Nucleosynthesis and mixing processes in Galactic bulge AGB stars ...

Nucleosynthesis and mixingprocesses in Galactic bulge AGBstars studied with high-resolution

spectroscopy

Stefan UTTENTHALER

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DISSERTATION

“Nucleosynthesis and mixing in Galactic bulgeAGB stars studied with high-resolution

spectroscopy”

angestrebter akademischer GradDoktor der Naturwissenschaften (Dr. rer. nat.)

Verfasser: Mag. rer. nat. Stefan UttenthalerMatrikel-Nummer: 9600316Dissertationsgebiet: AstronomieBetreuer: Mag. Dr. Thomas Lebzelter

Wien, im Oktober 2007

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Abstract

The present thesis deals with stars on the asymptotic giant branch (AGB) locatedin the Galactic bulge and the mixing and nucleosynthetic processes therein. Theseprocesses have been studied by means of the occurrence and the abundances ofkey elements such as Technetium (Tc), Lithium (Li), and Fluorine (F). For thispurpose high-resolution spectra in the visual and infraredspectral regions wereanalysed with respect to the presence and strength of absorption lines connectedto these elements. The spectra have been obtained with instruments of ESO’s VeryLarge Telescope (VLT) in Chile.

Because of its radioactive nature, Tc serves well as an indicator of recentdeep mixing processes (third dredge-up, 3DUP) to where nucleosynthetic pro-cesses are taking place within a star. In combination with other observables suchas the luminosity and the pulsation period, conclusions could be drawn on theoccurrence of 3DUP in the course of the stars’ evolution on the AGB. One re-sult of the studies is that the minimum luminosity required for 3DUP to occur,as predicted by theoretical evolution models, is in agreement with observations.Furthermore, masses of the stars could be estimated from their luminosity andpulsation period. The derived masses hint towards a relatively young age of thestars, in contrast to what is found from studies of other stellar types in the bulge,but well in line with a number of works on bulge AGB stars.

Surprisingly, Li was found in a few sample stars, and different scenarios forits enrichment in AGB stars are discussed. As the most promising explanationCool Bottom Processing (CBP), another mixing process that may operate on theAGB, was identified. A relatively uncharted field of researchwas entered with thisstudy, and the knowledge of CBP on the AGB could be expanded byour work.

The abundance of F was measured in one of the sample stars showing bothTc and Li. F is sensitive to the temperature in the nuclearly active zone of the star.Abundance determinations of F, particularly in AGB stars, are rare in the litera-ture. The measurements are of astrophysical interest because the star’s mass canbe estimated rather accurately and thus serves as a benchmark for the F productionin rather low mass AGB stars. The measurements are based on infrared spectraobtained with the CRIRES spectrograph at the VLT.

An additional Chapter is devoted to a comparison of stellar model atmo-spheres and synthetic spectra based on the MARCS and PHOENIXatmosphericcodes, respectively. The precise reason for the differences found in high-resolutionspectra could not be identified, nevertheless useful hints could be found.

The final Chapter deals with the author’s various technical contributions tothe CRIRES project in the course of the ESO studentship.

In the Appendices can be found a comparison of spectra of bulge Mira vari-ables, taken with the CRIRES and Phoenix infrared spectrographs, as well as thesource code to describe the polarisation properties of an optical element for thespectro-polarimetric mode of CRIRES.

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Zusammenfassung

Die vorliegende Dissertation beschaftigt sich mit Sternen am AsymptotischenRiesen Ast (AGB) im Bulge der Milchstraße und den darin ablaufenden Misch-und Nukleosynthese-Prozessen. Diese Prozesse wurden anhand des Auftretensund der Haufigkeit bestimmter chemischer Schlussel-Elemente wie Technetium(Tc), Lithium (Li) und Fluor (F) studiert. Dazu wurden hoch aufgeloste Spektrenim visuellen und infraroten Spektralbereich im Hinblick auf das Vorkommen unddie Starke von Absorptionslinien, die von den genannten Elementen herruhren,analysiert. Die Spektren wurden mit Instrumenten am Very Large Telescope(VLT) der ESO in Chile aufgenommen.

Aufgrund seiner radioaktiven Natur eignet sich Tc besonders als Indika-tor fur tiefgreifende Misch-Prozesse (des sogenannten dritten dredge-ups, 3DUP)in jungster Vergangenheit (weinge hunderttausend Jahre), die in Regionen desSterninneren reichen, in denen Nukleosynthese stattfindet. In Kombination mitanderen Kenngroßen der Sterne wie der absoluten Leuchtkraft oder der Pulsation-speriode konnten daraus Ruckschlusse auf das Auftreten des 3DUP im Laufe derEntwicklung am AGB gezogen werden. Ein Ergebnis der Studienist, dass dievon theoretischen Entwicklungsmodellen solcher Sterne vorhergesagte minimaleLeuchtkraft beim ersten Auftreten des 3DUP im Einklang mit den Beobachtungensteht. Weiters ließ sich aus der Leuchtkraft und der Pulsationsperiode der Sternebzw. dem Auftreten von Tc eine Masse von ca. 1.5 Sonnenmassenabschatzen.Das sich daraus ergebende junge Alter der Sterne bestatigtdie bekannten Un-stimmigkeiten zwischen Altersbestimmungen des Bulge aus AGB- und anderenSterntypen.

Uberraschender Weise wurde Li in einigen der untersuchten Sterne gefun-den, und verschiedene Deutungsmoglichkeiten wurden diskutiert. Als die wahr-scheinlichste Erklarung fur das Auftreten von Li erwies sich Cool Bottom Pro-cessing (CBP), ein weiterer Mischprozess, der am AGB auftreten kann. Daswenige publizierte Wissen zu CBP in AGB-Sternen konnte durch diese Arbeiterweitert werden.

Die Haufigkeit von F wurde in einem einzelnen Bulge-Stern gemessen,der sowohl Tc als auch Li zeigt. F ist ein Indikator fur die Temperatur in dernuklear aktiven Region des Sterns. Haufigkeitsbestimmungen von F, insbeson-dere in AGB-Sternen, existieren nur wenige in der Literatur. Die Messung istvon Interesse da die Masse des betreffenden Sterns recht gut abgeschatzt wer-den konnte und somit die Erzeugung von F in AGB-Sternen eher niedriger Masseeingeschrankt werden konnte. Diese Messungen basieren auf Infrarot-Spektren,welche mit dem Spektrographen CRIRES am VLT aufgenommen wurden.

Ein weiteres Kapitel beschaftigt sich mit einem Vergleichder Atmo-spharenstrukturen und synthetischen Spektren, die auf den MARCS bzw.

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PHOENIX Atmospharen-Codes basieren. Der genaue Grund fur die gefundenenUnterschiede in hoch aufgelosten Spektren konnte zwar nicht identifiziert werden,jedoch gewisse Hinweise darauf.

Das abschließende Kapitel widmet sich den verschiedenen technischen Bei-tragen des Autors zu CRIRES im Rahmen des ESO-Studenships.

Im Anhang findet sich ein Vergleich von Spektren von Bulge Mira Vari-ablen, aufgenommen mit den Infrarot Spektrographen CRIRESund Phoenix,sowie der Quellcode zur Beschreibung der Polarisationseigenschaften eines op-tischen Elements fur den Polarimetrie-Modus von CRIRES.

Contents

1 Introduction 11.1 AGB stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Evolution to and on the AGB . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Evolution to the AGB . . . . . . . . . . . . . . . . . . . . 61.2.2 Evolution on the AGB . . . . . . . . . . . . . . . . . . . 7

1.3 Nucleosynthesis and mixing in AGB stars . . . . . . . . . . . . . 111.3.1 The third dredge-up . . . . . . . . . . . . . . . . . . . . . 121.3.2 The s-process . . . . . . . . . . . . . . . . . . . . . . . . 141.3.3 Other elements produced on the AGB: Lithium and Fluorine 17

1.4 Atmospheres of AGB stars and models thereof . . . . . . . . . . .191.5 The Galactic bulge . . . . . . . . . . . . . . . . . . . . . . . . . 211.6 Why infrared astronomy? . . . . . . . . . . . . . . . . . . . . . . 24

2 Technetium in Galactic bulge AGB stars 252.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Sample selection . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3 Fore- and background contamination . . . . . . . . . . . . . . . . 292.4 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.5 Sample characteristics . . . . . . . . . . . . . . . . . . . . . . . 312.6 Tc detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.7.1 Membership in the bulge . . . . . . . . . . . . . . . . . . 382.7.2 Third dredge-up luminosity limit . . . . . . . . . . . . . . 392.7.3 The mass and age of the Tc stars . . . . . . . . . . . . . . 40

2.8 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 44

3 Lithium in Galactic bulge AGB stars 473.1 Analysis of the UVES spectra with respect to Li . . . . . . . . .. 473.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.1 Enrichment by massive binary companion . . . . . . . . . 513.2.2 Accretion of a (sub-)stellar companion . . . . . . . . . . . 52

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x CONTENTS

3.2.3 Cool Bottom Processing . . . . . . . . . . . . . . . . . . 523.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4 Comparison of MARCS and PHOENIX 59

5 Fluorine in a Galactic bulge AGB star 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 CRIRES Observations . . . . . . . . . . . . . . . . . . . . . . . 685.3 Stellar parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 695.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.5 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . 73

6 CRIRES 756.1 Some technical details of CRIRES . . . . . . . . . . . . . . . . . 756.2 Contribution to the CRIRES project . . . . . . . . . . . . . . . . 80

6.2.1 Model of the instrumental polarisation . . . . . . . . . . . 806.2.2 Focus measurements . . . . . . . . . . . . . . . . . . . . 886.2.3 Testing the slit viewer guiding algorithm . . . . . . . . . 896.2.4 CRIRES – UVES parallel observations . . . . . . . . . . 926.2.5 Linearisation of the science detector signal . . . . . . .. 98

A Spectral variability of bulge Miras 113

B Muller matrix source code 119

Chapter 1

Introduction

1.1 AGB stars

This thesis deals with a type of stars known as Asymptotic Giant Branch (AGB)stars, more specifically stars of this type located in the central bulge of our homegalaxy, the Milky Way, and what can be learned from them abouttheir evolution.AGB stars represent a late stage of evolution of stars which were born with aninitial mass between about 0.8 and 8 M⊙

1. Due to their short life time, AGB starsare a rare type of star, but of high importance for the evolution of their homegalaxy because of their significant contribution to the cosmic matter cycle. Also,they are highly complex objects. We first want to give an introduction to the innerstructure of an AGB star as illustrated in Figs. 1.1 and 1.3; in Section 1.2 we willthen turn to the description of how a star evolves to this “status quo”.

We start out the structural description in the centre of the star where a de-generatecoreof mainly carbon and oxygen (and a few other heavy elements, butno hydrogen or helium) is dwelling. “Degenerate” in this respect does not meanthat energy levels of some particles are degenerate with respect to some quantumnumber. Rather the dominant contribution to the pressure ofthe material comesfrom the degeneracy pressure of free electrons as a result ofPauli’s exclusion prin-ciple for fermions. The degeneracy pressure counter-acts the strong gravitationalpressure resulting from the layers above and prevents the core (and the star) fromfurther collapse.

Immediately above the core a spherical shell is located where4He is burnt to12C (and some16O) by the so-called triple-α process. The He-burning thus steadily

1The mass limits are not sharp and arise from different reasons. The upper limit comes from thefact that more massive stars end their life in a Supernova explosion. It is a function of the metalcontent of a star, its rotation, etc. The lower limit reflectsjust the fact that stars below this masssimply haven’t had enough time since the beginning of the universe in the Big Bang to evolve tothe AGB. Once the universe grows older, stars of∼ 0.5 M⊙ might well populate the AGB.

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2 CHAPTER 1. INTRODUCTION

Figure 1.1: Sketch of the structure of an AGB star from its centre to its outermost layers(J. Hron, priv. comm.).

increases the mass of the C-O core. TheHe-burning shellderives its fuel from aHe-rich layer. This He-rich layer is also the site of nucleosynthetic processes.For example, the lighter nuclei of elements like Ti, Fe, or Niare transformed toheavier nuclei of elements like Zr, Tc, Ba, or Pb (see Section1.3.2). The He-richlayer basically contains all chemical elements, except H, because H is burnt in aspherical shell above the He-rich shell into He. The H- and He-burning shells arethe energy sources of the star. All these regions are coveredwith a vastly extendedenvelope which is unstable against mass circulation by convection. Almost all ofthe star’s volume is filled by thisconvective envelope, as can be estimated fromthe scale at the bottom of Fig. 1.1. In stars with masses. 3 M⊙, a thin layer withdominant radiative energy transport separates the H-burning shell and the convec-tive envelope. The region between the He-burning shell and this radiative layerare of high interest in this thesis because it is the origin ofchemical abundancechanges on the surface of the AGB star.

The upper layers of the convective envelope are called theatmosphere. Forthe analysis of stars it is of high importance, since most of the electromagneticradiation originates from there and the star’s spectrum receives its overall shape

1.1. AGB STARS 3

(except for far-infrared features; for a critical discussion of the term “atmosphere”of an AGB star see Chapter 4 of Habing & Olofsson, 2004). Because of its impor-tance we want to discuss atmospheres of AGB stars and models thereof separatelyin Section 1.4, only the most striking features are presented here.

First of all, most AGB stars are obviously in a zone of the Hertzsprung-Russel diagram (HRD) where their atmospheres are unstable againstpulsation(Gautschy A., 1999). The mechanism responsible for the pulsation is the so-calledκ-mechanism resulting from periodic ionisation and recombination of H- and He-atoms in deep layers of the convective envelope. The pulsations have a number ofconsequences which have to be considered. The most apparentconsequence is thevariability in brightness of the star. It was this variability that led tothe discoveryof Mira Ceti, the first AGB star ever recorded in history, by the Friesian priest andastronomer David Fabricius in 1596 (although at that time itwas thought that thediscovered star was a Nova). AGB stars are variable on timescales between about50 to above 1 000 days. A change of temperature accompanies the brightnessvariations with the same period, with highest temperature close to the brightnessmaximum. The change in temperature is expressed also in a change of colour. Theamplitude of the light-curve depends on the wavelength under consideration, andis largest in theV-band. A good measure for the total (bolometric) variability is theamplitude in the near-IRK-band (see Nowotny, 2005, for a detailed discussion).

Based on the regularity of the light change and its amplitude, differentvari-ability typeson the AGB are distinguished. Irregular variables (Lb) do not havea prominent period of their light change, and the amplitude is rather small. How-ever, the irregularity is a rather poor criterion if photometric data are sparse. Semi-regular variables (SR or SRV) exhibit more regular light variations with ampli-tudes in theV-band≤ 2.m5. Based on their pulsation properties, surface tempera-tures, luminosities, and mass loss rates they are subdivided into SRa, SRb (Samuset al., 2004), and Mira-SR classes (Kerschbaum & Hron, 1992). Mira variables,finally, whose prototype star is Mira Ceti, exhibit regular light variations with adistinct period and amplitudes> 2.m5 in V. These classes of AGB variables prob-ably represent different evolutionary states along the AGB (cf. Section 1.2.2). Lband SR variables are probably placed on the early AGB, while Mira variables aremore evolved and populate the thermally pulsing AGB.

Together, SRVs and Miras make up a large part of the so-calledlong periodvariables(LPVs). In recent years a great deal about variability and pulsation ofLPVs was learned from light-curves obtained from micro-lensing surveys such asMACHO, OGLE, EROS, etc. For essential results, in particular the sequences inthe period-luminosity plane formed by LPVs, see e.g. Wood etal. (1999), Lebzel-ter et al. (2002), Ita et al. (2004), and Groenewegen & Blommaert (2005). Forthese sequences, period-luminosity relations can be established which are usefulin several respects, see Section 2.7. General consensus hasnow been reached that


Mira variables are fundamental mode pulsators, while SR variables also pulsatein the first and second overtone mode (Wood, 2007). This probably is an effect ofincreasing luminosity (and radius) along the AGB.

AGB stellar atmospheres are among the coolest of all stellaratmospheres.Due to the low temperatures,moleculesof different kinds can form in the atmo-sphere, which in turn strongly influence the structure of theatmosphere (Tsuji,1966; Jørgensen et al., 2001). Thus, the chemistry of the atmosphere becomes animportant point. The prevailing chemistry in an AGB atmosphere can be eitherC-rich or O-rich, depending on the C/O number ratio in the atmosphere. If C/Ois < 1 the chemistry will be O-rich (spectral type M), and C-rich if C/O is > 1(spectral type C). Stars whose C/O ratio is very close to unity (within a few per-cent) are assigned the spectral type S, and intermediate types MS and SC are used.The CO molecule is one of the most stable molecules and forms at temperatures ashigh as 4000 K. Any C and O available will be bound into CO untilthe least abun-dant of the two species is almost completely consumed in CO. Thus, if C/O< 1there will be a surplus of O atoms that can form other molecules containing O,and if C/O> 1 there will be a surplus of C atoms to form molecules containing C.Molecules forming abundantly in an O-rich environment are TiO, SiO, H2O, OH,and in very cool atmospheres VO. In a C-rich environment these will be replacedby CN, CH, C2, C3, HCN, C2H2, etc. Each molecule has its characteristic energylevels for rotation, vibration, and electronic transitions and thus will accordinglyshape the appearance of the star’s spectrum. For instance, the TiO molecule hasvery characteristic absorption bands in the visual and red spectral range which willbe mentioned at various occasions throughout the thesis. For theoretical descrip-tions of molecules and how to derive molecular line wavelengths and strengths,see e.g. Herzberg (1989), Bernath (2005), or Aringer (2000).

In principle, because the C/O ratio of the interstellar medium is alwayssmaller than unity, all stars are born O-rich. The reasons why C-rich stars existare nucleosynthetic and mixing processes in the deep interior of these stars whichlead to a progressive enrichment of C on the stars’ surface2. These processes arepresented in more detail in Section 1.3. Thus, a star may evolve from an O-rich toa C-rich chemistry during its AGB phase.

A feature of AGB stellar atmospheres not yet mentioned are dynamic ef-fects such asshock waveswhich build up in strongly pulsating atmospheres. Theycause not only characteristic emission lines from mainly H,Fe, and Mg, but alsoaid the formation ofdust grainsin cool layers of the atmosphere (see below). Thedust species formed in these layers depend on the prevailingchemistry of the at-mosphere. In the O-rich case, mainly silicates (e.g. forsterite) and Fe-, Mg-, and

2There exist, however, C-rich stars which are definitely not placed on the AGB. These stars havereceived their surplus C by mass transfer from a close binarycompanion who evolved through theAGB phase some time ago and is a White Dwarf now.

1.1. AGB STARS 5

Al-rich oxides (e.g. spinel) will form. In a C-rich environment, SiC and amor-phous carbon grains will dominate. Like atoms and moleculesin the optical andnear-IR part of the spectrum, different dust species have characteristic (emission)features in the far-IR (& 5µm). The study of the dust properties has developedinto a completely new field of AGB research, even with extensive laboratory workincluded (e.g. Posch et al., 1999). Pre-solar grains found in meteorites are believedto originate in the dust formation region of now extinct AGB stars and are usedto study different properties of their parent stars (e.g. Busso et al., 2003; Savina etal., 2004).

A decisive property of stars on the AGB is their high amount ofmass loss(10−7

− 10−4 M⊙ yr−1). For the consequences of mass loss on the further evolu-tion on the AGB, see Section 1.2.2. The mechanism(s) leadingto mass loss arelong debated. An early hypothesis has been that dust grains play a key role inthe acceleration of the outflow. The idea is that radiation coming from the staris re-radiated isotropically by the grains and thus createsa net force (radiationpressure) away from the star. The gas then dynamically couples to the dust andis “dragged along” with it. However, this simple idea does not fully withstanddeeper scrutiny, because the densities reached in a (hydrostatic) atmosphere arefar too low to efficiently form dust. A second mechanism is required to causeincreased densities in high atmospheric layers to favour dust formation. Here, dy-namic effects in the atmosphere come into play. Shock waves moving outwardfrom deep atmospheric layers compress, heat, and push outward the gas. Once ashock wave has passed, the relatively dense gas cools again and may form dustgrains, in particular of amorphous carbon in a C-rich atmosphere. Radiation pres-sure can act on the dust to accelerate it away from the star. Via dust-gas collisions,momentum is transferred to the gas, and the shell moves outward. The terminalvelocity of the wind is of the order of 10− 20 km s−1. Hydrodynamic model atmo-spheres with C-rich chemistry like those of Hofner et al. (2003) well reproduce theobserved outflow velocities, thus this mass loss scenario iswidely accepted (e.g.Fleischer et al., 2000; Nowotny et al., 2005a,b, see also Section 1.4). In O-rich en-vironments, the radiation pressure on silicate dust grainsis not sufficient to drivea stellar wind (Woitke, 2006). Mass loss rates and outflow velocities are howeverobserved to be quite similar for O-rich and the C-rich objects. Modifications tothe scenario described above are thus discussed (e.g. Hofner & Andersen, 2007).

The matter blown off the AGB star is generally summarised as thecircum-stellar envelope(CSE, not to be confused with theconvectiveenvelope!). Thedensity and temperature of the material decreases with increasing distance fromthe star and gradually merges with the interstellar medium (ISM). Besides thermal(rotational) line emission from CO, SiO, and many other molecules, the CSE isalso the region where strong naturalmaseremission from different molecules mayemerge, most prominently from SiO, H2O, and OH (hydroxyl). Maser emission


from the SiO molecule at 43 and 86 GHz comes from layers close to the photo-sphere where the stellar wind is being accelerated. H2O maser emission at 22 GHzoriginates from somewhat cooler layers further outward. OHmaser emission at1612 MHz finally is emitted from even cooler layers, where theinterstellar UVradiation field dissociates some of the H2O molecules. The maser emission of allmolecules exhibits a complex temporal and spatial behaviour that is not well un-derstood theoretically. Measurements of this radiation are performed with radioand sub-mm antennas (e.g. IRAM, JCMT, APEX, Effelsberg, Onsala, . . . ).

Depending on the mass loss rate the CSE may become optically thick. Inextreme cases the circumstellar reddening is so strong thatsome objects have onlybeen detected as IR sources. Since many of these stars show OHmaser emission,they are also calledOH/IR stars(Habing, 1993). OH/IR stars are thought to rep-resent the super-wind phase at the very final stage on the AGB,before the starmoves to the post-AGB sequence (see Section 1.2.2). The outflow velocity of theCSE as well as the radial velocity can be measured with high precision for OH/IRstars. For this reason these objects are also used as tracersin studies of the Galac-tic structure and dynamics (e.g. Blommaert, 1992; Sevenster, 1999; Habing et al.,2006).

The C-rich relative to OH/IR stars are the obscured carbon stars. Sincethey have a C-rich CSE, no maser radiation of the above mentioned moleculesis observed from them. Nevertheless, the circumstellar extinction is so strongthat the objects are almost undetectable in the optical partof the electromagneticspectrum. The most prominent representative of this objecttype is CW Leo, alsoknown as IRC+10216 (e.g. Menut et al., 2007).

1.2 Evolution to and on the AGB

1.2.1 Evolution to the AGB

The objects discussed in the following Chapters are estimated to have massesaround 1.5 M⊙ and are thus rated as rather low mass AGB stars. We can followschematically the evolution of a star of mass 1 M⊙ in a luminosity versus effec-tive temperature diagram from the main sequence (MS) to the AGB (Fig. 1.2).The evolution at 1.5 M⊙ is not much different from that at 1 M⊙, only somewhathigher luminosities and temperatures (at least on the MS) are reached, and theevolutionary time scales are shorter.

The evolution starts out on the zero age main sequence (ZAMS), where thestar burns hydrogen under radiative conditions in its core for ∼90% of its totallife time. H becomes gradually less and less in the core (inset (a)), while theluminosity and surface temperature increase. At point 4 thestar passes the turn off(TO), where the surface temperature reaches a maximum. WhenH is exhausted in

1.2. EVOLUTION TO AND ON THE AGB 7

the core, H burning advances in a shell around the He core (inset (b)). The He corecontracts which in turn leads to an expansion of the (convective) stellar envelope –the star begins to ascend the giant branch (RedGiant Branch, or RGB) for the firsttime. At the base of the RGB the surface convection zone (SCZ)extends deeplyinward to layers where partial H burning has occurred before. This phenomenonis called theFirst Dredge-Up(1DUP) and is illustrated in inset (c) of Fig. 1.2.The 1DUP marks the first episode in the star’s life where the surface abundancesare changed due to the mixing of nuclearly processed material (see Section 1.3).The most prominent isotopes enriched on the surface by 1DUP are 4He, 13C, and14N, being products of incomplete CN cycling. As a consequence, the 12C/13Cratio decreases from its initial value (≈ solar= 90) to between 4 and 20, and the12C/14N ratio decreases by a factor of about 2.5.

As the He core further contracts and heats up, the star’s envelope continuesto expand and the star “climbs” up the RGB. Due to neutrino cooling the tempera-ture maximum is not reached exactly at the core centre but somewhat displaced, asillustrated in inset (d). The triple-α process which burns three helium nuclei intoone12C nucleus thus ignites off-centre. For stars below 2.25 M⊙ in mass the coreis degenerate and the temperature gradient is very shallow inside the core. Thusthis ignition is rather violent and is therefore also calledthe “helium core flash”.After this event the star leaves the giant branch and moves quickly to the horizon-tal branch or the red giant clump, depending on its precise mass and metallicity.Henceforth the star burns4He to12C (and some16O) in the core and H to4He in ashell around the core. The development of the H and He fraction with time frompoints 10 to 14 is shown in inset (e) in Fig. 1.2.

Helium gets exhausted in the core at point 14, and the star begins to ascendthe giant branch a second time. The C-O core becomes electrondegenerate, andthe star’s main energy source is the He-burning shell. The convective envelope ontop of the (dormant) H-burning shell fills most of the star’s volume (inset (f)). Thestar has commenced the early AGB (E-AGB) phase.

1.2.2 Evolution on the AGB

The evolution on the AGB has been reviewed in many papers, most notably byIben & Renzini (1983), Vassiliadis & Wood (1993), Frost & Lattanzio (1995),Busso et al. (1999), and Habing & Olofsson (2004). The paper by Weigert (1966)is also very enlightening but is available only in German.

Fig. 1.3 shows a cross-section through a star located somewhere aroundpoint 15 in Fig. 1.2. The size of the core and of the burning shells is much exag-gerated to make them visible in this sketch. The scaling is rather according to themasses of the respective regions than to the spatial extension. In reality, the C-Ocore is of the size of the earth (about ten thousand kilometres), while the envelope


He shell

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Thermally pulsing AGBBeyond point 15 is the

9 = Core He Flash

Early AGB begins

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inset (b)

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10

Pulse = 15First Thermal

Beyond point 14 the

mass fraction

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ance

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11 1213

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Core He

= 14exhaustion

log(T)

67

45H

abu

ndan

ce

10

11

12

13

14

10 11 12 13

1110 12 13

14

14

inset (e)

conv

ectiv

een

velo

pe

conv

ectiv

een

velo

pe

He coreCO

Log(

L)

Log(Teff)

1 = ZAMS

65

7

2

3

4 = core Hexhaustion

mass fraction

mass fraction

mass fraction

H a

bund

ance

Figure 1.2: Schematic evolution of a star of mass M≈ 1M⊙ (Frost& Lattanzio, 1995).See Section 1.2.

1.2. EVOLUTION TO AND ON THE AGB 9

Figure 1.3: Cross-section through a typical TP-AGB star (not to scale).Taken fromwww.noao.edu/outreach/press/pr03/sb0307.html

has a radius one hundred times that of the sun (about one-hundred million kilo-metres). Not drawn in this sketch is the thin He-rich layer that separates the He-and the H-burning shell. This layer is the stage of rich nucleosynthesis processesdiscussed in Section 1.3.2. The total time typically spent on the AGB is around106 years, but is a non-monotonic function of the stellar mass.

The electron degenerate C-O core of the AGB star grows steadily duringthe evolution on the AGB3. It is the progenitor of the White Dwarf (WD) thatwill remain at the end of the star’s evolution. In the low massstars discussedhere, the core can grow up to half of the star’s MS mass. In the E-AGB phase,most of the star’s luminosity is produced by the He-burning shell. As the Herich shell becomes thinner the luminosity of the He-burningshell declines andthe H-burning shell gradually takes over. When the He-rich shell is sufficientlythin, the He-burning shell luminosity starts to oscillate.As has been shown bySchwarzschild & Harm (1965) and Weigert (1966), these oscillations eventuallydevelop into an instability of the He-burning shell called athermal pulse(TP).This phase of evolution is named TP-AGB. The main physical reasons for TPs arethe high temperature sensitivity of the specific energy production by the triple-αprocess (ǫ ∝ Tν, with ν between 30 and 40!) and the small thickness-to-radiusratio of the He-burning shell. TPs influence the star’s luminosity and surfacetemperature, hence pulsation properties, and possibly mass loss (Mattsson et al.,

3For stars with mass above∼ 8 M⊙ the core is no longer degenerate, thus carbon burning can igniteand the star will end its life in a Supernova explosion


2007).Depending on the star’s mass and mass loss, the total number of TPs expe-

rienced by the star and the inter-pulse period strongly vary. A star of 1 M⊙ mayexperience only a few TPs on the AGB with an inter-pulse period (with quies-cent evolution between two TPs) of up to 105 years, while at 5 M⊙ the numberof TPs reaches several dozens and the inter-pulse period declines to below 104

years (Vassiliadis & Wood, 1993). The number of thermal pulses is also stronglydetermined by the amount of mass lost during AGB evolution, which in turn de-pends on the initial metallicity. The pulse itself has a duration of the order of onehundred years.

Lb, SR, and Mira type variability probably are to be placed ondifferentparts of the AGB (Lebzelter & Wood, 2005, e.g.). Also the pulsation period ofthe star’s outer envelope is modulated by the thermal pulses. This is partly aresult of the change in stellar radius caused by the thermal pulses. The generaltrend is an increase of the pulsation period (and amplitude)as the star ascends thegiant branch. In a simplistic picture the star evolves from anon-variable star onthe Horizontal Branch to an SR variable on the E-AGB, and later on to a Miravariable. However, this evolution depends also on stellar mass, since SR variablesshowing lines of Tc are known (i.e. they are on the TP-AGB, e.g. Lebzelter &Hron, 1999).

During a TP cycle the surface luminosity as well as the luminosity deliveredby the He- and H-burning shells exhibit strong variation. In-between two TPs theH-burning shell is the main source of energy, while the He-burning shell producesonly 1 % of the total luminosity. When the He-burning shell instability develops,its luminosity sharply increases, while the H-burning shell is essentially shut offbecause of the decreasing temperature at the site of H-burning. After the TP, theHe-burning shell luminosity slowly declines and the H-burning shell takes overagain. The surface luminosity of course shows much smaller variations, but maychange by about 1.m0 in bolometric magnitudes.

The surface luminosity in the quiescent phase (between two successive TPs)gradually increases on the AGB. For low mass stars (M < 3 M⊙), where the con-vective envelope does not penetrate the H-burning shell, the star’s luminosity dur-ing the quiescent phase is directly related to the mass of theH-exhausted core,except for the early phase on the TP-AGB. This enabled Paczynski (1970) to es-tablish his well-known core mass-luminosity relation:L = 59 250· (MC − 0.522),whereL andMC are in solar units.

Mass loss is the process determining the further stellar evolution on theAGB, rather than nuclear burning. The star has previously lost mass on the RGB,but typically only a tiny fraction compared to that on the AGB. Since the finalmass of the WD is only a weak function of the star’s initial mass, high mass starslose a much bigger fraction of their mass on the AGB than low mass stars do. A

1.3. NUCLEOSYNTHESIS AND MIXING IN AGB STARS 11

final “super-wind” phase with mass loss rates up to 10−4 M⊙ yr−1 is thought to ter-minate the AGB evolution. Once the H-rich envelope is erodedto below 10−3 M⊙the star cannot retain its size and it shrinks. In the HRD (Fig. 1.2) the star movesoff the AGB to the left at constant luminosity, i.e. its surface temperature increases.The star has become a post-AGB object. At temperaturesTeff > 30 000 K the starenters the domain of the planetary nebula nuclei. The strongUV radiation fromthe hot photosphere ionises the mass shell ejected during the super wind phaseand before, which becomes observable as a planetary nebula (PN).

Finally, the decreasing mass of the residual convective envelope causes adecrease of the temperature at the H-burning shell so that nuclear energy produc-tion ceases. With the shut-down of the last burning shell, the star rapidly drops inluminosity and follows the WD cooling track. Depending on where in the TP cy-cle (during quiescent evolution or close to a TP) the super wind phase ejects mostof the star’s envelope, a so-called “late thermal pulse” mayoccur. The star thenmoves to the AGB once again on a very short time scale (years).This phenomenonhas been observed e.g. in Sakurai’s object (V4334 Sgr, Kauflet al., 2003b).

Besides this simple description of AGB evolution one must not forget themany details not yet understood due to uncertainties in modelling and the chal-lenging interpretation of observations. In particular uncertain are the aspects ofmass loss, mixing phenomena, and to some extent physical input data (nuclearcross-sections, etc.). Section 1.4 gives an idea of the complications involved inderiving observational quantities to constrain models of AGB evolution.

1.3 Nucleosynthesis and mixing in AGB stars

The nucleosynthesis in AGB stars has an effect on the rest of the world since even-tually the newly formed elements reach interstellar space and molecular clouds bymass loss from the AGB star, to be part of a new generation of stars and planetarysystems formed from these clouds. Hence, nucleosynthesis in (AGB) stars hasattracted researchers’ attention since a long time.

During the evolution on the AGB a broad range of nucleosynthetic processesoccur in the deep interior of the star. Generally, light atomic nuclei are fused tobuild up heavier nuclei, but one may distinguish two different types of reactionsregarding their energy release: (i) Reactions that are abundant and release a signif-icant amount of energy, hence they strongly influence the structure of the star, and(ii) reactions that release only a small amount of energy andwhose energy outputis negligible for the structure of the star. This division isof importance in numericcalculations of stellar evolution, since the reaction network can be narrowed downto speed up computations. The less energetic reactions can be treated afterwardsin more detail in a “post-processing” algorithm (e.g. Gallino et al., 1998).


In an AGB star, among others the following reactions belong to the firsttype. H is burnt to He in the H-burning shell through CNO cycling, which alsoturns almost all CNO nuclei into14N. In the He-burning shell the triple-α processburns4He into12C. Some of the12C is further processed into16O, and most of the14N captures two He-nuclei to become22Ne.

Reactions of the second type are manifold, with neutron capture reactionsbeing the most prominent ones. These reactions are intimately linked to the TPs(see previous Section), and an associated mixing phenomenon called the thirddredge-up. Understanding these processes is only possiblewith knowledge of thestructure of the H- and He-burning shells and the He-rich inter-shell region as afunction of time. This is best illustrated by a Kippenhahn diagram (mass vs. time)of this region (Fig. 1.4), which we will discuss in the following.

1.3.1 The third dredge-up

Each TP produces a large amount of energy. This energy cannotbe transportedoutwards efficiently enough by radiation, thus the He-rich shell betweenthe He-and the H-burning shell becomes convectively unstable. Theenergy is partly usedup to expand the star which causes the temporary shut-down ofH-burning. Thelower border of the convective envelope retreats outwards such that the convec-tive thermal pulse does not connect to it, as found by Iben (1977). When theTP ceases, the convective envelope border extends inwards to reach mass layerswhere H-burning and other nucleosynthetic processes have taken place before.The convective thermal pulse and the convective envelope hence overlap in mass(although not at the same time!) and the material in regions Aand B in Fig. 1.4is now mixed to the surface (“dredged up”). This event is thuscalled thethirddredge-up(3DUP)4. In this way, the effects of nuclear processing become visibleon the star’s surface. The most notable effect of 3DUP is the progressive enrich-ment of the envelope by products of He-burning, i.e. by12C. This is the root causeof the metamorphosis from an initially O-rich to a C-rich star. Smith & Lam-bert (1990) showed that the C-content of TP-AGB stars indeedincreases alongthe spectral type sequence M-MS-S. AGB stars are significantcontributors to theGalaxy’s C inventory, since C is a primary (i.e. no initial seed nuclei other than Hand He are required) product of AGB nucleosynthesis.

4The first and second dredge-up (1DUP and 2DUP, respectively)occur earlier in the evolution of astar. The 1DUP is experienced as the star ascends the RGB, while 2DUP happens only for moremassive stars (M > 4M⊙) when the He-burning shell is established at the end of core He-burning.Both the 1DUP and the 2DUP mix material to the surface which has undergone partial or full H-burning, thus they cause similar surface abundance changes. These include an increase of the13C,14N, and4He content, as well as a decrease of12C, 16O, and18O. The abbreviation TDU insteadof 3DUP is in use in the literature, too.


Figure 1.4: Kippenhahn diagram of the nucleosynthetically active regions of a TP-AGBstar. Horizontal gray bars in the He-rich inter-shell denote zones where protons are as-sumed to be ingested to create the13C-pocket.13C burns under radiative conditions in thegray area before ingestion because of the progressive heating of the region (Straniero etal., 1997). The slow neutron capture (s) products are then engulfed by the thermal pulse.Further processing occurs owing to neutrons from the22Ne(α,n)25Mg source may oper-ate at the base of the convective pulse in low mass stars. Region A between the H shelland the border of the convective zone and region B in the He inter-shell are mixed into theconvective envelope during 3DUP, and these regions salt theenvelope with freshly synthe-sised material. The remaining part of the He inter-shell region below B is also enriched ins-process nuclei and is partly mixed over subsequent cycles. See Sections 1.3.1 and 1.3.2for more details. Taken from Busso et al. (1999).

Third dredge-up in principle is a repeated mixing event on the AGB thatmay operate after every TP. Like all astrophysical phenomena involving mixing,it is not well understood theoretically. It is known that themass of the convectiveenvelope is a critical ingredient for 3DUP to occur. Below a certain value ofthe envelope mass, 3DUP will not occur. Thus, there may be TPsin the star’sevolution which will not be followed by a 3DUP event.


1.3.2 The s-process

In-between two TPs, free neutrons are abundant in the inter-shell region (see be-low). The free neutrons are captured mainly by seed (i.e. secondary) nuclei ofthe iron group (. . . , Mn, Fe, Co, Ni, . . . ). By such a capture thenucleus gainsin mass by one atomic mass unit. A particular nucleus captures neutrons until itreaches an isotope that is unstable againstβ−-decay with a half life time shorterthan the typical neutron capture rate of the nucleus. At low neutron densities,neutrons will be captured at a slow rate and the unstable nucleus will rather decayto turn into a nucleus of the element with next the higher atomic number thancapture another neutron. This is why this process is called the “slow neutron cap-ture process”, ors-processfor short5. Elements produced by the s-process arereferred to as s-elements. The s-process was first suggestedin the famous paperby Burbidge, Burbidge, Fowler, and Hoyle (B2FH, 1957). Excellent reviews ofthe s-process and other stellar nucleosynthetic processescan be found in Pagel(1997) and Wallerstein et al. (1997).

As mentioned, a nucleus moves one isotope to the right in the chart of nu-clides when a neutron is captured, and one isotope up and leftwhen theβ−-decayoccurs. Thus, as a consequence of repeated n capture, the nucleus will followa certain path in the chart of nuclides, called the s-processpath. Fig. 1.5 illus-trates this path in the region of the elements Zr to Rh. The thick red line is thes-process path at low neutron densities. Note that93Zr has a long half-life time of1.5× 106 years and thus can be treated as a stable nucleus in this context.

Of particular interest are isotopes whose half-lifes are comparable to theneutron capture rate. At these nuclei, a branching in the s-process path may occur.Examples for branching points are the isotopes95Zr and85Kr. The branching at95Zr is shown as a thin red line in Fig. 1.5. Both of the mentionedbranchingpoints were used by Lambert et al. (1995) to measure the neutron density at thesite of the s-process path. The authors could derive a very low upper limit onthe96Zr abundance (measured from band heads of the ZrO molecule),indicatingthat95Zr (τ1/2 = 64 d) decays rather than capturing another neutron to make96Zr.However, a more stringent criterion was found by Lambert et al. (1995) from thebranching at85Kr (which controls the Rb/Sr abundance ratio). Their measuredvalues indicate a neutron density which is in agreement withpredictions for theinter-pulse period in low mass AGB stars (∼ 107 cm−3), and in disagreement withthe neutron density during the TP itself.

An interesting element that lies on the s-process path is Technetium (Tc).The isotope of Tc with the longest half-life time created by the s-process is99Tc

5In contrast, in the “rapid neutron capture process”, or r-process, the neutron density is very highand very neutron-rich nuclei are formed before they decay tothe next higher element. The r-process is believed to occur under explosive conditions such as in Supernovae.


Zr 93

Tc 100

Zr 90 Zr 99Zr 98Zr 95

Tc 101

Mo 101

Nb 100

Tc 102Tc 97Tc 96Tc 94 Tc 95

Nb 91 Nb 94 Nb 95 Nb 96 Nb 97 Nb 98 Nb 99

Ru 97Ru 95Ru 94

Rh 96 Rh 97 Rh 98 Rh 99

Mo 93 Mo 99

Nb 92

Tc 93 Tc 98 Tc 99

Ru 103

Zr 97

Rh 100Rh 95 Rh 102 Rh 104Rh 101

Zr 92Zr 91 Zr 94 Zr 96

Mo 98

Nb 93

Mo 92 Mo 94 Mo 95 Mo 96 Mo 97 Mo 100

Ru 96 Ru 98 Ru 99 Ru 100 Ru 101 Ru 102

Rh 103

Figure 1.5: Section of the chart of nuclides between the elements Zr to Rh. Neutron num-ber increases to the right, and proton number increases upward. Black coloured back-ground indicates stable isotopes, pink coloured background represents isotopes decayingpredominantly via theβ+-decay, and light-blue coloured background stands for isotopespredominantly decaying via theβ−-decay. The thick red line is the s-process path followedat low neutron density, the thin red line indicates a possible branching at higher neutrondensities.

with τ1/2 = 2.1× 105 years. Due to its long half-life it is, in principle, also abranching point in the s-process path that controls the abundance distribution ofthe Ru isotopes.100Tc is produced in the s-process as well, but decaysβ− afteronly 16 s. 98Tc has a half-life time of evenτ1/2 = 4.2× 106 years, but is not cre-ated by the s-process because it is shielded by the stable98Mo. Thus,99Tc offersthe unique possibility to distinguish stars which underwent the s-processand the3DUP very recently from stars which have not (yet) experienced these events.Merrill (1952) was the first one to detect atomic absorption lines of Tc in spectraof late type stars, and many works have been published since on the subject. Inthe present thesis,99Tc has been used to identify AGB stars in the Galactic bulgethat underwent the s-process and the 3DUP very recently (seeChaper 2).

The s-process path leads all the way up to Pb and Bi, where it terminatesin a circle reaction because of an instability gap. Only during the r-process inSupernova explosions the neutron density is high enough to bridge this gap andtrans-lead elements (U, Th, etc.) are naturally created.


The enhancement factors of different s-elements are a strong function of thestar’s initial metal content. In metal-poor stars, more neutrons per seed nucleusare available, thus the heavier s-elements will be strongerenriched. The peak pro-duction of the heaviest s-elements Bi and Pb is reached at or below a tenth of thesolar metallicity, whereas at solar metallicity the elements like Sr, Y, and Zr (lights-elements with the neutron magic number 50) will be formed predominantly. Atintermediate metallicities, the heavy s-elements Ba, La, .. . , Eu (neutron magicnumber 82) reach their peak enhancement factors (see e.g. Fig. 12 of Busso et al.,1999).

A long standing discussion in the literature has been theneutron sourcethatdrives the s-process. The two suggested reactions are13C(α,n)16O and22Ne(α,n)25Mg. The originally suggested neutron source was22Ne, but general consensushas now been reached that this source is prevailing only in intermediate mass stars(& 3 M⊙, Garcıa-Hernandez et al., 2006), whereas13C is the dominant source inlow mass stars (≈ 1.5 M⊙, Lambert et al., 1995; Abia et al., 2001).22Ne is indeedabundant in the inter-shell region. However, the temperature of 300 million Kelvinrequired for the reaction22Ne(α,n)25Mg is reached only in intermediate mass stars.The “problem” with the13C-source simply is that protons are required in the inter-shell region to abundantly produce13C, but they are abundant only in and abovethe H-burning shell. It is now believed that, during the 3DUPepisode, protons aremixed down from the convective envelope into the inter-shell region to produce13C from the abundant12C (with β+-unstable13N as intermediate nucleus). Thelayer enriched in13C is called the13C-pocket(grey bars in Fig. 1.4). In earliermodels it was assumed that the13C only reacts in the convection zone created bythe thermal pulse. However, Straniero et al. (1997) realised that13C is also burnedunder radiative conditions in the quiescent evolution between two TPs. The nextconvective TP then engulfs the s-elements produced by the neutrons released fromthe reaction13C(α,n)16O and mixes them to layers where they can be reached bythe subsequent 3DUP event. Indeed, the22Ne-source may be very briefly (a fewyears!) ignited also in low mass stars at the base of the convective thermal pulse.

Note here that still many uncertainties are involved in the modelling of thedescribed processes. The size and density profile of the13C-pocket is not a resultof self-consistent calculations, but is rather a parameterin most of the currentmodels. Also, the precise physical mechanism responsible for building the13C-pocket is unclear.


1.3.3 Other elements produced on the AGB: Lithium and Flu-orine

We want to briefly discuss other interesting elements and their production pro-cesses on the AGB.

Besides the well established mixing events of the 3DUP,extra mixingpro-cesses may occur on the AGB. These processes lead to the production of lithium(see Chapter 3). Extra mixing is well established for RGB stars, at least from theobservational point of view (Gilroy & Brown, 1991; Charbonnel & Do Nascimi-ento, 1998), but relatively unexplored for AGB stars.

Li is destroyed during most of the evolutionary stages of a star, since even atlow temperatures (3×106 K) it captures protons to form4He (Bodenheimer, 1965).For instance, the sun has reduced its Li content by a factor of160 with respect toits initial (meteoritic) value by burning Li in the outer convective layers. Due toits fragility, lithium is an important diagnostic tool for stellar evolution (Rebolo,1991), but also has a high significance in the determination of cosmological pa-rameters (Spite & Spite, 1982; Korn et al., 2006).

Under certain circumstances, however, Li can be produced rather than de-stroyed by stars via the so-called Cameron-Fowler or7Be-transport mechanism(Cameron & Fowler, 1971). The reaction writes as3He(α,γ)7Be(e−,ν)7Li. 7Be isproduced at high temperatures deep inside the star, e.g. in the H-burning shell.If it captures an electron in this high temperature environment, the resulting7Liwill be quickly destroyed again. The clue of the Cameron-Fowler mechanism issome kind of mass circulation that transports7Be to layers of low temperaturesquick enough before it turns into7Li. In low mass AGB stars this mass circulationis usually hampered by a thin zone of radiative energy transport between the H-burning shell and the convective envelope. Some sort of extra mixing mechanism(which is not described by the classical convection criterion) may overcome thisbarrier. An observational hint for Li production by extra mixing (called “CoolBottom Processing”) in Galactic bulge AGB stars is presented in Chapter 3.

Li is naturally produced in high mass AGB stars (M & 3 M⊙) without theneed for extra mixing. In such stars, no radiative layer is present between theH-burning shell and the convective envelope. Another way ofthinking is thatthe bottom of the convective envelope reaches into the top ofthe H-burning shellwith temperatures close to 100 million K. This circumstanceis commonly named“Hot Bottom Burning” (HBB), but “Hot Bottom Convective Envelope” and “Con-vective Envelope Burning” are also in use. HBB has first been identified by Iben(1973). First observational evidences date back to Smith & Lambert (1989, 1990),later confirmed to be in agreement with HBB models (Smith et al., 1995). Most re-cently, Garcıa-Hernandez et al. (2007) measured Li abundances in massive Galac-tic AGB stars. In contrast to the Magellanic Cloud (MC) objects (Smith et al.,


1995), the Galactic Li-rich stars were not found to be enriched in s-elements. Thismight reflect a metallicity effect, but the precise reasons are still very unclear.

Other types of evolved stars with considerable (super-solar) Li abundancenot fulfilling the criteria for HBB are known in the literature. Most of these areK-type RGB-bump stars, for which a “Li-flash” has been suggested (Palacios etal., 2001). Objects of this type are presented in de la Reza etal. (1997). A Li-richred giant (probably RGB) has been reported by Smith et al. (1999). Only a fewlow luminosity S-type (Smith et al., 1995; Van Eck et al., 1998) and C-type (Abiaet al., 1991) Li-rich AGB stars are known.

An additional crucial effect of HBB is the fact that a C-rich star can be turnedinto an O-rich star again (or even prevent the star from becoming C-rich at all),since C is burnt into N in the envelope and its abundance is decreased again belowthat of O (Frost & Lattanzio, 1995). Thus, massive AGB stars are also significantcontributors to the N content of their home galaxy. For a recent observational con-firmation see McSaveney et al. (2007). Also note here that AGBstars with HBBdo not follow the core mass-luminosity relation (see Section 1.2.2) established forlow mass stars because they are lacking the radiative zone between the H-burningshell and the convective envelope. They can reach much higher luminosities thanpredicted by these relations as unprocessed material is continuously mixed intothe burning zone.

Another interesting element thought to be produced in AGB stars is Fluo-rine. The reason for the attention to this element is probably its elusiveness. Nouseful atomic absorption lines can be found in cool stars. Thus, no informationon F outside the solar system could be collected until Spinrad et al. (1971) firstdetected lines of the HF molecule inαOri. Up to date, the most elaborate work onF from the observational side is the one from Jorissen et al. (1992). They showedthrough the correlation with the abundance of carbon that AGB stars are indeedproducers of F. Theoretical works with quantitative estimates of F production inAGB stars can be found in Forestini et al. (1992), Mowlavi et al. (1996), Mowlaviet al. (1998), Karakas (2003), and Lugaro et al. (2004). These theoretical investi-gations in general show that the production of F on the AGB is astrong functionof mass. In low mass AGB stars, the F abundance is practicallyunaltered on theAGB. The peak F production occurs at stellar masses around 3 M⊙, depending onmetallicity. In these stars, the surface F abundance is predicted to be enhancedby 0.7 to 1.5 dex compared to the solar value. At still higher masses the F pro-duction decreases again, turning into adestructionfor masses& 5 M⊙ because ofthe increasing temperature at the base of the convective envelope (i.e. stars withHBB). In such stars, the behaviour of F is closely related to that of Li (Karakas,2003). The reaction chains leading to the formation of19F, the only stable isotopeof F, are too complex and lengthy to be reproduced here. We refer to the workby Forestini et al. (1992) for a discussion of the relevant reactions. The reaction

1.4. ATMOSPHERES OF AGB STARS AND MODELS THEREOF 19

chains involve the creation of15N, the lesser abundant isotope of N. The final stepis always15N(α,p)19F. The prevailing reaction destroying19F in the He-intershellis 19F(α,p)22Ne. In Chapter 5 we present observations of the F content of a Galac-tic bulge AGB star.

1.4 Atmospheres of AGB stars and models thereof

Since they are the interface between the processes deep inside the star and the out-side world, atmospheres need to be understood in order to interpret the spectra ofAGB stars. We therefore discuss atmospheres and models thereof in this Section.

AGB atmosphere models have been described in Aringer (2000), GautschyR. (2001), and Nowotny (2005). A good reference for the general description ofAGB atmosphere models is Chapter 4 of Habing & Olofsson (2004). The presentthesis uses model atmospheres previously developed among others by the worksjust mentioned to learn more about nucleosynthetic and mixing processes in theinterior of AGB stars.

The atmosphere of a star is generally defined as the region where most of its(electromagnetic) radiation originates from. AGB stellaratmospheres are charac-terised by their low densities, temperatures, and gravity,large extension, and dy-namic processes such as pulsations, shock fronts, dust formation, and mass loss.These properties lead to a number of difficulties encountered when one tries tomodel these atmospheres. Hence, the modelling of cool atmospheres still belongsto the most challenging tasks in stellar astrophysics.

The low temperatures provoke the formation of molecules which have tensof millions of absorption lines. The large opacity originating from the moleculesdetermines the structure of the whole atmosphere. Thus, anymodel calculationof a cool giant atmosphere has to include chemical reactionsamong atomic andmolecular species and complete opacity data. As has alreadybeen mentioned,the chemistry of the atmosphere may be either oxygen-rich orcarbon-rich. TheC/O ratio controls the main molecular species formed, hence the spectral locationof strong molecular absorption features, and influences thestructure of the atmo-sphere. Precise physical input data are required for modelling purposes, but theseare not available for all molecules (Aringer, 2005). The large extension of theatmospheres necessitates to take sphericity effects in the model construction (andin the radiative transfer for spectral synthesis) into account.

Neglecting dynamic time-dependent processes (pulsation,dust formation,mass loss) the atmosphere may be described by ahydrostaticmodel atmosphere.These models assume hydrostatic equilibrium, local thermodynamic equilibrium(LTE), and constancy of radiative plus convective flux. The program to calculatemodel atmospheres for this thesis (in the environment of theAGB working group


at the University of Vienna) is the MARCS (Model Atmospheresin a RadiativeConvective Scheme) code, with the original version described in Gustafsson et al.(1975). At present, a revised version of MARCS (Jørgensen etal., 1992) withspherical radiative transfer routines from Nordlund (1984), and new opacity datafrom the COMA program (Aringer, 2000) is used. MARCS treats convection ina local mixing-length theory and turbulent pressure is neglected. The radiativetransfer for spectral synthesis calculations is based on Windsteig et al. (1997).More details on the MARCS program can be found in Loidl (1997)and Aringer(2000). The spectral synthesis has recently been improved by Gorfer (2005).

Other codes for hydrostatic model atmospheres exist as well, for cool starsin particular the PHOENIX code (Hauschildt et al., 2003). Chapter 4 is devotedto a comparison of spectra from the MARCS and PHOENIX codes with observedspectra of cool stars at high resolution, and the inconsistencies found.

The hydrostatic approximation is quite successful in describing atmospheresof solar-type main sequence stars, and giants of spectral type K to early M withno or only mild pulsation. The situation changes, however, as soon as the atmo-sphere starts to pulsate strongly in late-type giants. Dynamic processes pose bigproblems for modelling since they render the simplifying assumptions of hydro-dynamic equilibrium and (likely) chemical equilibrium invalid. As an example,Aringer et al. (2002) identified strong H2O absorption bands in the IR of Mira vari-ables that cannot be satisfactorily reproduced by hydrostatic models. Of course,also kinematic effects cannot be described by hydrostatic models (Lebzelter etal., 1998; Nowotny et al., 2005b). A time-dependent handling of hydrodynam-ics, dust formation, and mass loss is required to do so. Models that take theseinto account have been presented by e.g. Hofner et al. (1998). They treat gasand radiation as two interacting fluids. The set of partial differential equationswhich arises from the conservation laws of these components(including equationof continuity, equation of motion, internal energy equation for the gas, and zerothand first moment equations of the spheric radiative transfer) are solved, and LTEis assumed. The iteration is started with a hydrostatic model. Dust is added asa third component, and its time evolution is specified by relations of its nucle-ation, growth, size distribution, and evaporation. Currently, the dust formation iswell understood only for C-rich environments, but not for O-rich environments(Woitke, 2006; Hofner & Andersen, 2007). The pulsation is taken into account byvarying the inner boundary of the atmosphere sinusoidally with a periodP and avelocity amplitude∆uP (piston).

In the most recent generation of dynamic models (Hofner et al., 2003), theradiative transfer is treated frequency-dependent, i.e. non-grey. The cooling andheating of different atmospheric layers introduced by molecules was not consid-ered properly by the grey radiative transfer. With the improvement of non-greyradiative transfer, molecular features are much better reproduced than in the older

1.5. THE GALACTIC BULGE 21

models. In some models, choosing a piston velocity higher than a critical valueleads to the effective formation of dust and a dust-driven outflow may develop.Tests of the kinematic predictions of the models have been performed by Nowotnyet al. (2005b). Transitions of different vibrational states of the CO molecule havebeen used to trace different regions of the atmosphere for a detailed comparisonwith observations. This approach has been done from observational side alreadybefore to constrain the inner structure of AGB atmospheres (e.g. Hinkle et al.,1982). The models of Hofner et al. (2003) were found to qualitatively reproduceline profile variations over the pulsation cycle, but predicted velocities (pulsationaland outflow) are generally smaller than observed.

1.5 The Galactic bulge

The objects analysed in this thesis are AGB stars located in the Galactic bulge. Thebulge of a disc galaxy like our Milky Way galaxy is a central “swelling” of thedisc and constitutes one of the galaxy’s stellar components. It can be particularlywell observed in galaxies that are viewed edge-on. Because of our special positioninside the Milky Way galaxy, we can discern also the Galacticbulge when we lookinto the Earth’s night sky. Fig. 1.6 shows a wide-angle photograph of the centralparts of our Milky Way galaxy, including the Galactic bulge.Also visible in thisphotograph are large dust clouds obscuring our view to the Galactic centre, at leastin the visible spectral range.

The shape of the bulge is not simply an oblate oval. Rather it can be de-scribed by a triaxial ellipsoid with an axis ratio 1.0 : 0.6 : 0.4 (Rich, 1998). Em-bedded in the bulge a disk instability called the “bar” is located. There have beenattempts to measure the orientation of the bar: Groenewegen& Blommaert (2005)determined an angle of 43◦ with respect to the plane of the sky from the zero-point of the period-luminosity relation of bulge LPVs (predominantly Miras) as afunction of Galactic longitude. This is very close to the value of 45◦ reported byWhitelock (1992), and the value of 46◦ found by Sevenster (1999). Measurementsof the bar orientation based on other methods than AGB and related populationssomewhat deviate from that (Groenewegen & Blommaert, 2005).

AGB stars in the Galactic bulge have received considerable attention inthe past. Searches for LPVs in the outer bulge have been conducted by e.g.Plaut (1971) and Wesselink (1987). The identified variableshave been studied inmore depth amongst others by Ng (1994), Schultheis et al. (1998), and Schultheis(1998). For works which include IR data of bulge AGB stars, Blommaert (1992)and Groenewegen & Blommaert (2005) certainly have to be mentioned.

It is generally believed that the bulge formed as a separate component earlyin the history of the Galaxy and thus contains an old stellar population. Works


supporting this hypothesis are e.g. Zoccali et al. (2003) and Zoccali et al. (2006).AGB stars in the Galactic bulge, however, do not fit into this picture of an earlyand fast formation of the bulge. Different indicators like luminosity, pulsationperiod, and the occurrence of 3DUP suggest a much younger age. This point isdiscussed in more detail in Section 2.7.3. Other hypothesessuggest the formationof the bulge later on in the assembly history of the Galaxy as the result of secularevolution of the disk; this type of bulge is called a “pseudo bulge” (Kormendy &Kennicutt, 2004). While some works favour a single old age ofthe bulge (Zoccaliet al., 2003) and a chemical composition different from that of the disk (Zoccali etal., 2006), “partial” mixing between bulge and disk populations is a possible wayto reconcile both age estimates. The existence of a Galacticbar makes secularevolution at least plausible.

AGB stars in the Galactic bulge offer the advantage of much more preciselyknown distance, and hence luminosity, compared to their solar neighbourhood sib-lings. This may sound puzzling in the first moment, but the limited accuracy of themeasured distances of solar neighbourhood AGB stars simplyis a result of theirlarge diameter. Some of them are larger than the base line available to distancedetermination by astrometry (e.g. the HIPPARCOS satellite) which significantlyhampers a precise measurement. Distance determination of the Galactic bulge,however, rely on methods different from parallax measurement. The distanceto the Galactic centre (Reid, 1993; Eisenhauer et al., 2003)and to the Galacticbulge (Carney et al., 1995; McNamara et al., 2000; Groenewegen & Blommaert,2005) may essentially be set equal and indeed agree on a valueclose to 8.0 kpc.Disadvantages in the study of bulge AGB stars that have to be kept in mind aretheir geometrical depth scatter within the bulge and the foreground contamina-tion. Nevertheless, in the outer parts of the bulge the depthscatter and foregroundcontamination are significantly reduced compared to inner bulge regions.

Furthermore, the number of known AGB stars in the bulge is large. Thelarge number of potential targets at very similar distance and the higher accuracyon luminosity are the reasons why the research on 3DUP indicators has been ex-panded from earlier works on field AGB stars (Lebzelter & Hron, 1999, 2003) tothe bulge6. The results of this research are presented in Chapter 2.

6The distances of AGB stars in the Magellanic Clouds (MCs) areeven better known, and theirgeometrical depth scatter is negligible. Foreground contamination can be safely ignored, too.However, given the size of current telescopes, AGB stars in the MCs are too faint to be amenableto high-resolution spectroscopy in the blue spectral range.

1.5. THE GALACTIC BULGE 23

Figure 1.6: Wide-angle photograph of the central parts of our Milky Way galaxy showingthe Galactic bulge (H. H. Heyer, ESO, priv. comm., publishedin Madsen& Laustsen,1986). North is up and East is left. The central plane of the Milky Way is indicated bythe thin white line. The brightest star north of the Galacticplane is Antares (α Sco).The approximate location of the Palomar Groningen field no. 3, where the bulge starscomprising the sample studied in Chapers 2 and 3 are located,is indicated by the whiterectangle.


1.6 Why infrared astronomy?

The author has been involved in the CRyogenic Infra-Red Echelle Spectrograph(CRIRES) project, and Chapter 5 is based on data acquired with this instrument.Why is the IR interesting for AGB research?

AGB stars emit the largest fraction of their energy in the IR region of theelectromagnetic spectrum because of their low temperatures compared to mostother stars. The flux peaks somewhere around 1µm, and it remains high through-out the near IR (Wien’s law for the maximum of black-body emission reads2897.8 µm/T [K], and AGB stars have effective temperatures around 3000 K).Warm dust in a thick CSE may produce a second flux peak in the farIR, the so-called IR excess. Because of absorption in the Earth’s atmosphere, observationsfrom space are of high importance for the study of CSEs of AGB stars. IR satel-lites like IRAS and ISO in the past, Spitzer in the present, and Herschel and theJames Webb Space Telescope in the future contributed and will contribute a lot toour understanding of these objects.

Besides the maximum flux, the IR has a number of other advantages forthe study of AGB stars. First, as will also be discussed in Chapter 4, the densityof spectral lines decreases when going to longer wavelengths. While in the bluerange basically no continuum is discernible in the spectra of AGB stars, the sit-uation improves much when observing in the IR regime. Even equivalent widthsmay be defined there (Ryde et al., 2007, and Chapter 5), aidingthe determinationof stellar parameters and abundances. Unblended spectral lines are much morefrequent (although not the rule) in the IR. Finally, IR radiation suffers less frominterstellar extinction than optical light (In theK-band at 2.2µm the extinction isonly ∼ 1/10 of the visual extinction). Thus, AGB stars in regions of the Galaxyotherwise inaccessible can be studied in the IR.

These and other advantages described in Chapter 6 make clearthat a lotabout AGB stars can be learned from the analysis of the IR radiation emittedby them. An instrument to study the IR radiation of AGB stars is the CRIRESspectrograph recently put into operation at ESO’s Cerro Paranal Observatory inChile, cf. Chapter 6. The cryogenic temperature of the instrument allows for a lowthermal background radiation, and the echelle set-up ensures high through-put tomake also distant and faint giant stars amenable to high-resolution spectroscopy.These are the reasons why IR spectrographs like CRIRES pointinto the futureof AGB research and work on such an instrument is exciting fora scholar in thisfield.

Chapter 2

Technetium and the third dredge-upin Galactic bulge AGB stars

Most of the content of this Chapter has been published in Uttenthaler S., Hron J.,Lebzelter T., Busso M., Schultheis M. & Kaufl H. U., 2007, A&A463, 251.

2.1 Introduction

In recent years, considerable progress has been made with regard to models forthe 3DUP and nucleosynthesis on the TP-AGB (Busso et al., 1999; Lugaro etal., 2003, and references therein). The different evolution models agree qualita-tively in the sense that the 3DUP is more efficient for more massive convectiveenvelopes (e.g. Straniero et al., 1997) and for lower metallicities (e.g. Straniero etal., 2003). However, the quantitative results are still model-dependent (Lattanzio,2002; Lugaro et al., 2003), and grids of new models covering awider range of stel-lar parameters are scarce. In general, observed abundancesof s-process elementsagree with the model predictions, at least qualitatively. For instance, the metal-licity dependence of the 3DUP is supported by observations (Busso et al., 2001;Abia et al., 2002). Nevertheless, observations not compatible with the modelshave to be mentioned here. For instance, Deroo et al. (2005) report the RV Taurivariable V453 Oph to be enriched in s-elements, but not in carbon. Simultaneousenrichment in C and s-elements is what is expected from AGB nucleosynthesisfollowed by 3DUP. Masseron et al. (2006) identify the metal-poor star CS 30322-023 as a TP-AGB star. Also this object combines clear s-process enrichment anda lack of C enhancement. Note that both V453 Oph and CS 30322-023 are verymetal-poor ([Fe/H] = −2.2 and [Fe/H] = −3.5, respectively).

A first attempt to directly check the conditions for the onsetof 3DUP obser-vationally has been made by Lebzelter & Hron (1999). Important constraints onthe minimum (core) mass (and hence luminosity) for 3DUP and its efficiency also

25

26 CHAPTER 2. TECHNETIUM IN GALACTIC BULGE AGB STARS

Figure 2.1: Predicted abundances (relative to Ti) of Zr and Tc as a function of pulsenumber for 1.5 M⊙, Z = 0.018 (full line), 2.5 M⊙, Z = 0.008 (dash-dotted line) and3.0 M⊙, Z = 0.020 (dotted line) stars. The thin horizontal lines correspond to a roughestimate of the detection threshold. Exactly the thresholdabundance for Tc was usedfor the synthetic spectrum with Tc in the lower panel of Fig. 2.3. Taken from Goriely&Mowlavi (2000).

come from the observed luminosity function of carbon stars in the LMC (Costa& Frogel, 1996) and in the Galaxy (Guandalini et al., 2006), together with syn-thetic stellar evolution calculations (Groenewegen & de Jong, 1993; Marigo et al.,1996).

Technetium (Tc) is among the elements produced by the s-process, and ithas no stable isotopes. The isotope of Tc with the longest half-life time producedin the s-process is99Tc with τ1/2 = 2.1× 105 years. In the following discussion,we always refer to the isotope99Tc when Tc is mentioned. For more details onTc see Section 1.3.2. The short half-life time makes Tc a reliable indicator ofthe 3DUP, because any Tc we see in a star must have been produced during itsprevious evolution on the TP-AGB. As becomes evident from Fig. 2.1, Tc shouldbe detectable at the surface after only a few thermal pulses (Goriely & Mowlavi,2000). It should be noted at this point that the absence of Tc does not necessarilymean the absence of TPs but rather the absence of 3DUP for several TPs. Thiscould be caused by an initial mass on the TP-AGB that is too low, or by a mass-loss rate at the end of the AGB-evolution that is too high (e.g. Busso et al., 1992).

A number of studies have been published on observations of Tcin spectraof late type stars, starting from the first observation by Merrill (1952), throughinvestigations by Dominy & Wallerstein (1986), Wallerstein & Dominy (1988),Smith & Lambert (1988), Smith & Lambert (1990), and Vanture et al. (1991), tostudies on S-stars (Van Eck & Jorissen, 1999) and C-stars (Barnbaum & Morris,1993). Important studies of Tc in large samples of LPVs have been conducted by

2.1. INTRODUCTION 27

Figure 2.2: Colour-luminosity diagram for the M-type field AGB stars with good HIP-PARCOS parallax searched for Tc lines in their spectrum by Lebzelter& Hron (2003).Open symbols denote non detections, filled squares represent stars showing Tc, and opentriangles mark unclear cases (possible). The full line marks the approximate minimumluminosity of an AGB-star when 3DUP sets in. The dotted line shows the approximatemaximum luminosity at this stage. Taken from Lebzelter& Hron (2003).

Little-Marenin & Little (1979), Little et al. (1987), and Lebzelter & Hron (1999).Most recently, Lebzelter & Hron (2003) studied the Tc content of a sample

of luminosity-selected Galactic field AGB stars. A significant number of starsabove the luminosity limit for 3DUP, indicated by mixing models, were found tonot show Tc in their spectra (Fig. 2.2). This can be explainedby the fact that thesecond important parameter for 3DUP is the mass of the envelope. It is suspectedthat the absence of Tc in a significant fraction of long-period Miras is due to areduction of the envelope mass below the critical limit by mass loss and/or dueto a low initial mass of the star. Due to the uncertainties in distance (based onHIPPARCOS parallaxes) of field stars, no definite conclusions could be drawn.

A sample of targets with more accurate distances is requiredto improvethe situation. Given the current accuracy of the distance measurements of AGBstars and the low flux in the blue spectral region of these stars, the only availabletargets for such studies can be found in the Galactic bulge. The distance to thebulge (8 kpc) is known rather accurately, and the depth of thebulge is low enough,at least in the outer parts, to have a fairly low depth-induced scatter in brightness(+0.m5/−0.m6, Schultheis et al., 1998). Using ESO’s VLT, exposure timesare short


enough to execute observations of a statistically relevantsample in a reasonabletime. Additionally, the bulge population is expected to be more homogeneousthan the disk population, because the widely absent C-starsindicate that high-mass stars are no longer present in the bulge. We therefore chose to observebright AGB stars in the Palomar Groningen field no. 3 (PG3).

It should be noted, however, that AGB variables in the bulge do not have thesame average properties as their disk counterparts, especially the SR variables.These differences might be explained by a different age-metallicity relation anda different pulsation mode for the bulge SRVs compared to the field SRVs. Fordetails we refer to Schultheis et al. (1998), while the work presented here focuseson dredge-up indicators rather than pulsation properties.

2.2 Sample selection

The selection of the sample was limited to oxygen-rich LPVs in the PG3 field,which is centred 10◦ south of the Galactic centre and covers an area of 6.◦5 × 6.◦5on the sky (cf. Fig. 1.6). It is located in the outer bulge where interstellar ex-tinction is rather low and the depth of the bulge is small. ThePG3 field has beenstudied extensively in the past (Wesselink, 1987; Blommaert, 1992; Ng, 1994;Schultheis, 1998; Schultheis et al., 1998) and periods are known for a consider-able number of variable stars.

To avoid foreground or background objects, we constructed alog P K-magnitude diagram based on near-IR photometry acquired at the ESO 1 m tele-scope at La Silla (see Schultheis et al., 1998, and references therein) and addi-tional data from DENIS (Epchtein et al., 1997) for some stars. The periods weretaken from Wesselink (1987). A range of±1.m0 around the logP− K relation forthe Sgr I field from Glass et al. (1995) was allowed for the potential targets to ac-count for the depth of the bulge and the intrinsic scatter in brightness (partly onlysingle-epoch measurements available). Stars outside thisrange were consideredto be in the foreground or background. The targets were chosen to be brighterthan the RGB tip (8.m2 in K0 at the bulge distance, see Tiede et al., 1995; Omontet al., 1999) to sample the AGB upwards. The distribution waschosen to be aboutequal between SR and Mira variables. This procedure resulted in a preliminarytarget list for the WFI observations (see Section 2.4).

2.3. FORE- AND BACKGROUND CONTAMINATION 29

2.3 Fore- and background contamination

Foreground confusion is a serious problem when observing inthe direction of thebulge. The density of stars drops fairly rapidly behind the bulge, and a star wouldhave to be extremely bright to fall on the period-luminosityrelation. Thus, back-ground contamination can be considered as low, and we can restrict the discussionto foreground contamination.

Since LPVs obey period-luminosity relation(s), their distance can be in-ferred from their position in such a diagram with a certain accuracy. However, themembership of single stars in the disk cannot be excluded if no kinematic infor-mation (proper motion) is available. Close-by M dwarfs in the Galactic disk andstars ascending the RGB can be excluded from our sample sinceneither fulfils thevariability criteria of LPVs.

To estimate the possible foreground contamination, we usedthe Besanconmodel of population synthesis (Robin et al., 2003). As a representative field, wecalculated the population of the central square degree of the PG3 field located atb = −10◦ and l = 0◦ using the observed photometric ranges (apparentK mag-nitude, (J − K)0 colour) as criteria (the extinction towards the PG3 field is ratherlow, see Section 2.5). No criteria for the pulsation could beincluded, but starswith too low a bolometric magnitude were treated as non-variable. The result in-dicates foreground AGB contamination at a level of 2.4%, which gives on averageless than 1 star in a sample of 27, the final number of objects. Thus, most probablyour sample is not affected by serious foreground contamination.

2.4 Observations

From the preliminary target list, 27 objects were selected for the UVES observa-tions. Details of this high-resolution optical spectrograph can be found in Dekkeret al. (2000). Pulsation phases of the targets were roughly estimated from pre-cedingB-band Wide Field Imager (WFI) observations obtained at the ESO/MPG2.2m telescope during two runs in April and May 2000 in service mode. Thesemeasurements were used for the final sample selection in an attempt to only ob-serve targets with their maximum brightness close to the time of the UVES obser-vations. The final object selection was also strongly drivenby the apparent targetbrightness at the time of the UVES observations in order to achieve the maximumsignal-to-noise (SNR) possible. Table 2.1 lists some basiccharacteristics of the fi-nal targets. In addition to the bulge objects, a few field AGB stars that have partlybeen checked for their content of Tc previously (see Lebzelter & Hron, 2003, andreferences therein) were observed.

The observations with UVES at ESO’s Very Large Telescope (VLT), CerroParanal/Chile, were carried out by Dr. Josef Hron between July 6 and July 9, 2000.


Table 2.1: Basic characteristics of the targets in our sample.

Name RA Dec Period [d] J0 [mag] K0 [mag] RV [km s−1] Tc?M45 18 12 48.5 -33 19 27 271.02 8.10 6.65 +19.8 noM100 18 13 38.5 -36 40 03 298.7 7.66 6.37 −37.3 noM143 18 14 13.6 -32 36 58 204.19 9.21 7.96 +17.6 noM195 18 15 07.7 -33 09 22 216.59 8.79 7.58 −142.8 noM277 18 16 15.4 -31 42 49 263.23 8.43 7.11 −34.5 noM315 18 16 45.0 -32 40 01 326.8 7.91 6.54 −61.9 noM331 18 16 57.6 -32 06 29 311.07 8.06 6.60 −31.8 noM626 18 21 32.5 -36 07 35 298.48 8.45 7.19 −67.7 yesM794 18 24 28.0 -32 30 51 303.54 7.39 6.04 −51.0 noM1147 18 33 06.2 -36 22 27 395.63 7.27 5.77 +1.0 yesM1179 18 33 54.7 -35 01 19 274.51 8.56 7.20 +61.8 noM1287 18 36 44.5 -32 25 43 312.5 7.95 6.64 +229.4 noM1313 18 37 35.5 -34 12 27 378.7 7.71 6.24 +14.1 noM1347 18 38 45.7 -34 33 28 426.6 7.47 5.99 +60.5 yesS70 18 13 05.6 -32 23 41 166.52 8.44 7.15 −77.2 noS328 18 16 56.2 -33 53 24 161.3 8.95 7.75 −117.9 noS639 18 21 42.3 -35 03 08 167.3 8.71 7.45 −88.7 noS719 18 23 18.4 -36 05 05 279.77 7.91 6.61 +69.4 noS942 18 28 09.0 -36 31 26 338.0 7.89 6.55 −77.8 yesS1002 18 29 22.8 -31 44 16 194.23 8.30 7.08 +33.0 noS1008 18 29 34.1 -34 08 27 232.14 7.97 6.72 −39.0 noS1059 18 30 42.8 -36 00 36 144.1 8.92 7.69 +18.0 noS1176 18 33 43.8 -31 27 35 184.1 8.27 6.94 +56.1 noS1204 18 34 38.8 -34 00 08 197.0 8.64 7.31 +236.5 noS1470 18 42 31.7 -35 59 28 184.08 8.55 7.34 −37.7 noS1517 18 27 19.1 -32 06 33 188.8 8.94 7.68 +80.2 noS1991 18 15 31.4 -31 58 40 124.7 9.17 8.02 −102.1 no

2.5. SAMPLE CHARACTERISTICS 31

The setting was chosen in order to cover the blue (central wavelength 4370 Å) andred (central wavelength 8600 Å) arm of the spectrometer simultaneously. Theobserved wavelength ranges thus were approximately 3770− 4900 Å (blue arm),6670− 8470 Å (red lower arm), and 8650− 10500 Å (red upper arm). With theblue arm, several resonance lines of neutral Tc were covered, among them thelines at 4238.19, 4262.27, and 4297.06 Å (wavelength in air,hereafter referredto as the “classical” lines). The slit width of the spectrograph was set to 0.′′7,which resulted in a resolution ofλ/∆λ � 50 000. The spectra were taken in the1× 2 binning mode. Cumulative exposure times ranged from 600 to7200 s, with3600 s as a typical value. All stars observed during the first night were observedagain on the second or third night because the exposure timeschosen on the firstnight were not sufficient.

The spectra were reduced with the ESO-provided pipeline written inMIDAS, version 2.1.0. For the spectra in the blue arm, “optimal” extraction wasused during the reduction process, whereas “average” extraction was used for thered arm. This procedure is recommended by the pipeline manual to optimise theSNR of the spectra. In optimal extraction, the pipeline performs a Gaussian fitto the signal profile in the spatial direction; the SNR is thencomputed from thedeviation of the profile from this fit.

The achieved SNR of the UVES spectra varies strongly with wavelength.For the regions around the Tc lines, the SNR provided by the UVES pipeline liesbetween 5 and 40 with the majority of the stars having an SNR of15 or better. Thefour stars with Tc (see Section 2.6) have an SNR of around 30 (M626, M1347,S942) and 5 (M1147), respectively. We demonstrate below that it is possible todecide whether Tc is present at such a low SNR.

2.5 Sample characteristics

Table 2.1 lists some basic characteristics of the observed targets. Column 1 liststhe stellar identifier, adopted from Wesselink (1987) whichcodes the variabilitytype: M stands for Mira variable, S for SR variable. The J2000coordinates incolumns 2 and 3 are the (rounded) positions as found in the 2MASS catalogue(Cutri et al., 2003).

The periods in column 4 are taken from Wesselink (1987). For two stars(S942 and M315), they give a low quality flag for the period determination. Usingtheir period measurement (176 and 173.6 d, respectively), these two objects wouldbe placed outside the range of the bulge in the logP− K diagram. We searchedthe literature and found a published period of 338 d for S942 based on photometricdata (Plaut, 1971). Note also that this star was classified asa Mira variable byPlaut (1971). For M315 a light curve from the MACHO survey could be extracted


(as a matter of fact, this star is the only one in our sample covered by the MACHOfields). Using the program PERIOD04 (Lenz & Breger, 2004) a robust period of326.8 d was determined.

The J0 and K0 magnitudes, found in columns 5 and 6 of Table 2.1, arethe de-reddened mean values of the ESO, DENIS, and 2MASS measurements.We thus have two to five measurements in both bands for our stars, with twomeasurements for only four of the objects (partly due to DENIS values with a badquality flag). The de-reddening was performed using the linear relation for thereddening in theBJ-band as a function of Galactic latitude as given in Schultheiset al. (1998). To translate this into the extinction in theJ- andK-bands, we usedthe relationR= AV/E(B− V) with R= 3.2 and the reddening law of Glass &Schultheis (2003). This results in an extinction of around 0.m1 in J and a few 0.m01in K.

To cross check our approach we also determined the extinction in K forthe respective object positions using the RGB fitting method, taking the RGB of47 Tuc as reference (following a suggestion by Messineo et al., 2005; Dutra et al.,2003). We extracted all objects 4′ around the target position from the 2MASS cat-alogue and constructed aKS versusJ − KS diagram. The computed shift relativeto the reference RGB resulted in a small (few 0.m01) or even negative extinctionvalue. This proves that there is no strong, patchy absorption in the direction ofany one of the sample stars, but it also proves that this method is too insensitive inthe outer bulge to reliably determine the extinction.

Note that five stars in our sample are redder than (J − K)0 = 1.4, a com-monly used limit to separate O-rich from C-rich AGB stars (Battinelli et al., 2007).However, we can confirm with our spectra that these stars are O-rich.

The radial velocities in column 7 of Table 2.1 were determined from theUVES spectra using a cross correlation technique with a synthetic spectrum as atemplate. For each of the blue, red lower, and red upper arm wavelength ranges, aregion of around 50 Å was used for the correlation. All three regions were chosento avoid very broad absorption as well as emission lines. Forthe respective regionin the red lower arm, the TiO band head at 7054 Å was covered, since this sharpfeature leads to a very accurate velocity measurement. The scatter of the derivedradial velocities from the three wavelength regions is of the order of 1 km s−1.

Taking a search radius of 30′′, a corresponding IRAS source could be foundfor eight of the sample stars (see also Blommaert, 1992). Theidentification waschecked using the 2MASSK-band images. Where available, the flux from theIRAS Faint Source Catalogue (Moshir et al., 1989) was taken;otherwise, theIRAS Catalogue of Point Sources (Joint IRAS Science W.G., 1994) entry wastaken, since the relative flux uncertainty quoted is lower inthe former. The IRAS-coloursK0 − [12] and [12]− [25] are summarised in Table 2.2. Note that colourswere not calculated using flux ratios but rather zero-point magnitudes for each

2.6. TC DETECTION 33

Table 2.2: IRAS colours of the objects that could be identified either inthe IRAS FaintSource Catalogue (Moshir et al., 1989) or in the IRAS Point Source Catalogue (JointIRAS Science W.G., 1994).

Name IRAS ident. K0 − [12] [12] − [25]M100 18102-3640 2.49±0.26 1.63±0.23M315 18134-3241 2.10±0.24 (1.78)M331 18136-3207 2.09±0.23 (1.92)M1147 18297-3624 2.37±0.10 0.64±0.15M1179 18305-3503 3.32±0.30 0.92±0.39M1313 18342-3415 2.37±0.19 0.93±0.26M1347 18354-3436 2.11±0.16 0.77±0.18S1204 18313-3402 2.50±0.12 (1.96)

filter. Zero points are 28.3 Jy in [12] and 6.73 Jy in [25] (Joint IRAS ScienceW.G., 1988). The errors are based on the relative flux uncertainty for the [12] and[25] flux as given in the respective catalogue and on the error-bar in K used inFig. 2.6. The respective colour value is quoted in brackets if a flux with qualityflag lower than 2 is involved, and no error is given for these cases.

The two stars with Tc in this small sample are the ones with thelongestpulsation period. They have the bluest IRAS [12]− [25] colour, but are otherwiseinconspicuous. From Fig. 21 of Whitelock et al. (1994) and using theK0 − [12]colour, we can estimate the mass loss of the IRAS sources in our sample to be inthe range−6.8 . log(M/M⊙ yr−1) . −6.0. Selecting optically bright targets forspectroscopy naturally avoids highly obscured (i.e. high mass loss) objects. Wetherefore assume that the “Tc yes” stars do not have a considerably higher massloss and intrinsic reddening than do the other stars in our sample.

2.6 Tc detection

To determine whether or not a star shows Tc, we first inspectedthe spectra visu-ally around the classical Tc lines together with synthetic spectra (Fig. 2.3). Thesynthetic spectra are based on the MARCS hydrostatic atmospheric models (seeSection 1.4 for more details). Atomic line wavelengths for the spectral synthesiswere taken from the VALD data base (Kupka et al., 1999)1. For Tc, theg f-valuesof Bozman et al. (1968) were used. The synthetic spectra wereconvolved witha Gaussian to reduce them to a resolution of 50 000, matching the resolution of

1As it seems not to be documented elsewhere, we note that the wavelengths of VALD are vacuumvalues below 2000 Å, for longer wavelengths they are standard atmosphere values!


0.00.5

1.0

1.5M626

0.00.5

1.0

1.5M1347

0.00.5

1.0

1.5

Flu

x (a

.u.) S942

0.00.5

1.0

1.5S719 (no Tc)

4236 4237 4238 42390.00.5

1.0

1.5

4261 4262 4263 4264Wavelength (A), in air

4296 4297 4298 4299

Figure 2.3: Regions around the three classical lines of neutral technetium covered bythe UVES spectra. The three upper panels show the stars with Tc detection and highsignal-to-noise ratio, the fourth panel shows a star without Tc. The central wavelengthsof the Tc lines are marked by the dotted vertical lines. The synthetic spectra with andwithout Tc in the lower panel are based on a hydrostatic MARCSatmospheric modelwith Teff = 3400 K, [Fe/H] = −0.5, logg = 0.0, one solar mass, solar C/O ratio, and amicro-turbulent velocity ofξ = 2.5km s−1. The spectrum with Tc was calculated with aTc abundance oflog(A(Tc)/A(H)) + 12.0 = 0.0 (cf. Fig. 2.1). The residual line at theposition of the 4297 Å Tc line in the spectrum calculated without Tc is due to chromium.All spectra are normalised so that the mean over the respective plotted region is 1.0.

the observed spectra. No additional macro-turbulence was assumed. This as-sumption was checked by determining the FWHM of a Gaussian fitto a selectionof a few strong, seemingly unblended lines of Fe, V, Ti, and Crin one of theobserved spectra with high SNR and the generic synthetic spectrum (see below).The assumption of zero macro-turbulence turned out to be acceptable, because theline-widths were never broader by more than 1.2 km s−1 in the observed spectrumcompared to the model spectrum.

On visual inspection of the extracted 1D spectra, three stars were identifieddisplaying Tc lines. In Fig. 2.3 we show sections of the observed spectra aroundthe classical Tc lines of these stars and of one star without Tc. In the lowest panel,


two synthetic spectra calculated with and without Tc, respectively, are shown. Thesynthetic spectra are based on a MARCS atmospheric model with Teff = 3400 K,[Fe/H] = −0.5, logg = 0.0, one solar mass, solar C/O ratio, and a micro-turbulentvelocity ofξ = 2.5 km s−1. The atmospheric parameters are not meant as a fit to thereal objects but rather are the result of an “educated guess”. The spectrum with Tcwas calculated assuming a Tc abundance of log(A(Tc)/A(H)) + 12.0 = 0.0 (cf.Fig. 2.1). According to Schatz (1983), the equilibrium Tc abundance resultingfrom the s-process is 0.37 on this scale.

Admittedly, the model spectra do not fit the observed spectravery well asthe lines seem to be much more pronounced in the model spectrathan what isobserved. Hence, we do not over-plot them on the observed spectra but plotthem separately in the lower panel of Fig. 2.3. The reason forthis discrepancyis not entirely clear. Reducing the metallicity for the model spectra calculation to[Fe/H] = -1.5 results in comparable line strengths. Such low metallicity is unre-alistic for stars of an inferred age of 3 Gyr and estimates that place the PG3 fieldslightly above the LMC in metallicity (Schultheis et al., 1998). Also, a highertemperature of the sample stars does not serve as an explanation, since in this caseno agreement in the strength of the TiO band heads could be found, and theJ − Kcolours are incompatible with a considerably higher temperature. Various authors(e.g. Merrill et al., 1962; Dominy & Wallerstein, 1986) reported on a similar phe-nomenon observed in field Miras and named – in the absence of a clear physicalexplanation – “line weakening”. This effect is apparently not accounted for in thehydrostatic model atmospheres used here. We were curious about the poor fit andperformed a comparison with spectra based on the PHOENIX atmospheric code,see Chapter 4.

In Fig. 2.3, the three stars classified as containing Tc by visual inspectionclearly show the Tc lines. At the position of the 4297 Å Tc linea somewhatweaker line appears also in the stars that were classified as not having Tc (lowerpanel). This line is caused by chromium (Little-Marenin & Little, 1979). In thethree stars identified to show the classical Tc lines by visual inspection, the Tclines at 3984.97, 4031.63, 4049.11, and 4095.67 Å measured by Bozman et al.(1968) and listed in the NIST atomic line database (http://physics.nist.gov/cgi-bin/AtData/lines form) are also clearly visible, whereas they are absent in theother stars. Plots of these lines are shown in Fig. 2.4.

For a more quantitative determination of the presence of Tc,we defined fluxratios between the Tc line centre and a pseudo-continuum point close to the lineposition. This continuum point was selected to be free of anyvisible absorptionfeatures in all observed spectra with good SNR, and in representative syntheticspectra. In a plot of this ratio versus the respective ratio for another Tc line, allstars that were identified to have Tc by visual inspection clearly separate fromthe other stars. This was done for several pairs of Tc lines, always giving the


0.0

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.u.)

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3983 3984 3985 3986 3987

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4030 4031 4032 4033Wavelength (A), in air

4047 4048 4049 4050 4051

4094 4095 4096 4097

Figure 2.4: Like Fig. 2.3, but for the subordinate lines of Tc at 3984.97,4031.63, 4049.11,and 4095.67 Å. No synthetic spectra were calculated for these lines.

same qualitative result. In Fig. 2.5 we show this ratio for the lines at 4238 and4262 Å, as these appear to be the strongest and least blended lines. The errorbars on the flux ratios were estimated by adding random noise with the magnitudeof the inverse SNR that was provided by the pipeline to the observed spectrum.The standard deviation in the flux ratio derived from 100 suchrealisations of thespectrum gives the error bar. M1147, a star not suspected of showing Tc based onthe visual inspection, separates from the compact group of “Tc no” stars as well,although not so obviously. Although this star is the brightest one in the sample inthe K-band, its flux in the blue spectral region is so low that the SNR per pixelaround the Tc lines is as low as 5 after one hour of integration. Taking the fluxratios of the other identified Tc lines and the error bars fromour simulation intoaccount, this star has to be classified as “Tc yes”, maybe witha somewhat reducedTc abundance with respect to the other “Tc yes” stars. For thefew other stars withlow SNR spectra, the occurrence of Tc can be definitively excluded based on theseflux ratios. We also include the flux ratio of the synthetic spectra shown in Fig. 2.3in this diagram.

The Tc-rich stars are among the coolest and longest-period objects in oursample; thus, we can exclude the possibility that any noteworthy Tc abundance


0.5 1.0 1.5 2.0 2.5Continuum/line ratio Tc 4238

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ontin

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/line

rat

io T

c 42

62

M626

M1147

M1347S942

VirER

HorR

Figure 2.5: Continuum-to-line flux ratios for the Tc lines at 4238 Å and 4262 Å. For theformer, the flux between 4239.4− 4239.7 Å (continuum) was ratio-ed to the flux in therange 4238.0− 4238.3 Å (line), while for the latter the wavelength ranges were 4261.3− 4261.5 Å and 4262.1− 4262.3 Å, respectively (see also Fig. 2.3). Six to ten pixelsaretypically covered by these ranges. We include the field starsR Hor and ER Vir (analysedby Lebzelter& Hron, 2003) in this plot. Also the star M1147 separates quiteclearly fromthe compact group of stars without Tc. This star was not suspected to have Tc from thevisual inspection of its spectrum due to the low SNR. The filled diamond symbols representthe flux ratios derived from the synthetic spectra plotted inFig. 2.3.

could have been overlooked in the increasing density of the line forest. On theother hand, Tc has been detected in significantly hotter fieldstars (e.g.o1 Ori,Lebzelter & Hron, 1999). Thus we may safely assume that, within the temper-ature range of AGB stars, the detection probability is independent of the star’stemperature.

Besides Tc, the carbon isotopic ratio12C/13C is certainly useful as anotherindicator of 3DUP. It can be determined from CO lines presentespecially in theK-band. The advantage of Tc lines as a 3DUP indicator is their complete indepen-dence from the star’s chemical history due to the radioactive nature of Tc. Thiscertainly is not the case for the12C/13C ratio, since it is at least influenced by theinitial isotopic composition and by the effects of the 1DUP and, in higher mass


2.0 2.2 2.4 2.6 2.8log(P/day)

9

8

7

6

5

K0 (

mag

)

RGB limit

Figure 2.6: Period K-magnitude diagram for our sample of LPVs in the Galactic bulge.Red squares and blue triangles represent Mira and SR variables, respectively. The filledsymbols are stars with a positive Tc detection. The solid line is thelog P − K relationfrom Glass& Schultheis (2003).

stars, the 2DUP. Additionally, Tc gives evidence of a recents-process as well. Forcomparison, we obtained near-IR CRIRES and Phoenix spectra(see Chapter 6 andAppendix A) of a few sample stars to study the12C/13C ratio and its correlationto the presence of Tc. The analysis is still going on and results will be publishedlater.

2.7 Discussion

2.7.1 Membership in the bulge

As the basis for the discussion of the bulge membership of thesample stars, weshow a logP−K diagram in Fig. 2.6. The error-bar inK is the statistical standarddeviation of the mean.

We plot the relation from Glass & Schultheis (2003, sequence“C”) insteadof the relation from Glass et al. (1995) that was used for the sample selection. The

2.7. DISCUSSION 39

former is an improved version of the latter. Although Glass &Schultheis (2003)note that “a very few extra observations could change the slope”, the rather steepslope of Glass & Schultheis (2003), which is based on single-epoch observationsin K, fits our multi-epoch data (two to five measurements inK) quite well. Thedotted lines 0.m6 above and 0.m5 below sequence “C” mark the range in magnitudedue to the finite depth of the bulge (Schultheis et al., 1998).In Glass & Schultheis(2003), sequence “C” extends in the range 2.2 < logP < 2.7. In the absence ofan alternative relation for the shortest period stars, we plot this over the wholediagram. The dashed line gives the approximate upper limit of the RGB (Tiedeet al., 1995; Omont et al., 1999; Zoccali et al., 2003). Usingthis PL-relation, allstars can be considered to be located in the bulge, within theerror bars.

Groenewegen & Blommaert (2005) published a logP− K relation for bulgeAGB variables based on OGLE light curves, as well as on 2MASS and DENISdata. Since their linear regression to sequence “C” is significantly below the datapoints for logP > 2.5 (see their Fig. 3), we do not use their relation here. Un-fortunately, none of our sample stars is covered by the OGLE survey. Even usingthe relation of Groenewegen & Blommaert (2005) and adoptingthe same range inmagnitude for bulge stars as before, only one of the Tc-rich stars (M1147) wouldbe placed in the foreground. Thus, the conclusion that AGB stars in the bulge withrecent dredge-up are identified is not altered.

Apparently, the SRVs fall mainly above the logP − K relation in Fig. 2.6.As the PG3 SRVs are in the same pulsation mode as the Mira variables (Schultheiset al., 1998), this can be explained by a selection bias towards brighter, i.e. closer,SRVs, as stars on the far side of the bulge may fall below the chosen RGB limit.Detection and non-detection of Tc is marked in this diagram by filled and opensymbols, respectively.

The “Tc yes” star with the shortest period is M626 with a period slightlybelow 300 d. The two stars with the longest period in our sample (M1347 andM1147) both show Tc. This compares well with the findings of Lebzelter &Hron (2003) where the fraction of “Tc yes” among Mira variables increases abovea period of 300 d. Following the variability classification of Plaut (1971), onlyMiras are found to show Tc in their spectrum (we still keep theSRV symbol forS942 in the figures).

2.7.2 Third dredge-up luminosity limit

To assess theoretical predictions of the minimum luminosity required for 3DUPto occur, we constructed a colour-luminosity diagram shownin the upper panel ofFig. 2.7. The bolometric magnitudes were calculated from the K brightness anda bolometric correction based on (J − K) using the relation of Kerschbaum et al.(in preparation). In their work, Kerschbaum et al. use near-IR and IRAS photom-


etry of a large collection of field LPVs and integrated over the linearly connectedphotometric values. Rationing this bolometric magnitude to the apparentK mag-nitude leads to a relation for the bolometric correction inK independent of thedistance to the objects. The relation derived is

BCK = −0.446+ 4.761(J − K)0 − 1.601(J − K)20 ·

Their relation leads to bolometric magnitudes that are 0.m06 brighter on averagethan when using the relation of Whitelock et al. (2000). Furthermore, a distancemodulus of 14.m5 to the bulge was assumed (McNamara et al., 2000).

In Lebzelter & Hron (2003) the minimum luminosity required for 3DUPwas estimated. It was derived from the luminosity evolutionof a 1.5 M⊙ model atthe time when 3DUP sets in (Straniero et al., 1997). At solar metallicity, 1.5 M⊙is about the minimum initial mass required for a star to experience 3DUP onthe AGB. This minimum luminosity corresponds to a bolometric magnitude ofMbol = −3.m9. As can be seen, all stars with positive Tc detection clearly fall abovethis line, confirming the theoretically estimated luminosity limit for 3DUP.

The scatter in magnitude of our sample stars around the logP− K relationmay be for various reasons: incomplete light-curve coverage, geometrical deptheffects within the bulge, or a scatter in mass and metallicity. For the lower panel ofFig. 2.7 we assume the scatter to be solely depth-induced (the periods are knownwith a much higher precision than theK-magnitudes). To correct for this scatter,we subtract (or add) the difference between measuredK-magnitude and the periodK-magnitude relation of Glass & Schultheis (2003) from (or to) the bolometricmagnitude. In other words, we use the logP− K relation to calculate a distancemodulus for every single star (see Fig. 2.6). Applying this correction, the “Tc yes”stars are the brightest objects at a given (J − K)0 colour.

2.7.3 The mass and age of the Tc stars

From stellar evolution models (Straniero et al., 2003) one would expect a mini-mum initial mass limit of 1.4 (Z = Z⊙/5) to 1.5 M⊙ (Z = Z⊙) for a star to experi-ence 3DUP. This implies a limiting age of the “Tc yes” stars inour sample of 3 to4 Gyr.

Various age estimates of the bulge can be found in the literature. Schultheiset al. (1998) give an age range of 5 to 10 Gyr from their study ofAGB variablesin the PG3 field. Zoccali et al. (2003) obtained colour-magnitude diagrams in thevisual and near-IR range and favour a single age of 10 Gyr, although an age of5 Gyr cannot be completely excluded from their analysis (TheWFI field studiedby Zoccali et al. (2003) does not overlap with the PG3 field, but is situated slightlycloser to the Galactic plane). Groenewegen & Blommaert (2005) studied the Mirapopulation in the OGLE bulge fields and derive an age of 1− 3 Gyr. Also Zoccali

2.7. DISCUSSION 41

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Figure 2.7: Bolometric magnitude vs.(J − K)0 of the sample stars, with symbols the sameas in Fig. 2.6. In the upper panel, the luminosity is plotted as directly derived from thenear infrared photometry, whereas in the lower panel it is corrected for the depth-inducedscatter using Fig. 2.6. Note that in the lower panel the overlap in luminosity between SRVsand Miras is much reduced. The dotted horizontal line marks the minimum luminosity atthe stage where 3DUP sets in. Isochrones from Girardi et al. (2000) are also representedin solid and dashed lines (see legend). For both isochrones,the tip of the AGB is wellbelow the observed AGB tip. The thick line in the lower panel is a 1.5 M⊙ evolutionarymodel track from O. Straniero (priv. comm.).


et al. (2003) find a number of stars that are significantly brighter than the estimatedRGB tip but do not interpret this as a sign of an intermediate-age population.Studies of the inner part of the bulge (van Loon et al., 2003) and of the Galacticbar (Cole & Weinberg, 2002) have found signatures of an intermediate age (1 toseveral Gyr) population on top of the main old component.

An interesting age indicator may come from the period distribution of theMiras in our sample. As argued by Hughes & Wood (1990), the period distributionof Miras found in the LMC can be understood as a combination ofan intermediateand an old population among these variables. Short-period Miras (around 200 d)are thought to be older and more metal-poor than their long-period counterparts(Hron, 1991). As our sample also includes both short- and long-period Miras,we may suspect that the bulge contains stars of a considerable age range as ananalogy to the LMC and the Galactic field. Groenewegen & Blommaert (2005)also conclude from the period distribution of the Mira starsin the OGLE fieldsthat the long-period stars must originate from an intermediate-age population. Theage discrepancy between bulge AGB and other stellar types isat least known sinceIben & Renzini (1983), the analysis presented here adds another piece of evidenceto the puzzle.

In Fig. 2.7 we include two isochrones from Girardi et al. (2000) with twoage-metallicity combinations (see legend). The original (J − K) colours of Gi-rardi et al. (2000) do not reach values above 1.3 and thus do not bracket the ob-servational data properly. This is probably related to the fact that the colours werederived from hydrostatic model atmospheres, while most of the red luminous starsare strongly pulsating objects with dynamic atmospheres. Therefore we chose anobservational approach and combined the effective temperatures of Girardi et al.(2000) with a (J − K) vs. Teff calibration determined from interferometric dataand near-infrared photometry of field Mira variables (see Schultheis et al., 1998).With our calibration, the isochrones reach redder (J − K) colours, thus becominga more realistic description of the observations. The younger isochrone (5 Gyr)covers almost the whole observed (J − K) range. Nevertheless, both parametersets have their AGB tip at a luminosity fainter by one magnitude than what isobserved. The picture is not changed in the second version (lower panel) of thediagram. The extension to red colours illustrates the general difficulty of trans-forming the effective temperature of a static evolutionary model into colours of astrongly pulsating atmosphere, a systematic investigation of this point is desirable.

The problem of the tip luminosity is discussed in the following. The iso-chrone of 2.82 Gyr age of Girardi et al. (2000) has an AGB tip luminosity ofMbol = −4.m8. Even taking the luminosity variation during a thermal pulse cycle(see next paragraph) into account thus slightly underestimates the AGB tip lumi-nosity. This implies that models with large overshoot from the envelope, like theones of Girardi et al. (2000), lead to somewhat lower luminosities than what is

2.7. DISCUSSION 43

observed.In the lower panel of Fig. 2.7 (corrected for the depth scatter), we include

an evolutionary model track from O. Straniero (priv. comm.)as thick line. Themodel used here is similar to the ones presented in Stranieroet al. (1997), exceptthat mass loss is taken into account in the current model. Thesame (J − K) vs.Teff calibration as for the isochrones was used to include the model track into thisdiagram. The parameters of the model are as follows: initialmass 1.5 M⊙, metal-licity Z = 0.02 (Z⊙), helium fractionY = 0.28, and Reimers mass-loss parameterη = 0.5 (Reimers, 1975). The track covers only the very last inter-pulse evolutionof this model, excluding the short-term luminosity spikes at the TPs themselves(the luminosity in between the preceding TPs is only slightly lower). The trackspans about 60 000 years. The evolution runs from the lower left end to the upperright end of the track. In other words, the luminosity increases between two TPswhile the temperature drops, until the next TP “resets” the star back to low lumi-nosity and high temperature. The bolometric magnitude varies by 0.m75 betweentwo TPs, whereas the temperature varies only slightly between 3176 and 3112 K.

The luminosity of the evolutionary model track matches thatof the “Tc yes”stars quite closely, especially the tip luminosity. Only the range in (J − K) of theobserved stars is wider than that of the model track, either because the “Tc yes”stars span a wider range in temperature or because of the mentioned problemsinvolved in theTeff to (J − K) transformation. In the light of these results, it isnot surprising to find stars which are more luminous than the tip of the Girardiisochrones. All “Tc yes” stars are found there, suggesting that these stars areindeed the most evolved and most massive ones in our sample.

Besides the evolutionary track of Straniero, the interpolation formulae ofStraniero et al. (2003) were used for a comparison with the present data set. Withthese formulae, the luminosity and the temperature at half the time between twosuccessive TPs can be calculated. Very good agreement with the observationaldata could be found by using the same parameters as for the full model track.

Trusting in the nucleosynthesis and stellar evolution models alone, our re-sults would require that the bulge includes a population of stars with an age around3 Gyr. On the other hand, if the age estimates of Schultheis etal. (1998) and Zoc-cali et al. (2003) are correct, then dredge-up – according toour findings – wouldoccur at a minimum mass significantly lower than 1.4 M⊙. This would then implythat the maximum AGB luminosity predicted by the stellar evolution models likethe ones from Straniero et al. (2003) is too low.

Finally, in Fig. 2.8 we present anMbol − log P diagram of our sample stars.The distribution of the objects is very similar to the one in Fig. 2.6. The solid linesshow theoretical linear pulsation models from Wood & Sebo (1996) for masses of1 M⊙ (lower line) and 1.5 M⊙ (upper line) in fundamental mode pulsation. As forthe evolution models, masses around 1.5 M⊙ are required to fit the brighter, long-


2.0 2.2 2.4 2.6 2.8log(P/day)

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Figure 2.8: Bolometric magnitude versus period of the sample stars. Thesymbols are thesame as in the previous figures. The dotted horizontal line marks the minimum bolometricmagnitude at the stage where 3DUP sets in. The solid lines arerelations for a 1 M⊙(lower line) and a 1.5 M⊙ (upper line) model star pulsating in fundamental mode (Wood& Sebo, 1996).

period pulsators in the present sample. This supports the solution discussed abovethat there is a young, more massive population present in theouter bulge and thatthe predictions of mixing theories are correct. However, one has to be aware ofthat the pulsation models used here are linear models. For fitting theMbol − log Psequence of Miras, non-linear models would be more appropriate (Lebzelter &Wood, 2005; Olivier & Wood, 2005). Thus, the pulsation argument has to be seenwith some caution.

2.8 Conclusions and outlook

We have presented high-resolution UVES/VLT spectra and near-IR photometry ofbulge AGB variables, aiming to detect the third dredge-up indicator technetium.The bulge membership of these stars was discussed using a period K-magnitudediagram. In a sample of 27 stars, four were found to have Tc, giving the first directevidence of recent or ongoing third dredge-up in these stars. For the distinction

2.8. CONCLUSIONS AND OUTLOOK 45

between “Tc no” and “Tc yes” stars, we compared the observed spectra to syn-thetic ones around the “classical” Tc lines. A more precise distinction is possibleusing flux ratios between the Tc line flux and a pseudo-continuum flux. Using thismethod, even for very low SNR spectra (down to SNR= 5), a reliable distinctionof this kind can be made.

In a colour-luminosity diagram of the sample stars, all objects with Tcclearly fall above the theoretical third dredge-up limit ofMbol = −3.m9, in agree-ment with model predictions. Many stars above the theoretical luminosity limitfor third dredge-up do not show Tc. There have been suggestions that Tc coulddecay (even below the detection limit) if 3DUP does not occurfor several TPs(Busso et al., 1992; Lebzelter & Hron, 2003). One may speculate that the starM1147 has a reduced Tc abundance with respect to the other three “Tc yes” stars,although it is one of the brightest (and most evolved) objects in the present sample.It is possible that this star on the AGB tip has lost so much mass that the envelopeis no longer massive enough to drive dredge-up, and Tc has already decayed to alower abundance level.

The observed AGB tip luminosity is well reproduced by full evolutionarymodel tracks, assuming an initial mass of 1.5 M⊙ and a Reimers parameterisedmass loss. Isochrones assuming large overshoot from the convective envelope arefound to somewhat underestimate the AGB tip luminosity, although a younger ageof the population would reduce this discrepancy.

From the period distribution, the period-luminosity diagram, and the detec-tion of Tc as incontestable indicator for 3DUP, a mass of about 1.5 M⊙ is requiredfor at least some of the sample stars. This implies an upper age limit of around3 Gyr for these stars, consistent with other findings of an intermediate age popu-lation in the bulge (van Loon et al., 2003; Groenewegen & Blommaert, 2005). Incontrast, Zoccali et al. (2003) do not find any signatures of an intermediate agepopulation, but favour a single age of 10 Gyr. A solution to this disagreementcannot be given here and must await future work on the Galactic bulge.

Chapter 3

Low-mass lithium-rich AGB stars inthe Galactic bulge: evidence forCool Bottom Processing?

In this Chapter we present on the discovery of Li-rich, low mass M-type AGB starsin the Galactic bulge and discuss different mechanisms for the Li enrichment. Formore details on the behaviour of lithium in stars see Section1.3.3.

The content of this Chapter has been published in Uttenthaler S., LebzelterT., Palmerini S., Busso M., Aringer B. & Lederer M. T., 2007, A&A 471, L41.This paper has been selected as a high-light of the week in A&AVolume 471-2(August 4, 2007).

3.1 Analysis of the UVES spectra with respect to Li

Spectra of the present sample of O-rich (M-type) Galactic bulge AGB stars havebeen originally obtained for a search for the radioactive element technetium inthese stars, which is an indicator of recent or ongoing 3DUP.For the descriptionof the UVES observations and results from the analysis with respect to Tc, seeChapter 2. This Chapter focuses on the analysis of these spectra with respect tothe abundance of lithium.

Since we aim at a determination of the abundance of Li and not only itsoccurrence (unlike for Tc, see Chapter 2), we need to estimate the stellar param-eters in order to perform spectral synthesis calculations.To determine the stellarparameters of our stars for the abundance analysis, we calculated a small gridof hydrostatic MARCS model atmospheres (cf. Section 1.4). The grid coveredthe following stellar parameter space:Teff = 2600− 3600 K in steps of 100 K,logg = −0.5 and 0.0, [M/H] = −0.5, 0.0, and+0.2. Ti was enhanced by 0.2 dexin the models (McWilliam & Rich, 1994). Due to their rather limited effect on

47

48 CHAPTER 3. LITHIUM IN GALACTIC BULGE AGB STARS

Table 3.1: Sample stars with positive Li detection. The bolometric magnitude is correctedfor depth effects within the bulge. For the determination of the Mbol values and Tc contentssee Chapter 2.

Name Mbol P (days) logǫ(Li) ∆ logǫ(Li) Tc?M45 −4.53 271.02 2.0 0.5 noM794 −4.78 303.54 1.1 0.4 noM1147 −5.27 395.63 0.8 0.4 yesM1347 −5.43 426.60 0.8 0.4 yes

the spectra the mass and the C/O ratio were fixed to the values 1.0 M⊙ and 0.48,respectively. The micro-turbulent velocity was set to 3 km s−1.

Synthetic spectra based on these model atmospheres were calculated for thetwo wavelength ranges 668− 674 nm and 700− 710 nm, respectively. The firstpiece covers (besides the Li line) the TiOγ(1,0)Rc andγ(1,0)Rb band heads, thesecond piece covers the TiOγ(0,0)Ra andγ(0,0)Rb band heads. These band headsare rather sensitive toTeff. The synthetic spectra were convolved with a Gaussianto reduce the resolution to the value of the observed spectra(R = 50 000), and anadditional macro-turbulence of 4 km s−1 was added in the convolution.

A χ2 minimisation method over the mentioned spectral ranges wasappliedto find the main parameters of the sample stars. As comparisonbetween the twospectral regions used for the fit showed, the temperature yielding the best fit dif-fered substantially between the two regions in many of the observed stars. Onaverage, the temperature derived from the region around theLi-line was lower byabout 100 K than the temperature derived from the second wavelength range. Wesuspect the reason for this is an underestimation of the TiOγ(1,0)Rc andγ(1,0)Rbband head strength in the line list used (Schwenke, 1998). A similar problem hasbeen reported in Reiners (2005) for other band heads of TiO. Thus, it seems pos-sible that several TiO bands are incorrect in their strength, and a revision of thecurrent line list is desirable.

Spectral synthesis calculations were applied in order to identify stars whichshow signs of Li line absorption. For these calculations we chose the model yield-ing the lowestχ2 value in the spectral region around the Li line, despite the ob-vious discrepancy regarding the derived temperature. The reason for this is thatthe background TiO absorption around the Li line is thus modelled as well as pos-sible. The four stars with a positive Li detection could all be fitted with a singleatmospheric model. This model hasTeff = 3000 K, logg = 0.0, and [M/H] = 0.0.

We assessed the content of s-process elements in our sample stars by in-vestigating the strength of the ZrO band head at 462 nm with respect to the TiOγ(0,0)Ra band head at 705.6 nm. Also, atomic line strengths ofthe s-elements Sr,

3.2. DISCUSSION 49

Y, Zr, Ba, La, Ce, Nd, and Sm in the range 400− 460 nm were inspected. Only thepreviously identified Tc-rich stars showed an increased strength of these features.

3.2 Discussion

For four stars a non-negligible Li abundance has to be assumed in order to givesatisfying fits to the observed spectra. Their determined Liabundances and bolo-metric magnitudes (corrected for the bulge depth scatter, see Section 2.7.2) aresummarised in Table 3.1. The error on the Li abundance given in the fifth columnwas estimated by varying the temperature of the atmosphericmodel by±100 K.For the other stars, an upper limit to the Li abundance was estimated. For the hot-ter stars (∼ 3400 K, SR variables), this upper limit is around logǫ(Li) = 0.6, for thecooler stars (∼ 3000 K, Mira variables), it is around logǫ(Li) = 0.11. Actually, ex-cellent fits to the spectra of the Li-poor stars can be achieved by fully neglecting Liin the spectral synthesis. Fig. 3.1 shows the observed spectrum of M45, the mostLi-rich star in our sample, along with synthetic spectra with differing Li abun-dance. Similarly, Fig. 3.2 shows the observed spectrum of M1347 together withtwo synthetic spectra assuming differing Li abundances for the spectral synthesis(left and right panel, respectively). The observed minus synthetic flux stronglysuggests that this star (and the star M1147) contains a non-zero amount of Li inits atmosphere.

The first thing we note is that the bolometric magnitudes of the stars listedin Table 3.1 are considerably below the luminosity expectedfor Li-enrichmentdue to HBB. [In models with rather extreme convective overshoot, HBB may startalready at luminosities as low asMbol ≃ −5.m0 (Karakas, 2003), but Li-enrichmentbecomes observable only atMbol ≃ −6.m0 (Smith et al., 1995; Vanture et al.,2007)]. Regarding the bolometric magnitudes of these stars, and also age con-siderations of the Galactic bulge, the HBB scenario is very unlikely to account forthe observed Li abundances.

A few stars with Li enrichment andMbol > −6.m0 have been reported in theliterature. Smith et al. (1995) identify a low luminosity, S-type star with veryhigh Li abundance in the SMC (HV 1645). They state a bolometric magnitudeof −4.m68 for that star. Abia et al. (1991) derivesMbol = −5.m0 for the C-richstar WX Cyg. Three S-stars below the HBB limit, namely NO Aur,π1 Gru andHR Peg, are listed by Van Eck et al. (1998).

Another remarkable thing about M45 and M794 in our sample is the ab-sence of Tc-lines from their spectra. Both stars do not show any other signs of s-process enhancement either, while M1147 and M1347 do show Tcand s-process

1Throughout this Chapter, the Li abundance is given on the scale logǫ(Li) = logN(Li)/N(H) + 12.The solar photospheric Li abundance on this scale is logǫ(Li) = 1.1.


Figure 3.1: Observed spectrum of the most Li-rich sample star M45 aroundthe 671 nmLi line together with the synthetic spectrum (blue line) used for the Li abundance deter-mination, assuming Li abundances oflogǫ(Li) = 1.8, 2.0, and2.2.

enhancement. Among a sample of Galactic MS- and S-type starsVanture et al.(2007) found three groups of stars with respect to the Li and Tc abundance: thosewithout Tc and Li, interpreted as the result of mass transferfrom a more massivecompanion; those with Tc and Li, which are intermediate-mass stars producing Lithrough HBB; and those with Tc but no Li, which are thought to be AGB stars be-low the HBB mass limit. One star of their sample, V441 Cyg, shows no Tc but isenriched in Li. This star as well as the low luminosity S- and C-type stars with Lifound before were interpreted as due to Cool Bottom Processing (see Sect. 3.2.3).

M1147 and M1347 may belong to the second group defined by Vanture etal. (2007), i.e. Li enrichment by HBB. Nevertheless, their luminosities are slightlybelow the HBB limit. The stars M45 and M794 in our sample seem to be indeeda novelty, since they are the first AGB stars detected with a considerable Li over-abundance, but no indications for a third dredge-up. From their variability andtheir location in the bulge CMD (Fig. 3.4) both stars are certainly on the AGB.In the following we will discuss these two stars in the light of the various Li-enrichment scenarios.

3.2. DISCUSSION 51

Figure 3.2: Observed spectrum of the star M1347, together with two synthetic spectraassuming no Li (left panels) andlogǫ(Li) = 0.8 (right panels) for the spectral synthesis,respectively. In the lower panels, the observed minus synthetic flux is plotted. The negativeresidual at the position of the Li line doublet (vertical dashed lines) can only be accountedfor by assuming a non-zero Li abundance. Such a residual is absent for the Li-poor stars.This demonstrates that a moderate Li abundance can only be detected using spectralsynthesis techniques.

3.2.1 Enrichment by massive binary companion

The Li-rich stars might have received Li-rich matter by windaccretion from aclose massive (M & 4 M⊙) binary companion which experienced HBB and mightbe a WD now. One might think that a possible mass transfer would have left itssignature not only in the presence of Li, but also in the abundance of s-process el-ements, since such a massive star can be expected to have undergone s-processingand 3DUP during its TP-AGB phase. This mass transfer would not have shownup in our search for Tc due to the short life time of this element. As men-tioned above, our Li-only stars show also no enhancement in the stable s-processelements. However, Li enrichment is expected to occur in early AGB phases(Karakas, 2003), when s-elements might still be absent. Moreover, intermedi-ate mass stars might not become very rich in s-elements, as their prevailing22Nesource never builds up large neutron exposures, and the massive envelope dilutes


extensively any new material dredged-up. Indeed, Garcıa-Hernandez et al. (2007)did not find enhanced ZrO band and atomic ZrI, NdII, and BaII line strengths intheir sample of massive Galactic Li-rich AGB stars, while Rbis enriched (Garcıa-Hernandez et al., 2006). This implies only a low s-process level in these stars. Incontrast, Smith et al. (1995) find a considerable level of s-process enrichment fortheir Li-rich AGB stars in the MCs. The difference in the behaviour of massiveAGB stars located in the MCs and in the Milky Way galaxy might be a metallicityeffect, but conclusive interpretation is not yet possible. It is not known how thebulge fits into this picture.

A possible WD companion may be detectable via an excess flux intheU-or B-band. MeanB- andR-band values for the two most Li-rich stars, M45 andM794, were found in the literature, but they did not turn out to be conspicuouslyblue in (B− R).

In conclusion, the massive binary companion hypothesis is not fully con-vincing, but cannot be ruled out on the basis of current observations.

3.2.2 Accretion of a (sub-)stellar companion

Siess & Livio (1999) investigated the response of the structure and abundances ofan AGB star to the accretion (“swallowing”) of a (sub-)stellar companion. Oneresult of their considerations is that the effect on the Li abundance might only bedetectable if a considerable mass (& 0.1 M⊙) is accreted to the envelope of theAGB star. Other expected effects of a brown dwarf accretion include the increaseof the mass loss rate and a spin-up of the envelope. These would be detectableas an IR excess and the rotational broadening of spectral lines, respectively. M45and M794, the two most Li-rich stars in our sample were not detected with IRAS,while M1147 and M1347 were. For the latter two, mass loss rates of the orderof 10−6.6 M⊙ yr−1 have been derived (cf. Section 2.5). Since these two stars arealso the brightest and longest period stars in our sample, this mass loss rate canbe expected due to normal evolution. Also, Siess & Livio (1999) estimate thefraction of stars with a low-mass companion which may be accreted during theevolution of the primary to 4− 8 percent. However, 15% of our small sample ofstars show Li. We conclude that the sub-stellar accretion scenario is unlikely toexplain the Li abundances observed in our sample stars.

3.2.3 Cool Bottom Processing

It is now known (see e.g. Kraft, 1994; Charbonnel, 2004) thatthe radiative layersbelow the convective envelope in evolved, low-mass red giants are the site of slowmixing phenomena, in addition to the convective dredge-up episodes. Such phe-nomena have been variously called “deep mixing”, or “extended mixing”, orCool

3.2. DISCUSSION 53

Bottom Processing(CBP), although this last name is relatively recent (Wasser-burg et al., 1995). The chemical stratification of a radiative layer hampers massmotions; hence, mixing can take place only after the H-burning shell has erasedany chemical discontinuity left by core H burning and by the 1DUP. When thisoccurs, the luminosity shows a bump, after which abundance changes related toextra-mixing begin to appear.

As to the physical origin of the extended mixing phenomena, very recentlya number of hypotheses have been presented, at least for RGB stars. Eggleton etal. (2006), on the basis of a 3D simulation, found that Rayleigh-Taylor instabili-ties below the convective envelope can develop due to the inversion of the meanmolecular weight gradient induced by3He burning. Alternatively, Charbonnel &Zahn (2007) suggested that the double-diffusive mechanism called “thermohalineinstability” should be at play. In principle, both these phenomena might occur alsoon the AGB, though detailed models have not been presented. Finally, Busso etal. (2007) explore the possibility that circulation of partially processed matter canbe accounted for by magnetic buoyancy induced by a stellar dynamo operating onthe RGB and on the AGB.

Independently of the still uncertain physical cause, we know that the bestestablished effect is a shift in the carbon isotopic mix (Gilroy & Brown, 1991),decreasing from the typical value of 25− 30 left by the 1DUP to 10− 15 for Pop-ulation I stars and down to 4 for Population II objects. Otherconsequences includeN enrichment and18O depletion (Charbonnel & Do Nascimiento, 1998). SimilarCBP episodes can occur later, during the thermally pulsing AGB stages, whereagain the sub-adiabatic zone below the envelope has a homogeneous molecularweight. Several authors (Boothroyd & Sackmann, 1999; Charbonnel & Balachan-dran, 2000) studied the possibility that7Li is affected by circulation phenomena.In particular it was noted that, on the RGB, Li enrichment is limited to phasesclose to the bump itself, so that it was suggested that Li production accompaniesthe early onset of extra-mixing (Charbonnel & Balachandran, 2000).

Let us illustrate what is found in stellar codes, using a model star of ini-tially 1.5 M⊙, with a Population I composition ([Fe/H] = −0.3; Busso et al., 2003;Straniero et al., 2003). Here production of7Li derives entirely from (bound orfree) electron captures on7Be. The synthesis of7Be can be followed through thecompetition of production and destruction:

dN(7Be)dt

= N(3)N(4)λ3,4 − N(7Be)N(p)λ7,p − N(7Be)λ7,e− (3.1)

where N(3), N(4), N(p) are the number abundances of3He, 4He and protons, andλ indicates the reaction rate. In high temperature regions (T > 2× 107 K) 7Beis completely ionised so that the contribution to e− captures coming from boundelectrons is suppressed. Here the synthesis of8B through p captures is efficient


and prevails.

For the mentioned stellar model the mass dependence of the rates for7Beproduction [λ(3He+ 4He)] and for its destruction through proton [λ(7Be+ p+)] orelectron [λ(7Be+ e−)] captures is shown in Fig. 3.3, for the case where p-capturesoccur without mass circulation. In this case7Be reaches an equilibrium concen-trationNe

7 that depends on the3He abundance maintained by H burning, and thatremains pretty low. In the same hot zones, and down toT ≥ 3 . . .4× 106 K, any7Li remaining captures protons and is very efficiently destroyed.

The same qualitative behaviour is maintained in presence ofcirculation phe-nomena too slow to save most of the produced7Be into regions of low T (where itdecays into7Li). Actually, any mixing phenomenon occurring at sufficiently lowrates (a few 10−8 M⊙/yr characterises Red Giants) would destroy Li in the enve-lope, carrying it to hot regions where it is burnt, while its replenishment through7Be saved at low T would remain too small to compensate.

In order to achieve a net and durable Li enhancement in the envelope itis required that a mixing mechanism of the type inferred by Cameron & Fowler(1971) carries7Be rather rapidly out of the high-temperature zone, typically to< 3× 106 K. On the one hand in such low-T regions the ionisation equilibriumof 7Be favours the presence of bound electrons, from which e− captures are in-creased. These dominate over p-captures (that are essentially shut off). On theother hand, in these layers any7Li produced would survive and the total inven-tory of 7Li to be carried to the envelope can be largely increased. We can havean estimate for the maximum7Li production if we consider the pure productionof 7Be in Equation 3.1, without destruction by p-captures, as ifit were quicklycarried to cool zones. Its derivative in time is shown in Fig.3.3 as (dN7/dt)p.The integral of that curve over the production region and over a period of oneyear provides themaximummass of Li that can be produced per year, amountingto 5.65× 10−13 M⊙/yr. In order to have the envelope (of about 1 M⊙) enrichedup to a mass fractionX(Li) = 2× 10−8 (≃ 10 times solar) we need to mix theproduced Li at a rateM > 3× 10−5 M⊙/yr, which is a rather fast circulation rate.Such high mixing rates have been so far suggested to occur only in rather ex-treme AGB cases, in order to explain some isotopic and elemental shifts thereinferred from measurements on pre-solar grains of AGB origin. They would pro-duce isotopic and elemental abundance changes (including Li) hardly distinguish-able from hot bottom burning effects (Nollett et al., 2003), but for much lowerstellar masses. In previous calculations with complete models (e.g. Boothroyd &Sackmann, 1999) Li production was obtained only adopting very fast circulationrates (M ≃ 10−4 M⊙/yr). This result is in line with our rather rough estimate forthe lowerM limit (3 × 10−5 M⊙/yr).

3.2. DISCUSSION 55

Figure 3.3: Rates for7Be production and destruction in the radiative layers belowtheconvective envelope (dotted and dashed lines). The abscissa shows the distance in massfrom the deepest layers affected by CBP, so that the convective envelope is at the right,outside the plot area. Also plotted is the7Be equilibrium abundance (Ne7) and its pro-duction rate (without destruction) if an infinite3He reservoir is available(dN7/dt)p. Thismimics the supply from the3He present in the envelope in case of extended mixing. Modelcalculations and figure kindly provided by Maurizio Busso and Sara Palmerini.


3.3 Conclusions

We conclude that the Li abundance measured for M45 is probably to be ascribedto the onset of rather extreme CBP phenomena on the AGB. This interpretationwould be in line with suggestions by Nollett et al. (2003) andis the first hint fordeep mixing coming from an M-type AGB star. As a consequence of the efficientmixing, we expect the12C/13C ratio to be close to the equilibrium value of 3.5.A remarkable14N enhancement at the surface would occur only if zones of rela-tively high temperature (logT > 7.4) were involved in the mixing episodes. Thisenhancement is instead expected in any case if HBB was at play. We leave thesepredictions for a subsequent verification of the consistency of our explanation.CRIRES observations have been applied for Period 81 to determine the C/O and12C/13C ratio, as well as the N abundance, in the Li-rich and comparison objects.At this stage we can only consider CBP as the most likely hypothesis, but we can-not derive too strong conclusions against the other interpretations, in particularthe binary wind accretion hypothesis, on the basis of current observations.

Our findings also suggest that the conditions for CBP and those for the thirddredge-up are independent. CBP is expected to be favoured atlow masses, whilebelow a certain mass limit (depending on the metallicity) dredge-up of s-processedmaterial does not occur. The Li-rich stars M45 and M794 should therefore beTP-AGB objects of low mass (M ≤ 1.3− 1.5 M⊙), where very efficient CBP canoccur, while the core is not massive enough to drive dredge-up.

Despite the lack of a physical explanation for the origin of CBP, a few hintscan be found from the investigation of the present homogeneous sample. Judgingfrom Fig. 3.4, the luminosities and temperatures of the Li-rich stars without Tcare similar to the Tc-rich stars. Also, the pulsation periods are comparable: TheLi-only stars M45 and M794 have periods of around or just slightly below 300 d,which is about the minimum period of the Tc stars.

M45 and M794 have Li abundances higher than the two Tc stars M1147 andM1347. M626 and S942, the two remaining Tc stars, do not show Li at all. It isquite thinkable that in the mass range of our sample stars Li production via CBPsets in before 3DUP occurs, or for masses slightly lower thannecessary to drivedredge-up. We note that the radiative layers below the convective envelope aresub-adiabatic, chemically homogeneous zones where no molecular weight barrierhampers the circulation of matter, so that the onset of CBP should be much easierthan formal dredge-up.

In any case, since not all of the stars with pulsation periodsaround or above300 d and luminosities comparable to the Li-rich stars do show this element, veryspecial conditions have to be met in order for CBP to work at the rather extremerates necessary. Which these conditions are remains a question to be answered.

3.3. CONCLUSIONS 57

1.1 1.2 1.3 1.4 1.5 1.6(J - K)

0

-3.0

-3.5

-4.0

-4.5

-5.0

-5.5

-6.0

Mbo

l

3DUP limit

Figure 3.4: Bolometric magnitude versus(J − K)0 of our sample stars. Open circlesare stars with positive Li detection, the size of the circle corresponds to the determinedabundance of Li. Symbols with a cross denote stars with positive Tc detection. The dashedhorizontal line indicates the estimated lower luminosity limit for 3DUP.

Chapter 4

Comparison of MARCS andPHOENIX spectra andatmospheres, or: A grain of salt

During the course of analysing spectra of bulge AGB stars taken with UVES it wasnoted that the synthetic spectra calculated from the MARCS hydrostatic atmo-spheres were a rather poor fit to the observed spectra (Section 2.4), especially inthe blue spectral region. The observations will be described in Chapter 2. Spectrallines simply are much stronger in synthetic spectra than in observed spectra. Thisdiscrepancy seems to be independent of the star and the adopted model parame-ters, as long as AGB stars are under consideration. This point is also discussedin Section 2.6, where the phenomenon is identified with the “line weakening”observed also by other authors.

The question is, if this is a general feature of hydrostatic models. Due tothe mentioned difficulties in modelling and for comparison reasons, we askedfor spectra based on models generated with the PHOENIX1 code (Hauschildtet al., 2003). The spectra were kindly provided by Dr. P. H. Hauschildt fromthe Hamburg University Observatory (priv. comm.). All PHOENIX model atmo-spheres used for the comparison have solar metallicity, log(g[cm s−1]) = 0.0, onesolar mass, micro-turbulent velocityξ = 2.0 km s−1, and cover a range in effectivetemperature characteristic for AGB stars. The PHOENIX models come in twoflavours with respect to the treatment of dust. The “dusty” case permits the for-mation of dust in layers with temperatures below 4000 K and its opacity is takeninto account. In the PHOENIX atmospheres, dust plays a majorrole at effec-tive temperatures at and below 2500 K. In the “cond” case the dust is assumedto “rain out” and accordingly generates no opacity. In the following we refer

1Please note here the difference between the PHOENIX atmospheric code and the Phoenixinfraredspectrograph, see Appendix A. Note also the different use of upper and lower case.

59

60 CHAPTER 4. COMPARISON OF MARCS AND PHOENIX

only to the “cond” models. The PHOENIX spectra cover the samewavelengthrange as the UVES observations (see Section 2.4) and have a spectral resolutionof R= λ/∆λ = 1.5× 106.

The MARCS models used here were calculated and kindly provided by B.Aringer. A (small) difference between PHOENIX and MARCS models is thatthe latter are calculated withξ = 2.5 km s−1 by standard. All other atmosphericparameters are identical to the ones of the PHOENIX models. Like the “cond”PHOENIX models, MARCS does not take into account the formation and opacityof dust, hence the differences found cannot be due to a different treatment of dust.The MARCS spectra are calculated withR = 3 × 105; this is fully sufficient toresolve the profiles of even the narrowest absorption lines in observed (UVES)AGB spectra. The synthetic MARCS and PHOENIX spectra discussed here havebeen convolved with a Gaussian to reduce them to the approximate resolutionof the observed spectra of around 50 000 (see Chapter 2). The difference in theoriginal resolution does not play any role in the comparisonpresented here.

On comparison between MARCS and PHOENIX spectra, considerable dif-ferences between them became apparent. One would expect similar spectra foridentical stellar parameters; this is however not the case.As a typical example,Fig. 4.1 shows a MARCS and a PHOENIX spectrum compared to an observedspectrum of the Galactic field AGB star ER Vir. This star is oneof the field AGBstars that have been observed with UVES along with the bulge sample (cf. Sec-tion 2.4). It is a SRb variable with a rather short pulsation period of 55 d, thespectral type is M4III. This star was chosen because the effects of pulsation on theatmosphere and on the spectrum are rather small. For instance, no apparent emis-sion lines are present in the blue spectral range of its UVES spectrum; emissionlines of primarily H, Fe, and Mg are observed in many of the bulge Miras andare a sign of strong shock waves traversing the atmosphere (e.g. Willson, 1971).Also, the observed velocity amplitude of ER Vir is rather small (2 – 2.5 km s−1,Lebzelter, 1999). Furthermore, the SNR of the observed spectrum of ER Vir ishigher than that of the bulge stars, around 40 in the blue spectral range.

The atmospheric models used for the comparison in Fig. 4.1 have an effec-tive temperature of 3700 K. At this temperature, the strengths of the TiO bandheads (e.g. at 7056 Å) are well reproduced. If this is regarded as an estimate forTeff of ER Vir, an error of±100 K has to be assumed. Note that dust does not playa major role at this temperature. The metallicity of both models used for Fig. 4.1is identical to the solar metallicity.

A general problem of comparing synthetic to observed spectra of cool starsis the lack of a continuum region not contaminated by atomic or molecular lines.This is particularly true for the optical domain where densely spaced atomic linesoverlap and absorb at practically every wavelength. Normalisation of the syn-thetic spectra to the observed one is thus not unambiguous. For example, in the

61

Figure 4.1: Comparison of spectra based on the MARCS code (red graph) andon thePHOENIX code (blue graph) with an observed spectrum of ER Vir(black graph), for twodifferent manners of normalisation. In the upper panel, the normalisation was done suchthat all three spectra have an identical mean value over the plotted wavelength range,while in the lower panel the normalisation was done with respect to the maximum fluxin the plotted wavelength range. Note the different scale on the y-axes. The observedspectrum is flux calibrated in units of10−11 erg s−1 cm−2 Å−1.

upper panel of Fig. 4.1 the normalisation of the synthetic spectra to the observedone was done such that all of them have an identical mean valueover the plottedwavelength range. In contrast, in the lower panel the spectra are normalised tothe maximum value within this wavelength range. Note that this maximum valuemay be reached at a different wavelength in each of the spectra. Note also that theprecise value to which the normalisation is done depends on the wavelength rangeunder consideration. Apparently, the normalisation procedure does not play a sig-nificant role for the PHOENIX spectrum since the contrast between line cores and“quasi-continuum” points is very comparable to that of the observed spectrum.For the MARCS spectrum, however, the normalisation procedure makes a hugedifference because the contrast between line core flux and quasi-continuum flux ismuch larger. This difference would be even greater in a comparison with a cooler,later-type Mira variable. Note also that a number of quasi-continuum points line


up at almost the same flux level in the PHOENIX and in the observed spectrum,while in the MARCS spectrum such a quasi-continuum is not discernable. Theproblem of normalisation has to be kept in mind throughout the thesis and is ageneral difficulty in the abundance analysis of AGB stars.

The line lists used for the synthesis of the spectra shown in Fig. 4.1 are notidentical. For the MARCS spectra the VALD database was used (Kupka et al.,1999), whereas the PHOENIX spectra utilise the Kurucz list (Kurucz, 1995). Theformer seems to be more complete, e.g. the line at∼4005.2 Å is missing in thePHOENIX spectrum.

In short, the difference between the MARCS and the PHOENIX based spec-tra is that the absorption lines in the MARCS spectra are muchstronger than inthe PHOENIX spectrum. This becomes more apparent in Fig. 4.2which showsa piece of spectrum around 7400 Å. The density of spectral lines decreases whengoing to longer wavelengths. In Fig. 4.2, some quasi-continuum becomes evidentalso in the MARCS spectrum. Here, the normalisation was donewith respect tothe maximum flux in the plotted region. Included in the plot isa MARCS spectrumcalculated and kindly provided by B. Plez (priv. comm.). Theunderlying modelhas a mass ofM = 15 M⊙ andξ = 2.0 km s−1, all other parameters are identicalwith the MARCS model calculated in Vienna. Note that the massassumed for theatmospheric model has a negligible effect on the resulting spectrum, as long aslogg is kept constant. Differences in the line lists used for the synthesis of the twoMARCS spectra are obvious. Also, the depths of the most prominent lines in theplotted region (all of metallic origin) are not identical for the two MARCS spectra.This probably is a consequence of the small difference in the micro-turbulent ve-locity assumed (ξ = 2.0 km s−1 for the spectrum by B. Plez vs.ξ = 2.5 km s−1 forthe Vienna MARCS spectrum). The lines in the PHOENIX spectrum are muchweaker compared to the two MARCS spectra. The line strengthsof the observedspectrum of ER Vir are met closer by the PHOENIX spectrum, albeit not perfectly(no fine-tuning was applied!).

The difference between the synthetic spectra from the different codes isstriking, although the input stellar parameters are eitheridentical or very similar.This calls for an explanation. A first idea might be that the model atmospheresdiffer in their structure. For a comparison between the model structures we showthe gas temperature vs. gas pressure in Fig. 4.3. The plot shows the structureof the three models used for Fig. 4.2. The graphs almost overlap over a broadrange in temperature and pressure. The PHOENIX model has a flat temperaturedependence on the gas pressure in the thin outermost layers of the atmosphere,which results from extrapolation. Some deviation between the MARCS modelsand the PHOENIX model also exists for the innermost parts of the atmosphere. Inthe PHOENIX model, contrary to the MARCS models, the gas pressure does notdrop with increasing temperature. At least a large fractionof this deviation can be

63

Figure 4.2: Comparison of the original MARCS and PHOENIX spectra, basedon themodel atmospheres shown in Fig. 4.3, with an observed spectrum of ER Vir. The stronglines are all of atomic origin. The spectra based on the MARCSmodel atmospheres ratheroverestimate the depth of the observed lines. The normalisation was done with respect tothe maximum flux in the spectral region shown.

ascribed to a different choice in the mixing length parameterαML = l/Hp (wherelis the mixing length andHp is the local pressure scale height). For the PHOENIXmodels,αML = 2.0 is assumed, whereas for the MARCS modelsαML is 1.5. Theconvective energy flux dominates over the radiative energy flux in these deep lay-ers. A different choice inαML therefore influences the stratification only in deeplayers of the atmosphere.

As a check, spectra of the three models shown in Fig. 4.3 were synthe-sised with the COMA code (Aringer, 2000), version 06. To do so, the MARCSmodel by B. Plez and the PHOENIX model were brought into a format readable toCOMA. The spectral synthesis was performed with atomic lines from the VALDdatabase and molecular line lists available (most notably TiO) using solar abun-dances. The resulting spectra are plotted for the region around 7400 Å in Fig. 4.4.Not much of a surprise the spectra are almost identical with line depths similar tothose of the original MARCS spectra, also for the PHOENIX model. The extrap-


Figure 4.3: Temperature-pressure stratification of the two MARCS models (Vienna/COMA code and the version of B. Plez, priv. comm.), and a PHOENIX model providedby P. H. Hauschildt (priv. comm.). The spectra shown in Figs.4.1 and 4.2 are based onthese models. All models have an effective temperature of 3700 K, a surface gravity oflogg = 0.0, and solar metallicity. The MARCS models differ by their mass and theirmicro-turbulence. The Vienna model has M= 1M⊙ andξ = 2.5km s−1, while the modelby B. Plez has M= 15M⊙ and ξ = 2.0km s−1. The PHOENIX model has M= 1M⊙andξ = 2.0km s−1. The deviation between MARCS and PHOENIX models in deep layers(high Tgas) can be ascribed to a different choice of the mixing length parameterαML .

olation of the PHOENIX model at low temperatures as well as the small deviationin deep layers do not cause significant differences in the resulting spectra. Thelatter can be understood because the spectrum is predominantly formed in muchhigher layers where the convective energy flux is small and the precise choice ofthe mixing length parameter has negligible influence on the structure of the atmo-sphere. The similarity between model structures is also supported by the compa-rable broad-band colours derived from both codes (Kucinskas et al., 2005, 2006).The check performed here is a hint that the cause of the differences between theoriginal MARCS and PHOENIX spectra is located in the spectral synthesis cal-culation (radiative transfer), and not in the creation of the atmospheric modelsthemselves.

65

Figure 4.4: The same as Fig. 4.2, only with all the spectra synthesised with the COMAcode, version 06 (Aringer, 2000), from the model atmospheres shown in Fig. 4.3.

The question which of the spectra exhibits the “correct” line depths cannotbe answered by the discussion so far. In principle, the line depths delivered by thePHOENIX spectrum are closer to the ones observed in ER Vir, but in fact this starmight have a metallicity considerably lower than solar. In Fig. 4.5 the observedspectrum of ER Vir as well as the PHOENIX spectrum are shown together witha (Viennese) MARCS spectrum based on a model atmosphere witha tenth of thesolar metallicity, but otherwise unaltered parameters. The atomic absorption linesin the MARCS spectrum are considerably reduced in strength,but are still strongerthan in the PHOENIX spectrum. In the blue spectral range a pseudo-continuummay be defined now. However, the absorption lines are still somewhat strongerin the MARCS spectrum than in the PHOENIX spectrum, a stronger reductionthan 1 dex would be required to equal the lines in strength. Ifindeed ER Vir isa metal poor star (say≤ 1/10 the solar metallicity), then the MARCS spectrumwould exhibit more realistic line depths, whereas the PHOENIX spectrum wouldunderestimate them. Such a low metallicity seems, however,rather unrealisticfor a Galactic disc star (After all, ER Vir was just chosen as an example here, andsimilar assumptions would have to be made for other stars). In any case, a possible


Figure 4.5: Comparison of the PHOENIX spectrum and a MARCS spectrum based ona model with a tenth of the solar metallicity. The two plots onthe left hand side showa section around 4000 Å with normalisation to the mean (top) and normalisation to themaximum flux (bottom) in the plotted wavelength region (cf. Fig. 4.1). The panel on theright hand side shows a section from the red part of the spectrum (cf. Fig. 4.2). Theobserved spectrum is flux calibrated and in units of10−11 erg s−1 cm−2 Å−1.

lower metallicity of ER Vir would not solve the discrepancy found between thetwo radiative transfer codes!

To find the root cause of the discrepancy between MARCS and PHOENIX,a detailed comparison of the source codes is required, whichis beyond the scopeof this thesis. We just want to note that the results of abundance analyses of coolgiant (AGB) atmospheres are to be taken with a grain of salt until the problem isresolved.

It should finally be mentioned that, despite the poor fit to theobserved AGBspectra in the blue spectral range, MARCS based spectra satisfactorily reproducespectra of stars such as Arcturus (α Boo) and hotter, especially in the IR domain.Thus, abundances derived from IR spectra (see the followingChapter) will beless affected by the found discrepancies. Also, low-resolution spectra and coloursderived from the MARCS and PHOENIX code are found to be widelyconsistentwith each other (Kucinskas et al., 2005, 2006).

Chapter 5

The fluorine abundance in aGalactic bulge AGB star measuredfrom CRIRES spectra

The content of this Chapter has been submitted to the Astrophysical Journal.

5.1 Introduction

Fluorine (F) is probably the element whose nucleosyntheticorigin is least known.The reason for the scarcity of knowledge is the fragility of its only stable isotope(19F) and the lack of measurable atomic lines in the optical spectral range in nor-mal stars. Apart from UV measurements of highly ionised F in very hot stars(Werner et al., 2005) and optical measurements of neutral F in extreme heliumstars (Pandey, 2006), the only source of information on stellar F abundances arevibration-rotation lines of the hydrofluoric acid (HF). TheHF molecule is effi-ciently formed in cool stellar atmospheres (types∼K0 and later), and a numberof strong lines appear in the near-IRK-band. The first identification of stellar HFlines has been made by Spinrad et al. (1971); lines of this molecule have beenused by Jorissen et al. (1992) to measure F abundances outside the solar systemfor the first time.

Several astrophysical sites for the synthesis of F have beenproposed. It hasbeen confirmed by Jorissen et al. (1992) through the correlation with the abun-dance of carbon that AGB stars are indeed producers of F. Whether or not AGBstars are themainproducers of F is still a matter of debate. Cunha et al. (2003)in this respect rather suggested that19F is created by neutrino nucleosynthesis(ν-process) during core collapse in supernovae of Type II (SNII). However, Fe-derman et al. (2005) did not find a clear indication for enhanced F abundancesresulting from theν-process in a region shaped by past supernovae.

67

68 CHAPTER 5. FLUORINE IN A GALACTIC BULGE AGB STAR

Under the conditions of the He-intershell and repeated TPs in AGB stars(see Sections 1.2.2 and 1.3.3),19F is produced among many other elements viacomplex reaction chains, or destroyed viaα captures forming22Ne. At very highneutron densities, also n captures lead to a destruction of F. For the relevant re-actions we refer to Forestini et al. (1992). The processed matter is brought to thestellar surface via 3DUP mixing events, which may operate after each thermalpulse (see Section 1.3).

Only few stellar systems have been investigated with respect to the abun-dance of F: BesidesGalacticfield red giants (Jorissen et al., 1992), similar starshave been observed in the globular cluster M4 (Smith et al., 2005), as well as inω Cen and the LMC (Cunha et al., 2003). Smith et al. (2005) addedF to the listof elements known to vary in globular cluster stars and drew conclusions on theearly-cluster chemical pollution. Nevertheless, F abundance determinations from3DUP-AGB stars are rare.

Here we report the measurement of the F abundance in a MS type bulgeAGB variable, i.e. an AGB star with an O-rich chemistry enriched in s-processelements. It is the first measurement of this kind in a star of the Galactic bulge.The measurement is of astrophysical interest because the star’s mass can be esti-mated rather accurately. The observations have been carried out with the CRIRESinfra-red spectrograph which is described in Chapter 6.

5.2 CRIRES Observations

One star observed during the first CRIRES commissioning run in June 2006 wasthe bulge Mira variable M1347 (Wesselink, 1987), also knownas Plaut 3-1347or V2017 Sgr (J2000 coordinates: 18h 38m 45.s7, -34◦ 33′ 28′′). With a Galacticlatitude of about−12.◦6 it belongs to the outer bulge. The observations of M1347were carried out on June 07, 2006. A large part of the near-IRK-band was ob-served, although the analysis presented here is limited to two wavelength settingscovering the range 2.253− 2.310µm. The slit-width was set to 0.′′2; thus, themaximum resolution of 100 000 (3 km s−1 equivalent) was achieved. The integra-tion time was 60 s for each of the four nodding positions per setting. A hot star atsimilar airmass was observed just after the science target.The raw frames were re-duced with the CRIRES pipeline (version 0.2.3), and the 1D science and standardstar spectra were wavelength-calibrated using the numerous telluric absorptionlines present on all of the four detector arrays. The wavelength-calibration wasdone separately for the science and telluric standard star spectrum because of thelimited reproducibility of the echelle grating position. Finally, the science spec-trum was divided by the standard star spectrum to correct forthe telluric linesand the illumination pattern as well as possible. Note, thatthe telluric lines are

5.3. STELLAR PARAMETERS 69

strong enough to use them as wavelength calibrator, but theyare weak enough tobe corrected for by standard star division; thus they have negligible influence onthe abundance measurements presented here. The SNR of the spectrum was esti-mated from an overlapping region on chip #3 that was observedin both settingsto be close to 100.

5.3 Stellar parameters

M1347 has previously been observed together with a larger sample of bulge AGBstars with the UVES spectrograph (see Section 2.4) on July 08, 2000 (= LD2451733.6). It was found to show absorption lines of technetium (Chapter 2)and lithium (Chapter 3). Tc is an indicator of recent or ongoing s-process and3DUP in an AGB star. As probably all genuine bulge AGB variables this star isO-rich. Because of the O-rich chemistry and signs of s-process enrichment it isclassified as type MS (Stephenson, 1984). The (slightly sub-solar) Li content oflogǫ(Li) = +0.8 in this star probably results from a different mixing phenomenoncalledCool Bottom Processing, although other enrichment scenarios could not becompletely excluded (see Section 3.2).

The mass and luminosity of M1347 are rather well constrained, thus itsabundances can be easily compared with the expectations from models of stellarevolution and nucleosynthesis. From Fig. 3 of Straniero et al. (2003) the masscan be limited to the range 1.4M⊙ < M < 2.0M⊙ over a wide range in metallic-ity (0.15Z⊙ < Z < Z⊙). Due to its age, no high-mass stars (& 2 M⊙) reachingC/O > 1 are present anymore in the bulge. Below 1.4 M⊙ no dredge-up occursat all, preventing a star to become s-process enriched. Notethat the former con-straint would not hold for a disk star, since a disk star couldbe a higher massstar on its way to C/O > 1 experiencing one of its first 3DUP events on the AGB.Additional constraints come from theMbol − P diagram. Using linear pulsationmodels M1347 is placed slightly above 1.5 M⊙ (cf. Fig. 2.8). The luminosity at adistance of 8 kpc is measured to beL � 11700L⊙ (Mbol = −5.m43), and the periodis 426.26 d (see Chapters 2 and 3).

The CRIRES observations on JD 2453895.9 were carried out 5.07 light cy-cles after the UVES observations. We thus assume that, despite the star’s vari-ability, M1347’s atmosphere was in a very similar state at the time of CRIRESobservations compared to the UVES observations. We estimated atmospheric pa-rameters from the UVES spectra by comparing them to a grid of synthetic spectrabased on MARCS atmospheric models (Section 1.4). Aχ2 minimisation methodwas used to find the parameters of the model best fitting the TiOband headsγ(0,0)Ra (705.6 nm) andγ(0,0)Rb (709.0 nm) band heads in the UVES spectra (cf.Section 3.1). The parameters found for M1347 areTeff = 3200 K, logg = −0.5,


[M /H] = 0.0, ξ = 3.0 km s−1, M = 1 M⊙, C/O = 0.48, and [Ti/H] = +0.21. Thisreference model atmosphere has been used for the spectral synthesis calculationsperformed for the abundance analysis from the CRIRES spectra. We want to notehere that the stellar mass assumed for the model atmosphere has a negligible effecton the spectrum and therefore is no indication of the real mass of the star.

5.4 Analysis

The lines R12 to R28 of the vibrational 1−0 band of the HF molecule fall in theobserved spectral range. The lines R12 and R13 are, despite the high resolution,hopelessly lost in the12CO 2−0 band head (∼ 2293.5 nm) and cannot be used forabundance analysis. Lines above R23 are very weak and could not be identified.The lines blue-wards of the12CO 2−0 band head however are well suited for theanalysis. We want to note here that all previous abundance analyses based on HF,except that of Jorissen et al. (1992), rely on a single line ofthat molecule!

A calculated line list of the HF molecule was kindly providedby R. H. Tip-ping (priv. comm.). From this list log(g f) values and the excitation potential of thelines could be derived and used for spectral synthesis calculations. Additionally,a measured line list by Webb & Rao (1968) is available which isalso incorpo-rated into the HITRAN data base (Rothman et al., 2005). This list contains onlylines up to the R14 line of the 1−0 band. We compared synthetic spectra based onthese lists for the lines in common and found very good agreement. For instance,Fig. 5.1 shows a comparison for the R14 line. This proves thatthe calculatedlist of Tipping is quite accurate. Since the Tipping data reaches to higher rota-tion quantum numbers than the HITRAN list, we only used the former for theabundance analysis.

The TiO band heads used for the temperature determination are also sen-sitive to the metallicity [M/H] of the star, leading to a temperature− metallic-ity degeneracy. We thus attempted to verify the adopted metallicity from atomiclines situated in the range observed with CRIRES. The reliability of log g f val-ues of atomic lines in the relevant wavelength range contained in the VALDdatabase (Kupka et al., 1999) was checked by comparing a corresponding syn-thetic spectrum with an observed Arcturus (αBoo) spectrum (Hinkle et al., 1995).Four lines turned out to be well suited for the metallicity determination: a Naline at 2208.969 nm, a Ca line at 2282.718 nm, and two Fe lines at 2274.514and 2283.870 nm, respectively. From these lines we determine a metallicity of[M /H] = −0.17±0.14, where the error comes from the scatter among the valuesfrom the individual lines. This agrees well with the peak metallicity of bulge RGB

1Note that the parameters here are different from those used in Chapter 3 for the measurement ofthe Li abundance. In Chapter 3 the parameters are chosen in order to best fit the Li line region.

5.4. ANALYSIS 71

Figure 5.1: The HF 1−0 R14 line calculated with the HITRAN and the Tipping list, re-spectively. Opacity sources other than HF have been neglected for these spectra. Thereference model described in Section 5.3 has been used to calculate the spectra. No con-volution has been applied, i.e. the spectra have the original resolution of R= 300 000.

stars ([M/H] = −0.1; Zoccali et al., 2003), and is just slightly below solar metallic-ity. The structure of an atmosphere model does not change much when reducingthe metallicity from 0.0 to−0.17 (Aringer, 2005). Also, the strength of the HFlines is rather insensitive to the overall metallicity, as long as [F/H] stays constant.We thus decided to proceed with the spectral synthesis calculations based on thereference model atmosphere (i.e. at solar metallicity), and add+0.17 dex to the Fabundance measured from it.

Finally, spectral synthesis calculations were performed to determine the Fabundance from the ten identified and measurable HF lines in the observed spec-tral range. A solar reference value logǫ(F) = 4.56 was adopted (Grevesse &Sauval, 1998). Table 5.1 lists the identified lines with their calculated wavelength,g f value, excitation potentialξ, measured equivalent width, and the best-fit [F/H]value derived from the respective line. In the spectral synthesis calculations forthe analysis, all atomic species and molecular lines from CO, CH, C2, SiO, CN,TiO, H2O, OH, VO, CO2, SO2, HCl, CH4, FeH, CrH, and ZrO were included toaccount for blending lines as well as possible. An additional macro-turbulence of4.0 km s−1 has been added in the spectral synthesis (Chapter 3). For best-fit modelspectra see Fig. 5.2.

From Table 5.1 it becomes obvious that the F abundances required to fit thedifferent HF lines have quite some spread. (The results for linesobserved in bothspectrograph wavelength settings are consistent with eachother, i.e. the differenceis < ±0.1 dex.) This is most of all because some of the observed lines are blends,and many lines from the other molecular line lists used for spectral synthesis have


Table 5.1: Lines of the HF molecule identified in M1347. The values of thewavelength,g f , andξ are taken from the calculated list of R. H. Tipping (priv. comm.)

Line λ (nm) g f(10−5) ξ(103cm−1) EW (mnm) best-fit [F/H]R14 2289.305 11.41 6.276 43.6 +0.07a

R15 2283.316 11.18 6.865 43.5 +0.17a

R16 2278.453 10.87 7.489 36.1 +0.27R17 2274.711 10.47 8.148 47.7 +0.67a

R18 2272.085 9.993 8.841 55.9 +0.37R19 2270.575 9.449 9.566 29.8 +0.32a

R20 2270.180 8.843 10.32 26.2 +0.62a

R21 2270.903 8.185 11.11 31.0 +0.97R22 2272.749 7.483 11.93 9.8 +0.37R23 2275.724 6.748 12.78 11.6 −0.03a

a The line is observed in both spectrograph wavelength settings, and the mean of theirrespective EW and abundance determination is given.

uncertain wavelength and/or g f value. Also, dynamic and mass loss effects lead tothe formation of spectral lines and line profiles which cannot be reproduced withhydrostatic atmospheres (Nowotny et al., 2005b, and Appendix A). Theoretically,the HF lines are expected to decrease in strength with increasing rotation quantumnumber. Some lines clearly deviate from this trend; these are the R17, R20, andR21 line. For them, a blend of unknown origin and strength hasto be assumed.The R18 line is blended, too. Also R23, the highest-lying line, is problematic. Itprobably consists of a blend in the observed as well as in the synthetic spectrum,with only a minor contribution by HF. Taking into account only the contributionfrom HF in the spectral synthesis leads to a good fit of this line at [F/H] = +0.57.We thus exclude these lines in the determination of the average F abundance. Themean value of the F abundance from the remaining five lines (R14, R15, R16,R19, and R22) is [F/H]= +0.25. The differences between observed and syntheticEWs of these lines reach least squares at [F/H] = +0.16.

Several sources of error have to be taken into account. Firstof all, the erroron the F abundance due to an error in the temperature has been estimated on theR16 line. A model with 100 K higher temperature has been used for this in thespectral synthesis. This leads to a F abundance increased by0.15 dex. The errordue to the (uncertain) continuum placement can be estimatedfrom lines observedin both wavelength settings; it amounts to around 0.1 dex. Finally, the error onthe overall metallicity contributes another 0.14 dex. Thissums up to a total errorof ±0.21 dex. The use of a hydrostatic model atmosphere for a variable star mayinduce an additional systematic error which we cannot estimate here.

5.5. CONCLUSIONS AND OUTLOOK 73

Figure 5.2: The R14 to R23 lines of HF in M1347 (black graph with dots) and their best-fit model spectrum (blue graph), with the according F abundance given in the legend. Thecentral wavelengths, marked by the vertical dashed lines, are given in Table 5.1. The tickmarks on the x-axis are 0.1 nm apart.

5.5 Conclusions and Outlook

The fluorine abundance in M1347 is probably slightly super-solar. Note, however,that the solar system meteoritic F abundance is somewhat uncertain, and probablyreduced with respect to that in normal K-M giants of the solarneighbourhood(cf. Jorissen et al., 1992). From this point of view, the F abundance of M1347 isperfectly normal for its metallicity, and no increase due tointernal nucleosynthesisand dredge-up needs to be assumed.

The measured F abundance can be compared to theoretical predictions ofAGB evolutionary and nucleosynthesis calculations. A widerange of stellar mas-ses and metallicities are covered e.g. by the calculations of Karakas (2003). Forstars below 2 M⊙ (cf. Figures C1 to C6 in Karakas, 2003) no change of the Fsurface abundance on the TP-AGB is predicted. Only at highermasses (∼ 3M⊙)a considerable increase is expected. Assuming that the F we see in M1347 isthe initial abundance and that it has not been altered on the TP-AGB, we caninterpret the measured F abundance as a confirmation of the predictions of detailednucleosynthesis calculations like those of Karakas (2003).


A deeper investigation of the nucleosynthetic origin of F isdesired. Weare currently devising a CRIRES observing program aimed at determining the Fabundance in high-mass AGB stars of the Magellanic Clouds. The observationshave been scheduled for November 2007. The goal is to observethe predictedup-turn of F production at masses of∼ 3 M⊙, and the Fdestructionat even highermasses around 5 M⊙. The measurement presented here is thus useful to pinpointthe F production in low mass stars.

Chapter 6

CRIRES – the CRyogenic InfraRedEchelle Spectrograph at ESO’s VLT

CRIRES is mounted to the Nasmyth focus A at the 8.2 m Unit Telescope #1 (Antu)of ESO’s VLT on Cerro Paranal, Chile. The instrument has beendescribed indetail in Kaufl et al. (2004) and Kaufl et al. (2006b), thus the description herewill be somewhat limited. More information on CRIRES can also be found onthe Internet at www.eso.org/instruments/crires/. Following a short technical anddesign description, an overview of the author’s various technical contributions tothis spectrograph project will be given.

6.1 Some technical details of CRIRES

CRIRES has been installed at the telescope in early 2006 and saw “first light”on June 04, 2006, followed by several commissioning and science verificationruns. It is offered to the community since the beginning of Period 79 (April01,2007). The installation of CRIRES at the telescope marks thecompletion of theoriginal plan for the first generation VLT instrumentation.CRIRES is designedfor high spectral resolution (λ/∆λ up to 105, corresponding to∆v ≃ 3 km s−1) andoperates in the spectral range 0.95− 5.3µm. A curvature sensing adaptive optics(AO) system feed is used to minimise slit losses and to provide diffraction limitedspatial resolution along the slit. A mosaic of four Aladdin III InSb arrays packagedon custom-fabricated ceramics boards has been developed. This provides for a4096×512 pixel focal plane array, to maximise the free spectral range covered ineach exposure. Insertion of gas cells to measure high precision radial velocitiesis possible. For the measurement of stellar magnetic fields and Zeeman-Doppler-imaging, especially of cool stars, a polarimetric mode willbe implemented (seeSect. 6.2.1). The scientific potential of the spectro-polarimetric mode is describedin more detail in Kaufl et al. (2003a).

75

76 CHAPTER 6. CRIRES

Figure 6.1: Optical layout of CRIRES. See text for more details.

6.1. SOME TECHNICAL DETAILS OF CRIRES 77

Figure 6.1 shows a sketch of the optical layout of CRIRES. Thelight fromthe telescope Nasmyth focus (f/15) enters from the upper right. Not shown in theFigure is the calibration unit which is in the optical path before the de-rotator.It consists of the previously mentioned gas absorption cells, a Neon arc lampand a Thorium-Argon (ThAr) hollow cathode lamp for wavelength calibrationexposures, as well as a Halogen lamp and an infrared glower incombination withan integrating sphere for flat fielding purposes. Instead of the gas cells, aλ/4retarder on a motorised mount can be introduced into the ray path to use CRIRESfor spectro-polarimetry. After the de-rotator the ray pathis folded by four mirrors,one of which is a deformable mirror. The latter is part of the Multi-ApplicationsCurvature Adaptive Optics (MACAO) system, described in detail in Paufique et al.(2006). The light required for the measurement of the wavefront distortion due toatmospheric turbulence is branched offwith a dichroic mirror. This mirror is at thesame time the entrance window to the cryostat which hosts thespectrograph andreflects light with wavelength shorter than∼ 950 nm. Thus, the AO works closeto theR-band. The curvature sensing wavefront sensor consists of an array of 60lens-lets, a fibre bundle, and 60 avalanche photo diodes. Corresponding signalsto correct the wavefront with the help of the deformable mirror are generated bya real time computer (RTC). All of these optics in front of thecryostat windoware called the “warm optics” part since it is kept at ambient temperature (andpressure). It has been commissioned separately before the spectrograph itself inApril 2006 (Kaufl et al., 2006a).

After the cryostat window, the “cold optics” part starts with the temperaturekept at∼ 65 K inside the cryostat. Such low temperatures are requiredto keepthe ambient background radiation low, and are one of the key features of the latestgeneration of IR spectrographs. The pre-slit optics of CRIRES consists of a four-mirror re-imager that reduces the focal ratio to∼ f/7.5. A cold pupil stop placedbetween the second and the third mirror of the re-imager blocks thermal emissioncoming from outside the cryostat.

Close to the cold pupil stop a Wollaston prism manufactured from MgF2

can be inserted utilising a motorised mount for the spectro-polarimetric mode.This prism splits, when inserted, the light into two orthogonally polarised andspatially separated beams to allow, in combination with theretarder wave plate(see Sect. 6.2.1), for the measurement of the circular polarisation of the incidentlight. The separation between the two beams will be about 5′′, corresponding toabout 58 pixels, on the science detector focal plane. After the Wollaston, a linearpolariser can be inserted to compensate the different efficiency of reflection andtransmission of subsequent optical elements with respect to the two beams.

The fourth mirror of the re-imager reflects the light into thespectrographentrance slit. The slit jaws act like a mirror and reflect somelight into the slitviewer, an IR camera equipped with a 1024× 1024 Aladdin III detector array. Its


Figure 6.2: CRIRES without the lid of the cryostat during re-integration in the opticallaboratory on Cerro Paranal. Photo kindly provided by Jean-Louis Lizon (ESO).

pixel scale is 45 milli arc-seconds (mas) per pixel. A filter wheel with J-, H-,andK-band as well as neutral density filters allow for slit-viewing and guiding inthese selected bands. The main spectrograph slit is adjustable between 0.′′2 and3.′′0.

After passage of the entrance slit the light is directed, by means of twofurther mirrors, to the pre-disperser prism which is mounted in quasi-Littrow con-figuration. This prism is manufactured from zinc-selenide (ZnSe) and is coatedwith gold on the back side. ZnSe is transparent to infrared light and has a ratherhigh refractive index of∼ 2.45. Due to the gold coating, the light is reflected backand crosses the prism twice. The pre-disperser together with the intermediate slit(not shown in Fig. 6.1, but placed close to the small folding mirror below the pre-disperser), acts to pre-select the light before entering the echelle grating. Thus,an overlap of adjacent echelle orders on the science detector is largely avoided.From the pre-disperser the light is directed to the three mirror anastigmat (TMA)which acts first as a collimator and then as a camera to image the spectrum ontothe science detector. The spectrum is created by the 40×20 cm echelle grating. Its31.6 grooves/mm are blazed at an angle of 63.◦5. After the second passage through

6.1. SOME TECHNICAL DETAILS OF CRIRES 79

Figure 6.3: CRIRES mounted to Antu (UT1) at Nasmyth focus platform A. Thesize ofthe spectrograph vessel can be estimated from comparison tothe computer screen andkeyboard on the lower left. The “black box” contains the de-rotator and MACAO adaptiveoptics system. Photo kindly provided by Dr. Hans Ulrich Kaufl (ESO).

the TMA the spectrum is imaged onto the four Aladdin III InSb detector arrayswhich are kept at an even lower temperature of∼ 25± 0.1 K. The four arrayshave 1024×512 pixels with a scale of 86 mas/pixel and are mounted on a custom-fabricated ceramic board. Thanks to the detector mosaic, CRIRES has a largeinstantaneous wavelength coverage of∼ 2.5 percent of the central wavelength.

Figure 6.2 gives an indication of how the setup looks like in reality. It showsa photo of CRIRES taken in the integration hall of the Paranalcontrol building.The dichroic entrance window is on the upper right of the cryostat vessel, at about2 o’clock. The pre-slit optics is at the upper left inside theblack metallic box,while the trapezoidal box contains the TMA. The echelle grating is hidden belowthe TMA. Figure 6.3 finally shows the spectrograph fully mounted and ready foroperation at the VLT UT1 Nasmyth platform A. The instrument is mounted invessel with 3 m diameter and 1 m height. Including its supportstructure, the totalweight of the instrument is 6.2 tons, spread between 2 tons for the warm part and4.2 tons for the cold part.


6.2 Contribution to the CRIRES project

The author got involved in the CRIRES project in the course ofa research stipendgranted by the University of Vienna (March− September 2004) and the ESO Stu-dentship (October 2004− December 2006). The work was carried out mainlyunder the supervision of Dr. H. U. Kaufl, ESO Garching, the Instrument Re-sponsible for CRIRES. The involvement culminated in the participation in threecommissioning and science verification runs at the Paranal Observatory, Chile, inMay and August 2006, and in January 2007. The following sub-sections give anoverview of the various technical contributions to CRIRES by the author whichcan be summarised under these headlines: model of the instrumental polarisation,focus measurements, testing the slit viewer algorithm, CRIRES− UVES parallelobservations, and linearisation of the science detector signal.

6.2.1 Model of the instrumental polarisation

The first assignment to work on for CRIRES was to study the wavelength- andtime-dependence of instrumental polarisation, and the feasibility of a model ofinstrumental polarisation based on first principles. If feasible, such a modelshould be constructed in order to predict the “parasitic” instrumental polarisationof CRIRES as a function of wavelength.

The goal of CRIRES’ spectro-polarimetric mode is to measurethe circularpolarisation of the incident light at high spectral resolution (i.e., the profile of in-trinsic spectral lines resolved). For this purpose, a rotating quarter-wave plate willbe installed close to the VLT focal plane in the calibration unit. The measure-ment will be carried out in combination with a cryogenic Wollaston prism whichsplits the light into two parallel beams of orthogonal polarisation. Ultimately,also linear polarisation should be measured to unambiguously reconstruct stellarmagnetic surface maps.

The infrared range has advantages over the optical range forthis kind ofobservations, e.g. an increased ratio of Zeeman-splittingto intrinsic line widths,and a decreased contrast between the star spot continuum andthe photosphericcontinuum which deepens absorption lines originating in magnetic star spots (seeKaufl et al., 2003a).

A proposed concept is to realise the quarter-wave plate by anassembly ofoptical elements including a Fresnel rhomb. A Fresnel rhombis a prism-likedevice that employs two total internal reflections to introduce a total phase-shiftof 90◦ (π/2 radians) on the two orthogonally linearly polarised components of theincident light. This means that a beam of light linearly+45◦ (−45◦ ) polarisedentering the rhomb becomes right (left) circularly polarised on exit.

The optical layout of the Fresnel rhomb assembly is sketchedin Fig. 6.4.

6.2. CONTRIBUTION TO THE CRIRES PROJECT 81

Figure 6.4: Sketch of the Fresnel rhomb assembly to provide theλ/4 phase shift betweenthe orthogonally linearly polarised components of the incident light. The real assemblywill be just slightly larger than this sketch.

Light from the telescope enters from the left. The light beamis divergent, sincethe assembly is placedafter the Nasmyth focus (f/15) of the telescope. The lightenters the Fresnel rhomb on its front face, with the central ray being perpendicu-lar to that face. Like the pre-disperser prism, the Fresnel rhomb is manufacturedfrom ZnSe. The light experiences two total internal reflections on the sloped faceswhich provide theπ/2 phase shift. The light exits the rhomb again through a per-pendicular face and gets reflected back to its original path via two silver coatedmirrors so that it proceeds on its way to the spectrograph. Thus, six optical sur-faces have to be taken into account for the description of polarisation introducedby the Fresnel rhomb assembly. For modelling purposes, a program in C waswritten to simulate the polarisation effect of the Fresnel rhomb assembly (Ap-pendix B).

In the description of the instrumental polarisation, all optical elements up tothe Wollaston prism have to be taken into account. After the Wollaston, only therelative intensity of the two beams is of importance, because the circular polar-isation is measured differentially from the intensity of the two beams emanatingfrom the Wollaston. Thus, the optical elements following the Wollaston do notneed to be modelled in depth. To correct the different respective efficiency of re-flection and transmission for the two beams (which is probably only the case forthe echelle grating), a linear polariser will be inserted. This device is rotated untilequal intensity for the two beams on the science detector is reached. Differentintensity will then only be present in Zeeman-active lines.

The discussion in this Section will be limited to a description of the Fresnelrhomb assembly. The polarising effect of all other elements in the ray path up tothe Wollaston (tertiary mirror, field de-rotator, AO mirrors, entrance window, fore-optics, pre-disperser) can be deduced from this example. The respective Mullermatrices are only a function of the wavelength, thus rotation can be ignored for


them. An exception might be the entrance slit whose effect on the polarisationcan probably not be constructed from first principles. Nevertheless, its influenceprobably can be neglected when the slit is opened wide enough(i.e. larger than apoint source under given seeing conditions).

The effect of an optical element on the polarisation state of a lightbeampassing through can be described in the framework of the Muller matrix formal-ism, see the book by Collett (1992)1. The formulae used in the following can befound in that book. The Muller matrix is a 4× 4 matrix that summarises the in-fluence of an optical element (or several of them) on the Stokes parameters of alight beam. The Stokes parameters are a measure of the beam intensity (I ), linearhorizontal or vertical polarisation (Q), linear±45◦ polarisation (U), and right orleft circular polarisation (V). We use the Stokes parameters as defined in Collett(1992):

S =

IQUV

=

E20x + E2

0y

E20x − E2

0y

2E0xE0y cosδ2E0xE0y sinδ

(6.1)

whereE0x andE0y are the amplitudes of the electric field component of a plainelectromagnetic wave in orthogonal directionsx andy (perpendicular to the direc-tion of propagation):

Ex(t) = E0x cos [ωt + δx(t)] (6.2)

Ey(t) = E0y cos[

ωt + δy(t)]

(6.3)

andδ is the difference in phaseδx − δy.The Stokes vector of the light beam that passed an optical element is derived

by multiplying the Muller matrix of that element with the Stokes vector of the in-cident light beam. To account for multiple optical elements, the Muller matricesof the single optical elements are multiplied with each other, with the Muller ma-trix of the first element passed by the light beam on the very right, and the Mullermatrix of the last element passed by the light beam on the veryleft. Only then themultiplication with the Stokes vector is performed. Thus, the total Muller matrixof several elements always stays a 4× 4 matrix, regardless of the number of opti-cal elements. In this formalism, the Muller matrix of an ideal quarter-wave platewould be

1The Muller matrix formalism is sufficient only in the case of incoherent light. For coherent lightthe Jones calculus has to be applied.


Mπ/2, ideal = τ ×

1 0 0 00 1 0 00 0 0 −10 0 1 0

, (6.4)

where the transmissionτ ideally is 1. We now follow the ray path in the Fresnelrhomb assembly to assess how well this requirement is met.

First we have to take into account a rotation of the assembly,which is de-scribed by the Muller matrix of rotation by an angleθ:

Mrot(θ) =

1 0 0 00 cos(2θ) sin(2θ) 00 − sin(2θ) cos(2θ) 00 0 0 1

. (6.5)

At θ = 0, the assembly is assumed to be vertically oriented.The first optically active surface is the front face of the Fresnel rhomb, where

the light beam enters the ZnSe prism from air. For perpendicular incidence on thissurface, its influence is a back reflection of a certain fraction of the beam, but oth-erwise the polarisation state will not be changed. For rays diverging from thecentral ray we have to introduce an angle of incidenceφ, measured to the perpen-dicular. These inclined rays will not only be diminished by the back reflection,but influenced in their state of polarisation, because the reflectance differs forlight with polarisation parallel and perpendicular to the plane of incidence. Thecorresponding Muller matrix is that of a dielectric surface:

Mds(θ) = τ ×

cos2(φ − r) + 1 cos2(φ − r) − 1 0 0cos2(φ − r) − 1 cos2(φ − r) + 1 0 0

0 0 2 cos2(φ − r) 00 0 0 2 cos2(φ − r)

,

(6.6)whereτ is calculated from

τ =sin(2φ) sin(2r)

2(sin(φ + r) cos(φ − r))2. (6.7)

Here, r is the refracted angle which follows from Snell’s law: sinφ =nZnSe(λ) sinr. At normal incidence,τ reduces toτ = 4nZnSe(λ)/(nZnSe(λ) + 1)2,which is also the value for transmittance (without anti-reflection coating). Mate-rial constants likenZnSe(λ) are the only measured values required to construct themodel of instrumental polarisation from first principles.nZnSe(λ) has been mea-sured and follows a so-called three-term Sellmeier formula(Browder & Ballard,1987):


n2ZnSe(λ) − 1 =

4.46395λ2

λ2 − 0.20108+

0.46132λ2

λ2 − 0.39311+

2.88289λ2

λ2 − 47.04759(6.8)

for 0.54µm ≤ λ ≤ 18.2µm. For instance, atλ = 2.6µm, the refractive index ofZnSe is very close to 2.44, resulting in a transmittance of 0.825.

After the dielectric surface, two total internal reflections follow. These arethe most important optical surfaces in the Fresnel rhomb assembly, since theyprovide theπ/2 phase shift between the linearly polarised components of the in-coming light ray. The Muller matrix for the total internal reflection is

Mtotal reflection(θ) =

1 0 0 00 1 0 00 0 cosδ − sinδ0 0 sinδ cosδ

, (6.9)

whereδ is calculated from

tan(δ/2) =− cosφ

√

n2ZnSe(λ) sin2 φ − 1

n2ZnSe(λ) sin2 φ

(6.10)

andφ is the angle of incidence on the surface. This angle is of course differentfrom the angle of incidence on the front face of the prism, andan angle conversionhas to be applied. Again, some elements of the Muller matrixdepend on therefractive index of ZnSe, which is a function of wavelength (Equ. 6.8). We wantto note here that, due to the fixed angles of the rhomb, the phase shift of exactlyπ/2 is met only for one specific wavelength, and then only for thecentral ray. (Atdifferent wavelengths rays other than the central one might experience a phaseshift preciselyπ/2 as well.)

Next, the light exits the Fresnel rhomb, and the Muller matrix of that surfaceagain is that of a dielectric, only with the angle of incidence and of refractioninterchanged.

The Fresnel rhomb alone would deflect the light by several cm from itsoriginal path. To direct the light back to its original path and subsequently into thespectrograph, two mirrors coated with silver are employed.The metallic reflectionhas a considerable influence on the light’s polarisation state. The Muller matrixof a metallic reflection is represented by2

2It should be noted that the corresponding equation in Collett (1992, Equ. 47 on page 493) is inerror. The signs of the elements M34, M43, and M44 have wrong signs there. This becomes clearalso from the subsequent calculations in the mentioned book.


Mmetal mirror(θ) =12

ρ2S+ ρ

2P ρ

2S− ρ

2P 0 0

ρ2S− ρ

2P ρ

2S+ ρ

2P 0 0

0 0 2ρSρP cos∆ 2ρSρP sin∆0 0 −2ρSρP sin∆ 2ρSρP cos∆

. (6.11)

∆ = φS − φP is the relative phase shift between the electric fields perpendicularand parallel to plane of incidence, andρS andρP are the absolute values of thereflection coefficients for the electric fields, respectively. The subscripts S and Pderive from the German “senkrecht” (perpendicular) and “parallel”. The reflectioncoefficients are obtained from

rS = ρSeiφS =cosφ −

√

n2 − sin2 φ

cosφ +√

n2 − sin2 φ

, (6.12)

rP = ρPeiφP =n2 cosφ −

√

n2 − sin2 φ

n2 cosφ +√

n2 − sin2 φ

, (6.13)

wheren is the complex refractive index of the metal (here silver),n = η + iκ.Measurements of these material constants can be found in theliterature

(Schulz, 1954; Bennett & Bennett, 1966; Johnson & Christy, 1972; CRC Hand-book of Physics & Chemistry, 2002). Fig. 6.5 shows the collected data for thereal (η) and the imaginary (κ) part of the refractive index of silver. The agreementbetween different data sources (and experimental techniques!) in the case of thereal part of the refractive index of silver is at best qualitative. At around 1µm,the spread among the different data sources is considerable. In the case of theimaginary part the different data sources agree over the whole wavelength rangealso quantitatively.

In order to have a value of the refractive index at any desiredwavelengthin the working range of CRIRES, fits to the experimental data were performed.For the real part, we decided to use only the values of Bennett& Bennett (1966)and Johnson & Christy (1972) in the range 0.9µm ≤ λ ≤ 6.0µm for the lin-ear fit to the (logλ, logη) data. The resulting fit follows the relation logη =2.0641 logλ − 1.2997. For the linear fit to the (logλ, logκ) data, all four litera-ture sources could be used to establish the relation logκ = 1.0177 logλ + 0.8535.Fig. 6.6 shows the fits and the data points used for them. The program for sim-ulating the instrumental polarisation (Appendix B) evaluates the linear fits at thewavelength under consideration to get the refractive indexof silver. Of course, theuncertainty in the material constants introduces some source of error in the modelof the instrumental polarisation. For example, the uncertainty in η introduces an


Figure 6.5: The real (top) and imaginary (bottom) part of the refractiveindex of silver.The different data sources have been colour coded (see legend).

error in the overall output Stokes vector of a few 0.1 % at 1µm, decreasing tolonger wavelengths. This is certainly a limitation to the accuracy of a model ofinstrumental polarisation based on first principles.

It should also be noted here that different definitions of the complex refrac-tive index are found in the literature. In the book by E. Collett the definitionreadsn = η(1 − iκ). In the experimental literature, however, the definition readsn = η − iκ. Hereκ just summarisesηκ in the definition of Collett. One has tobe aware of this when comparing different data sources and when calculating theelements of the Muller matrix of a metallic reflection. Figures 6.5 and 6.6 showκas defined in the experimental literature, i.e.n = η − iκ.

Finally, after the two silver coated mirrors, a back-rotation by an angle−θhas to be applied (Equ. 6.5).

The code of the C program to simulate the Fresnel rhomb assembly can befound in Appendix B. The functioning of the program is rathersimple. First, the


Figure 6.6: Fit to the real (top) and imaginary (bottom) part of the refractive index ofsilver in thelog− log plane.

input Stokes parameters, the wavelength under consideration, as well as the angleof incidence (on the front face of the prism) and the angle of rotation are readfrom the command line. The Muller matrix is initialised as an identity matrix.Then the Muller matrix is consecutively sent to different sub-routines (functions)together with the wavelength and the angle of incidence to calculate the Mullermatrix of the different elements. When calculating the Muller matrix elements forthe metallic mirrors, functions able to handle complex numbers are required. Tothis end, the GNU Scientific Library (GSL) was included in thecode. A matrixmultiplication is performed at the end of each function to calculate the total Mullermatrix. Angle conversions are performed to use the correct angle of incidencefor every optical element. Finally, the total Muller matrix is sent to a functionthat prints the matrix, the (normalised) output Stokes vector, and the transmittedintensity.

As an example of how well an idealλ/4-plate is realised by the Fresnel


rhomb assembly, the Muller matrix at 2µm for an angle of incidence and of rota-tion equal to 0◦ is given here (to be compared with Equ. 6.4):

M2µm = 0.673

1.000 0.003 0.000 0.0000.003 1.000 0.000 0.0000.000 0.000 0.035 −0.9990.000 0.000 0.999 0.035

(6.14)

This shows that the Fresnel rhomb assembly also introduces acertain fractionof linear polarisation. This is primarily a result of the reflections from the twore-directing mirrors. For this reason, it is considered by ESO to introduce aquarter-wave plate manufactured from a bi-refringent crystal. Apart from thisresult, studying the instrumental polarisation with the M¨uller matrix formalism isan instructive exercise to understand the symmetry of the problem, as well as time(rotation) and wavelength dependences.

CRIRES’ spectro-polarimetric mode is not fully implemented yet. Cur-rently, calibration lamps emitting linearly and circularly polarised light are beinginstalled in the CRIRES calibration unit. Close-by early type stars can be used asunpolarised light sources. Ultimately, also linear polarisation should be measured.For this goal, aλ/2-plate has to be inserted which will be manufactured from abi-refringent crystal in any case. The model developed herewill be further usedto calibrate instrumental polarisation.

6.2.2 Focus measurements

CRIRES has four different focal planes. They are located at each of the two slits(entrance and intermediate) and at the two detectors (slit viewer and science).In order to optimise instrument performance, the slits and detectors need to bealigned to these focal planes. The alignment can only be measured precisely oncethe instrument is integrated and cooled down to its operating temperature. Thus,after the re-integration at the observatory in May 2006 the alignment had to bemeasured to correct the positions of the slits and detectorsduring a subsequentintervention.

The method to measure the position of the slits and detectorsrelative totheir focal planes involved a pinhole located in the CRIRES calibration unit. Thispinhole was mounted on ax-y-z stage (a small mount movable in all three spacecoordinates) and was illuminated from the back by a HeNe laser as monochro-matic light source. To measure the focus position of the slits and the detectors,two different procedures had to be applied: For the detectors, the goal was to opti-mise the image quality in terms of the full width at half maximum (FWHM) of thepinhole image on the detectors. For the slit viewer, these measurements were per-formed with all the different filters available (J-, H-, K-band and neutral density


filters). The focal plane of the slits can be found by maximising the flux throughthe (almost closed) slit. Another method to find the focus position of the slit canbe applied with the slit opened: When moving the pinhole image across the slitedge, the focus is where the decrease (or increase) in flux is sharpest. The “bestfocus” position of all four focal planes are ideally reachedat a single position ofthe pinhole along the ray path (x-direction).

The image data were taken by Dr. Jean-Francois Pirard (ESO).The pinholeimages could, in a large part, not be fitted with a 2D Gaussian.Thus it was decidedto write a dedicated IDL program to analyse the image data with a more sophisti-cated method. In addition to a Gaussian fit the FWHM was determined from thestatistical spread of the flux on the detector. The program reads information nec-essary for the analysis, e.g. the name(s) of the image frame(s) to analyse, the nameof an optional bad pixel mask and a dark frame, etc., from an input file. From thisinput it decides whether one or several image frames have to be analysed. If sev-eral frames are to be analysed, the average frame can be used to better locate theposition of the pinhole image on the detector; due to bad detector cosmetics andimperfect bad pixel correction this turned out to be difficult for some of the singleimage frames. A dark frame (if available) is subtracted fromthe images and badpixels are replaced by the median value of its closest eight neighbours. Cuttingout a rectangular sub-image (with user-provided coordinates of the lower left andupper right corner) proved to stabilise the code. From the (cleaned) average framethe x- andy-coordinate of the pinhole image is determined. Around the pixel ofmaximum flux a box is constructed to estimate and subtract theresidual back-ground. The centre-of-mass coordinate of the cleaned and background-subtractedpinhole image is then derived, together with its extension in x- andy-direction.Also, a 2D Gaussian fit is performed. The resulting values areprinted and canthen be further analysed as a function of the pinhole position.

The displacement of the slits and detectors from their best focus locationswere measured during commissioning in August 2006. The predicted correctionswere applied during an intervention in September 2006. The re-focusing provedto be successful (see also Section 6.2.4).

6.2.3 Testing the slit viewer guiding algorithm

A slit viewer guiding algorithm was developed by ESO for CRIRES to centrethe target of spectroscopic observations on the spectrograph entrance slit. In thecase where the (point-like) target is at the same time the slit viewer guiding star, aproblem arises as a matter of principle. On the one hand, as much light as possiblefrom the target should be transmitted through the slit (in-between the slit jaws).On the other hand, slit viewer guiding should be possible by calculating the actual(true) position of the guide star from the residual light reflected by the slit jaws


to centre the target on the slit. (This implies that under perfect seeing conditionsand/or perfect AO correction slit viewer guiding on the target isactually impos-sible!) This is not a trivial task, because in these residual“wings” of the guidestar only a small fraction of the total light flux is present. To assess how well theslit viewer algorithm can indeed reproduce the guide star position if it is close toor partly in the slit, observations of a binary star system have been obtained andanalysed. This is a crucial point because only a reliable andstable guiding allowsfor optimal slit through-put and maximum spectral resolution.

The binary system observed during the last CRIRES commissioning run inJanuary and February 2007 was HD 73461. The apparentJ-band magnitude ofthe two components is 7.m11 and 7.m97, respectively, the separation inferred fromthe CRIRES observations is about 7.′′083. The strategy of the measurements was totake slit viewer images of both components while the primarycomponent driftedacross the slit. When the primary component is far away from the slit the influenceof the slit on the measured position can be neglected. However, when the primaryis close to or actually in the slit the measured position willbe influenced by theslit, unless the target position is perfectly predicted (measured) by the guidingalgorithm. Since the distance between the components is known from the off-slitmeasurements, the influence of the slit on the position measurement can be tested.

Fig. 6.7 shows results of this test for slit widths of 0.′′2 and 0.′′4, respec-tively. Similar measurements have been performed at slit widths of 0.′′3, 0.′′6, and0.′′8. The results for these slit widths are qualitatively the same, but are not shownhere. We plot the deviation of the distance between the binary components fromits mean value as a function of thex-coordinate of the secondary (the slit is ver-tically oriented on the 10242 pixel slit viewer detector, and thex-axis is definedto be horizontal, i.e. it runsacrossthe slit). The green graph represents the re-sults as obtained from the (adapted) CRIRES slit viewer guiding algorithm, whilethe red graph represents the results from the routine that was used for the focusmeasurements (see Sect. 6.2.2). The actual guiding algorithm employs a centre-of-mass determination, too, to derive the coordinates of the guiding star, but doesso in a three step loop with successively smaller boxes for source extraction andbackground subtraction.

A perfect prediction of the true guiding star position wouldmean a zero de-viation for all positions relative to the slit. The smaller the deviation from the meanseparation, the closer the predicted position to the true position. The actual slitviewer algorithm has somewhat smaller maximum deviations from the mean, andthus gives slightly better results than the routine used forthe focus measurements.As the primary component approaches the slit from the left, the measured binaryseparation increases. This means that the guiding algorithm over-estimates thedistance of the guide star from the slit centre; the much brighter residual “wing”

3Brosche & Sinachopoulos (1989) measured a separation of 7.′′54.


Figure 6.7: Deviation of the measured binary separation from its mean value, for a slitwidth of 0.′′2 (top) and 0.′′4 (bottom). Note the different scale on the y-axis.

on the left side of the slit dominates over the faint wing on the right side of the slitin the centre-of-mass determination for predicting the guide star position. Whenthe guide star moves slightly off-centre to the righthand side of the slit, the situa-tion becomes just opposite and the deviation exhibits a sharp “jump” and becomesnegative. The semi-amplitude of the resulting curve gives an indication of howstrongly the guiding algorithm over-estimates the distance of the guide star fromthe true slit centre. Table 6.1 summarises these semi-amplitudes measured for theadopted slit widths.

The described over-estimation creates some temporal instability of the spec-trum on the science detector, eventually degrading the spectrum and decreasingthe spectral resolution in long exposures (> a few seconds). Thus, a stable guidingnot only increases the spectrograph through-put but also the spectral resolution.For these reasons, a damping term is included in the guiding algorithm to reducethe “oscillating behaviour” resulting from the slit distance over-estimation. In


Table 6.1: Semi-amplitudes of the deviation from the mean binary separation as foundfrom the CRIRES slit viewer guiding algorithm for different slit widths.

slit width semi amplitude semi amplitude(′′) (SlV pixel) (′′)0.2 1.4 0.0630.3 1.9 0.0860.4 3.3 0.1490.6 4.7 0.2120.8 5.9 0.266

principle, the deviation measured here can be used to correct the predicted positionof the target and thus improve the guiding algorithm. However, these deviationsare dependent on the observing conditions, most of all on theseeing. Eventu-ally, an improved algorithm for the prediction of the sourceposition is sought for,which is probably not based on a centre-of-mass determination.

One more thing is worth noting here. A faint third object was identified inthe field of view of the CRIRES slit viewer images, about 3.′′34 (74.2 slit viewerpixels) to the south-east of the primary. No information on this third object wasfound in the literature, nor could it be identified in sky surveys like DSS2, due toits faintness and the small separation from the much brighter primary component.In fact HD 73461 could be a triple system. Proper motion measurements arerequired to draw definite conclusions.

6.2.4 CRIRES – UVES parallel observations

CRIRES has an overlap in wavelength with UVES, the UV-visualEchelle Spec-trograph (Dekker et al., 2000), which is mounted at the Nasmyth B focus of VLTUT2 (Kueyen). Both instruments can operate between about 0.95 and 1.05µm.This wavelength range is of high interest for a number of applications, e.g. Nissenet al. (2007) and Reiners et al. (2007). To get a comparison ofthe performancein the overlapping wavelength range, parallel observations of one target with bothinstruments have been carried out during the CRIRES commissioning runs in June2006 and February 2007. The respective target was observed simultaneously withboth instruments to ensure identical ambient conditions (airmass, seeing, etc.). InJune 2006 the starµ Velorum (spectral type G5IIIa, 2MASSJ-band magnitude1.m154) was observed (actually, the dominating primary in thisbinary system);in February 2007 the target wasβ Columbae (K2III, 2MASSJ-band magnitude1.m296). In June 2006 the six blue-most nominal (n) and interlaced (i) wavelengthsettings (orders 54 to 59) were observed with CRIRES. In the February 2007 run


only four nominal wavelength settings were observed (orders 54, 56, 57, and 59).Only the results from detector chips #2 and #3 will be shown here, because con-tamination from adjacent orders is present on chips #1 and #4in these settings.The data were reduced with the most recent CPL-based instrument pipelines (ver-sion 3.3.1 of the UVES pipeline, version 1.3.1 of the CRIRES pipeline).

The UVES pipeline offers the possibility, by the usage of ESO-providedresponse curves derived from spectro-photometric standard stars, to derive flux-calibrated spectra corrected for the extinction by the Earth’s atmosphere. Spectro-photometric standard stars for the infrared have yet to be established, thus thisoption is not yet offered by the CRIRES pipeline. For this reason the flux from theCRIRES pipeline is not corrected for extinction and instrument through-put. Thisprevents a quantitative comparison of the two instruments in terms of the mea-sured flux. Still, it is interesting to see the change in measured flux between theJune 2006 and February 2007 observing runs. Figures 6.8 and 6.9 show the fluxesmeasured by CRIRES and UVES, respectively. The starµ Vel is brighter thanβ Col in the observed wavelength region, as indicated by theJ-band magnitude.Thus, the flux in the UVES spectrum ofµ Vel (June 2006) is higher by a factorof about two than the flux ofβ Col (February 2007). Contrary to this, the fluxmeasured by CRIRESincreasedbetween June 2006 and February 2007. This isprobably a result of adjustments carried out during the intervention in September2006. During this intervention the instrument through-putwas improved, and alsothe detectors were re-focused (see Sect. 6.2.2).

The best measure for the instrument performance is the SNR achieved, cal-culated from the flux/error ratio. It was normalised to the square-root of the ex-posure time and the resolution element of the respective instrument. Figures 6.10and 6.11 show the results of the June 2006 and February 2007 observations incomparison. For both figures the same scale on they-axis was chosen to make adirect comparison possible. As expected from the behaviourof the measured flux,also the SNR of the UVES spectrum decreased when going fromµ Vel to β Col.On the other hand, the SNR measured from the CRIRES spectra increased con-siderably. The bottom line of this comparison is that starting from around 980 nmCRIRES now performs better than UVES in terms of SNR. This is confirmed bySiebenmorgen et al. (2007), based on observations by Reiners et al. (2007), whofind that UVES requires roughly twice the observing time of CRIRES to reach thesame SNR for similar flux levels and spectral resolution around 1µm.

The results of this comparison have been included in the CRIRES user man-ual, issue 81.1.


Figure 6.8: Flux ofµ Vel as measured by CRIRES and UVES in June 2006. The nominal(n) and interlaced (i) orders of CRIRES are plotted in blue and turquoise, respectively.


Figure 6.9: As Fig. 6.8, but forβ Col observed in February 2007.


Figure 6.10: SNR (measured in s−1/2Å−1) of the CRIRES− UVES parallel observationsof µ Vel in June 2006. The nominal (n) and interlaced (i) orders ofCRIRES are plotted inblue and turquoise, respectively.


Figure 6.11: As Fig. 6.10, but forβ Col observed in February 2007.


6.2.5 Linearisation of the science detector signal

Infrared detector arrays have seen dramatic improvements during the last twodecades, both regarding their size and sensitivity. Detectors commonly used ininstruments like CRIRES are arrays of diodes operated in reverse-biasing. Eachdiode (pixel) acts as a small capacity. A bias voltage is applied to the capacity,which is discharged by (IR) photons producing electron-hole pairs. To measurethe photon flux, the voltage is sampled at the beginning and atthe end of theexposure. From their design, the diodes are intrinsically non-linear, because thecapacity increases as the voltage decreases. This is fundamentally different fromdetectors used in the optical range (. 1µm). Because of the non-linearity, an ex-posure of twice the integration time at the same photon flux will not yield exactlytwice the measured flux, but rather a little less. In many kinds of measurementsthis does not introduce a large error. However, there are situations where a precisereconstruction of the real flux bylinearisation is necessary. In the case of theCRIRES detectors this is necessary because of the odd-even effect between pixelcolumns (mainly on detector chips #1 and #4) and pixel rows (mainly on detectorchips #2 and #3). It is not precisely known where this odd-even effect comes from,but due to its orientation it is believed to be related to the detector read-out.

The aim is to derive a formula to “linearise” the detector signal, i.e. to re-construct the real flux. We assume a set of image frames (with the measured fluxfm in each pixel) with an increasing integration timetint. The dependence offm ontint may be described by a second-order polynomial:

fm = a+ b · tint + c · t2int. (6.15)

We want to determine the real fluxfr as a function of the measured flux for eachpixel: fr = fr( fm). Assuming a light source that is constant in time, the real flux( fr) is linearly related totint. This meansfr = const. · tint, or

tint = fr/const. (6.16)

At times close to 0, the quadratic term in Equ. 6.15 can be neglected, thus theslope of fm and fr at tint = 0 are the same:

d fmdtint

(tint = 0) =d frdtint

(tint = 0) (6.17)

d fmdtint

(tint = 0) = b+ 2c · tint = b,d frdtint

(tint = 0) = const. ⇒ const. = b

(6.18)We insert this relation now in Equations 6.15 and 6.16:


Figure 6.12: Simple demonstration of the power of signal linearisation to get rid of theodd-even effect.

frb= tint (6.19)

fm = a+ b · tint + c · t2int = a+ b ·

(

frb

)

+ c ·

(

frb

)2

= a+ fr +cb2· f 2

r (6.20)

Using the well-known relation to solve quadratic equations, this can be translatedinto the two solutions

f 1,2r =

−b2± b2

√

1− 4c(a− fm)/b2

2c(6.21)

where the ”+” solution is the one to be used in this case. Thus, with an array ofcoefficientsa(i, j), b(i, j), andc(i, j) determined from a quadratic fit tofm vs. tint

for every pixel, the real flux in every pixel can be reconstructed (below some levelof overexposure). The coefficients might depend only on the read-out mode andthe wavelength at which the set of frames was taken.

Fig. 6.12 shows a simple demonstration of how the odd-even effect is di-minished by applying the derived signal linearisation algorithm. The CRIRES


observations ofβ Columbae, obtained for the comparison with UVES, have beenused for this purpose. The spectral lines visible in Fig. 6.12 are around 1052 nmand of telluric origin. Since detector chip #4 shows a very pronounced odd-eveneffect, it has been chosen for this demonstration. The spectra have not been re-duced with the ESO CRIRES pipeline, but are rather reduced with a self-writtenIDL routine which uses simple flux summation over columns to extract the spec-trum. For demonstration purposes this is fully sufficient. In Fig. 6.12 the spectrahave been offset by 0.04 in flux for clarity.

The black graph shows a spectrum directly extracted from theraw frame,without division by a flat field frame, hence also the general slope. The odd-eveneffect amounts to a flux difference of around 10% between adjacent pixel columns.In the spectrum divided by the flat field prior to extraction (blue graph), the odd-even effect is reduced to about 1%, but is still clearly visible. Weaklines aredifficult to discern. The red graph finally shows a spectrum where the raw spec-trum as well as the flat field frame have been linearised according to the equationsabove prior to division by the flat field. The non-linearity coefficients for this ex-ample have been derived from a series of exposures with increasing integrationtime at a wavelength of around 3.7µm. Since there might exist chromatic effects(which have not been investigated yet), an even better correction can be expectedfrom a corresponding data set recorded at the wavelength setting of the actualobservations. In any case, the residual odd-even effect is certainly considerablybelow 1%.

The described algorithm for linearising the flux has been implemented inthe ESO CRIRES pipeline as criresspecdetlin recipe.

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Appendix A

Spectral variability of bulge Mirasfrom CRIRES and Phoenix spectra

Two Mira variables of the bulge sample have been observed with both CRIRESand the Phoenix spectrograph at the Gemini South telescope.These stars arethe Tc- and Li-rich star M1347, and the Li-only star M794 (however, the Li-content of the stars had not been analysed at the time of theseobservations). Theobservations can be used to investigate the temporal spectral variablity of Miravariable stars in theK-band. Here we present a qualitative comparison betweenthe Phoenix and the CRIRES spectra of these stars.

The observations with Phoenix have been carried out, reduced, and kindlyprovided by Dr. Thomas Lebzelter and Dr. Kenneth Hinkle (NOAO). Phoenix isa high-resolution near-IR spectrograph comparable to CRIRES mounted to theGemini South telescope at Cerro Pachon, Chile. The maximumspectral resolu-tion of Phoenix isR= 75 000, not far from the CRIRES resolution. However, theinstantaneous wavelength coverage is much smaller than that of CRIRES sinceonly one 1024× 1024 InSb Aladdin II array is available. The wavelength cov-erage of 0.51 percent translates into about 10 nm in theK-band. More infor-mation on Phoenix can be found in the papers by Hinkle et al. (1998, 2000,2003), and on the Internet at www.noao.edu/usgp/phoenix/phoenix.html andwww.gemini.edu/sciops/instruments/phoenix/phoenixIndex.html, respectively.

The Phoenix observations of both stars have been carried outon July 03,2004 (JD 2453189.8). Spectra at three different slit positions with 60 s exposuretime each have been obtained at a slit width of 3 pixels, corresponding to a spectralresolution ofR = λ/∆λ = 50 000. The wavelength calibration was done usingtelluric lines in a hot standard star, and the observations cover the range∼ 2358−2368 nm. The spectra were corrected for telluric lines usingobservations of theB3V star HR 472.

The CRIRES observations of M1347 were obtained during commissioning

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114 APPENDIX A. SPECTRAL VARIABILITY OF BULGE MIRAS

on June 09, 2006 (JD 2453895.9, Chapter 5), shortly after first light. M794 wasobserved during CRIRES science verification under program no. 60.A-9079A onOctober 11, 2006 (JD 2454019.6). The nominal spectral resolution of the ob-servations of M1347 was 75 000 (slit-width 0.′′3), while for M794 it was 50 000(slit-width 0.′′4). The exposure time at each of the four slit positions was 60s. Bothdata sets and the corresponding standard star observationswere reduced with theCRIRES pipeline (version 0.2.3). The wavelength calibration of each detectorchip was done using the numerous telluric lines in the observed spectrum. Forthis purpose, line positions were measured in the observed spectrum as well as ina telluric transmission model (A. Seifahrt, priv. comm.) using a Gaussian fit to theline. The telluric transmission model has been computed with the PcLnWin pro-gram (www.ontar.com/Software/ProductDetails.aspx?item=PcLnWin) with linedata from the HITRAN data base (Rothman et al., 2005). A radial ve-locity correction has been applied. The spectra of the bulgestars weredivided by a standard star spectrum obtained at similar air mass to cor-rect for telluric absorption lines and the spectrograph illumination pattern(continuum tilt). Prior to division, the 1D spectrum of detector chips#1 and #4 have been convolved with a Gaussian of width 2.0/2.3548 pix-els using the IDL routine gausconvol.pro (www.astro.washington.edu/deutsch-bin/getpro/library08.html?GAUSCONVOL) to reduce the odd-even effect. Theflux linearisation had not been implemented in the pipeline version used here (cf.Sect. 6.2.5).

The flux was normalised to have a maximum of 1.0 in the observedwave-length range. The observations were carried out (among others) in the wavelengthsettings 24/1/n and 24/1/i. The reference wavelengths, i.e. the wavelengths thatfall on the central pixel column of chip #3, are 2382.2 and 2388.6 nm, respec-tively (see Tables 4a-f and 5a-f of the CRIRES manual, issue 81.1). Because ofgaps between the detector chips of CRIRES, no single chip of CRIRES covers thewhole range of the Phoenix observations.

The Figures A.1 and A.2 show a juxtaposition of the Phoenix and theCRIRES spectra of the stars M1347 and M794, respectively. For a comparisonof the spectra it is of importance to know the difference in pulsation phase of theobservations. Both stars are Mira variables and therefore significant variations inthe spectrum have to be expected (see e.g. Lebzelter et al., 1998, and Chapter 1).For M1347 the time difference is 706.1 d, corresponding to a phase difference ofabout 1.66 pulsation cycles (P = 426.60 d). For M794, the time difference be-tween the observations is 829.8 d, corresponding to a phase difference of about2.73 pulsation cycles (P = 303.54 d). Since these bulge variables are not moni-tored regularly, the absolute pulsation phase at which the observations have beencarried out is not known.

First of all, the CRIRES spectra from the different detector chips agree very

115

Figure A.1: K-band spectra of the bulge AGB star M1347 taken with CRIRES andPhoenix, respectively. The CRIRES spectrum from the interlaced (i, blue) setting cov-ers the detector gap of the nominal (n, green) setting.

nicely with each other, giving an impression of the high SNR.For M1347 the SNRhas been estimated to be∼ 100 from two overlapping regions (see Chapter 5).Due to the identical exposure time and similarK-band magnitude, the SNR of thespectrum of M794 is comparable to this value. Most of the features seen are thus“real” and no artefacts from the reduction process or standard star division.

A striking feature in the comparison of the two diagrams is that the spectrumof M794 seems even more crowded and more complicated than that of M1347.From this, a lower temperature may be estimated for M794 thanfor M1347. In-deed, the temperature-sensitive TiO band heads observed inthe UVES spectra arestronger in M794 than in M1347. Also, the variability amplitudes are higher forM794 than for M1347: In theB- andR-band, M794 has an amplitude of 6.m75 and4.m20, respectively, while M1347 has amplitudes of 4.m20 and 3.m80, respectively(Wesselink, 1987).

The similarity between the spectra at different epochs is rather limited.While the general trend in the spectra retains the same, onlyfew features ap-pear at the same position and with the same strength at the twoepochs. In thisrespect, it is especially interesting to note the appearance of lines in the Phoenix


Figure A.2: As Fig. A.1, but for the star M794.

spectrum of M1347 which are absent in the CRIRES spectrum, e.g. at∼2361.7,and∼2364.1 nm. These lines practically coincide with strong water lines listed inthe computed list by Barber et al. (2006) and the measured HITEMP list (Roth-man et al., 2005). We thus ascribe them to H2O. Also the line at∼2362.0 nmhas a much increased strength in the Phoenix spectrum compared to the CRIRESspectrum. At this position no line due to H2O can be found in the mentionedlists. However, this is not unexpected because the lists arenot complete, and thisline might well be due to water. The variation of the H2O line strength probablymeans that M1347 was in a somewhat cooler phase of its light cycle at the timeof the Phoenix observation than at the time of the CRIRES observation. Probablythe star was close to its minimum phase of the visual light cycle (when the sur-face temperature also roughly reaches its minimum) during Phoenix observations,whereas during CRIRES observations it was closer to its maximum phase whenalso the temperature was higher. Regarding the phase difference of the observa-tions of 1.66 light cycles this is well possible.

Also, the variability of the strong, almost equally spaced lines at∼ 2358.5,2360.8, 2363.2, 2365.6, and 2368.0 nm is intriguing. They appear more prominentin the spectrum of M1347 (Fig. A.1). All these are blends of COlines, each

117

Figure A.3: CO lines of the Mira M1347 as observed with CRIRES (left panel) andPhoenix (right panel). The flux is plotted as a function of velocity from the centres (fluxminima) of the two CO line blends at 2363.2 (including 2–0 P7)and 2365.6 nm (includ-ing 2–0 P8), respectively. The flux of the P7 line is shifted by+0.1 for clarity, and i andn orders are over-plotted. Note the blue-shifted componentin both lines in the CRIRESspectrum which is absent in the Phoenix spectrum.

containing a line of the 2–0 P branch. In some cases (2363.2 and 2365.6 nm)two almost equally strong lines constitute the blend, and the two componentsare resolved in the CRIRES spectrum. Additionally, in the CRIRES spectrumof M1347 a blue-shifted third component becomes visible in these lines. Alsoother, weaker lines show line splitting with a blue-shiftedcomponent. Fig. A.3shows the lines at 2363.2 nm (including 2–0 P7) and 2365.6 nm (including 2–0P8) of M1347 over-plotted in a close-up for a comparison of their structures. Theadditional component is clearly absent in the Phoenix spectrum (right panel ofFig. A.3), but certainly not because of the slightly reducedspectral resolution.The shift between the additional component and the blue component of the blendis ∼ −15 km s−1, a typical velocity observed in atmospheres of Mira variables.Also the lines at∼ 2358.5 and 2360.8 nm show a “bump” on their blue wing, butthey are not split. These multiple line components are most probably caused byvelocity fields within the stars’ atmosphere Nowotny et al. (2005a,b).


Figure A.4: Illustration of the spectral change in the range of the Phoenix observationsexpected from hydrostatic models when decreasing the effective temperature from 3200 to2900 K.

Finally, Fig. A.4 illustrates the spectral change that is predicted from hy-drostatic model atmospheres when the effective temperature is decreased from3200 to 2900 K. This range is realistic for the temperature variation in Mirastars between maximum and minimum light phase. In general, all lines becomestronger when the temperature is decreased. A few lines become visible only atTeff = 2900 K. Some of these lines can be ascribed to the water molecule, e.g. theline at 2364 nm. However, no line splitting (additional linecomponents) are seenin these spectra, because hydrostatic models were used for their synthesis.

Appendix B

The C source code for the Mullermatrix calculation

1

2 /*

3 Program to calculate the Mueller matrix of the Fresnel assembly

4 used in CRIRES as a quarter wave plate. The Mueller matrices of

5 the single optical surfaces are computed and printed as well.

6

7 Input on command-line:

8 ./fresnel I Q U V wavelength angle-of-incidence angle-of-rotation

9 Example:

10 ./fresnel 1 0 0 1 2.0 2.0 0.0

11 -> Completely right circularly polarized light of 2.0 microns

12 wavelength, incident at +2 deg on the air-ZnSe interface with

13 a non-rotated assembly.

14 */

15

16

17 #include <stdio.h>

18 #include </usr/include/gsl/gsl_complex_math.h>

19 #include </usr/share/doc/gsl-1.1.1/gsl_complex_math.h>

20 #include <complex.h>

21 #include <math.h>

22 #include <stdlib.h>

23

24

25 /* Define some abbreviations of the lengthy names of complex

26 functions: */

27

28 #define add_real gsl_complex_add_real

119

120 APPENDIX B. MULLER MATRIX SOURCE CODE

29 #define mul_real gsl_complex_mul_real

30 #define sub_real gsl_complex_sub_real

31 #define div_real gsl_complex_div_real

32 #define add_cplx gsl_complex_add

33 #define mul_cplx gsl_complex_mul

34 #define sub_cplx gsl_complex_sub

35 #define div_cplx gsl_complex_div

36 #define csqrt gsl_complex_sqrt

37 #define pow_real gsl_complex_pow_real

38 #define conjg gsl_complex_conjugate

39 #define pi 3.14159265

40

41

42 /* For more information, look up the gsl reference manual! */

43

44 double pow();

45 double cos();

46 double sin();

47 double asin();

48 double sqrt();

49 double atan();

50 double exp();

51 double log10();

52

53

54 /* Index of refraction of ZnSe as a function of wavelength, from

55 Bowder & Ballard, 1987. */

56 float eta(float lambda)

57 {

58 float a,b,c;

59 a=4.46395*pow(lambda,2)/(pow(lambda,2)-pow(0.20108,2));

60 b=0.46132*pow(lambda,2)/(pow(lambda,2)-pow(0.39211,2));

61 c=2.88289*pow(lambda,2)/(pow(lambda,2)-pow(47.04759,2));

62

63 return sqrt(a + b + c + 1);

64 }

65

66

67 /* Real part of index of refraction of silver as a function of

68 wavelength. */

69 float n(float lambda)

70 {

71 return pow(10.0,log10(lambda)*2.06405 - 1.29969);

72 }

121

73

74

75 /* Imaginary part of index of refraction of silver as a function of

76 wavelength. */

77 float kappa(float lambda)

78 {

79 return pow(10.0,log10(lambda)*1.0176529 + 0.85352284);

80 }

81

82

83

84 /* This function multiplies the mueller matrix of an optical

85 element with the matrix m, which the total mueller matrix up

86 to this element. The multiplication is performed from the

87 left! */

88

89 int matrixmult(float mueller[4][4],float m[4][4])

90 {

91 float temp[4][4];

92 int i,j,k;

93

94 for(i=0;i<4;i++)

95 {

96 for(j=0;j<4;j++)

97 {temp[i][j]=0.0;

98 for(k=0;k<4;k++)

99 /* Result is stored in temp. */

100 temp[i][j]=temp[i][j]+mueller[i][k]*m[k][j];

101 }

102 }

103

104 for(i=0;i<4;i++)

105 for(j=0;j<4;j++) /* temp is assigned to m. */

106 m[i][j]=temp[i][j];

107 /* Function matrixmult() leaves changed m. */

108

109 return 0;

110 }

111

112

113

114 /* Function to apply the rotation matrix on the mueller matrix. */

115 int rotation(float m[4][4], float theta)

116 {


117 float mueller[4][4];


119 int i,j,k;

120

121 for(i=0;i<4;i++)

122 for(j=0;j<4;j++)

123 mueller[i][j]=0.0;

124

125 mueller[0][0]=mueller[3][3]=1.0;

126 mueller[1][1]=mueller[2][2]=cos(2*theta);

127 mueller[1][2]=sin(2*theta);

128 mueller[2][1]=-mueller[1][2];

129

130 printf("\n\n Muellermatrix of rotation is: \n\n");

131

132 for(i=0;i<4;i++)

133 {printf("\n");

134 for(j=0;j<4;j++)

135 printf("%7.4f ", mueller[i][j]);

136 }

137

138 matrixmult(mueller,m);

139

140 return 0;

141 }

142

143

144

145 /* Mueller matrix of the air - ZnSe surface (light entering the

146 Fresnel rhomb). */

147 int AirZnSeInterface(float m[4][4], float lambda, float phi)

148 {


150 float vorfaktor,r,n; /* Auxiliary variables. */

151 int i, j;

152

153 n=eta(lambda);

154 for(i=0;i<4;i++)

155 for(j=0;j<4;j++)

156 mueller[i][j]=0;

157

158 if (phi==0.0)

159 {vorfaktor=4*n/pow(n+1,2);

160 mueller[0][0]=mueller[1][1]=mueller[2][2]=mueller[3][3]=vorfaktor;

123

161 }

162

163 else

164 {r=asin(sin(phi)/n);

165 vorfaktor=sin(2*phi)*sin(2*r)/(2*pow(sin(phi+r)*cos(phi-r),2));

166 mueller[0][0] = mueller[1][1] = vorfaktor*(pow(cos(phi-r),2)+1);

167 mueller[0][1] = mueller[1][0] = vorfaktor*(pow(cos(phi-r),2)-1);

168 mueller[2][2] = mueller[3][3] = 2*vorfaktor*cos(phi-r);

169 }

170

171 printf("\n\n Muellermatrix of Air-ZnSe interface: \n\n");

172 for(i=0;i<4;i++)

173 {printf("\n");

174 for(j=0;j<4;j++)


176 }

177


179

180 return 0;

181 }

182

183

184

185 /* Mueller matrix of the ZnSe - air surface (light exiting the

186 Fresnel rhomb). */

187 int ZnSeAirInterface(float m[4][4], float lambda, float phi)

188 {


190 float vorfaktor, r, n; /* Auxiliary variables. */

191 int i, j;

192

193 n=eta(lambda);

194 for(i=0;i<4;i++)

195 for(j=0;j<4;j++)

196 mueller[i][j]=0;

197

198 if (phi==0.0)

199 {vorfaktor=4*n/pow(n+1,2);

200 mueller[0][0]=mueller[1][1]=mueller[2][2]=mueller[3][3]=vorfaktor;

201 }

202

203 else

204 {r=asin(sin(phi)*n);


205 vorfaktor=sin(2*phi)*sin(2*r)/(2*pow(sin(phi+r)*cos(phi-r),2));

206 mueller[0][0] = mueller[1][1] = vorfaktor*(pow(cos(phi-r),2)+1);

207 mueller[0][1] = mueller[1][0] = vorfaktor*(pow(cos(phi-r),2)-1);

208 mueller[2][2] = mueller[3][3] = 2*vorfaktor*cos(phi-r);

209 }

210

211 printf("\n\n Muellermatrix of ZnSe-Air interface: \n\n");

212 for(i=0;i<4;i++)

213 {printf("\n");

214 for(j=0;j<4;j++)


216 }

217


219

220 return 0;

221 }

222

223

224

225 /* Mueller matrix of the silver coated mirrors that reflect the

226 light back to the original ray path. */

227 int mirror(float m[4][4], float lambda, float phi)

228 {



231 int i,j,k;

232 float a;

233 gsl_complex c_n, c_r_s, c_r_p, b, c_i;

234

235 GSL_SET_COMPLEX (&c_i, 0, 1);

236 c_n=add_real(mul_real(c_i, -kappa(lambda)), n(lambda));

237 a=cos(phi);

238 b=csqrt(sub_real(pow_real(c_n,2),pow(sin(phi),2)));

239 c_r_s=div_cplx(mul_real(sub_real(b,a),-1),add_real(b,a));

240 c_r_p=div_cplx(sub_cplx(mul_real(mul_cplx(c_n,c_n),a),b),(add_cplx

(mul_real(mul_cplx(c_n,c_n),a),b)));

241

242

243 /* Initialisation of Mueller matrix elements */

244 mueller[0][0]=mueller[1][1]=0.5*GSL_REAL(add_cplx(mul_cplx(c_r_s,

conjg(c_r_s)),mul_cplx(c_r_p,conjg(c_r_p))));

245 mueller[0][1]=mueller[1][0]=0.5*GSL_REAL(sub_cplx(mul_cplx(c_r_s,

conjg(c_r_s)),mul_cplx(c_r_p,conjg(c_r_p))));

125

246 mueller[0][2]=mueller[0][3]=mueller[1][2]=mueller[1][3]=0;

247 mueller[2][0]=mueller[2][1]=mueller[3][0]=mueller[3][1]=0;

248 mueller[2][2]=mueller[3][3]=0.5*GSL_REAL(add_cplx(mul_cplx(c_r_s,

conjg(c_r_p)),mul_cplx(c_r_p,conjg(c_r_s))));

249 mueller[2][3]=0.5*GSL_REAL(mul_cplx(sub_cplx(mul_cplx(c_r_s,conjg(

c_r_p)),mul_cplx(c_r_p,conjg(c_r_s))),gsl_complex_negative(c_i

)));


251

252 printf("\n\n Muellermatrix of silver coated mirror: \n\n");

253 for(i=0;i<4;i++)

254 {printf("\n");

255 for(j=0;j<4;j++)


257 }

258


260

261 return 0;

262 }

263

264

265

266 /* Mueller matrix of the total internal reflection inside the

267 Fresnel rhomb. */

268 int ZnSeRhomb(float m[4][4], float lambda, float phi)

269 {



272 float delta,n;

273 int i,j,k;

274

275 n=eta(lambda);

276 delta=2*atan(-cos(phi)*sqrt(pow(n*sin(phi),2)-1)/(n*pow(sin(phi)

,2)));

277

278 /* Initialisation of Mueller matrix elements */

279 for(i=0;i<4;i++)

280 for(j=0;j<4;j++)

281 mueller[i][j]=0.0;

282

283 mueller[0][0]=mueller[1][1]=1;

284 mueller[2][2]=mueller[3][3]=cos(delta);

285 mueller[3][2]=sin(delta);



287

288 printf("\n\n Muellermatrix of total internal reflection: \n\n");

289 for(i=0;i<4;i++)

290 {printf("\n");

291 for(j=0;j<4;j++)


293 }

294


296

297 return 0;

298 }

299

300

301

302 /* Make the final output. */

303 int Ausgabe(float Stokes[4], float m[4][4], char *s)

304 {

305 int i,j;

306 float temp[4];

307

308 printf("\n\n Total Mueller-matrix after %s is:\n", s);

309

310 for(i=0;i<4;i++)

311 {printf("\n");

312 for(j=0;j<4;j++)

313 printf("%7.4f ", m[i][j]);

314 }

315

316 printf("\n\n Normalized Stokes-vector after %s is:\n\n", s);

317

318 for(i=0;i<4;i++)

319 {temp[i]=0.0;

320 for(j=0;j<4;j++)

321 temp[i]=temp[i]+m[i][j]*Stokes[j];

322 printf("%7.4f\n", temp[i]/temp[0]);

323 }

324

325 printf("\n Intensity after %s is:\n\n%7.4f\n\n", s, temp[0]);

326

327 return 0;

328 }

329

127

330

331 int main(int argc,char *argv[])

332 {

333 int i;

334 float lambda, phi, theta;

335 float Stokes[4];

336 float m[4][4]={{1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}};

337 char s[100];

338

339

340 /* Read in the values from the command line. */

341 /* First four values in command line are the four

342 Stokes parameters of input beam. */

343 Stokes[0]=atof(*++argv);




347 /* Fifth value is the wavelenght. */

348 lambda=atof(*++argv);

349 /* Sitxth value is the incident angle in degrees;

350 it is converted to radians. */

351 phi=atof(*++argv)*pi/180.0;

352 /* Last value is the rotation of the assembly

353 by an angle theta (converted to rad). */

354 theta=atof(*++argv)*pi/180.0;

355

356 /* Do a sanity check on the input Stokes parameters. */

357 if((sqrt(pow(Stokes[1],2)+pow(Stokes[2],2)+pow(Stokes[3],2))/

Stokes[0])>1.0)

358 {printf("Stokes Parameters are not physical !!!\n");

359 return 1;}

360

361

362

363 /* Send the mueller matrix through the various optical elements: */

364 /* Rotation of Fresnel assembly by an angle theta! */

365 i=rotation(m,theta);

366

367 /* Air-ZnSe Interface */

368 i=AirZnSeInterface(m,lambda,phi);

369

370 /* Angle conversion. */

371 phi=asin(sin(phi)/eta(lambda));

372 phi=62.5*pi/180.0-phi;


373

374 /* 1st total internal reflection in ZnSe-Rhomb. */

375 i=ZnSeRhomb(m,lambda,phi);

376

377 /* 2nd total internal reflection in ZnSe-Rhomb. */

378 i=ZnSeRhomb(m,lambda,phi);

379


381 phi=62.5*pi/180-phi;

382

383 /* ZnSe-air interface. */

384 i=ZnSeAirInterface(m,lambda,phi);

385


387 phi=asin(sin(phi)*eta(lambda));

388 phi=45.0*pi/180.0+phi;

389

390 /* 1st reflection from silver-coated mirror. */

391 i=mirror(m,lambda,phi);

392

393 /* 2nd reflection from silver-coated mirror. */

394 i=mirror(m,lambda,phi);

395

396 /* Back rotation of Fresnel assembly. */

397 i=rotation(m,-theta);

398

399 sprintf(s,"back-rotation");

400 Ausgabe(Stokes,m,s);

401

402 return 0;

403 }

404

405

406 /*

407 compilation command: gcc fresnelassembly.c -L/usr/include/gsl -lgsl

408 -lgslcblas -lm -o fresnel

409 */

List of abbreviations

1DUP First Dredge-Up2DUP Second Dredge-Up2MASS Two Micron All Sky Survey3DUP Third Dredge-UpAO Adaptive OpticsAGB Asymptotic Giant BranchCBP Cool Bottom ProcessingCPL Common Pipeline LanguageCRIRES CRyogenic InfraRed Echelle SpectrographCSE CircumStellar EnvelopeDENIS DEep Near-Infrared Survey of the southern skyE-AGB Early Asymptotic Giant BranchEW Equivalent WidthESO European Southern ObservatoryFWHM Full Width at Half MaximumGSL GNU Scientific LibraryHBB Hot Bottom BurningHIPPARCOS High Precision Parallax Collecting SatelliteHRD Hertzsprung-Russel DiagramIDL Interactive Data LanguageIR InfraRedIRAS InfraRed Astronomical SatelliteIRAM Institut de Radio Astronomie MillimetriqueISM Interstellar MediumISO Infrared Space ObservatoryJCMT James Clerk Maxwell TelescopeLb Irregular variablesLMC Large Magellanic CloudLPV Long Period VariableLTE Local Thermodynamic EquilibriumMACAO Multi-Applications Curvature Adaptive OpticsMACHO MAssive Compact Halo ObjectsMCs Magellanic CloudsMARCS Model Atmospheres in a Radiative Convective Schememas milli arc-secondsMS Main SequenceNOAO National Optical Astronomy ObservatoryOGLE Optical Gravitational Lensing Experiment

PG3 Palomar Groningen survey field no. 3PN Planetary NebulaRGB Red Giant BranchRTC Real Time DisplaySCZ Surface Convection ZoneSMC Small Magellanic CloudSNIa SuperNovae of type IaSNII SuperNovae of type IISR Semi-Regular variableSRV Semi-Regular VariableTMA Three Mirror AnastigmatTO Turn OffTP Thermal PulseSNR Signal-to-Noise RatioUT Unit TelescopeUVES Uv and Visual Echelle SpectrographVLT Very Large TelescopeWD White DwarfZAMS Zero Age Main Sequence

List of Figures

1.1 AGB structure Sketch . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Schematic evolution of a star of massM ≈ 1M⊙ . . . . . . . . . . 81.3 Cross-section through a TP-AGB star . . . . . . . . . . . . . . . 91.4 Kippenhahn diagram of TP and 3DUP . . . . . . . . . . . . . . . 131.5 S-process path in the chart of nuclides . . . . . . . . . . . . . . .151.6 ESO photograph of the bulge . . . . . . . . . . . . . . . . . . . . 23

2.1 Predicted abundances of Zr and Tc . . . . . . . . . . . . . . . . . 262.2 Colour-luminosity diagram of field AGB stars . . . . . . . . . .. 272.3 Classical Tc lines . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4 Subordinate Tc lines . . . . . . . . . . . . . . . . . . . . . . . . 362.5 Continuum-to-line flux ratios of Tc lines . . . . . . . . . . . . .. 372.6 PeriodK-magnitude diagram of the bulge sample stars . . . . . . 382.7 Bolometric magnitude vs. (J − K)0 of the bulge sample stars . . . 412.8 Bolometric magnitude vs. period diagram of the bulge sample stars 44

3.1 Observed spectrum of the most Li-rich sample star M45 . . .. . . 503.2 Observed spectrum of the star M1347 around the 671 nm Li line . 513.3 Rates for7Be production and destruction . . . . . . . . . . . . . . 553.4 Bolometric magnitude vs. (J − K)0 of the bulge sample stars with

Li identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.1 Comparison of MARCS and PHOENIX spectra around 4000 Å . . 614.2 Comparison of MARCS and PHOENIX spectra around 7400 Å . . 634.3 MARCS and PHOENIX model atmosphere structures . . . . . . . 644.4 Spectra based on MARCS and PHOENIX models, synthesised

with COMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.5 Synthetic MARCS spectrum with 1/10 solar metallicity . . . . . . 66

5.1 The HF 1−0 R14 line from different line lists . . . . . . . . . . . 715.2 Fits to the observed HF R14 to R23 lines . . . . . . . . . . . . . . 73

6.1 Optical layout of CRIRES . . . . . . . . . . . . . . . . . . . . . 76

131

132 LIST OF FIGURES

6.2 CRIRES in the optical laboratory on Paranal . . . . . . . . . . .. 786.3 CRIRES mounted to UT1 . . . . . . . . . . . . . . . . . . . . . . 796.4 Sketch of the Fresnel rhomb assembly . . . . . . . . . . . . . . . 816.5 Real and imaginary index of refraction of silver . . . . . . .. . . 866.6 Fit to the real and imaginary index of refraction of silver . . . . . 876.7 Binary separation in the guiding algorithm test . . . . . . .. . . . 916.8 Flux measured by CRIRES and UVES in June 2006 . . . . . . . . 946.9 Flux measured by CRIRES and UVES in February 2007 . . . . . 956.10 SNR of the CRIRES and UVES spectra of June 2006 . . . . . . . 966.11 SNR of the CRIRES and UVES spectra of February 2007 . . . . .976.12 Demonstration of signal linearisation . . . . . . . . . . . . .. . . 99

A.1 CRIRES and Phoenix spectra of M1347 . . . . . . . . . . . . . . 115A.2 CRIRES and Phoenix spectra of M794 . . . . . . . . . . . . . . . 116A.3 Kinematic structure in CO lines of M1347 . . . . . . . . . . . . . 117A.4 Illustration of the spectral change in the range of Phoenix obser-

vation from hydrostatic models . . . . . . . . . . . . . . . . . . . 118

List of Tables

2.1 Basic characteristics of the bulge sample stars . . . . . . .. . . . 302.2 IRAS colours of IRAS detected bulge sample stars . . . . . . .. 33

3.1 Abundances of Li-rich bulge sample stars . . . . . . . . . . . . .48

5.1 Lines of the HF molecule identified in M1347 . . . . . . . . . . . 72

6.1 Semi-amplitude of binary separation . . . . . . . . . . . . . . . .92

133

Acknowledgements

Like probably every thesis, also this one would not have beenfeasible in the cur-rent form without the support, help, and positive influence of many people. Iwould thus like to thank these helping “hands and heads”.

First of all I would like to thank the members of the AGB working groupat the Institute for Astronomy at the University of Vienna, foremost my thesissupervisor Thomas Lebzelter. The constant interchange of ideas with him, bothduring my time in Munich and in Vienna, fundamentally formedthe present work.Most of all I want to thank him for that he always found the timeand leisure todeal with my requests and questions.

Josef Hron deserves particular thank. The largest part of this thesis is basedon a data set of optical spectra of bulge AGB stars taken by him. I gratefullycould use this outstanding data set for my work. Especially Iowe the more thantwo years of ESO studentship in Garching near Munich to both Josef Hron andThomas Lebzelter. This would not have come into reality without their support.

Special thanks go to my supervisor at ESO, Hans Ulrich Kaufl,for his sup-port and for involving me into the CRIRES project. This allowed me to makeirreplaceable experience with a top-level instrument, as well as to get to know theworld class observatory on Cerro Paranal during my three trips to Chile in theframework of CRIRES commissioning and science verification.

I wish to thank Bernhard Aringer for calculating model atmospheres and forthe instructive conversation. Thanks to him also for the common mountaineeringtours (and the pains thereby suffered;-)!

Michael Lederer contributed with his model atmosphere calculations – inparticular for the measurements of lithium (Chapter 3) – to the success of thiswork. Many thanks for this!

The works of Walter Nowotny formed my understanding of dynamic effectsin atmospheres of AGB stars as well as in spectra thereof. Appendix A developedin a large part from discussions with him. I wish to thank him for this and for hisalways exhilarating mind.

I also wish to thank Michael Gorfer for his improvements of the COMAcode, and at the same time I would like to apologise for ruining his master thesis(see footnote 1 in Chapter 2).

I acknowledge Ernst Dorfi for help in administrative issues during the prepa-ration of the thesis, as well as for his educational lectureson astrophysics.

The time in Munich would not have been nearly as pleasant and entertain-ing without the many friendly and open-minded colleagues (students, fellows,and staff) both in Garching and Chile, and from the neighbouring Max-Planck-Institutes. Many of these became friends and companions. Itwould remain anincomplete list if I tried to name them all. Representatively thanked are only mylong-term office mate Yuri Beletsky and his wife Anna, whom I wish lots of joywith little Elena Maria, my dear friend from home Brigitta Eder, as well as BrunoLeibundgut, my boss at ESO, for circumspectly leading the ESO Science Divi-sion. Due to all these people, the time in Munich became unforgettable.

I wish to thank also the co-authors of my papers not yet mentioned. Theseare Maurizio Busso and Sara Palmerini, who deliver the theoretical back groundto the observations, as well as Mathias Schultheis, who crucially contributed withhis broad knowledge of the Galactic bulge to the success of the journal articles.

I acknowledge financial support during my undergraduate andgraduatestudies by the Stipendienstelle Wien, the University of Vienna, ESO, and the Aus-trian Science Fund FWF.

Likewise I wish to thank all my friends for their continued moral support.I have to particularly thank Roland Ottensamer for his help with LATEX and otheruseful advises.

My parents have to be thanked for giving freedom to my dreams,and fortheir support during my studies.

Dear Julia, I want to thank you for the wonderful time we are spendingtogether, and I am looking forward to everything that may come.

Wie wahrscheinlich jede Doktorarbeit, so ware auch diese ohne die Un-terstutzung, Hilfe und den positiven Einfluss vieler Menschen nicht in der vor-liegenden Form entstanden. Ich mochte daher an dieser Stelle all diesen helfenden“Handen und Kopfen” danken.

Zuerst mochte ich mich bei allen Mitgliedern der AGB Arbeitsgruppe amInstitut fur Astronomie der Universitat Wien bedanken, allen voran bei meinemBetreuer Thomas Lebzelter. Der standige Gedankenaustausch mit ihm, sowohlwahrend meiner Zeit in Munchen als auch in Wien, haben die vorliegende Arbeitwesentlich geformt. Vor allem mochte ich ihm aber dafur danken, dass er jederzeitdie Muße gefunden hat, sich mit meinen Anliegen und Fragen zubeschaftigen.

Josef Hron gebuhrt besonderer Dank. Der großte Teil dieser Arbeit fußtauf einem von ihm aufgenommenen Datensatz von optischen Spektren von AGB-Sternen im Bulge. Dankenswerter Weise durfte ich diesen hervorragenden Daten-satz fur meine Arbeit verwenden. Sowohl Josef Hron als Thomas Lebzelter ver-danke ich speziell meinen gut zweijahrigen Aufenthalt in Garching bei Munchenim Rahmen des ESO Studentships, der ohne ihre Vermittlung nicht zustandegekommen ware.

Meinem Betreuer bei der ESO, Hans Ulrich Kaufl, mochte ich Dankaussprechen fur seine Unterstutzung und besonders fur die Einbindung in dasCRIRES Projekt. Dadurch konnte ich unersetzbare Erfahrungmachen und Ein-blick bekommen in ein Spitzen-Instrument, sowie bei meinendrei Reisen nachChile im Rahmen der CRIRES Kommissionierung und Science Verification dasWeltklasse-Observatorium am Cerro Paranal kennen lernen.

Bedanken mochte ich mich bei Bernhard Aringer fur die Berechnung vonModellatmospharen und die aufschlussreichen Gesprachemit ihm. Vielen Dankauch fur die gemeinsamen Bergtouren (und die dadurch erlittenen Schmerzen;-)!

Auch Michael Lederer hat mit den von ihm berechneten Modellatmospharen– insbesondere fur die Messung von Lithium (Kapitel 3) – zumGelingen derArbeit beigetragen, vielen Dank dafur!

Die Arbeiten von Walter Nowotny haben mein Verstandnis derdynamischenEffekte in Atmospharen von AGB-Sternen sowie in deren Spektren gepragt. An-hang A ist zu einem großen Teil aus Gesprachen mit ihm entstanden. Dafur undfur sein stets aufheiterndes Gemut mochte ich ihm danken.

Ich mochte Michael Gorfer fur seine Verbesserungen im COMA Codedanken. Ich muss mich aber gleichzeitig bei ihm dafur entschuldigen, dass ichseine Diplomarbeit halb “ruiniert” habe (siehe Fußnote 1 inKapitel 2).

Auch Ernst Dorfi mochte ich danken fur die Hilfe in administrativen An-gelegenheiten in Rahmen der Fertigstellung dieser Arbeit,sowie fur seine bilden-den Astrophysik-Vorlesungen.

Die Zeit in Munchen ware bestimmt weniger angenehm und kurzweiligverlaufen ohne die vielen freundlichen und aufgeschlossenen Kollegen bei ESOsowohl in Garching als auch in Chile, seien es Studenten, Fellows oder Staff,aber auch bei den angrenzenden Max-Planck Instituten, von denen viele zu Freun-den und weiteren Wegbegleitern wurden. Es konnte nur eine unvollstandige Listebleiben, wurde ich versuchen, sie alle hier aufzuzahlen.Stellvertretend bedanktseien hier nur mein Langzeit-Burokollege Yuri Beletsky und seine Frau Anna, de-nen ich viel Freude mit der kleinen Elena Maria wunsche, meiner lieben Kolleginaus der “Heimat” Brigitta Eder, sowie Bruno Leibundgut, meinem Chef bei ESO,fur die umsichtige Leitung der ESO Science Division. Durchall diese Menschenhabe ich die Zeit in Munchen ganz besonders genossen.

Dank auch an die Co-Autoren meiner Publikationen, die noch nicht erwahntwurden. Das sind Maurizio Busso und seine Studentin Sara Palmerini, die das the-oretische Ruckgrat zu den Beobachtungen liefern, sowie Mathias Schultheis, dermit seinem breiten Wissen uber den galaktischen Bulge wesentlich zum Gelingender Artikel beigetragen hat.

Nicht zuletzt mochte ich mich bei allen Einrichtungen bedanken, von denenich im Laufe des Diplom- und Doktoratstudiums finanziell unterstutzt wurde, na-mentlich die Studienbeihilfenstelle Wien, die Universit¨at Wien, die ESO und derFWF.

Ebenso mochte ich allen meinen Freunden danken, vor allem fur die kon-tinuierliche moralische Unterstutzung. Roland Ottensamer muss ich zusatzlichfur seine Hilfe mit LATEX und andere nutzliche Ratschlage danken.

Meinen Eltern mochte ich danken dass sie meinen “Traumereien” freienLauf gelassen haben, und fur ihre Unterstutzung im Studium.

Liebe Julia, ich danke dir fur die wunderbare Zeit die wir miteinander ver-bringen, und ich freue mich auf alles was noch vor uns liegen mag.

Curriculum VitaeMag. rer. nat. Stefan UTTENTHALER

Personal Data:

Date of birth: 30. 09. 1978Place of birth: A – 4680 Haag am Hausruck, AustriaParents: Elisabeth (nee Lehner) and Rupert Martin FlorianUttenthalerCitizenship: Austria, EuropeMarital status: unmarried

Dec. 2007: Expected defence of PhD thesis, title: “Nucleosynthesis and mix-ing in Galactic bulge AGB stars studied with high-resolution spectroscopy”under the supervision of Mag. Dr. Thomas Lebzelter

Jan. 2006 – Dec. 2007: Employment in a Project by the AustrianScience Fund(FWF)

Oct. 2004 – Dec. 2006: ESO Studentship at ESO headquarters inGarching nearMunich, Germany; participation in the VLT/CRIRES infra-red spectrographproject, in particular during commissioning and science verification observ-ing runs in May 2006, Aug. 2006, and Jan./Feb. 2007

Mar. 2004 – Sept. 2004: Research Stipend granted by the University of Vienna,working title: “An instrumental polarisation model for theinfra-red spec-trograph CRIRES at ESO’s VLT”

Oct. 2003: Start of PhD studies of Astronomy at the University of Vienna

Oct. 2002 – Sept. 2003: Civilian service

06 Sept. 2002: Final Physics diploma exam passed with distinction. Diplomathesis title: “Experiments on Coherence and Decoherence ofMolecularMatter Waves”, supervisor: Prof. Dr. Anton Zeilinger

Aug. 2000 – Jan. 2001: ERASMUS stipend at the University of Århus, Denmark

Oct. 1996: Start of undergraduate studies of Physics and Astronomy at the Uni-versity of Vienna

Sept. 1992 – June 1996: High-school in A – 4910 Ried im Innkreis, Upper-Austria, final school-leaving exam passed on June 05, 1996.

Nucleosynthesis and mixing processes in Galactic bulge AGB stars ...

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