Theoretical Studies on Brown Dwarfs and Extrasolar Planets Dissertation zur Erlangung des Doktorgrades des Department Physik der Universität Hamburg verfasst von René Heller aus Hoyerswerda Hamburg, den 09. Juli 2010 Gutachter der Dissertation: Prof. Dr. Günter Wiedemann Prof. Dr. Stefan Dreizler Prof. Dr. Wilhelm Kley Gutachter der Disputation: Prof. Dr. Jürgen H. M. M. Schmitt Prof. Dr. Peter H. Hauschildt Datum der Disputation: 24. August 2010 Vorsitzender des Prüfungsausschusses: Dr. Robert Baade Vorsitzender des Promotionsausschusses: Prof. Dr. Jochen Bartels Dekan der Fakultät für Mathematik, Informatik und Naturwissenschaften : Prof. Dr. Heinrich Graener iii Contents I Opening thoughts 1 1 Abstract 3 2 Celestial mechanics 7 2.1 Historical context ......................................... 7 2.2 Classical celestial mechanics .................................. 9 2.2.1 Visual binaries ....................................... 10 2.2.2 Double-lined spectroscopic binaries ........................... 10 2.3 Tidal distortion .......................................... 11 2.4 Orbital evolution ......................................... 11 2.5 Feedback between structural and orbital evolution ...................... 12 3 Brown dwarfs and extrasolar planets 15 3.1 Formation of sub-stellar objects ................................. 15 3.2 The brown dwarf desert ..................................... 16 3.3 Evolution of sub-stellar objects ................................. 17 4 The observational bonanza of transits 19 4.1 Photometry ............................................. 19 4.1.1 Transit dynamics ..................................... 20 4.2 Spectroscopy ............................................ 21 4.2.1 The Rossiter-McLaughlin effect ............................. 21 4.2.2 Transit spectroscopy ................................... 22 II Publications 25 5 Tidal effects on brown dwarfs and extrasolar planets 27 5.1 Tidal effects on brown dwarfs: application to 2M0535 05 .................. 27 − 5.2 Constraints on habitability from obliquity tides ....................... 43 5.3 Tidal constraints on planetary habitability .......................... 59 5.4 Tidal effects on the habitability of exoplanets: GJ581 d ................... 67 6 Transits of extrasolar planets 71 6.1 Transit detections of extrasolar planets I. ........................... 71 6.2 Transit detections of extrasolar planets II. .......................... 81 6.3 Albedo and eccentricity determination of exoplanets ..................... 89 6.4 The Photometric Software for Transits (PhoS-T) ....................... 95 III Closing thoughts 101 7 Summary and outlook 103 A Appendix 105 A.1 Auf der Suche nach extrasolaren Transitplaneten ...................... 105 v List of Figures 2.1 Cosmic background radiation .................................. 8 2.2 Radial velocities of a stellar binary ............................... 10 2.3 Tidal distortion and semi-major axes-eccentricity correlation ................ 12 3.1 Brown dwarf desert ........................................ 16 3.2 Evolution tracks of young brown dwarfs ............................ 18 3.3 Evolution tracks of stellar and substellar objects ....................... 18 4.1 Light curve of the transiting exoplanet HD209458b ..................... 20 4.2 Simulations of the Rossiter-McLaughlin effect ........................ 21 4.3 Atmospheric transmission spectrum of the transiting exoplanet HD198733 b ...... 22 7.1 Transit path of the Earth as a projection on the celestial plane ............... 104 xi List of Symbols Proportional ∼ Approximately ≈ Is equivalent to ≡ , Is equal to by definition ≔ Is defined by ≕ Defines x x is rounded up to the next natural number ⌈ ⌉ Infinity ∞ ln(a) loge(a) log(a) log10(a) π Ratio of a circle’s circumference to its diameter ( 1)n π = 4 ∞ − 3.14159 · n=0 2n+1 ≈ P 1 c Speed of light c , 299,792,458 m s− G Gravitational constant G 6.673 10 11 m3 kg 1 s 2 ≈ · − − − M Solar mass M 1.988 1030 kg ⊙ ⊙ ≈ · 27 MJ Jupiter mass MJ 1.8986 10 kg ≈ · R Solar radius R 6.96 108 m ⊙ ⊙ ≈ · 7 RJ Jupiter radius RJ 7.1492 10 m ≈ · AU Astronomical unit AU 149.598 109 m ≈ · Myr Megayear Myr 31, 536, 000, 000, 000 s ≈ FAUST. Ich bin nur durch die Welt gerannt! Ein jed Gelüst ergriff ich bei den Haaren, Was nicht genügte, ließ ich fahren, Was mir entwischte, ließ ich ziehn. Ich habe nur begehrt und nur vollbracht Und abermals gewünscht und so mit Macht Mein Leben durchgestürmt: erst groß und mächtig, Nun aber geht es weise, geht bedächtig. Der Erdenkreis ist mir genug bekannt. Nach drüben ist die Aussicht uns verrannt; Tor, wer dorthin die Augen blinzelnd richtet, Sich über Wolken seinesgleichen dichtet! Er stehe fest und sehe hier sich um: Dem Tüchtigen ist diese Welt nicht stumm! Was braucht er in die Ewigkeit zu schweifen? Was er erkennt, läßt sich ergreifen. Er wandle so den Erdentag entlang; Wenn Geister spuken, geh er seinen Gang, Im Weiterschreiten find er Qual und Glück, Er, unbefriedigt jeden Augenblick! SORGE. Wen ich einmal mir besitze, Dem ist alle Welt nichts nütze: Ewiges Düstre steigt herunter, Sonne geht nicht auf noch unter, Bei vollkommnen äußern Sinnen Wohnen Finsternisse drinnen, Und er weiß von allen Schätzen Sich nicht in Besitz zu setzen. Glück und Unglück wird zur Grille, Er verhungert in der Fülle, Sei es Wonne, sei es Plage, Schiebt ers zu dem andern Tage, Ist der Zukunft nur gewärtig, Und so wird er niemals fertig. Johann Wolfgang Goethe, “Faust” (Zeilen 11433 – 11466) Part I Opening thoughts Chapter 1 Abstract With our human self-reflection we embody the fact that the Universe thinks about itself. About 13.75 billion years after a Big Bang, dead matter became something that is able to say “Je pense, donc je suis.”, or “I think, therefore I am”. For several thousands of years, we are wondering what it means ‘to be’, what that is which has being, where did it all come from and – why. In quest of answers to these questions, some dig into the shortest scales of matter, so they may penetrate the power that holds the Universe together. Others study the forms of life or explore the human brain, some believe in an omnipotence and some, finally, use devices to look deep into the sky. About 20 years ago, these stargazers – astronomers, who used to name celestial objects in former times, and astrophysicists, who study their physical qualities – discovered the first planet that orbits a distant star. Over the intervening years, the number of such confirmations has increased to several hundreds. Moreover, scientists discovered objects, which are neither stars nor planets, but have intermediate masses. These ‘brown dwarfs’ constitute the connecting link between the two regimes. And both, stars as well as planets, can only be understood comprehensively in their context with brown dwarfs. The mere number of these so-called extrasolar planets, or exoplanets, does not tell us too much about our cosmological context. We want to study them. This thesis aims at the gravitational interaction of stellar and substellar objects and at the possibilities for their exploration. The picture of an isolated planet that orbits its host star undeviatingly and forever is obsolete. Recent discoveries have shown that the fate of planets in close orbits is determined by star-planet interaction. And tidal effects turned out to play a key role. Even more, the structure of young brown dwarfs essentially depends on the tidal processes driven by close companions. Part I of this book, with its Chaps. 2 to 4, gives an introduction to the basic physics and to the objects we will deal with. In Part II, which makes up the cumulative contingent of my publications, Chap. 5 is dedicated to the tidal effects on brown dwarfs. This issue had not been considered before. Here, we point out how tidal processes affect the energy budget of these substellar objects and how they cause deviations from the standard evolution tracks of isolated brown dwarfs. We apply different established tidal models to the case of the currently only known eclipsing brown dwarf binary, and we identify their differences as well as possibilities for their validation or falsification. In the following, I address the impact of tidal effects on the habitability of exoplanets. As we find, the concept of the so-called (circumstellar) ‘habitable zone’ requires a revision in due consideration of tidal processes. Chapter 6 is devoted to the prediction of extrasolar planet transits and data analysis. We present sky maps of the expectation values of transits as a projection on the celestial plane. We also introduce a mathematical model, which allows for the deduction of the planet’s orbital eccentricity, orientation of periastron, geometric albedo, its radius as a fraction of the stellar radius, its orbital period, and the inclination of the orbital plane with respect to the observer’s line of sight. In Part III, I take the liberty to conclude, and in the appendix, finally, I present a German popular science publication of my studies on extrasolar transiting planets. 4 CHAPTER 1. ABSTRACT Abriss Die menschliche Selbstreflexion macht uns zu einem Hort, an dem das Universum über sich selbst nachdenkt. Nach ca. 13,75 Milliarden Jahren ist aus toter Materie etwas entstanden, das „Je pense, donc je suis.“ sagt, oder „Ich denke, also bin ich“. Seit einigen tausend Jahren fragen sich Menschen, was das Sein ist, woher alles Seiende kommt, wie es anfing und – warum. Auf der Suche nach Antworten auf diese Fragen schauen manche in die kleinsten Teilchen, um dort zu finden, was die Welt im Innersten