1 INTRODUCTIONarXiv:1001.2010v3 [astro-ph.EP] 17 Jun 2010Transits and OccultationsJoshua N. WinnMassachusetts Institute of TechnologyWhen we are fortunate enough to view an exoplanetary system nearly edge-on, the star and planetperiodically eclipse each other. Observations of eclipses—transits and occultations—provide a bonanzaof information that cannot be obtained from radial-velocitydataalone,suchastherelativedimensionsof the planet and its host star, as well as the orientation of the planet’s orbit relative to the sky plane andrelative to the stellar rotation axis. The wavelength-dependence of the eclipse signal gives clues about thethe temperature and composition of the planetary atmosphere. Anomalies in the timing or other propertiesof the eclipses may betray the presence of additional planetsormoons. Searchingforeclipsesisalsoaproductive means of discovering new planets. This chapter reviews the basic geometry and physics ofeclipses, and summarizes the knowledge that has been gained through eclipse observations, as well as theinformation that might be gained in the future.1. INTRODUCTIONFrom immemorial antiquity, men have dreamed of aroyal road to success—leading directly and easily to somegoal that could be reached otherwise only by long ap-proaches and with weary toil. Times beyond number, thisdream has proved to be a delusion.... Nevertheless, thereare ways of approach to unknown territory which lead sur-prisingly far, and repay their followers richly. There isprobably no better example of this than eclipses of heav-enly bodies. —HenryNorrisRussell(1948)Vast e xp an se s o f sc ie nt ific te r ri t o ry h av e b ee n t raver sedby exploiting the occasions when one astronomical bodyshadows another. The timing of the eclipses of Jupiter’smoons gave the first accurate measure of the speed of light.Observing the passage of Venus across the disk of the Sunprovided a highly refined estimate of the astronomical unit.Studying solar eclipses led to the discovery of helium, therecognition that Earth’s rotation is slowing down due totides, and the confirmation of Einstein’s prediction for thegravitational deflection of light. The analysis of eclipsingbinary stars—the subject Russell had in mind—enabled aprecise understanding of stellar structure and evolution.Continuing in this tradition, eclipses are the “royal road”of exoplanetary science. We can learn intimate details aboutexoplanets and their parent stars through observations oftheir combined light, without the weary toil of spatially re-solving the planet and the star (see Figure 1). This chaptershows how eclipse observations are used to gain knowledgeof the planet’s orbit, mass, radius, temperature, and atmo-spheric constituents, along with other details that are other-wise hidden. This knowledge, in turn, gives clues about theprocesses of planet formation and evolution and provides alarger context for understanding the properties of the solarsystem.An eclipse is the obscuration of one celestial body by an-other. When the bodies have very unequal sizes, the passageof the smaller body in front of the larger body is a transitand the passage of the smaller body behind the larger bodyis an occultation.Formally,transitsarecaseswhenthefulldisk of the smaller body passes completely within that ofthe larger body, and occultations refer to the complete con-cealment of the smaller body. We will allow those terms toinclude the grazing cases in which the bodies’ silhouettesdo not overlap completely. Please be aware that the exo-planet literature often refers to occultations as secondaryeclipses (a more general term that does not connote an ex-treme size ratio), or by the neologisms “secondary transit”and “anti-transit.”This chapter is organized as follows. Section 2 de-scribes the geometry of eclipses and provides the founda-tional equations, building on the discussion of Keplerian or-bits in the chapter by Murray and Correia. Readers seekingamoreelementarytreatmentinvolvingonlycircularorbitsmay prefer to start by reading Sackett (1999). Section 3 dis-cusses many scientific applications of eclipse data, includ-ing the determination of the mass and radius of the planet.Section 4 is a primer on observing the apparent decline instellar brightness during eclipses (the photometric signal).Section 5 reviews some recent scientific accomplishments,and Section 6 offers some thoughts on future prospects.2. ECLIPSE BASICS2.1 Geometry of eclipsesConsider a planet of radius Rpand mass Mporbiting astar of radius R!and mass M!.TheratioRp/R!occursfrequently enough to deserve its own symbol, for which wewill use k,indeferencetotheliteratureoneclipsingbinarystars. As in the chapter by Murray and Correia, we chooseacoordinatesystemcenteredonthestar,withtheskyinthe X–Y plane and the +Z axis pointing at the observer(see Figure 2). Since the orientation of the line of nodesrelative to celestial north (or any other externally definedaxis) is usually unknown and of limited interest, we might1Fig. 1.— Illustration of transits and occultations. Only thecombinedfluxofthestarandplanetisobserved. Duringatransit, the fluxdrops because the planet blocks a fraction of the starlight. Then the flux rises as the planet’s dayside comes into view. Thefluxdropsagain when the planet is occulted by the star.as well align the X axis with the line of nodes; we place thedescending node of the planet’s orbit along the +X axis,giving Ω=180◦.The distance between the star and planet is given byequation (20) of the chapter by Murray and Correia:r =a(1 −e2)1+e cos f, (1)where a is the semimajor axis of the relative orbit and fis the true anomaly, an implicit function of time dependingon the orbital eccentricity e and period P (see Section 3 ofthe chapter by Murray and Correia). This can be resolvedinto Cartesian coordinates using equations (53-55) of thechapter by Murray and Correia, with Ω=180◦:X = −r cos(ω + f), (2)Y = −r sin(ω + f)cosi, (3)Z = r sin(ω + f) sin i. (4)If eclipses occur, they do so when rsky≡√X2+ Y2isalocalminimum.Usingequations(2-3),rsky=a(1 − e2)1+e cos f!1 − sin2(ω + f) sin2i. (5)Minimizing this
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