Mitigating stellar signals in the quest for other Earths

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Thesis

Reference

Mitigating stellar signals in the quest for other Earths

DUMUSQUE, Xavier

Abstract

After having found hundreds of extra-solar planets, the radial-velocity (RV) technique starts to be limited by intrinsic stellar signals. Indeed, at the level of the best spectrographs, one starts to see the effects induced by stellar pressure waves, convection, surface activity coupled with stellar rotation, and magnetic cycles. The questions of how to extract and analyse the different stellar signals from RV data, and how to mitigate their contributions have been studied in detail. In addition, optimizing the observational strategy to look for planets can also help in mitigating short-term stellar signal effects. As a result, a few dozen of the lowest mass planets known so far have been discovered following the work performed in this thesis. Among these planets, we have discovered Alpha Centauri Bb, the lightest extra-solar planet detected so far with the RV technique, and the closest one to our Solar System.

DUMUSQUE, Xavier. Mitigating stellar signals in the quest for other Earths. Thèse de doctorat : Univ. Genève, 2012, no. Sc. 4504

URN : urn:nbn:ch:unige-265026

DOI : 10.13097/archive-ouverte/unige:26502

Available at:

http://archive-ouverte.unige.ch/unige:26502

Disclaimer: layout of this document may differ from the published version.

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Université de Genève Faculté des Sciences Département d’Astronomie Professeur Stéphane Udry

Universit´e de Porto Facult´e des Sciences

D´epartement de Physique et d’Astronomie Docteur Nuno C. Santos

Mitigating stellar signals in the quest for other Earths

Th` ese

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences,

mention Astronomie et Astrophysique

par

Xavier DUMUSQUE

de

Rennaz (VD, Switzerland)

Th`ese N^o 4504

Gen`eve

Observatoire Astronomique de l’Universit´e de Gen`eve 2012

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R´ ESUM´ E

Depuis l’Antiquité, toutes les civilisations avancées se sont posées la question de l’existence d’autres mondes au delà du Système Solaire. Avec la centaine de milliards d’étoiles con- stituant notre Galaxie, l’unicité du Système Solaire semblait absurde. Cependant, il a fallu attendre 1995, date à laquelle la première planète extrasolaire fût découverte autour d’une

´etoile similaire au Soleil, pour confirmer l’existence d’autres mondes. Avec une masse ´egale

`

a la moitié de celle de Jupiter et une période orbitale de seulement quatre jours, ce Jupiter chaud n’était en rien ressemblant aux planètes présentes dans notre Système Solaire. Au fil des ans et de l’amélioration des techniques de détection, de nouveaux types de planète ont

été détectés. C’est le cas des mini-Neptunes, des super-Terres, des mondes de lave, ou des planètes océans. Tous ces types de nouveaux mondes sont absents du Système Solaire et re- flètent l’incroyable diversité de la nature. Une variété d’architecture des systèmes planétaires est aussi observée avec la découverte de planètes circumbinaires, de systèmes multiplanétaires extrêmement compacts ainsi que de planètes sur des orbites rétrogrades par rapport au sens de rotation de l’étoile hôte. Nous connaissons aujourd’hui plus de 800 planètes, sans prendre en compte plus de 2’300 candidats qui attendent d’être confirmés. Ces découvertes ne représen- tent peut-être que la partie émergée de l’iceberg et le perpétuel progrès de l’exoplanétologie rend cette science excitante.

Il existe aujourd’hui une dizaine de méthodes pour découvrir ces autres mondes. Néanmoins, la technique des vitesses radiales et celle des transits comptabilisent à elles seules la grande majorité des découvertes. La première méthode consiste à mesurer l’infime vitesse de déplace- ment de l’étoile perturbée par la planète qui orbite autour. La deuxième technique quant à elle mesure la faible décroissance de flux de l’étoile lorsqu’une planète passe devant. Ces deux techniques sont complémentaires, l’une donnant une information sur la masse minimale d’une planète, l’autre sur le rayon de l’objet détecté. Ainsi, la densité moyenne de la planète peut- être calculée, ce qui permet d’étudier sa composition interne. De plus, lorsqu’une planète transite, une petite fraction de la lumière de l’étoile passant à travers son atmosphère peut nous renseigner sur sa composition chimique. C’est ainsi qu’aujourd’hui nous sommes en mesure de savoir que des éléments tels que le sodium, l’hydrogène, le carbone, l’oxygène et l’eau existent sur certaines planètes.

La technique des vitesses radiales, qui ne cesse d’´evoluer en pr´ecision, permet aujourd’hui

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de découvrir des planètes aussi légères que la Terre, cependant sur des orbites beaucoup plus courtes. Cette extrême précision a aussi révélé la nature agitée des étoiles. Il est maintenant possible d’observer les effets induits par des ondes de pression se propageant à la surface des étoiles, par la convection, par la présence de taches stellaires, ainsi que par les cycles magnétiques des étoiles. La Terre induit un effet sur le Soleil d’un ordre de grandeur inférieur aux différents signaux stellaires. Cela soulève une question essentielle : ”Sera-t- il possible d’atteindre ce niveau de précision en considérant les différents types de signaux propres aux étoiles ?”. Les pessimistes sont convaincus que cela ne sera pas réalisable, alors que les optimistes argumentent qu’avec une analyse poussée et une bonne compréhension de ces phénomènes, nous pourrons un jour détecter une jumelle de la Terre. J’ai toujours été quelqu’un d’optimiste et la majeure partie de mon travail de thèse se focalise sur l’étude des signaux intrinsèques stellaires et le développement de nouvelles techniques permettant de réduire leurs impacts et ainsi repousser les limites de la méthode des vitesses radiales.

Cette thèse se concentre sur la caractérisation des différents types de signaux stellaires per- turbant les mesures de vitesse radiale et les manières de réduire leurs contributions. Une première étape du travail a consisté en l’étude d’une stratégie observationnelle permettant à la fois de moyenner l’effet des signaux à courte période et d’échantillonner correctement les signaux à plus longue période afin d’étudier leur comportement et ainsi trouver des solutions pour réduire leur impact. Cette stratégie d’observation a, par la suite, été appliquée au suivi de dix étoiles et a permis la découverte de sept planètes de petite masse. Ce résultat, dé- montrant l’efficacité d’une telle stratégie, reflète également la grande proportion des planètes de petite masse. Les récentes analyses statistiques arrivent à la conclusion qu’au moins 50 % des étoiles de type solaire présentent un compagnon planétaire.

L’étude des données obtenues par le spectrographe HARPS, le meilleur instrument actuel pour la recherche de planètes avec la technique des vitesses radiales, a permis de caractériser les signaux stellaires induits par l’activité des étoiles. Cette activité se caractérise par l’apparition de taches sombres et brillantes à la surface des étoiles, dont le nombre varie en fonction du cycle magnétique. L’effet des taches ainsi que des cycles magnétiques a été étudié et des solutions intéressantes ont été trouvées pour réduire leur impact. Les cycles magnétiques induisent un effet, en vitesse radiale, corrélé avec la variation de l’activité. L’amplitude d’un tel signal dépend de la température effective ainsi que de la metallicité des étoiles. Pour ce qui est du signal induit par la présence de taches sur la surface d’une étoile, ce dernier peut être modélisé en ajustant des sinuso¨ıdes à la période de rotation de l’étoile et ses harmoniques.

L’impact sur les vitesses radiales de ces effets d’activité peut ainsi être réduit.

Ces quatre ans d’effort continu visant à réduire l’impact des différents signaux stellaires s’achèvent avec la découverte de la planète la plus légère jamais détectée par la technique des vitesses radiales. Ayant une masse très proche de celle de la Terre, cette planète orbitant autour de Alpha du Centaure B est aussi la plus proche du Système Solaire. Une analyse complexe utilisant de nouvelles techniques pour réduire l’impact des différents signaux stellaires a permis d’arriver à cette importante découverte. Avec une période orbitale de trois jours, cette planète est sûrement plus ressemblante à unmonde de lavequ’à une planète où il fait bon vivre. La précision atteinte après avoir réduit l’effet des différents signaux stellaires permettrait de détecter une planète de quatre fois la masse de la Terre dans la zone habitable d’une étoile similaire au soleil. Ce résultat représente donc une étape importante vers la détection d’une jumelle de la Terre. Nous vivons à une époque excitante.

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FOREWORDS

After centuries of wondering if other worlds were present beyond the Solar System, the first extra-solar planets were discovered about twenty years ago. With hundreds of billions of stars in our Galaxy, there was little doubt about the existence of other planets in our close neighborhood. However we had to find the first one to spark things off. The number of discoveries never stopped growing: at present, there are more than 800 extra-solar planets discovered, and over 2’300 candidates awaiting confirmation. The first planets found around solar-type stars were Hot Jupiters, i.e. Jupiter-mass planets orbiting extremely close to their parent star, something inconceivable at the time. Then came the discovery of mini- Neptunes,super-Earths,lava worlds, andocean planets. All these types of planets are absent from our Solar System and show the incredible diversity in mass, in size, and in orbital period. A variety in architecture of the systems has also been observed, with the discovery of circumbinary planets, bodies that orbit not one but two stars, very compact multi-planetary systems or planets orbiting on retrograde orbits. This is perhaps only the tip of the iceberg and going from one surprise to the next makes exoplanetology a more and more exciting subject.

Nowadays, several different techniques are used to search for exoplanets. The two major methods, Doppler radial-velocimetry and transit photometry, account for the big majority of detections. The first technique measures the gravitational stellar wobbles induced by a companion orbiting its parent star, and the second one detects the small decrease in stellar flux that occurs when a planet passes in front of the stellar disc. Radial velocimetry and transit photometry are complementary, one giving the minimum mass of planets, the other their radius. The combination of both yields the planet’s real mass and average density, which can then be used to infer the composition of these other worlds. In addition, when a planet transits its parent star, a tiny fraction of the stellar light will pass through the atmosphere of the planet, allowing us to obtain information about the principal constituent of the planet’s atmosphere. Thus, sodium, hydrogen, carbon, oxygen, and water vapor have been found in the atmosphere of a few extra-solar planets.

The meter per second precision in radial velocimetry has revolutionized our understanding of exoplanets. Small-mass planets down to the size of the Earth have been detected, nevertheless on short-period orbits. Gas giants similar to the ones in our Solar System have also been

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found. Unfortunately for planet searches, this precision also revealed previously unnoticed signal sources that are related to the stars themselves. Indeed, one starts to see the effect induced by pressure waves propagating on the surface of stars, convection, surface activity coupled with stellar rotation, and even magnetic cycles. There is a serious debate underway in the exoplanet community about whether it will ever be possible to derive a radial-velocity orbit with an amplitude of a tenth of a meter per second for a star like the Sun, as will be required to detect an Earth twin. The pessimists argue that such a planetary signal will be completely masked by intrinsic stellar signals. The optimists though think that with carefully designed observing protocols and data analysis, it will be possible to correct for these astrophysical effects.

The main work performed during these four years of PhD has been focused on characterizing the different stellar signals that are affecting radial-velocity measurements, and to find ways to mitigate them. The first step was to find an optimum observational strategy that was capable of both averaging out high-frequency stellar signals, and sampling efficiently low- frequency signals to characterize them and finds ways to correct them. This observational strategy was then used to follow a small sample of ten stars that were all presenting at the time a very low level of radial-velocity variation. Out of this small sample, seven small-mass planets were discovered. Besides proving the efficiency of such an approach, this results also points out that small-mass planets are common. Recent statistical studies carried out on HARPS andKepler results arrive to the conclusion that more than 50 % of solar-type stars harbor at least a planet.

Precise radial-velocity measurements obtained with HARPS allowed us to characterize the behavior of activity-related stellar signals, such as variations induced by the presence of magnetic features on a rotating star, or radial-velocity perturbations produced by sun-like magnetic cycles. Ways to correct these long-term effects have been investigated and interesting outcomes were found. The RV effect induced by a magnetic cycle depends not only on the strength of the cycle, but also on basic stellar properties like the effective temperature and the metallicity. Cool and metal poor stars are less affected by magnetic cycles than hotter and more metal rich stars, making them better candidate to search for low-mass planets.

Knowing the basic stellar properties and the strength of a magnetic cycle, it is possible to estimate the amplitude of the radial-velocity signal induced. Regarding the radial-velocity variation produced by magnetic features rotating with the star, it can be modeled fitting sine waves at the rotational period of the star and its harmonics. In conclusion, the effects of activity-related stellar signals can be mitigated.

These four years of continuous efforts trying to reduce the effect of stellar signals finish with the discovery of the smallest mass planet found so far with the radial-velocity technique.

Nearly having the mass of the Earth, this planet is also the closest one to the Solar system, as it orbits around Alpha Centauri B. The extraction of the tiny signal completely overwhelmed by stellar signals was difficult. An important effort has been carried out to mitigate these perturbing signals, which lead to an interesting result. This planet has been discovered on a short-period orbit of three days, being more a lava world, than a peacefully Earth twin.

However the precision reached after mitigating stellar signals would allow the detection of a planet four times more massive than the Earth in the habitable region of a solar-type star.

This result represents a major step towards the detection of an Earth twin in the immediate vicinity of the Sun. We live in exciting times.

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THANKS

A thesis is often seen as the work of a single person. However, the research presented in this manuscript has been possible thanks to the help of many people that gave me new ideas when I was lost, that motivated me when I was exhausted, that simply listened to me when I had to speak to someone.

My greatest thanks go to Stéphane and Nuno who supervised my work during these four years. The enthusiasm of Nuno, his expertise in the field of exoplanets, and all the time shared together, made of my stay in Porto an incredibly interesting moment. After spending two years in Portugal with Nuno, I came back to Geneva where Stéphane took me under his wing. Even if he was extremely busy, being director of the observatory and head of the Geneva exoplanet’s group, he always found time to get interested in my work, read my papers before submission, supported me for proposals and fellowships. Stéphane is a very optimist person, extremely competent, and it was a great honor to work for him during my PhD.

He also taught me a lot about different political aspects, which is an invaluable help for my future career.

The exoplanet’s group in Geneva is boiling with enthusiasm, new ideas and expertise. All these qualities in a very friendly environment have made of my stay in Geneva an excep- tional experience. Special thanks to Damien S´egransan and Christophe Lovis for always taking time to help me on difficult topics, to Francesco Pepe for his invaluable knowledge on instrumentation, to Michel Mayor always getting interested into people’s work.

Thanks also to Marion, my office mate, with who I spent pleasant moments, to Richard Anderson, Johannes Sahlmann, Amaury Triaud, Monika Lendl, Janis Hagelberg in Geneva, and Ahmed Grigahc`ene, Nanda Kumar, Giancarlo Pace, Pedro Figueira, Micha¨el Bazot in Porto for all the great moments shared together.

I would also like to acknowledge my friend that studied physics with me. Pierre, Audrey, Gaetan, Imam, and Elisabeth, without your company, I would never be where I am today.

There are plenty of persons that I could not acknowledged here, all my friends inside or outside of the University, but they know how much they count for me.

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A mon père qui est maintenant quelque part dans les étoiles A ma mère qui à toujours été lá pour moi A mon frère pour tous les moments partagés A ma sœur qui restera toujours dans mon cœur A Minette que j’aime tant ....

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CHAPTER 1 INTRODUCTION

”I don’t know where I’m going, but I’m on my way.”— Carl Sagan

I think that everyone has once looked toward the sky during a clear night, and in front of these millions of stars, has asked himself the natural question: ”Are we alone in the Universe?”. This question has interested all the important civilizations, Egyptians, Mayas, Greeks, Romans. . . until the discovery of the first extra-solar planet that gave a first part of the answer. The history that conducted to this first discovery is fascinating, and it makes a good starting point to this thesis.

1.1 Historical introduction to extra-solar planets

The idea of the ”plurality of worlds” in the universe is not a modern topic. Already twenty centuries ago, Greek philosophers like Epicurus expressed their deep feeling that other worlds should exist in infinite numbers in the universe.

Across the last two millennia, that question remained a philosophical discussion. It is only more recently, during the 20th century, that the supposed existence of other worlds harboring life has been at the root of numerous published fictions. However, it is interesting to notice that prior to 1940, astronomers were giving an extremely low probability for the existence of other worlds in the Milky Way. In total, the number of planets in our Galaxy should be inferior to ten. This very pessimistic number was the result of the scenario proposed by Sir Jeans, which required very rare events to form the gaseous nebulae needed for planetary formation. A dynamical interaction of very close stellar flybys was considered the main cause leading to the formation of the gaseous nebulae, in which planets are formed. Such a close encounter is extremely rare. With the abandon of Jean’s scenario in the 40’s, the old paradigm of planetary formation drastically changed and immediately the estimated number of possible planetary systems in the Milky Way jumped to billions.

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In the modern view, an updated version of theSolar Nebular proposed by Swedenborg, Kant and Laplace during the 18th century, the origin of the nebulae needed to start planetary formation is the result of the stellar formation mechanism itself. During the collapse of a turbulent and inhomogeneous molecular cloud, perturbations in the density are at the origin of stars that naturally become surrounded by rapid rotating discs of gas and dust particles (accretion disc). The existence of these discs deduced from theoretical works has been first detected by the infrared radiation emitted by their dust. The Hubble Space Telescope obtained a beautiful confirmation of the existence of these accretion discs in 1995 (O’dell &

Wong, 1996).

Victor Safronov proposed the most accepted mechanism of planetary formation in 1969. In the inner parts of the accretion disc formed around the new star, where the temperature is high enough to prevent condensation of water ice and other substances on grains, coagulation of purely rocky grains leads to a slow formation of planetesimals. Once the size of a planetesimal reaches about one kilometer, runaway accretion accelerate the growth of the objet until a medium size of about 1’000 kilometers. At this stage, material for accretion becomes more rare, because a large number of medium sized objects have been created. These objects will continue accreting, however more slowly. Being massive, these proto-planetary cores will start interacting between each other. A chaotic process will follow, which will end either in the ejection of these cores out of the system, or in the merging of several cores, forming telluric planets. In the outer regions of the disc, beyond the ice line, the presence of condensed ice around grains enhances the rapid formation of planetesimals because grains will be more sticky. This leads to the formation of more massive proto-planetary cores that will start to accrete slowly the hydrogen and helium gas in the disc once they have reached about ten times the mass of Earth. When the mass reaches approximatively thirty Earth-masses, a runaway process occurs ending up in the formation of gas giants like Jupiter or Saturn. The accretion of gas can only appear during the few millions years corresponding to the presence of gas in the disc. This means that massive planets can only form if the initial growth from small dust grains to planetesimals, helped by the presence of ice, is fast enough compared to the lifetime of gas in the accretion disc.

The new planetary formation theory, partly confirmed by the measured infrared emission from proto-stars, was predicting billions of extra-solar planets. Therefore, many scientists got involved in this new topic of astrophysics and started to develop new observational technique to detect such planets. Because planets just reflect light form their parent star, planets are extremely faint and directly detecting such objects was impossible at the time. Indirect methods measuring the gravitational stellar wobbles induced by a companion orbiting its parent star were then used. Astrometry, measuring the displacement of the star on the sky in comparison with reference stars, and the radial-velocity technique, measuring the Doppler spectral shift induced by the stars’ movement was the two original methods to search for planets. These techniques were already used since the beginning of the 20th century to study binary stars. In 1993, the new ELODIE spectrograph is installed at the Observatoire de Haute-Provence in France, on a 2 meter-class telescope. This instrument was capable of reaching a radial-velocity precision slightly below ten meters per seconds. In spring 1994, Michel Mayor and Didier Queloz start their program to search for extra-solar planets. After a few months of observation, they found that 51 Peg was showing a radial-velocity periodic variability. This signal was however corresponding to a planet of a half Jupiter-mass, on a four-day orbit. Such a planet is absent from our Solar System and was not explained at the time by the planetary formation theory. The two scientists decided therefore to be careful before announcing any discovery, and waited one more year to see if the signal was permanent.

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1.2 State of the exoplanet field 3 In summer 1995, the variability of 51 Peg is still present, and the detection of the first extra- solar planet orbiting around a solar-type star is announced in October, at the Cool Stars meeting taking place in Florence. The planet is then rapidly confirmed by two American scientists, Geoff Marcy and Paul Butler. With a big impact on the media, this discovery that opened the way to the detection of other worlds and that allowed to answer part of the question, ”are we alone in the Universe”, has been at the origin of the great adventure that we are continuing today.

Six years before the announcement of the planet orbiting 51 Peg, Dave Latham and collab- orators, including Michel Mayor, announced the first promising candidate orbiting around HD 114762 (Latham et al., 1989). However, with a minimum mass 11 times that of Jupiter, this object is at the limit of being a brown dwarf, that is a sub-stellar object which is too low in mass to sustain hydrogen fusion reactions in its core. Currently, the limit between brown dwarfs and giant planets is arbitrarily set to 13 Jupiter-mass, however there is some debate concerning what criterion to use for defining the separation between a brown dwarf and a giant planet. This object was therefore interesting and showing that the precision to find exoplanets was near reach. Three years later, in 1992, Wolszczan and Frail announced the discovery of two extra-solar planets orbiting a pulsar. There were not searching for planets at the time, but for new millisecond pulsars. However, by chance, one of their new pulsars, PSR B1257+12 was showing tiny periodic variations betraying the presence of orbiting planets. These two super Earth-mass planets (3 and 4.3 Earth-mass), orbiting on period longer than 50 days, were confirmed in 1994 after the effects of their mutual interaction has been detected. However a pulsar, characterized by very energetic events, is not the best place in the Universe to search for potential life as we know it. This explains why this discovery, although very interesting, did not sparks things off.

1.2 State of the exoplanet field

Since the discovery of the first exoplanet orbiting a solar-type star by Michel Mayor and Didier Queloz in 1995 (Mayor & Queloz, 1995), the number of known planets has not stopped growing: at present, there are more than 800 confirmed planets with minimum mass estimates¹, and over 2’300 transiting planet candidates detected with the Kepler satellite that are awaiting confirmation (Batalha et al., 2012; Borucki et al., 2011).

The first exoplanets discovered were single, very massive, and on very short-period orbits, the so-called hot Jupiters. Then came the discovery ofmini-Neptunes, planets five to ten times the mass of the Earth but covered by a thick layer of ice, super-Earths, rocky bodies with masses five to ten times the one of the Earth (e.g. Fressin et al., 2011; Mayor et al., 2011;

Pepe et al., 2011; Mayor et al., 2009b,a; Udry et al., 2007), lava worlds (Alpha Centauri B b, Kepler-10 b, Corot-7 b Dumusque et al., 2012; Fressin et al., 2011; L´eger et al., 2009; Queloz et al., 2009), and ocean planets (Kepler-22 b,55 Cnc e,GL 1214 Borucki et al., 2012; Gillon et al., 2012; Charbonneau et al., 2009). All these types of planets are completely absent from our Solar System and show the incredible diversity in mass, in size, in orbital period.

Note that giant planets much more similar to the solar system giants have also been found (e.g. Wright et al., 2008). In these last years, super-Earth planets far enough from their

1see The Extrasolar Planets Encyclopaedia website (http://exoplanet.eu), and the Exoplanet Data Explorer website (http://exoplanets.org).

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host stars to possibly harbor liquid water on their surface have been detected (Kepler-22 b, HD 88512 b, and Gl 581 d Borucki et al., 2012; Pepe et al., 2011; Wordsworth et al., 2011;

Mayor et al., 2009b). In addition, planets down to the size or mass of the Earth have been announced (Dumusque et al., 2012; Gautier et al., 2012; Muirhead et al., 2012). All these exciting discoveries point towards one of the major goal of the exoplanet field: detecting one day an Earth-twin, i.e. an Earth-mass planet orbiting in the habitable zone of its parent star.

Besides this variety in mass, in size, and in orbital period, a variety in architecture of the systems has also been observed, with the discovery of very eccentric orbits (e.g. Naef et al., 2001), circumbinary planets, bodies that orbit not one but two stars (e.g. Schwamb et al., 2012; Doyle et al., 2011), very compact multi-planetary systems (e.g. Lissauer et al., 2011a;

Lovis et al., 2011b) or planets orbiting on retrograde orbits (e.g. Triaud et al., 2010; Queloz et al., 2010).

With the important number of discovered extra-solar planets, statistical study can be performed to infer and test planetary formation scenarios. Spectroscopic observations with HARPS and photometric measurements carried out byCorot and Kepler show that massive planets orbiting on short periods, the so-called hot Jupiters, are rare and normally single, while small-mass planets tend to belong to multiple planetary systems (Mayor et al., 2011;

Lissauer et al., 2011b; Latham et al., 2011). In addition, it has been shown that more than 50 % of solar-type stars harbor at least one planet of any mass and with period up to 100 days, and that most of the small-mass planets belong to multi-planetary systems (Mayor et al., 2011). Therefore small-mass planets are extremely frequent, which was expected from some theories of planetary formation (e.g. Mordasini et al., 2009). In addition, the frequency of massive planet depends on the metallicity of the host star. Metal-poor stars form very few of these massive planets (Santos et al., 2011), while almost 25 % of metal-rich stars ([Fe/H]>0.3) host at least one planet (Santos et al., 2004b). This dependency does not seem to hold for Neptune-mass planets (Sousa et al., 2008). Many other statistical properties can be found in Mayor et al. (2011), as well as in Udry & Santos (2007).

Following these exciting discoveries and statistical studies, a lot of efforts are done on trying to characterize these exoplanets. When the planet is transiting the star, a fraction of the light will pass through the planet’s atmosphere, which will allow us to probe its composition. This can be done by studying the transit depth at different wavelengths. Indeed, if a chemical spices is present in the atmosphere, it will absorb the stellar light at a given wavelength, which will induce a deeper transit at this wavelength because an observer will see the size of the planet plus its atmosphere. This technique, called transit spectroscopy, has been carried out for a few giant planets close to their host stars: HD 189733 b (Lee et al., 2012; Gibson et al., 2011; D´esert et al., 2011b), HD 209458 b (Vidal-Madjar et al., 2011; Snellen, 2005), and for GJ 1214 b, a six Earth-mass planet orbiting a light M dwarf (Berta et al., 2012; Bean et al., 2011; D´esert et al., 2011a). Two interesting exoplanets detected by the RV technique, therefore orbiting bright stars, have been discovered to transit recently. These two planets, 55 Cnc e (Gillon et al., 2012; Demory et al., 2011) and GJ 3470 (Bonfils et al., 2012), are excellent candidates to carry out transmission spectroscopy.

The majority of extra-solar planet detections have been achieved thanks to the development of two major methods, the photometric transit technique, and the spectroscopic radial-velocity (RV) technique. The first technique measures the decrease of stellar light that occurs when a planet is eclipsing its parent star. This event is repeatable every orbital period and several

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1.2 State of the exoplanet field 5 transits are necessary to confirm the periodicity of the signal, and therefore its planetary origin. This technique is simple to implement, however, it mainly provides information about the planet radius. More problematic, the signal induced by a transiting planet can be mim- icked by other physical events. For example if a background binary star is eclipsing in the field of view of the aimed star, it can produce the same effect as a planet passing in front of the stellar disc. Detecting the planet using the RV technique is therefore mandatory to confirm the planet origin of transiting candidates². This RV technique is an indirect method used to detect planets. It measures, using the Doppler effect, the gravitational stellar wobble induced by the planetary companion orbiting its parent star. Contrary to the transit technique, this method does not require the planet to transit, which allows for the detection of planets on many more stars. Unfortunately, because we only have access to the star’s velocity in the direction of the line of sight (radial velocity), we cannot have access to the inclination i of the system, and only the minimum massMsiniof the planet can be determined.

The photometric transit and the spectroscopic RV techniques are complementary, the first one giving information on the radius of the planet, and the second one on the minimum planetary mass. Note that if the planet is transiting, the inclination of the system is known and we can have an estimate of the real planetary mass. These two techniques give therefore access to the mean planetary density that can be used to infer some information about the planet’s internal composition.

At present, the best available instruments for the two different techniques are the HARPS spectrograph for RVs, and the Kepler photometric satellite for transits. HARPS is able to reach a precision level slightly better than the meter per second (0.8 m.s⁻¹), which allows us to detect super Earth-mass planets at the limit of the habitable region: HD 85512 b (3.5 Earth- mass at 58 days of period, Pepe et al., 2011), Gl 581 d (6 Earth-mass at 66 days of period, von Paris et al., 2011; von Braun et al., 2011; Kaltenegger et al., 2011a; Wordsworth et al., 2011), and Earth-mass planets close to their parent star like Alpha Centauri B b (1.1 Earth-mass at 3.24 days Dumusque et al., 2012). In the case ofKepler, the satellite can detect a luminosity variation of about 25 parts per million on a magnitude 12 star for a 5-hour integration³, which allows us to detect Earth radius planets (e.g. Kepler-20 e, and f, Gautier et al., 2012), and even smaller (e.g. Kepler-42 b, c, and d, Muirhead et al., 2012). These other worlds, equal in size or smaller than the Earth, orbit relatively close to their parent stars. However, because the transit depth is independent of the orbital period⁴, detecting an Earth-size planet in the habitable region should be possible. Unfortunately, one faces two difficulties. First, when the orbital period raises, the probability for a planet to transit the star goes rapidly down to zero because of geometrical probability. Secondly, several transits are needed to confirm the periodic variation of the signal, and improve the significance of the signal in the case of detections that are at the limits of instrumental precision. A longer orbital period implies less transit detected, and therefore, less precision. This explains why only one super Earth- size planet in the habitable region have been discovered so far (Kepler-22b, 2.4 Earth radius at 290 days of period, Borucki et al., 2012). The Kepler mission has been extended until 2016, and hopefully, these additional years will perhaps lead to the discovery of a habitable Earth-size planet.

2except in some special cases of multi-planetary transiting systems where the central time of transit is modified due to planet-planet interaction.

3SeeKeplerGuest Observer website, http://keplergo.arc.nasa.gov/CalibrationSN.shtml

4If you compare the separation between the planet and the star, with the distance between us and the star, an observer can be supposed at infinity, implying that transit depth does not change with orbital period.

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Unfortunately, HARPS is installed on a southern telescope (Chili, La Silla observatory), while Kepler is pointed towards the northern sky. Therefore, the best spectroscopic and photometric instruments cannot be used together to confirm some of the Kepler candidates and obtain planetary densities. This deficiency is now rectified, with the development and installation in May 2012 of the HARPS-N spectrograph (an improved copy of HARPS) on the TNG telescope in La Palma. After several inherent technical and software problems, the instrument is now giving science quality data. Note that only a few Kepler candidates will be confirmed with HARPS-N, because the majority of stars in the Kepler field of view are unfortunately too faint to be followed with Doppler spectroscopy.

1.3 Techniques to detect exoplanets and characterize them

Besides the two major detection and characterization techniques, radial velocimetry and transit photometry, that discovered the majority of extra-solar planets, other techniques exist, but the number of planet discovered with them is for the moment marginal. Some of these techniques are however very promising for the next future, when the precision of the instruments will reach the level of planetary signatures. An overview of all the different techniques to find and characterize extra-solar planets is given in the following.

Figure 1.1: Exoplanets detected prior to December 2011, and detection limits for the different exoplanet detection techniques (credits: Keith Horne, University of St Andrews).

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1.3 Techniques to detect exoplanets and characterize them 7 1.3.1 The radial-velocity technique

As its name states, this technique consists of measuring the radial velocity of a star using the relative Doppler shift of its spectral lines. It is an indirect method that measures the gravitational stellar wobbles induced by a companion orbiting its parent star. This technique has been used since the beginning of the 20th century to detect binary stars. It was therefore a logical way to use this technique for planet detection. With the discovery in 1989 of a 11 Jupiter-mass companion orbiting HD 114762 (Latham et al., 1989), the planet limit was getting closer by the end of the 80’s. We had to wait for six years until the detection of the first recognized exoplanet orbiting a solar-type star was announced (51 Peg b, Mayor &

Queloz, 1995). One thing remarkable about that discovery was that the planet has a half Jupiter-mass on an orbit as short as four days. This was a great surprise at the time, because such ahot Jupiter is absent from our Solar System, and because planetary formation theories were showing that anin situformation of such a massive planet was impossible. We know now that the majority of these planets are formed beyond the ice line, far from their parent stars, and then migrate inside the planetary accretion disc towards the central star (e.g. Ward, 1986;

Goldreich & Tremaine, 1980, 1979). Recent observations have shown that disc-migration is not the only effect responsible of migration; planet-planet scattering (e.g. Capobianco et al., 2011; Naoz et al., 2011; Kirsh et al., 2009; Hahn & Malhotra, 1999), as well as Kozai cycle effects may play a role as well (e.g. Libert & Delsate, 2012; Fabrycky & Tremaine, 2007).

Until the beginning of the 21st century, the RV technique was the only successful method to search for planets. HD 209458 b and HD 189733 b had been found transiting their parent star, however, these planets were already known by RV surveys. The geometrical probability that a planet transits its parent star is small, and therefore observing one by one each star, as the RV technique, is poorly efficient. The change came with dedicated ground-based wide field surveys that were able to search for transit over several thousands of star at the same time.

The first planet detected by transit was OGLE-TR-56 (Konacki et al., 2003) using the OGLE facility, and then came dozens of detection brought by the TrES, superWASP and HATNet surveys. More recently, dedicated space-based telescopes have been launched. The first of them,Corot, has for example allowed the discovery of the first super-Earth in transit in 2009.

Followed now byKepler, that has discovered thousands of planetary candidates, the transit method has become since a few years the most efficient method to search for exoplanets.

However, the RV technique it is still very important because it is the most reliable technique to confirm a detection. Indeed photometric transit can lead to false positive, even with the precision ofKepler (Santerne et al., 2012), and the detection of a transiting candidate requires to be confirm by the RV technique. Note than in few cases where transit timing variation can be measured (see Sec. 1.3.3), one can confirm an exoplanet candidate and obtain its real mass without requiring RV measurements. In addition, while transit survey are looking towards faint and distant stars, radial velocimetry is focusing on bright and near stars, the most important targets to conduct planet characterization (e.g. Lee et al., 2012; Vidal-Madjar et al., 2011). Finally the probability to find a planet with the transit technique fall down rapidly when the orbital period of the planet increase. Therefore the RV technique is still more efficient to find planets on long-period orbits.

Among the existing instruments dedicated to planet search using the RV technique, the HARPS spectrograph is the reference in term of precision. Reaching a precision of 0.8 m.s⁻¹ on bright targets, HARPS allowed us to find the lightest planet ever found with the RV technique. Its extreme precision also permits to detect super Earth-mass planet orbiting

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their parent star in the habitable zone, i.e. at a distance from the parent star at which water, if present, would be liquid (Gl 581 d (Mayor et al., 2009a), HD 85512 b (see Fig. 1.2, Pepe et al., 2011)). In the next future, new generation instrument like ESPRESSO on the VLT will be able to reach the 0.1 m.s⁻¹ precision level, and on the longer term, spectrographs for Extremely Large Telescopes (ELTs) should reach a precision even lower.

Figure 1.2:RVs of HD 85512, folded in phase with the orbital period of the planetP_p= 58.43 days. The weak amplitude of the planetary signal found, K = 0.77 m.s⁻¹, highlights the extreme precision of the HARPS spectrograph (from Pepe et al., 2011).

10¹ 10² 10³

Period [days]

10^-3 10^-2 10^-1 10⁰ 10¹

Minimum mass [M©]

PSR B1257+10c PSR B1257+10d

PSR B1257+10b

Mercury

Venus Earth

Mars radial velocity

pulsar timing

Figure 1.3:Comparison between the detection limits for the radial-velocity technique in red (optimal case, Dumusque et al. (2011c)) and for the pulsar timing technique assuming a time accuracy of 15 microseconds in blue. Black dots represents the 3 planets found around PSR B1257+12, and green dots corresponds to the telluric planets in our Solar System.

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1.3 Techniques to detect exoplanets and characterize them 9 1.3.2 The pulsar-timing technique

A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. If this beam of emission is pointing toward Earth during the rotation of the pulsar, a periodic signal can be detected. A pulsar is the remnant left after the supernova of an old massive star; it is therefore not the best place to search for extra-solar planets. However, due to the very short rotational period of some pulsars, a few milliseconds, and due to the extreme periodicity of the signal in function of time, any tiny perturbation of the pulsar can be detected. Imagine a planet orbiting around a millisecond pulsar, what would be the detection limit in mass? Could a small-mass planet like Earth on a one-year orbital period be detected? According to Wolszczan & Frail (1992), who detected the first extra-solar planets orbiting a pulsar with a rotational period of 6.2 milliseconds, the typical uncertainty in the Time of Arrivals (TOAs) derived from one-minute pulse integration is fifteen microseconds.

Because the emission travel space at the speed of light, fifteen microseconds corresponds to a displacement of the pulsar by 4.5 km. For a one-year orbital period, the radial-velocity of the pulsar that could be detected is therefore 0.014 cm s⁻¹ (for 4.5 km of displacement in 1 year)!

The effect of Earth on the Sun is 9 cm s⁻¹, and even if a pulsar is slightly more massive than our star, although less than three solar mass according to theory and observation (Thorsett et al., 1999), an Earth-like planet could easily be detected. When comparing Fig. 1.1 with Fig. 1.3, the pulsar timing method is by far the most powerful technique to search for small- mass extra-solar planets. However, this detection technique cannot really be compared with other methods to look for extra-solar planets, because it only allows searching for planets orbiting pulsars.

Wolszczan & Frail (1992) announced the discovery of two planets orbiting the same millisecond pulsar, PSR B1257+12. Figure 1.4 shows the signal of the two planets as announced in 1992. The presence of these two signals with different periods was much more difficult to explain by other phenomena, like for example free precession of the neutron star (Nelson et al., 1990), and interstellar or circum-pulsar propagation effect (Fruchter et al., 1988). In addition, these two planets, 3.4 and 2.8 Earth-mass at an orbital period of 66.6 and 98.2 days (as originally reported), are close to a 3:2 resonance. This offers the unique opportunity to measure the pulsar delay in TOAs induced by the gravitational interaction between the two bodies (Rasio et al., 1992; Malhotra, 1993; Peale, 1993). Two years later, Wolszczan (1994) presents new observations of the pulsar, where the gravitational interaction between the two planets was detected, confirming definitively the existence of planets around pulsars.

The planets around PSR1257+57 are very close to circular orbit. This is in contradiction with the hypothesis that the planets have survived to the supernovae leading to the neutron star.

The modern view of planetary formation around pulsars starts with a binary composed of a primary neutron star and a white dwarf or dwarf secondary. The secondary is evaporated by the high radiation coming for the neutron star, a part of this evaporation fall on the pulsar, spinning it up to millisecond rotational period, and the rest forms a protoplanetary disk around the pulsar, resulting in formation of planets by the disc-accretion scenario.

After this first discovery and more then twenty years of research, the number of planets around pulsars amounts to only 5. In 1993, a Jupiter-like planet has been found orbiting PSR B1620-26 (Backer et al., 1993; Rasio, 1994; Thorsett et al., 1999; Sigurdsson et al., 2003;

Sigurdsson & Thorsett, 2005). An additional planet, twice the mass of the moon, has been confirmed by Wolszczan et al. (2000) around PSR B1257+12. Finally, recently in 2011, an

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Figure 1.4: Signal of the first two extra-solar planets detected around the pulsar PSR B1257+12 (from Wolszczan & Frail, 1992).

object with a mass of Jupiter has been announced on a very short-period orbit, 0.09 days, orbiting PSR B1719-14 (Bailes et al., 2011). However, the minimum density of 23 grams per cubic centimeter of this object suggests that it may be an ultralow-mass carbon white dwarf.

This system may thus once has been an ultra compact low-mass X-ray binary, where the companion narrowly avoided complete destruction.

1.3.3 The photometric transit method

The transit method searches for the small decrease in stellar flux that occurs when a planet is passing in front of the stellar disc (see Fig. 1.5). Among the indirect methods to search for exoplanets, transit detection is the easiest one to think of, surely because this phenomenon has been observed since a long time for Venus in our solar system. Indeed, the transit of Venus was first predicted in 1627 by Johannes Kepler and first observed by Jeremiah Horrocks in 1639. This event happens in pairs eight years apart that are separated from each other by 105 or 121 years.

The first detection of an exoplanet transiting its host star has been made in 2000 for the hot Jupiter HD 209458 b (Charbonneau et al., 2000), already known from radial-velocity measurements (Mazeh et al., 2000). This detection definitely proved that these objects found with the radial-velocity technique were planets and not binaries on very inclined orbit, as some scientists were still arguing at the time. Since then, the number of detected transiting planet has increased incredibly thanks to dedicated ground-based wide filed surveys likeTrES, superWASP or HATNet (Pollacco et al., 2006; Bakos et al., 2004; Brown & Charbonneau, 2000, 5 planets for TrES, 79 planets for superWASP, and 41 for HATNet detected so far), and space-based mission likeCorot and Kepler (Borucki et al., 2010; Auvergne et al., 2009, 23 planets discovered forCorot and 77 planets and more than 2000 candidates forKepler).

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1.3 Techniques to detect exoplanets and characterize them 11

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



Fig. 1.— Illustration of transits and occultations. Only the combined flux of the star and planet is observed. During a transit, the flux drops because the planet blocks a fraction of the starlight. Then the flux rises as the planet’s dayside comes into view. The flux drops again when the planet is occulted by the star.

as well align theXaxis with the line of nodes; we place the descending node of the planet’s orbit along the+X axis, givingΩ = 180^◦.

The distance between the star and planet is given by equation (20) of the chapter by Murray and Correia:

r= a(1−e²)

1 +ecosf, (1) wherea is the semimajor axis of the relative orbit andf is the true anomaly, an implicit function of time depending on the orbital eccentricityeand periodP (see Section 3 of the chapter by Murray and Correia). This can be resolved into Cartesian coordinates using equations (53-55) of the chapter by Murray and Correia, withΩ = 180^◦:

X = −rcos(ω+f), (2) Y = −rsin(ω+f) cosi, (3) Z = rsin(ω+f) sini. (4) If eclipses occur, they do so whenrsky ≡√

X²+Y²is a local minimum. Using equations (2-3),

rsky= a(1−e²) 1 +ecosf

!

1−sin²(ω+f) sin²i. (5) Minimizing this expression leads to lengthy algebra (Kip- ping 2008). However, an excellent approximation that we will use throughout this chapter is that eclipses are centered

around conjunctions, which are defined by the condition X = 0and may be inferior (planet in front) orsuperior (star in front). This gives

f_tra= +π

2 −ω, f_occ=−π

2 −ω, (6) where here and elsewhere in this chapter, “tra” refers to transits and “occ” to occultations. This approximation is valid for all cases except extremely eccentric and close-in orbits with grazing eclipses.

Theimpact parameterbis the sky-projected distance at conjunction, in units of the stellar radius:

b_tra = acosi R_!

"

1−e² 1 +esinω

#

, (7)

b_occ = acosi R_!

"

1−e² 1−esinω

#

. (8)

For the common case R_! $ a, the planet’s path across (or behind) the stellar disk is approximately a straight line between the pointsX=±R_!√

1−b²atY =bR_!. 2.2 Probability of eclipses

Eclipses are seen only by privileged observers who view a planet’s orbit nearly edge-on. As the planet orbits its star, its shadow describes a cone that sweeps out a band on the celestial sphere, as illustrated in Figure 3. A distant observer within the shadow band will see transits. The open- ing angle of the cone, Θ, satisfies the conditionsin Θ = 2

Figure 1.5: Change in flux received on Earth as a planet orbits its parent star (from Winn, 2010).

Compare to the radial-velocity method, the transit technique requires simple instrumentation, and thousands of stars can be observed at the same time. Unfortunately, the probability that a planet transits is very low, and goes rapidly to zero with increasing orbital period, making the transit detection technique inefficient to search for long-period planets.

Similar to the pulsar timing technique, it is possible to detect non-transiting planet by measuring delays in the middle time of binary or planet transits. Indeed, if a planet orbits one star of a binary system, its gravitational pull out will influence the movement of its parents star around its binary companion, and will induce change in the binary transit time. A similar behavior can happen if two planets are orbiting the same parent star, with at least one planet transiting. Dynamical interaction can occur between these two planets, especially if they are in mean motion resonance⁵, which will induce variation in the transit timing. Planet transit timing variation (TTV) has been observed for the first time on multi-planetary transiting systems found with the Kepler satellite (Holman et al., 2010).

The transit method allows us to obtain the planet radius, when the stellar radius is known. It is therefore an essential complementary method to the radial-velocity technique that can only have access to the minimum mass of a companion. First, if a planet transits, the minimum mass estimated with the RV method is the real mass because the orbit is align with the line of sight, and secondly the average density of the planet is known. This parameter is essential to constrain planetary formation theories and obtain information about planet compositions

5The dynamical situation where the ratio of the orbital periods of two orbiting objects can be expressed as the ratio of two small integers

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Figure 1.6:The transit of Venus in 2012. This event happens in pairs eight years apart that are separated from each other by 105 or 121 years. The next transit will not happen until 2117 (Credit: NASA/SDO).

(see Fig. 1.7). Note that in special cases where TTVs are measured, it is also possible to obtain an estimation of the real mass of the planets, without requiring RV measurements.

When a planet transits, the angle between the planet orbital spin and the parent star rotation spin can be obtained using radial-velocity measurements. Holt (1893) predicted that if a star is eclipsed by another one for which the rotation spin aligned with the orbital spin, it would cover first the approaching hemisphere, blueshifted, thus making the overall light appear redder.

As it makes its way across the stellar disc, the transit reaches the redshifted hemisphere, thus creating an anomalous blueshift. Because redshift means positive radial velocity and blueshift negative one, an align transit seen using the radial-velocity method will first induce a anomalous increase compared to the mean radial velocity of the star, symmetrically followed by a decrease. Depending on the angle between the stellar rotation spin and the orbital spin, the companion will mask portions of the star that have different speeds in RV (and therefore different level of blueshit or redshift by Doppler effect), inducing different transit shapes (see Fig 1.8). This phenomenon, called the Rossiter-McLaughlin effect, has been observed for the first time on binaries by Rossiter (1924) and McLaughlin (1924). The first measurement of this effect for a planet has been carried out by Queloz et al. (2000). An important change came when H´ebrard et al. (2008) announced a misaligned transit on X0-3, however some doubts was still there because of an incomplete transit sequence. The observation that vanished out the idea that all planets were on coplanar orbits with their star’s equatorial plane was the measurement of the clear misaligned transit of WASP-8b (see Fig. 1.9, Queloz et al., 2010).

This important result, and the other discovery of misaligned transits (25 out of a total of 58 Rossiter-McLaughlin effects measured⁶ pointed out that disc migration theory cannot

6See Rene Heller’s Holt-Rossiter-McLaughlin Encyclopaedia, http://ooo.aip.de/People/rheller/content- /main spinorbit.html

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1.3 Techniques to detect exoplanets and characterize them 13

Figure 1.7: Mass-radius relationship for small-mass planets. Planets Kepler-11 b to Kepler- 11 f are represented by filled circles with their letters written above. Other transiting extra- solar planets in this size range are shown as open squares, representing, in order of ascending radius, Kepler-10 b, CoRoT-7 b, GJ 1214 b, Kepler-4 b, GJ 436 b and HAT-P-11 b. The triangles (labeled V, E, U and N) correspond to Venus, Earth, Neptune and Uranus, respectively.

The colors of the points show planetary temperatures. The solid black curve corresponds to models of planets with Earth-like rock-iron composition. The higher dashed curve corresponds to 100% H₂O, all other curves use a water or H₂/He envelope on top of the rock-iron core. We note that multi-component and mixed compositions (not shown above), including rock/iron, H₂O, and H₂/He, are expected and lead to even greater degeneracy in determining composition from mass and radius alone (from Lissauer et al., 2011a).

Figure 1.8: Different configuration of the Rossiter-McLaughlin (RM) effect, where λis the angle between the stellar rotation spin and the spin of the planetary orbit, and bthe impact parameter (b = 0: central transit, |b| = 1: grazing transit). The trajectories all have the same impact parameter and produce the same transit light curve, but they differ in λ and produce different RM curves (from Gaudi & Winn (2007), colored by A. Triaud).

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Fig. 4.Top: radial velocity measurement phased with the transit (mid- transit is at 0). Black triangles are CORALIE data and red dots HARPSdata. Bottom: normalized transit photometry measurement of WASP-8. Black triangles indicates SuperWASP data and red dots the R-band Euler photometry data. The best-fit model is superimposed in blue.

were determined in a similarly way to the work ofGillon et al.

(2009) and used as additionalT_effand loggdiagnostics (Smalley 2005).

The Li



6708 Å line is detected in the spectra indicating an abundance of log A(Li/H)+12=1.5±0.1, which implies an age of 3−5 Gyr according to Sestito & Randich (2005). However, Israelian et al.(2009) noted that stars with planets have lower lithium abundances than normal solar-type stars, so the lithium abundance may not be a good age indicator for them.

The rotational broadeningvsiniwas measured by fitting the observed HARPS profiles of several unblended Fe



lines. A typical value of macroturbulencev_mac=2 km s⁻¹ was adopted and an instrumental profile determined from telluric absorption lines.

We found that vsini = 2.0 ± 0.6 km s⁻¹, which is typical of a G dwarf of intermediate age.

3.2. Analysis of the planetary system

This whole data set was found to detect without doubt a planet transiting the starWASP-8. We analyzed together the photometric (WASP and Euler data) and the radial velocity data, including the spectroscopic transit sequence in this context. Our model was based on the transit modeling by Mandel & Agol (2002) and the radial velocity description byGiménez(2006). The best- fit model parameters and their error bars were computed using a MCMC convergence scheme that solves all parameters together. For details of the code and fitting techniques, we refer to

Table 1. Stellar parameters of WASP-8 derived from spectroscopic analysis.

Teff 5600±80 K [Na/H] +0.22±0.07

logg 4.5±0.1 [Mg/H] +0.21±0.04

ξt 1.1±0.1 km s⁻¹ [Si/H] +0.29±0.09 vsini 2.0±0.6 km s⁻¹ [Ca/H] +0.24±0.12 [Fe/H] +0.17±0.07 [Sc/H] +0.23±0.05 log A(Li/H)+12 1.5±0.1 [Ti/H] +0.24±0.08 [V/H] +0.30±0.08

dist 87±7 pc [Cr/H] +0.17±0.09

age 3−5 Gyr [Co/H] +0.29±0.07

[Ni/H] +0.23±0.07 Notes.The quoted error estimates include those given by the uncertainties inTeff, logg, andξt, as well as atomic data uncertainties.

Fig. 5.Comparison of the best-fitting stellar parameters from the transit profile and spectroscopic analysis with evolutionary models interpo- lated at [Fe/H]=0.17. The isochrones are 100 Myr, 1 Gyr, 5 Gyr and 10 Gyr. The evolutionary tracks are indicated for 0.9, 1.0 and 1.1Msun.

Triaud et al.(2009);Collier Cameron et al.(2007). To obtain a coherent solution, we determined the mass of the star by comparing the spectroscopically-determined effective temperature and the stellar density outcome of the MCMC adjustment, with evolutionary tracks and isochrones of the observed metallicity from the stellar evolution model ofGirardi et al.(2000). We converged iteratively on a stellar mass of 1.04(+0.02−0.09)M_"and an age younger than 6 Gyr (see in Fig.5).

The free parameters of our model were the depth of transitD, the width of transitW, the impact parameterb, the periodP, the epoch of transit centre T0, the RV semi-amplitude K, e cos ω andesin ω(ebeing the eccentricity andωthe angle of the peri- astron), andV sin I cos βandV sin I sin β, withV sin Ibeing the projection of the stellar equatorial rotation, and β the projection of the angle between the stellar spin axis and the planetary orbit axis. In addition, we employed free normalization factors for each lightcurve (WASP and Euler) and each set of radial velocity (γHforHARPSandγ_C forCORALIE), which en- abled variations to be made in instrumental zero points. From these parameters, physical parameters were derived to charac- terise the planetary system. The best-fit set of parameters that minimize theχ²_r (reducedχ²is 0.86) are listed in Table2as well as their related computed physical parameters. With this best-fit solution one computes for the CORALIE data χ² = 204 with 48 measurements, and for HARPS dataχ² = 188 with 82 measurements which implies that additional jittering is present that is not accounted for by the fitted model. Since the main deviation is related to theCORALIE data, the uncertainties in the orbital Page 3 of4 Figure 1.9: Transit of WASP-8b, the first clear detection of a misaligned transit, i.e. the

orbital spin of the planet is opposite to the stellar rotation spin (from Queloz et al., 2010).

Figure 1.10:Comparison of the measured wavelength-dependent planet-to-star radius ratios to transmission spectroscopic models from Miller-Ricci & Fortney (2010), for GJ 1214 b. Ob- servations are in black and theoretical atmospheric models in colors. From the observations, it is possible to rule out solar metallicity models, but not solar metallicity models without CH₄ (from D´esert et al. (2011a)).

Mitigating stellar signals in the quest for other Earths

Thesis

Reference

Mitigating stellar signals in the quest for other Earths

Mitigating stellar signals in the quest for other Earths

Th` ese

Xavier DUMUSQUE

R´ ESUM´ E

FOREWORDS

THANKS

CONTENTS

CHAPTER 1

INTRODUCTION

1.1 Historical introduction to extra-solar planets

1.2 State of the exoplanet field

1.3 Techniques to detect exoplanets and characterize them

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