulence velocity has a negligible impact on Na, Si and Ti. Its greater influence on Fe i, Fe ii and Ca may be due to larger equivalent widths measured for lines of these elements. Lines with large EWs are more affected by the microturbulence velocity because they correspond to absorption highest in the stellar atmosphere, where vt is the strongest. These variations are in agreement with the variations found by Carretta et al (2013), their results being revealed in a smaller scale because they made smaller perturbations (Teff ± 50K, log(g) ± 0.20 dex, [Fe/H] ± 0.10 dex and vt ± 0.10 dex). The same conclusions were driven by Cordero et al. (2013) in their study of 164 giant stars in 47 Tucanae (NGC 104). Therefore the adopted model atmosphere uncertainties seem appropriate. Chapter 5

Discussion

5.1 Radial dependences of abundances

The purpose of this section is to study the inﬂuence of the distance from the cluster centre on the chemical abundances of the elements measured in Chapters 2 and 3. Radial variations are seen in other studies (e.g. Carretta et al. 2013), and they point to the second generation of stars being generally more centrally condensed than the ﬁrst generation. The same variations could appear in this study. The distance has been calculated using the right ascension and the declination. The distance is expressed in degrees and was derived using the equation:

Dist = p(∆RA)2 + (∆Dec)2 (5.1) where ∆RA is the diﬀerence, expressed in arcminutes, in right ascension between the selected star and the cluster center, determined via

∆RA = (RAstar − RAcl) ∗ cos(Dec) (5.2) and ∆Dec is the diﬀerence in declination between the selected star and the cluster center, determined via

∆Dec = (Decstar − Deccl) (5.3)

69 CHAPTER 5. DISCUSSION 70

The centre of NGC 362 is located at RA = 01h23m14.26s, Dec = –70◦ 50’ 55.6”. The histogram of the distribution of distances is plotted in Figure 5.1. Distances have been converted to arcminutes for easier interpretation. The distance from the centre of NGC 362 ranges from 0.25 to 6.00 arcminutes. Overall the distribution is virtually ﬂat over all radii.

Figure 5.1: Histogram of the distribution of the distance from the centre of the cluster.

5.1.1 Iron abundance

[Fe/H] is plotted as a function of the distance from the centre of NGC 362 in Figure 5.2. There is a very weak correlation between the two variables plotted in Figure 5.2: the correlation coeﬃcient is 0.23, any linear trend would have fairly low statistical signiﬁcance. A wider range of [Fe/H] is found in the centre of the cluster (typically where Dist < 1.00 arcmin) than around the edges (where Dist > 4.00 arcmin). This spread in [Fe/H] was also observed in Section 2.4, but does not appear CHAPTER 5. DISCUSSION 71

Figure 5.2: [Fe/H] against the distance from the centre of NGC 362. Error bars are added based on the errors calculated in 4.1. in the literature. It is not visible in the Hertzsprung-Russell diagram either1 (see Figure 2.1). The following causes can be considered:

• The stars in this study are unusual, partly composed of AGB stars, maybe post-AGB stars that could have a variation in [Fe/H] due to various surface and depletion eﬀects (Moehler et al. 1998, van Winckel 2003).

• The warmer stars are likely to be variable, lying in the instability strip where the local thermodynamic equilibrium (LTE) is broken. As ATLAS9 grids were generated assuming that the stars are in LTE, MOOG derivations would be inaccurate for these speciﬁc stars.

• There could also be an observational issue. As the FLAMES ﬁbres are a ﬁnite width, they could be detecting light from more than one star. The stars

1Metal-poor stars are warmer at a given luminosity, as their atmospheres don’t have the added opacity from metal lines. Consequently light escapes easier and the stellar atmosphere can cool more eﬀectively. The star is therefore smaller and hotter. Hence, a spread in [Fe/H] translates into a spread in temperature of the RGB and AGB, which is not seen in NGC 362. CHAPTER 5. DISCUSSION 72

aﬀected would have a spectrum polluted by the blended star, causing errors in equivalent width measurements. This would most likely occur in the more crowded areas of the cluster - i.e. at the centre. This would cause a spread in metallicity which is greatest at the centre.

Moehler et al. (1998) claim that the depletion would affect preferentially iron. The reason is that iron is a highly condensible element, therefore it can be stuck into dust grains while the other elements remain in a gaseous state. The iron grains will eventually be forced away from the star by stellar winds, and the iron-poor gas can fall back onto the star, depleting the iron but not the hydrogen. This would decrease the average metallicity of the cluster affected by the phenomenon, but it is not what can be observed for NGC 362. This evidence goes against the first assumption. The [Fe/H] behaviour with the effective temperature was studied in Figure 2.8, but did not reveal a clear trend. The warmer stars do not show an extreme iron abundance ratio. This result goes against the first and second hypothesis. [Fe/H] has been plotted against the surface gravity in Figure 5.3. A clear correlation is visible, the gradient being 0.24 ± 0.04. The correlation coefficient is reasonably high, 0.62, meaning that this trend can be trusted. This would partially explain the scatter of iron abundances. This behaviour might reveal some late AGB or post-

AGB stars, but it also highlights the sensitivity of the derivation of Fe ii equivalent widths, consisting of six lines compared to the 73 Fe i lines in this region. The possible inaccuracy would have directly impacted the surface gravity determination, resulting in a different iron abundance value. A lot of scatter has been introduced in the metallicity by letting gravity be a free parameter. Most studies fix this parameter based on the photometric colour of the star. This helps deriving more accurate iron abundances, but does not determine the gravity independently. This thesis would have provided surface gravities to calculate the mass loss in AGB stars (cf. McDonald et al. 2011), but the derivation is not accurate enough to do so. In fact, the surface gravity is the biggest cause of uncertainty in the data. It might be better to fix it for further work on this dataset. CHAPTER 5. DISCUSSION 73

Figure 5.3: [Fe/H] against the surface gravity derived from the spectroscopic measurements.

Abundances would be determined more accurately, at the expense of independent information about the stellar gravity. CHAPTER 5. DISCUSSION 74

5.1.2 Sodium abundance

Figure 5.4 shows the relationship between [Na/Fe] and the distance from the centre of NGC 362. Despite the large scatter already observed in Section 3.2, no linear dependence emerges from this figure, the correlation coefficient being almost equal to zero. Stars located between 2.00 and 4.00 arcmin from the centre reveal a lesser spread, which is likely to be due to an effect of small-number statistics. Observation of extra stars within this radius bin would prove that this absence of scatter is not real.

Figure 5.4: [Na/Fe] against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 75

5.1.3 Silicon abundance

[Si/Fe] is plotted against the distance from the cluster centre in Figure 5.5. No linear correlation is found as the correlation coeﬃcient is 0.22.

Figure 5.5: [Si/Fe] against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 76

5.1.4 Calcium abundance

Figure 5.6 displays the calcium abundance, plotted against the distance from the centre of NGC 362. No linear trend is emerging from this ﬁgure. The correlation coeﬃcient is 0.28, too low for a linear trend to be trusted.

Figure 5.6: [Ca/Fe] against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 77

5.1.5 Titanium abundance

The behaviour of [Ti/Fe] with the distance from the centre of NGC 362 is shown in Figure 5.7. The large uncertainties for the titanium abundances prevent any linear trend to be observed. The correlation coeﬃcient between [Ti/Fe] and the distance from the centre is 0.13.

Figure 5.7: [Ti/Fe] against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 78

5.1.6 α-element abundance

The behaviour of the α elements is interesting to study because it is an average value of calcium, silicon and titanium. This reduces the scatter in the data and it might be easier to notice a trend. [α/Fe] has been plotted against the distance in Figure 5.8. The shape is very similar to [Ti/Fe] against the distance. No correlation appears from this ﬁgure, as the related correlation coeﬃcient is practically zero.

Figure 5.8: [α/Fe] against the distance from the centre of NGC 362.

The absence of real trend in titanium and α-element abundances against the distance could be attributed to the bias in [Fe/H]. It is interesting to look at the abundances relative to hydrogen to remove this bias. [α/H] and [Ti/H] have been plotted against the distance in Figure 5.9 and Figure 5.10 respectively. [α/H] does not reveal a trend, the correlation coeﬃcient being close to zero. [Ti/H] is not correlated to the distance from the cluster centre either. The related correlation coeﬃcient is 0.16, too small to reveal a linear dependence. No dependence with radius has been found for all the abundances derived in this CHAPTER 5. DISCUSSION 79

Figure 5.9: [α/H] against the distance from the centre of NGC 362. study. The correlation coeﬃcients are too low to believe that a linear trend exists. CHAPTER 5. DISCUSSION 80

Figure 5.10: [Ti/H] against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 81

5.2 Comparison of stellar parameters

In this section, the eﬀective temperatures of the stars derived with MOOG (Section 2.3) are compared with the ones obtained from spectral energy distribution ﬁtting of literature photometric data, taken from Boyer et al. (2009). The luminosity derived photometrically has been added in the fourth column. The luminosity values range

from 32 to 237 L . Only 10 out of 56 stars have a luminosity greater than 100 L .

Table 5.1: Comparison between spectroscopic and photometric eﬀective temperatures

Star Teffspec Teffphot ∆Teff Lphot

384 4575 5057 –482 257 490 4825 5131 –306 196 417 4975 5500 –525 241 200 4850 5525 –675 175 273 4700 5135 –435 196 254 4900 4070 830 72 232 5125 5354 –229 88 319 5250 5381 –131 90 013 5050 5340 –290 69 045 4925 5027 –102 46 161 5400 5411 –11 58 685 5475 5512 –37 47 049 5325 5521 –196 47 168 5575 5654 –79 45 002 5350 5527 –177 48 646 5200 5528 –328 46 694 5250 5530 –280 50 687 5275 5541 –266 46 217 5350 5563 –213 48 CHAPTER 5. DISCUSSION 82

Table 5.1 – Continued

Star Teffspec Teffphot ∆Teff Lphot

684 5375 5614 –239 45 664 5375 5635 –260 45 320 5100 6143 –1043 112 286 4950 5406 –456 128 237 5325 6500 –1175 108 602 5025 5343 –318 87 315 5200 5404 –204 75 467 5050 5875 –825 73 565 5550 5907 –357 73 564 5175 5457 –282 63 670 5000 5484 –484 56 607 5225 5487 –262 62 005 5175 5500 –325 52 601 5025 4844 181 49 686 4900 4916 –16 47 603 5075 5007 68 44 172 5000 5022 –22 40 662 5100 5055 45 32 522 5100 5062 38 38 260 5050 5071 –21 37 597 5125 5129 –4 35 067 5075 5161 –86 30 426 4925 5150 –225 42 022 5175 5531 –356 50 590 5575 5542 33 51 040 5550 5551 –1 47 CHAPTER 5. DISCUSSION 83

Table 5.1 – Continued

Star Teffspec Teffphot ∆Teff Lphot

385 5225 5561 –336 56 195 5475 5572 –97 46 625 5275 5613 –338 45 651 5550 5613 –63 48 074 5550 5635 –85 46 044 5525 5641 –116 51 312 5400 5644 –244 47 430 5500 5646 –136 44 637 5725 5663 62 48 108 5750 5675 75 46 692 5250 4988 262 34

Average 5211 5417 –206 70

The comparison reveals that overall our results disagree with the photometric derivation. The average difference in effective temperatures is –206 K, with the spectroscopic temperatures being lower. A large spread in ∆Teff can be observed, the standard deviation being 301 K. The standard deviation is biased by three stars which show huge differences: 254

(∆Teff = 830K), 320 (∆Teff = –1043K), 237 (∆Teff = –1175K). The photometric

measurements for these stars are either very low (Teffphot = 4070K for 254) or very high (Teffphot = 6500K for 237 and Teffphot = 6143K for 320). It is possible that the photometry may have lacked precision for those stars. The new average and standard deviation values are respectively –192 K and 209 K. The average difference

in effective temperatures among stars with Teffphot < 5300 K (–71 K, σ = 210 K) is considerably less than that of stars with Teffphot > 5300 K (–233 K, σ = 194 K). CHAPTER 5. DISCUSSION 84

The reasons for the diﬀerences observed are similar to the reasons for the scatter of [Fe/H] shown in 5.1.1:

• Some stars could be blended, the FLAMES ﬁbres picking up more than one star. This would cause errors in spectroscopic temperatures because the inaccurate equivalent widths derived after the polluted spectrum would impact the eﬀective temperature calculated via MOOG. It would also cause errors in photometric temperatures because it is harder to isolate the brightness of a single star when it is blended with others.

• Some stars could sit in the instability strip and be variable, having a changing eﬀective temperature depending on when they are observed.

• Errors in both photometric and spectroscopic temperatures should also be considered. The estimated error on the spectroscopic eﬀective temperature is ∼100 K (Section 4.1) and the estimated error on the photometric data is likely to be ∼100–200 K.

If the assumptions are combined, most of the diﬀerences are resolved. The blended

stars can be revealed by plotting Teffspec – Teffphot against the radial distance, as a scatter would appear at small radii, the issue affecting more the inner stars than the outer stars. The plot is shown in Figure 5.11. It exposes the larger scatter at small radii, typically where the distance is less than 1.00 arcminute. The three stars biasing the average temperature difference are found in this radius box. The difference is then virtually flat over the larger radii. Therefore one of the temperature measurements has probably been affected by some blended stars, probably in at least five cases, considering Figure 5.11. Both temperatures are displayed in Figure 5.12:

Teffspec against the radial distance and Teffphot versus the radial distance. Teffspec is low for two stars at small radii. Teffphot is very hot for one star and very cold for another, compared to the others at small radii. CHAPTER 5. DISCUSSION 85

Figure 5.11: Teﬀspec – Teﬀphot against the distance from the centre of NGC 362.

Figure 5.12: Teﬀspec (in red) and Teﬀphot (in blue) against the distance from the centre of NGC 362. CHAPTER 5. DISCUSSION 86

The photometric data is more likely to be affected by blending because of the apertures used. Each FLAMES fibre has an aperture of 1.2”. The Spitzer photometry used to fix the mid-IR colours of the stars has an Airy disc that is 2” across, making the blending of stars unavoidable with the instrumentation used.

5.3 Comparison with the literature

A summary of the previous results is provided before the comparison with the literature.

• [Fe/H] shows an unexpected scatter mainly due to the variations in the S/N ratio from star to star. It is not related to the distance from the centre of the cluster.

• [Na/Fe] reveals a large star-to-star variation, regardless of the radius.

• [Si/Fe] exposes an anticorrelation to [Fe/H] but no correlation to the distance from the cluster centre has been found.

• [Ca/Fe] dependence with [Fe/H] is not clear, the correlation coeﬃcient being equal to 0.44. It is not correlated to the distance from the centre of the cluster.

• [Ti/Fe] is not correlated to [Fe/H] or the projected distance and shows a wide scatter.

• [Fe/H] does not show a trend with the eﬀective temperature but is correlated to the surface gravity of the stars. The correlation between [Fe/H] and g is suspected to be the cause of the scatter in [Fe/H] and overall in the other abundance ratios. It is likely to be the reason behind the unclear correlations between abundances.

The study of Carretta et al. (2013) provides the best comparison tool because it possesses a large number of stars (92), limiting the small-number statistics. They also have derived the abundances of the same elements as this study. The comparison CHAPTER 5. DISCUSSION 87 between the two studies will help clarify the scatters observed in the previous sections as it is not yet clear if they are real or due to errors in derivations.

5.3.1 Comparison of the iron abundances

Figure 5.13 shows the behaviour of the iron abundance as a function of the effective temperature for the two studies. These studies focus on different stages of the stellar evolution: RGB stars for Carretta, with Teff between 3850 and 5200 K, and mostly

AGB stars for this study, containing stars with Teﬀ between 4600 and 5800 K.

Figure 5.13: Comparison of [Fe/H] against Teﬀ . The red crosses correspond to this study and the blue crosses correspond to Carretta et al. (2013). The blue plot was generated with the data taken from the VizieR data service.

This figure brings to light the huge scatter of iron abundance found in this study compared to Carretta et al. for which the scatter is considerably less. As mentioned previously, the main reason for this scatter is the determination of the surface gravity. The trend in Figure 5.3 should be virtually flat, meaning that [Fe/H] would lie between –1.10 and –1.40. This result would be closer to the metallicities CHAPTER 5. DISCUSSION 88 derived by Carretta et al. the remaining differences being due to measurement errors (studied in Chapter 4).

5.3.2 Comparison of the sodium abundances

[Na/Fe] is plotted against [Fe/H] for the two studies in Figure 5.14. Despite the larger range in [Fe/H] for this study, the [Na/Fe] values are reasonably close, both studies having abundances between –0.40 and 0.80 dex. The uncertainties are very large due to the star-to-star variations but the similar trends between the two studies suggest that they may be real. The uncertainties are larger for this study, mostly because of the small number of sodium lines available in the wavelength region: two lines against four for Carretta, √ which introduces an additional error of the order of 2. Overall the two studies reveal an enhancement in the sodium abundance, the mean [Na/Fe] being 0.11 dex (Table 3.2), equivalent to an enrichment of a factor ∼ 1.3 compared to the Sun.

Figure 5.14: Comparison of [Na/Fe] against [Fe/H]. The red dots correspond to this study and the blue dots correspond to Carretta et al. (2013). CHAPTER 5. DISCUSSION 89

5.3.3 Comparison of the silicon abundances

Figure 5.15 displays the silicon behaviour as function of [Fe/H]. The star-to-star variations are much higher for this study than Carretta et al. The silicon abundance ranges from 0.15 to 0.35 dex in Carretta’s study whereas it ranges from –0.10 to 0.60 dex in this study. The uncertainties are higher for this study once again, the reason being a smaller number of lines (two Si lines for this study against 10 for √ Carretta et al.) which introduces an additional error of the order of 5 ∼ 2.25.

Figure 5.15: Comparison of [Si/Fe] against [Fe/H]. The red dots correspond to this study and the blue dots correspond to Carretta et al. (2013). CHAPTER 5. DISCUSSION 90

The stars with extreme metallicity, ∼ –0.8 or ∼ –1.6, exaggerate the trend for this study. If the plot with red dots is analysed only for the region where –1.30 < [Fe/H] < –1.10 dex, the star-to-star variations are less noticeable and the trend is virtually flat. It is interesting to focus on this region because it is where the accuracy on the measurements is believed to be the best for this study. It can be considered that the anticorrelation observed in Figure 5.15 is due to the scatter of [Fe/H] and might not be real. (Si) vs [Fe/H], plotted in Figure 5.16, can confirm this assumption: the star-to-star variations are smaller over the range of iron abundances. The silicon spread among the stars in the cluster is likely to be very small. The trends in (X) vs [Fe/H] do not have a real significance because [Fe/H] still affects (X) (see 5.3.4), so these trends are likely to be a consequence of the spread in [Fe/H]. The mean silicon abundance is in agreement between the two studies and also reveals an enhancement compared to the Sun: [Si/Fe] = 0.25 dex which correspond to an enrichment factor of ∼ 1.8.

Figure 5.16: (Si) against [Fe/H]. CHAPTER 5. DISCUSSION 91

5.3.4 Comparison of the calcium abundances

The comparison of the calcium abundances has been made in Figure 5.17. [Ca/Fe] shows star-to-star variations in this study, the abundances ranging between 0.20 to 0.60 dex whereas Carretta et al. did not ﬁnd considerable variations, their abundances being between 0.30 and 0.40 dex.

Figure 5.17: Comparison of [Ca/Fe] against [Fe/H]. The red dots correspond to this study and the blue dots correspond to Carretta et al. (2013).

The behaviour of the calcium abundance relative to hydrogen as function of the iron abundance, plotted in Figure 5.18, shows that there are still star-to-star variations as a correlation can be observed. There is a smaller range of (Ca) in the region where –1.30 < [Fe/H] < –1.10 dex, the calcium abundance ranging from 5.40 to 5.60 dex. This range is closer to the one determined in Carretta’s study. If all the [Fe/H] values are considered, the range is 0.90 dex, from 5.10 to 6.00 dex. It proves that [Fe/H] still aﬀects the other elements abundance relative to hydrogen, which can be explained by the inﬂuence of [Fe/H] on the model atmosphere parameters. CHAPTER 5. DISCUSSION 92

These parameters are ﬁxed based on the equality of the ionised states of iron. An inaccurate derivation for iron will result in inaccurate temperature or gravity which can have impact on [Ca/H] and [Ca/Fe]. The uncertainties are higher for Carretta’s study which contained seven Ca lines compared to the four lines in this study. The mean calcium abundance is in agreement between the two studies, this study showing [Ca/Fe] = 0.38 dex, equivalent to an enrichment factor of ∼ 2.4 compared to the Sun.

Figure 5.18: (Ca) against [Fe/H].

5.3.5 Comparison of the titanium abundances

[Ti/Fe] is plotted against [Fe/H] for the two studies in Figure 5.19. A very large scatter can be observed in the data from this work, whereas data from Caretta et al. exhibits a virtually ﬂat trend. The abundance ratios are substantially diﬀerent as this study contains ratios between 0.10 and 1.20 dex compared to ratios between 0.10 and 0.20 dex for Carretta et al. Even by taking values of [Fe/H] between –1.30 CHAPTER 5. DISCUSSION 93 and –1.10 dex, the wide scatter is still discernible. [Ti/H] was plotted as a function of the distance from the centre of the cluster in Figure 5.10 and the spread is also visible there, abundances relative to hydrogen ranging between 3.80 to 4.80 dex. The reason for these star-to-star variations can be attributed to the derivation errors for the titanium lines because of the proximity with the 6562 AH˚ α line as explained in Section 3.5. The previous results from Shetrone & Keane (2000), Gratton (1987) and Pila- chowski et al. (1983) are closer to the abundance of Carretta et al. Therefore the titanium results from this study might not be particularly trustworthy. It is assumed that the titanium abundance relative to iron is expected to be closer to 0.20 dex.

Figure 5.19: Comparison of [Ti/Fe] against [Fe/H]. The red dots correspond to this study and the blue dots correspond to Carretta et al. (2013). CHAPTER 5. DISCUSSION 94

5.4 Enrichment history of NGC 362

The chemical enrichment of NGC 362 can be estimated from the abundance ratios and the trends determined in this study. The comparison with Carretta et al. (2013) helped clarifying which spreads were expected and which ones were due to the scatter in [Fe/H] or derivation errors. Sodium, silicon, calcium and titanium are mainly produced by massive stars

(Mstar ≥ 10M ) during different nuclear burning stages (carbon burning for Na, oxygen burning for Si, explosive oxygen burning for Ca and Ti). Eventually a massive star will produce a Type II SN explosion and release these elements to the ISM (Arnett & Thielemann 1985, Thielemann & Arnett 1985, Woosley & Weaver 1995). According to theoretical yields shown in Figure 5.20, the generation of stars born after this enrichment will show [Na/Fe] between –0.20 and 0.60 dex, [Si/Fe] between 0.40 and 0.70 dex, [Ca/Fe] between 0.20 and 0.40 dex and [Ti/Fe] about –0.20 dex (Nomoto et al. 2006). The high [Na/Fe] and [Ca/Fe] abundance ratios determined in this study confirm that the targeted stars are formed after enrichment by Type II SN explosions. But the silicon and titanium abundances are different from the predicted SN yields. [Si/Fe] is about 0.20 dex lower and [Ti/Fe] is about 0.70 dex higher. Even assuming the Carretta et al. abundance of [Ti/Fe] = 0.20 dex, the titanium abundance would still be 0.40 dex higher than the predicted yields. Nomoto et al. claim that the theoretical yield for titanium can be increased if a bipolar (jet-like) explosion occurs instead of a spherical explosion. Although the blue model curve differs from the abundances derived in this study, the underlying data roughly agree. As these data were obtained from stars enriched by Type II SNe, it is probably more reliable. CHAPTER 5. DISCUSSION 95

Figure 5.20: Theoretical yields (blue curve) for the chemical enrichment due to Type II SN explosions, taken from Nomoto et al. (2006). The black dots correspond to observational data of stars enriched from Type II SNe. The yields cover the range of [Fe/H] derived in this thesis: the derived abundances have been added in red.

Another enrichment mechanism in the ISM are Type Ia SNe which produce larger quantities of iron compared to lighter elements, increasing the [Fe/H] ratio while decreasing the other ratios (Nomoto et al. 1997). It should not have had a great inﬂuence in the chemical enrichment of NGC 362 because the [x/Fe] vs [Fe/H] plots do not reveal a pronounced anticorrelation after comparison with Carretta et al. (2013). More importantly, the α elements are still enriched compared to iron, so the ratio cannot have been lowered that much. Chapter 6

Conclusion

This thesis has studied the chemical enrichment of the Galactic globular cluster NGC 362. The abundances of iron, silicon, calcium and titanium have been determined in 56 HB, AGB and RGB stars. The average abundances are in agreement with the literature, except for titanium which shows a higher abundance by ∼0.40 dex. The titanium lines used were contaminated by the 6562 AH˚ α line. A large spread was discovered in [Fe/H], which was not seen in the most detailed previous study, carried out by Carretta et al. (2013). As the spread is symmetric, the average [Fe/H], [Na/Fe], [Si/Fe] and [Ca/Fe] values are presumed to be correct. The large range in [Fe/H] is reflected in a wide range in [Na/Fe], [Si/Fe], [Ca/Fe]. Two possible explanations were identified: the scatter could be due to blended stars, which appear because of the size of the apertures in the FLAMES fibres during the observations. The spread could also be caused by the fact that none of the model atmosphere parameters (Teff , log(g), [Fe/H] and vt) are determined prior to the analysis. The parameters are fixed by iteration using MOOG software, but the strong correlation found in [Fe/H] vs log(g) shows that this method is inaccurate for this sample of stars. The same method has been used in different clusters, such as 47 Tuc (Cordero et al. 2013) or NGC 288 (Hsyu et al. 2014). The S/N was not high enough in this sample to perform with the same accuracy. It will be preferable for future studies on these data to fix the gravity via photometric measurements.

96 CHAPTER 6. CONCLUSION 97

Most of the trends shown in this study are due to the spread in [Fe/H]. The only trusted trend is the anticorrelation between [Na/Fe] and [Fe/H]. The radial dependence of the abundances has also been studied. No real trends are emerging from the plots, but the iron abundance reveals a larger scatter at the centre of the cluster, showing evidence of the blending of stars. The effective temperatures derived in this study have been compared with the photometric temperatures, calculated by Boyer et al. (2009). Overall our temperatures are ∼200 K colder. The difference is particularly noticeable for the stars near 5500K, belonging to the beginning of the horizontal branch according to the photometry. If their real temperature is ∼5300K, these stars might be part of the AGB. The surface gravity measurements were not sufficiently accurate to calculate the mass loss in evolved stars in NGC 362. The method would have been similar to the one used by McDonald et al. (2011) in the study of mass loss in ω Centauri. The enhancement in α-element abundance is proof that NGC 362 has been enriched mostly by Type II SNe, and the contribution of Type Ia SNe seems very limited. Bibliography

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