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Introduction Introduction Onething is certain about this book: by thetimeyou readit, parts of it will be out of date. Thestudy of exoplanets,planets orbitingaround starsother than theSun, is anew andfast-moving field.Important newdiscoveries areannounced on a weekly basis. This is arguablythe most exciting andfastest-growing field in astrophysics.Teamsofastronomersare competing to be thefirsttofind habitable planets likeour ownEarth, andare constantly discovering ahostofunexpected andamazingly detailed characteristics of thenew worlds. Since1995, when the first exoplanet wasdiscoveredorbitingaSun-like star,over 400 of them have been identified.Acomprehensive review of thefield of exoplanets is beyond thescope of this book, so we have chosen to focus on thesubset of exoplanets that are observedtotransittheir hoststar (Figure 1). Figure1 An artist’simpression of thetransitofHD209458 bacrossits star. Thesetransitingplanets areofparamount importancetoour understanding of the formation andevolutionofplanets.During atransit, theapparent brightness of the hoststar drops by afraction that is proportionaltothe area of theplanet: thus we can measure thesizes of transitingplanets,eventhough we cannot seethe planets themselves.Indeed,the transitingexoplanets arethe onlyplanets outside our own Solar System with known sizes.Knowing aplanet’ssize allows its density to be deduced andits bulk compositiontobeinferred.Furthermore, by performing precisespectroscopicmeasurements during andout of transit, theatmospheric compositionofthe planet can be detected.Spectroscopicmeasurements during transitalsoreveal information about theorientation of theplanet’sorbitwith respect to the stellar spin.Insomecases,light from thetransitingplanet itself can be detected;since thesize of theplanet is known,thiscan be interpreted in terms of an empirical effective temperature for theplanet. That we can learnsomuch about planets that we can’t directly seeisatriumphoftwenty-firstcentury science. 11 Introduction This book is dividedintoeight chapters, thefirstofwhich sets thesceneby examiningour ownsolar neighbourhood, anddiscussesthe variousmethods by which exoplanets aredetected usingthe Solar System planets as testcases. Chapter 2describes howtransitingexoplanets arediscovered, anddevelopsthe related mathematics.InChapter 3wesee howthe transitlight curveisused to derive precisevalues for theradius of thetransitingplanet andits orbital inclination.Chapter 4examinesthe known exoplanet population in the context of theselection effects inherentinthe detectionmethods used to findthem. Chapter5discussesthe information on theplanetaryatmosphere andonthe stellar spin that can be deduced from spectroscopicstudies of exoplanet transits.In Chapter6thelight from theplanet itself is discussed, while in Chapter 7the dynamics of transitingexoplanets areanalyzed.Finally,inChapter 8webriefly discussthe prospects for furtherresearch in this area, including theprospects for discovering habitable worlds. Thebook is designedtobeworked through in sequence; some aspects of later chaptersbuild on theknowledge gained in earlier chapters. So,while you could dipinatany point,you will findifyou do so that you areoften referredback to concepts developedelsewhere in thebook. If thebook is studied sequentially it providesaself-contained,self-study courseinthe astrophysics of transiting exoplanets. Aspecial comment shouldbemadeabout theexercises in this book. Youmay be tempted to regard them as optionalextras to help you to revise. Do not fall into this trap! Theexercises arenot part of the revision,theyare part of the learning. Severalimportant concepts aredeveloped through theexercises andnowhere else. Therefore you shouldattempt each of them when you come to it. You will findfullsolutions for all exercises at the endofthisbook, butdotry to complete an exerciseyourself first beforelooking at the answer. An Appendix containingphysical constants is includedatthe endofthe book; usethese values as appropriate in your calculations. Formostcalculations presented here, useofascientificcalculatorisessential. In some cases,you will be able to work outorderofmagnitude estimates without the useofacalculator, andsuchestimates areinvariably useful to check whether an expression is correct. In some calculations you mayfind that useofacomputer spreadsheet, or graphing calculator, providesaconvenient meansofvisualizinga particular function.Ifyou have accesstosuchtools, pleasefeel freetouse them. 12 Chapter 1Our Solar Systemfromafar Introduction In 1972 aNASA spacecraftcalled Pioneer 10 waslaunched. It is the fastest-moving human artefact to have leftthe Earth: 11 hours after launch it was furtherawaythanthe Moon. In late 1973 it passedJupiter,taking the first close-up images of thelargest planet in our Solar System.For 25 yearsPioneer 10 transmitted observations of thefar reaches of our Solar System back to Earth, passing Plutoin1983 (Figure 1.1). Figure1.1 Thetrajectories of Pioneer 10 andother space probes.The heliopauseis theboundary between the heliosphere, which is dominated by thesolar wind, and interstellar space. Thesolar wind is initially supersonic andbecomessubsonicatthe terminationshock. Note: all objects are much smaller than they have been drawn! At final radiocontact, it was 82 AU (or equivalently 1.2 × 1013 m) from theSun. It continuestocoast silently towards thered star Aldebaran in theconstellation Taurus.Itis68 light-years to Aldebaran, anditwill takePioneer 10 twomillion yearstocoverthisdistance. During this time, of course, Aldebaran will have moved. Anysinglestar mayhave Figures 1.2 and1.3 show theSun’splace in our Galaxy. The 10-light-year severaldifferent names. This is scale-barinFigure 1.2a is 2000 times theradius of Neptune’s orbit:Neptuneis especially true of bright stars, thefurthest planet from theSun showninFigure 1.1. Thestructure of ourown e.g. Aldebaran is alsoknown as α Solar System showninFigure 1.1 is invisiblytinyonthe scale of Figure 1.2a. To Tau. We have generally render them visible, all the starsinFigure 1.2a areshown largerthantheyreally tried to adopt thenames most are. Interstellar space is sparsely populated by stars. Thesuccessive parts of frequently used in the exoplanet Figures 1.2 and1.3 zoom out from theviewofour immediate neighbourhood. In literature. Figure 1.2b we seeamore or lessrandom patternofstars, which includes theHyadescluster andthe bright starsinUrsaMajor.All thestarsshown in Figure 1.2b belong to our local spiral arm, which is called theOrion Arm. 13 Chapter 1Our Solar System from afar (a) (b) Figure 1.2 (a) Thestarswithin 12.5 light-years of theSun. (b) Thesolar neighbourhood within 250 light-years. 14 Introduction (a) Figure1.3 (a)Our part of the Orion Arm andthe neighbouring arms. (b) Our MilkyWay (b) Galaxy. Figure 1.3a showsour sector of theGalaxy:aview centred on theSun, which is anondescript star lostinthe hostofstarscomprisingthe Orion Arm. The bright starsofOrion,familiar to many peoplefrom thenaked-eye nightsky, areprominentinthisview: they give our local spiral armits name.Finally, Figure 1.3b showsour entireGalaxy. 15 Chapter 1Our Solar System from afar Exercise 1.1 Pioneer 10 is coastingthrough interstellar space at aspeed of approximately 12 km s−1.Confirm thetimethatitwill taketocoverthe 68 light-years to Aldebaran’spresent position. Hint:The Appendixgives conversion factorsbetween units. ■ The nearest stars and planets Planets have been detected around 6 of the 100 neareststars(October2009), including theSun. Throughoutthisbook, wherenew results arefrequent, we indicate in parenthesesthe date at which astatementwas made,aswedid in theprevioussentence. Table1.1 lists theseven known planetarysystems within 8 pc. Ta ble1.1 Starswithin 8 pc with known planets.(In accordancewith the IAUwelist 8 planets in the Solar System;wewill not comment further on the status of Plutoand similar dwarfplanets.) Confusingly, thestandard NameParallax, Spectral V M Mass Known symbol for astronomical V (alias) π/arcsec type(M%)planets parallax is π,which is more frequently used as the symbol Sun—G2V −26.72 4.85 1.00 8 for theconstantrelating the ε Eri 0.309 99 K2V 3.73 6.19 0.85 1 diameter andcircumference of a (GJ144) ±0.00079 circle. Usually it is easytowork out which meaning is intended. GJ 674 0.220 25 M3.0V 9.38 11.09 0.36 1 ±0.00159 GJ 876 0.212 59 M3.5V 10.17 11.81 0.27 3 (ILAqr) ±0.00196 GJ 832 0.202 52 M1.5V 8.66 10.19 0.45 1 (HD204961) ±0.00196 GJ 581 0.159 29 M2.5V 10.56 11.57 0.30 3 (HOLib) ±0.00210 Fomalhaut 0.130 08 A3V 1.16 1.73 2.11 (αPsA/GJ881) ±0.00092 Thesedata were taken from theinformationonthe 100 neareststarsonthe Research Consortium on Nearby Stars(RECONS) website, which is updated annually.Fomalhaut, which is nearby,but not one of the 100 neareststars, wasaddedbecause theplanet Fomalhautbwasrecently discovered, as we will seeinSubsection 1.1.1. Table1.1 givesthe values of theparallax, π,the spectral type, the apparent Vbandmagnitude,V,and theabsoluteVband magnitude, MV,aswell as the stellar mass andthe numberofknown planets.Itisverynoticeable that overhalf of thesenearby planet host starsare Mdwarfs,the lowest-mass, dimmest andslowest-evolvingmain sequencestars. By the time you readthis, more nearby planets will probably have been discovered. Theneareststarshavedistances directly determinedbygeometryusing trigonometric parallax,and theRECONS sample (Figure 1.4)includes 249 16 Introduction systemswithin 10 pc,orequivalently 32.6 light-years,all with distances known to 10%orbetter. 72%ofthe starsare Mdwarfs.Mdwarfs arethe faintestmain sequencestars, so
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