iii Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Paul HEEREN born in: Kulmbach, Germany Oral examination: 20.07.2021 v Testing Planet Candidates around Giant Stars: Computation and Analysis of High Precision Radial Velocities Referees: Prof. Dr. Andreas QUIRRENBACH Prof. Dr. Henrik BEUTHER vii “The fact that we live at the bottom of a deep gravity well, on the surface of a gas covered planet going around a nuclear fireball 90 million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be.” Douglas Adams ix RUPRECHT-KARLS-UNIVERSITÄT HEIDELBERG Abstract Testing Planet Candidates around Giant Stars: Computation and Analysis of High Precision Radial Velocities by Paul HEEREN The radial velocity (RV), or Doppler, technique is one of the most successful meth- ods in the search for exoplanets; with more than two decades of RV measurements 1 acquired for some stars, and thanks to a precision around 1 m s− and better reached by modern spectrographs, it allows to explore an ever greater variety of planetary systems. In this PhD dissertation, I present my contributions to the RV survey of G- and K-giant stars, which is conducted by the Exoplanet Group at the Landesstern- warte (LSW) Heidelberg. The aim is to track planet candidates in the sample, and thus strengthen our understanding of planet occurrence rates around these types of stars and discern between planetary signatures and false positives caused by intrin- sic stellar variations. My work can be split into two parts: First, I was involved in the Waltz telescope project, which will act as a successor to the CAT telescope at Lick observatory and allow to continue the RV survey of giant stars with an LSW-owned telescope. I describe my work on opto-mechanical components which enabled to reach first light on-sky, and I present results from early observations. My main task in the project was the build-up of the Waltz DRS (data reduction software), which will be used to reduce acquired spectra and extract RVs. I detail the structure of the software and implementation of mathematical methods, and discuss first test results on early Waltz and archived Lick spectra. The second part of my work concerns the analysis of the highly eccentric stellar bi- nary ε Cygni, which is part of the K-giant sample. RV data obtained at Lick, with the SONG telescope on Tenerife, and from the literature show short-period variations in addition to the long signal caused by the stellar companion, which might hint at a planetary companion on a S-type orbit around the primary. I present Keplerian and dynamical models and constrain the orbit of the stellar companion; however, in combination with a stability analysis of the system, the models deem the planet hypothesis to be highly unlikely. I examine possible alternative explanations for the short-period RV variations and find tidally induced stellar oscillations as a plausible cause. x Zusammenfassung Prüfung von Planetenkandidaten um Riesensterne: Berechnung und Analyse von hochpräzisen Radialgeschwindigkeiten Die Radialgeschwindigkeits-Technik, oder auch Doppler-Technik, ist eine der erfol- greichsten Methoden zum Auffinden von Exoplaneten. Mit mehr als zwei Jahrzehn- ten gesammelter Messungen für manche Sterne, und mit Hilfe moderner Spektro- 1 graphen, die eine Präzision von 1 m s− und besser erreichen, erlaubt diese Methode eine immer größere Vielfalt von Planetensystemem zu erforschen. In dieser Dis- sertation stelle ich meine Beiträge zur Radialgeschwindigkeitsstudie von G- und K- Riesensternen vor, die von der Exoplanetengruppe an der Landessternwarte (LSW) Heidelberg durchgeführt wird. Sie hat zum Ziel, Planetenkandidaten in der Stich- probe aufzuspüren, und damit unser Verständnis der Planetenvorkommen um diese Sterntypen zu verbessern und zwischen von Planeten verursachten Signalen und falsch-positiven Signaturen aufgrund von stellaren Variationen zu unterscheiden. Meine Arbeit lässt sich in zwei Bereiche aufteilen: Einerseits war ich am Waltz- Teleskop-Projekt beteiligt, das als Nachfolger des CAT-Teleskops am Lick-Observa- torium dienen und damit eine Weiterführung der Radialgeschwindigkeitsmessun- gen von Riesensternen an einem Teleskop der LSW erlauben wird. Ich beschreibe meine Arbeit an optisch-mechanischen Komponenten, mit denen erste Beobach- tungen am Himmel erreicht werden konnten, und ich präsentiere Resultate dieser Beobachtungen. Meine Hauptaufgabe im Projekt war es, die Datenreduktionssoft- ware Waltz DRS aufzubauen, die zur Reduktion der aufgenommenen Spektren und Extraktion der Radialgeschwindigkeiten eingesetzt wird. Ich beschreibe den Aufbau der Software und die Einbindung der mathematischen Methoden, und diskutiere er- ste Testergebnisse an frühen Waltz- und archivierten Lick-Spektren. Der zweite Teil meiner Arbeit betrifft die Analyse des stark exzentrischen Doppel- sternsystems ε Cygni, das Teil der K-Riesen-Stichprobe ist. Radialgeschwindigkeits- messungen vom Lick-Observatorium, vom SONG-Teleskop auf Teneriffa, und aus der Literatur zeigen neben dem langen Signal, das durch den stellaren Begleiter verursacht wird, auch kurzperiodische Variationen, die auf einen planetaren Be- gleiter auf einem S-Orbit um den Primärstern hindeuten könnten. Ich präsentiere Kepler- und dynamische Modelle und grenze den Orbit des stellaren Begleiters ein; in Kombination mit einer Stabilitätsanalyse des Systems lassen die Modelle die Plan- etenhypothese jedoch als sehr unwahrscheinlich erscheinen. Ich untersuche mög- liche alternative Erklärungen für die kurzperiodischen Radialgeschwindigkeitsvari- ationen und halte gezeiteninduzierte stellare Oszillationen für eine plausible Ur- sache. xi Acknowledgements I would not have been able to perform the work presented in this dissertation, let alone write it, without the help of a large network of people around me who sup- ported me in many different ways, some more direct, others probably without even knowing about their helping me. The latter will hopefully know after having read my acknowledgements. Science is teamwork, and I have discussed my research with more people than I can possibly recall. Of greatest importance and influence on my work however was the feedback of my supervisors, Andreas Quirrenbach and Sabine Reffert: Their detailed suggestions helped to open up many alleged dead-ends, and I am grateful for the chances they have given me, and for the responsibilities they have trusted me with. Furthermore, I want to thank Martin Kürster, third advisor on my IMPRS thesis committee, who always has an open ear for ones worries and knows how to find an encouraging response. Also I am thankful to Henrik Beuther, who agreed to act as second referee of this thesis, and to Joachim Wambsganss and Fred Hamprecht, for joining my defence examination panel. And to the proofreaders of this work, Sabine Reffert and Steffi Yen: Thank you so much for your invested time, and the helpful and very constructive comments! During my PhD, I dove head-on into the field of planetary dynamics, and my grat- itude goes out to Trifon Trifonov and Man Hoi Lee who would always readily pro- vide me with learning material and answers to my questions. For my work on the Waltz telescope project, I got a lot of fruitful advice (e.g. about how not to break things) from Walter Seifert, Otmar Stahl, Julian Stürmer and Rob Harris, who I would like to thank here. Still, the Waltz instruments would not be standing and functional without the workshops of the LSW, and my thanks go out to Jochen Ti- etz, Edwin Lutz, and particularly Lutz Geuer for his competent work (talking about "Lutz-precision"). My work on the Waltz DRS profited greatly from the help and advice of several experts in the field: René Tronsgaard Rasmussen, who shared his pyodine code with me; Rafael Brahm and Andres Jordan, who guided me when I started working with the CERES package; and notably Frank Grundahl, who not only shared his many experiences (and some frustrations) with RV analysis codes with me, but also supplied me with SONG data to test the Waltz DRS on. A productive workspace however not only requires work-related help, but also a socially comfortable environment — and for creating this, I want to thank all my colleagues, fellow PhD students (viva la generacion 13), bachelor and master stu- dents, and the institute staff members. Particularly, I am grateful for having met all the wonderful characters of the LSW gang; heated discussions, pranks gotten out- of-hand, collective lunching (and dining, some drinking), puzzles, movies, birthday gifts and songs. Finally, with a global pandemic raging during the final year of my PhD, I am thank- ful to my flatmates who created a home worth of spending much more than just one lockdown in. I also got by with a little help of my friends, with whom I can take ev- erything with the earnest sarcasm it deserves. I want to thank Anujeema, for feeling so close despite being so far. And I am grateful for my family, who always reassured me of my ability to write this dissertation (even whilst not being fully seated). Most of all to my parents: You taught me to marvel at life, and to follow my heart rather than any outer expectations. Thank you! xiii Contents Abstract ix Acknowledgements xi Contents xiii 1 Introduction 1 1.1 The Radial Velocity (RV) method ...................... 4 1.1.1 Orbital parameters from radial velocities ............. 5 1.1.2 Design and performance of high-resolution spectrographs . 7 1.1.3 Reduction of spectra ......................... 10 1.1.4 The iodine-cell method ........................ 14 1.2 Exoplanets around evolved stars ...................... 17 1.2.1 The Lick RV survey of evolved stars . 17 1.2.2 Occurrence rate of planets as function of stellar mass and metal- licity .................................. 18 1.2.3 Overall occurrence rate and period distribution of planets . 19 1.3 RV variations beyond the Keplerian model .