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Radial Velocity Variations in Red Giant Stars: Pulsations, Spots and Planets

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Radial Velocity Variations in Red Giant Stars: Pulsations, Spots and Planets RADIAL VELOCITY VARIATIONS IN RED GIANT STARS: PULSATIONS, SPOTS AND PLANETS RADIAL VELOCITY VARIATIONS IN RED GIANT STARS: PULSATIONS, SPOTS AND PLANETS Proefschrift ter verkrijging van de graad van Doctor aan de Universiteit Leiden, op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden, volgens besluit van het College voor Promoties te verdedigen op 18 september 2007 klokke 13:45 uur door Saskia Hekker geboren te Heeze in 1978 Promotiecommissie Promotor: Prof. dr. A. Quirrenbach Sterrewacht Leiden Landessternwarte Heidelberg Promotor: Prof. dr. C. Aerts Katholieke Universiteit Leuven Radboud Universiteit Nijmegen Co-promotor: Dr. I. A. G. Snellen Sterrewacht Leiden Overige leden: Prof. dr. E. F. van Dishoeck Sterrewacht Leiden Prof. dr. K. H. Kuijken Sterrewacht Leiden Prof. dr. P. T. de Zeeuw Sterrewacht Leiden Dr. M. Hogerheijde Sterrewacht Leiden Dr. J. Lub Sterrewacht Leiden Dit proefschrift is tot stand gekomen met steun van No pain, no gain Contents 1 Introduction 1 1.1 Redgiantstars................................... 2 1.2 Observations ................................... 4 1.2.1 Iodinecell................................. 4 1.2.2 SimultaneousThAr............................ 4 1.3 Oscillations .................................... 5 1.3.1 Excitationmechanism .......................... 9 1.3.2 Asymptoticrelation. 10 1.3.3 Scalingrelations ............................. 10 1.4 Starspots...................................... 11 1.5 Sub-stellarcompanions . ... 12 1.6 Why can oscillations, spots and companions be observed as radial velocity vari- ations?....................................... 14 1.7 Lineprofileanalysis.............................. .. 15 1.7.1 Moments ................................. 15 1.7.2 Amplitudeandphasedistribution . ... 16 1.7.3 Linebisector ............................... 16 1.7.4 Lineresidual ............................... 18 1.7.5 Examples................................. 18 1.8 Thisthesis..................................... 22 2 Pulsations detected in the line profile variations of red giants: Modelling of line moments, line bisector and line shape 27 2.1 Introduction.................................... 28 2.2 Observationaldiagnostics. ..... 29 2.2.1 Spectra .................................. 29 2.2.2 Cross-correlationprofiles. ... 30 2.2.3 Frequencyanalysis ............................ 32 2.3 Theoreticalmodediagnostics. ..... 34 2.3.1 Discriminant ............................... 35 2.3.2 Amplitudeandphasedistribution . ... 36 2.4 Simulations .................................... 38 2.4.1 Dampingandre-excitationequations . .... 41 2.4.2 Frequencies................................ 44 vii Radial velocity variations in Red Giant stars: pulsations, spots and planets 2.4.3 Amplitudeandphasedistribution . ... 45 2.5 Interpretation .................................. 47 2.6 Discussionandconclusions. .... 48 3 Precise radial velocities of giant stars. I. Stable stars 51 3.1 Introduction.................................... 52 3.2 Observations ................................... 52 3.3 Results....................................... 53 3.4 Discussionandconclusions. .... 54 3.4.1 Statistics ................................. 54 3.4.2 Variability................................. 54 3.4.3 Standardstarsample ........................... 61 3.4.4 Referencestars .............................. 61 3.4.5 Sub-stellarcompanionsandpulsations . ...... 62 4 Precise radial velocities of giant stars. III. Variability mechanism derived from statistical properties and from line profile analysis 65 4.1 Introduction.................................... 66 4.2 Radialvelocityobservations . ..... 67 4.3 Radial velocity amplitude - surface gravity relation . ............. 68 4.4 CompanionInterpretation. .... 70 4.4.1 Massdistribution............................. 71 4.4.2 Semi-majoraxisdistribution . ... 72 4.4.3 Perioddistribution . 73 4.4.4 Eccentricitydistribution . ... 73 4.4.5 Ironabundance .............................. 74 4.4.6 Summarycompanioninterpretation . ... 75 4.5 Lineshapeanalysis ............................... 75 4.5.1 Lickdata ................................. 76 4.5.2 SARGdata ................................ 77 4.5.3 Results .................................. 79 4.5.4 Discussionofthelineprofileanalysis . ..... 86 4.6 Conclusions.................................... 87 5 Precise radial velocities of giant stars. IV. Stellar parameters 91 5.1 Introduction.................................... 92 5.2 Observations ................................... 93 5.3 Effective temperature, surface gravity, and metallicity.............. 93 5.3.1 Comparisonwiththeliterature . ... 94 5.3.2 ComparisonwithLuck&Heiter(2007) . .. 97 5.3.3 Metallicityincompanionhostinggiants . ...... 97 5.4 Rotationalvelocity .............................. .. 99 5.4.1 Macroturbulence............................. 100 5.4.2 Comparisonwiththeliterature . 101 5.5 Summary ..................................... 101 viii Contents Summary and Future prospects 115 Bibliography 121 Nederlandse Samenvatting 123 Curriculum Vitae 131 Acknowledgements 133 ix CHAPTER 1 Introduction N this Chapter some background information on the main topics of this I thesis will be described. First, I will describe the red giant phase of stars, why stars in this phase are of particular interest, and some open questions. Subsequently, I will discuss two different spectroscopic calibration methods that are widely used to observe radial velocity variations, namely iodine cell and simultaneous ThAr observations. Both methods reach accuracies of order ms−1, but are based on different strategies. I will continue with some background information on oscillations, starspots and sub-stellar companions. These phenomena can all cause variations in the observed radial velocity, but expose different characteristics of the star. Oscillations reveal in a quasi-direct way the internal structure of a star, while starspots provide information on the magnetic field(s) of the star. Detection of sub-stellar companions contributes to present knowledge on the formation and evolution of planetary systems. Following the description of these phe- nomena, I will discuss why they can cause similar observational results in radial velocity measurements. A variation, or a lack of variation, in spectral line shape plays an important role in distinguishing between the different phenomena, and, therefore, spectral line shape diagnostics are presented together with some examples for oscillations, spots and companions. An overview of the contents of the subsequent chapters of this thesis is provided at the end of the introduction. 1 Radial velocity variations in Red Giant stars: pulsations, spots and planets 2. Collapse toward center, becoming hotter than 3. Increased fusion rate in before. ¢ ¢ £ shells, causing expansion. ¢ ¢ £ ¢ ¢ £ Expansion takes energy, ¢ ¢ £ so surface cools and ¤ ¤ ¥ ¥ reddens. ¤ ¤ ¥ ¥ ¡ 1. Burn−up of hydrogen ¡ ¡ ¡ ¡ at center. ¡ ¦ ¦ § § ¦ ¦ § § 4. Star expands greatly and reddened luminosity ¨ ¨ © increases because area is ¨ ¨ © ¨ ¨ © so much increased, even though it is cooler. Figure 1.1: The evolution of a red giant. 1.1 RED GIANT STARS It is generally thought that stars are born in an interstellar cloud, which collapses under its own gravity. The mass of this cloud is one of the parameters determining the mass of a star. Dur- ing the main sequence life of stars, energy is generated in the core by fusion of hydrogen to helium. The star is in hydrostatic equilibrium in this phase with equal, but opposite, pressure and gravitational forces. Over time the star develops towards an object with a core of pure helium surrounded by a hydrogen shell. The temperature in the core is not (yet) sufficient to fuse helium to carbon. Without a source of energy generation, the helium core cannot support itself against gravitational collapse. Consequently, the core starts to collapse, which results in a temperature increase. Due to this temperature rise, the fusion in the hydrogen shell increases, and the outer layers of the star will expand and cool. The collapse of the core continues until it reaches a temperature of 100 million degrees, at which fusion of helium to carbon starts. The star expands and cools further due to the increased heating in the core, and eventually progresses to an equilibrium phase. This evolution is schematically shown in Figure 1.1. Red giant stars are of particular interest for several reasons: 1. Every star with a mass between 0.4 and 10 times the mass of the sun should eventually go through a red giantphase. Only in the red giantphase carbon and more heavy elements are formed, the basis of all life, and, therefore, this is an important phase in stellar evolution. 2. A large fraction of the brightest stars are red giants. Not only the number of stars is large, but they are also observable over large distances, which make them potential reference stars for e.g. astrometry. 3. Research on red giants is a way to learn more about massive stars. Massive stars on the main sequence rotate rapidly and are very hot. As a result, they do not have many spectral 2 Introduction lines, and the ones they have, are broadened due to rotation. When these stars turn off the main sequence, they cool down and their rotational velocity decreases, which increases the number of spectral lines and narrows them. In this phase, it becomes possible to perform spectroscopic measurements to detect small radial velocity variations. 4. Red giants are ideal targets for stellar oscillation
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