The Dynamic Atmospheres of Red Giant Stars

Spectral Synthesis in High Resolution

Walter Nowotny

revised version (December 2006)

The Dynamic Atmospheres of Red Giant Stars Spectral Synthesis in High Resolution

Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium Doktor der Naturwissenschaften

an der Fakult¨at f¨ur Geowissenschaften, Geographie und Astronomie der Universit¨at Wien

eingereicht von Ing. Mag.rer.nat. Walter Nowotny-Schipper Institut f¨ur Astronomie T¨urkenschanzstr. 17 A–1180 Wien, Austria

Wien, November 2005

Das sch¨onste Gl¨uck des denkenden Menschen ist, das Erforschliche erforscht zu haben und das Unerforschliche ruhig zu verehren.

J.W. von Goethe

And all that is now And all that is gone And all that’s to come and everything under the sun is tune but the sun is eclipsed by the moon.

Pink Floyd (from ”The dark side of the moon”)

Contents

Abstract v

1 Introduction 1 1.1 Setting the stage – stellar evolution and the general propertiesofAGBstars. . . . 1 1.1.1 EvolutiontowardstheAGB ...... 1 1.1.2 Fundamental properties, nucleo-synthesis, convectiveprocesses ...... 2 1.1.3 Pulsation and photometric variability ...... 4 1.1.4 Masslossandthefading...... 5 1.1.5 AGB stars as members of stellar populations ...... 5 1.2 AtmospheresandspectraofAGBstars...... 7 1.2.1 Generalremarks ...... 7 1.2.2 The pulsating photosphere and molecular features ...... 9 1.2.3 Circumstellar dust and the development of a stellar wind ...... 14 1.2.4 Regions of line formation – studying atmospheric dynamics in AGB stars . 16 1.2.4.1 Theoccurenceofmolecularfeatures ...... 16 1.2.4.2 Theconceptofopticaldepth ...... 17 1.2.4.3 LineformationinAGBstars ...... 19 1.2.4.4 Obtaining information on dynamics in different atmospheric depths 21 1.3 Atmospheric kinematics of AGB stars and observed line profilevariations . . . . . 24 1.3.1 Generalremarks ...... 24 1.3.2 MolecularlinesofCOintheNIR...... 26 1.3.2.1 Second overtone lines – CO ∆v=3...... 27 1.3.2.2 First overtone lines – CO ∆v=2 ...... 32 1.3.2.3 Fundamental mode lines – CO ∆v=1 ...... 33 1.3.3 Otherfeaturesobserved ...... 34 1.3.4 Deducing a stratigraphy for AGB atmospheres ...... 37 1.3.5 Carbon-richLPVs ...... 40 1.3.5.1 COfeatures ...... 40 1.3.5.2 CNlines–animportanttoolforCstars ...... 41 1.3.5.3 TheC-typeMiraSCep ...... 43 1.3.6 A note on studying the dynamics of stellar systems ...... 44 1.4 Aimandstructureofthethesis ...... 48

i 2 AGB atmospheres from the numerical point of view 51 2.1 Dynamicmodelatmospheres ...... 52 2.1.1 Generalremarks ...... 52 2.1.2 The models for atmospheres and winds used in this thesis...... 52 2.1.2.1 Basicingredients...... 53 2.1.2.2 Atmospheric models selected for the line profile modelling. . . . . 55 2.1.2.3 Somecomputationaldetails...... 57 2.1.3 Naming convention for radial velocities ...... 62 2.1.4 Some remarks on stellar parameters – real stars vs. models ...... 62 2.1.4.1 Period, luminosity, amplitude, mass ...... 62 2.1.4.2 Effective temperature, surface gravity ...... 63 2.1.4.3 Elementalabundances,C/Oratio ...... 64 2.1.4.4 Consequences...... 64 2.2 Spectralsynthesis...... 64 2.2.1 Spectral features chosen for the line profile modelling ...... 64 2.2.2 Opacity treatment (COMA)...... 65 2.2.3 Mergingdifferentopacitysources ...... 69 2.2.4 Radiative transfer and deriving RVs from synthetic spectra ...... 72 2.2.5 Influence of velocities on optical depth and line formation ...... 73 2.2.6 Visual phases of observations vs. bolometric phases ofmodels...... 77

3 Synthetic line profiles 81 3.1 Modelling line profile variations – the history so far ...... 81 3.1.1 Generalremarks ...... 81 3.1.2 Pulsating model atmospheres (Australia–Heidelberg models) ...... 82 3.1.3 Dust-driven wind models (Berlin models) ...... 83 3.1.4 Combined atmosphere and wind models (Vienna models) ...... 84 3.2 Reproducing the global (velocity) structures of Miras ...... 85 3.2.1 Probingthepulsatinglayers...... 85 3.2.1.1 CO ∆v=3lines...... 85 3.2.1.2 CNlines ...... 87 3.2.2 Probing the dust-forming region – CO ∆v=2 ...... 90 3.2.3 Probing the outflow – CO ∆v=1 ...... 93 3.2.4 TheoverallpictureconcerningRVs ...... 94 3.2.5 Resume ...... 96 3.3 A closer look at CO ∆v=3lines...... 97 3.3.1 LineformationinmodelS...... 97

ii 3.3.2 Miras and semi-regular variables (SRVs) ...... 100 3.4 Gasvelocitiesvs.measuredRVs...... 104 3.5 Stepstowardsrealisticmodels...... 105 3.5.1 Fitting models to observations of selected targets (e.g.SCep) ...... 105 3.5.2 Larger velocity amplitudes in the pulsating layers ...... 108 3.6 Quasi-static, warm molecular envelopes and dynamic modelatmospheres...... 112

4 Conclusions and future prospects 113

Bibliography 117

Abbreviations 128

Danksagung / Acknowledgements 129

iii iv Abstract

Light is the only1 source of information we have to study distant stars. Our knowledge about the state of the matter inside stars has been gathered by analysing star light (photometry, spectroscopy, interferometry, polarimetry, etc.). Of central importance in this context are stellar atmospheres, which are the transition regions from the optically thick stellar interiors where the electromagnetic radiation is generated to the optically thin outer layers from where the photons can leave the star. However, the atmosphere of a star is not only the region where most of the observable radiation is emitted or in other words the layers which are ”visible from outside”. The atmosphere also leaves an imprint on the stellar spectrum as the radiation passes through, most of the line spectrum is formed there. Thus, the light serves as a probe for the physical processes within stellar atmospheres,2 especially spectroscopy is one of the major tools in stellar astrophysics. Applying the underlying physical principles in numerical simulations (model atmospheres, synthetic spectra) is the second – complementary and necessary – step towards a deeper understanding of stellar atmospheres and for deriving stellar parameters (e.g. Teff , L, log g, chemical composition) of observed objects. This thesis is dedicated to the outer layers of Asymptotic Giant Branch (AGB) stars, which have rather remarkable properties compared to atmospheres of most other types of stars. AGB stars represent low- to intermediate mass stars at a late stage of their evolution. Forming a sub-group among all red giants, they exhibit large extensions, low effective temperatures and high luminosities. The evolutionary phase of the AGB – complex but decisive for stellar evolution – is characterised by several important phenomena as for example nucleo-synthesis in explosively burning shells (thermal pulses), convective processes (dredge up), large-amplitude pulsations with long periods or a pronounced mass loss. Red giant stars generally have extremely extended atmospheres with extensions on the same order as the radii of the stars themselves (a few 100 R⊙). Within these cool and relatively dense environments, molecules can efficiently form. They have many internal degrees of freedom leading to a large number of possible transitions (electronic, vibrational, and rotational) and numerous ab- sorption lines/bands. Thus, molecules significantly determine the spectral appearance of late-type stars which have characteristic line-rich spectra in the visual and infrared. At the upper part of the AGB, the stars become unstable to strong radial pulsations (e.g. Mira variables). Due to the large size variations of the stellar interior, the outer layers are levitated and the atmospheric struc- ture is periodically modulated. Triggered by the pulsation, shock waves emerge and propagate outwards through the atmosphere. Efficient dust condensation can take place in the wake of the shock waves (post-shock regions). Due to the large absorptivity of the formed dust grains, radiation pressure results in an outwards directed acceleration with the outflowing dust particles dragging along the surrounding gas. This leads to the development of a rather slow but dense stellar wind. The just mentioned dynamic effects3 – pulsations of the stellar interior and dust-driven winds – have substantial influence on the evolution of the outer layers of these red giants. As a conse- quence, the atmospheres of evolved AGB stars can eventually become even more extended. Being 1Exceptions may be neutrinos from the sun or gravitational waves in the future. 2Note that spectroscopy provides primarily information about the atmosphere of a star, meaning the physical (e.g. T/p/ρ) and chemical (e.g. elemental abundances) properties of the spectrum-forming region. The optically thick stellar interior is a priori not visible, it may influence the spectral appearance indirectly though (e.g. features of nucleo-synthesis products, transformation from M-type to C star in the case of AGB stars). 3neglecting convection

v time-dependently changed on global and local scales, the resulting atmospheric structure strongly deviates from a hydrostatic configuration (e.g. shock fronts). Especially important in the context of this thesis are the complex, non-monotonic velocity fields with macroscopic motions on the order of 10km·s−1, severly affecting the shapes of individual spectral lines (Doppler effect). Observational studies have demonstrated that time series high-resolution spectroscopy in the near infrared (where AGB stars are bright and well observable) represents a valuable tool to study atmospheric kinematics of red giants. The spectra of these stars are densely populated by numerous absorption lines, making very high spectral resolutions (λ/∆λ of a few 104) necessary. It turns out that spectral features of different vibration-rotation bands (or molecules) originate in separated regions of different atmospheric (geometrical) depth. The movements of the layers there can heavily influence the appearance of molecular line profiles in observed spectra (e.g. broadening, line doubling). Radial velocities (RV) derived from (Doppler-) shifts in wavelength of spectral lines provide clues on the gas velocities in the line-forming region of the respective feature. Monitoring line profiles of different individual molecular lines allows to probe atmospheric kinematics throughout the extended AGB atmospheres. Thus, we can trace the velocity field within all regions of the dynamic outer layers of AGB stars over time – and thereby the mass loss process – by repeated spectroscopic observations. Particularly useful in this context is the CO molecule, which is very stable against dissociation (due to its high bond energy) and therefore present at all depths. Three different vibration-rotation band systems originate in quite separated regions and are well observable in spectral windows of the earth’s atmosphere. The corresponding NIR features nicely trace all layers from deep inside the atmosphere out to the cool wind region. Variations of CO line profiles can be used to systematically explore structure and dynamics of AGB atmospheres at different depths. For example, line splitting as a function of phase provides information about how shock waves progress up through the atmosphere. Spectral features of CN are prominent in visual and NIR spectra of carbon-rich AGB stars and can in addition to CO be used to infer velocity information. Modelling the cool and very extended atmospheres of evolved AGB stars remains challenging due to the intricate interaction of different complex phenomena (convection, pulsation, radiation, molecular and dust formation/absorption, acceleration of winds). Standard hydrostatic models are not an adequate approach in the context of this thesis as they neglect the strong influence of dynamics on atmospheric structure and line profiles. Dynamic model atmospheres are con- structed to simulate and understand the physical processes taking place in the outer layers of AGB stars, for example they are crucial for our understanding of the mass loss process. A combined and self-consistent solution of hydrodynamics, frequency-dependent radiative transfer and a detailed time-dependent treatment of dust formation/evolution is needed to reproduce the complex, tem- porally variable structures of AGB atmospheres properly. In this thesis, we utilised models for long period variables with well-pronounced and regular pulsations as well as moderate mass loss rates (Miras). These models represent the scenario of pulsation-enhanced dust-driven winds and provide a consistent and realistic description from the deep and dust-free photospheric layers (dominated by the pulsation of the stellar interior) out to the dust-forming layers and beyond to the stellar wind region. Taking into account the effects of dust in a consistent way is (so far) only possible for carbon-rich chemistries, therefore we concentrated on model atmospheres for C-type Miras in the work presented here. The aim for this thesis was to see, if observed line profiles variations can be comprehended with state-of-the-art dynamic model atmospheres. The typical behaviour of different spectral fea- tures is an important observational aspect which should be reproduced by self-consistent numerical simulations. On the one hand, insights gained by such a line profile modelling may help to inter- pret the observed complex multi-component profiles. On the other hand, reproducing the temporal variability of various molecular line profiles is a crucial test for the atmospheric models. The com- parison of modelling results with observations (i) tells us whether the models resemble structures and dynamics of real AGB atmospheres, (ii) may put constraints on probable mass-loss mecha- nisms, (iii) may provide information on the interrelation of pulsation and mass loss, and (iv) may be a criterion to constrain the stellar parameters for observed targets. In practice, a ’dynamic model

vi atmosphere’ provides snapshots of the time-dependent atmospheric structure (ρ, T, p, ugas, etc.) at several instances of time. On the basis of these and under the assumption of LTE, opacities for var- ious sources are calculated (especially the molecular contributions by using line lists), which serve as input for the subsequent radiative transfer computations. Because of the diverse movements of atmospheric layers in different depths, it is essential to include the influence of macroscopic velocities on the interaction between matter and radiation in this step of the spectral synthesis. Thus, a code for solving spherical radiative transfer which takes into account velocity effects was used to model the complex line profiles and their variations. One major goal for this thesis was to find out if the used dynamic model atmospheres can reproduce the global atmospheric structures of typical pulsating and mass-losing AGB stars (Mira variables), especially the characteristic velocity behaviours in zones of different atmospheric depths. This should allow the simultaneous modelling of spectral lines originating in various layers with one single dynamical model. The only C-rich Mira with a reasonable time series of high-resolution NIR spectroscopy, SCep, served as the reference for the chosen atmospheric model. Synthetic spectra, containing selected CO (∆v=1,2,3) and CN lines, were calculated based on several phases of this model. The results of this modelling – line profile variations, derived RVs (for individual components), estimated regions of line formation – were then compared in detail to observational results of SCep and other Miras. It could be shown that the behaviour of different types of molecular features (known to probe different atmospheric regions) could qualitatively be reproduced by our modelling. Although some differences (e.g. RV amplitudes) remain, this comparison reveals that the global velocity structure of the model (from the deep pulsating photosphere out to the stellar wind region) is in qualitative agreement with velocities derived from spectroscopic observations. Thus, the advanced dynamic model atmospheres used here show fundamental agreement with dynamic processes (pulsation, dust formation, mass loss process) occurring in real Mira atmospheres. By using various dynamic model atmospheres (different stellar parameters, with/without mass loss) we could reproduce the differing behaviour of CO ∆v=3 lines as found in spectroscopic studies of different types of LPVs. Some models were able to reproduce the very characteristic line profile variations of Miras with line doubling at phases of light maximum, leading to S-shaped discontinuous RV curves over the lightcycle (interpreted by a shockwave propagating through the line-forming region). A small parameter study resulted in a model that shows even quantitative agreement with the typical velocity behaviour of second overtone CO lines in Mira spectra (shape and amplitude of RV curve). Another model yielded the same variations as observed for semi-regular variables (SRVs). More detailed investigations suggest that the puzzling finding of observational evidence for shock waves but no line doubling at the same time may be explained by optical depth effects for this type of LPVs. In addition, we studied a few other issues related to the overall topic as for example: the conver- sion factor between measured radial velocties and actual gas velocities in the line-forming region; the shift between bolometric phases φbol and visual ones φv for the dynamic model atmosphere used; or broad-band lightcurves from synthetic spectra based on a dynamic model (reproducing nicely the decrease in amplitude from the visual to the IR as well as the known relation ∆K≈∆mbol).

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