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Onething is certain about this book: by thetimeyou readit, parts of it will be out of date.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 although they predominate in thesolar neighbourhood, they aremore difficult to detect than othermore luminous stars, particularly at large distances.

250 239

200 cts

je 150 of ob

er 100 numb 50 44 18 21 18 8 0 0 4 6 4 0 WD O B A F G K M L T P stars brown dwarfs

Figure1.4 Knownobjects within 10 parsecs (RECONS 2008). The leftmostcolumnshows white dwarfs,columns 2–8 show starssubdividedby spectral type, columns 9and 10 show Land Tclassbrown dwarfs,and the lastcolumnshows known planets,including eightinour ownSolar System. Thestarsinthe censusare overwhelminglyMdwarfstars, i.e. low-mass main sequencestars. Thecensusillustrated in Figure 1.4 is likely to be more representative of stellar demographics than asamplelimited by apparent brightness wouldbe. Thenumbers in this censusinclude theSun andits eight planets.The 362 objects represented in Figure 1.4 arecomprised of 170 systemscontaininga singleobject, 58 doublesystems(either binary starsorstar plus singleplanet systems),and 21 multiple systems, including our ownSolar System.New objects arebeing discoveredcontinually,and this censusgrewby20% between January 2000 andJanuary 2008. While not quite close enough to be includedinTable 1.1, or in thecensus illustrated in Figure 1.4, HD 160691 at adistance of 15.3 pc deserves a mention: it has 4 known planets.The recently discoveredplanet GJ 832 bis agiantplanet with an orbital period between 9 and 10 years: i.e. it has pronouncedsimilarities to thegiantplanets in our ownSolar System. GJ 832 bhas mass MP =0.64 ± 0.06 MJ,where MJ is themassofJupiter, i.e. 1898.13 ± 0.19 × 1024 kg. Theproperties of its hoststar,GJ832, are giveninTable 1.1.

17 Chapter 1Our Solar System from afar

● With referencetoTable 1.1, what is the distance to the nearestknown exoplanetarysystem? ❍ ε Eri(GJ 144) hasthe largest parallax of all known exoplanetarysystems, with π =0.309 99 ± 0.000 79 arcsec. Thedistance, d,inparsecs is givenby d 1 = , pc π/arcsec so thedistance to ε Eriis0.309 99−1 pc,or3.226 pc.The uncertainty on the parallax measurementis0.25%, so theuncertainty in the distance determinationisapproximately 0.25%of3.226 pc.Hence, to foursignificant figures,the distance to the nearestknown exoplanetarysystem is 3.226 ± 0.008 pc.ConvertingthistoSIunits, 1 pc is 3.086 × 1016 m, so the distance to GJ 144 is (9.96 ± 0.02) × 1016 m. As you can seeinFigure 1.2b, Aldebaran is actually an extremely nearby star when we consider our place in the MilkyWay Galaxy, so theexample of Pioneer 10’sjourneyshows just howdistantthe starsare,compared to the interplanetarydistances in our ownSolar System.Until 1995, we knewofno planets orbitingaround otherstarssimilar to our ownSun. Giventhe distances involved,and theextremedimness of planets compared to main sequencestars, this is hardly surprising.

Stars, planets and browndwarfs This book will primarily discussgiantplanets andtheir hoststars. Objects with masses too small to ignite hydrogen burning in their cores, yetmassive enough to have fuseddeuterium,are knownasbrowndwarfs.Thisimplies that brown dwarfs have masses lessthanabout 80 MJ.While thereisno universally agreed definition, giantplanets areoften defined as objects that arelessmassive than brown dwarfs andhavefailed to ignite deuterium burning.Adoptingthisdefinition, planets have masses lessthanabout 13 MJ. Stars, brown dwarfs andgiantplanets form asequenceofdecliningmass. Figure 1.5a compares twoexamples of main sequencestarswith twobrown dwarfs,one oldand one young, andgiantplanets with masses of 1 MJ and 10 MJ.Itisclear that thebrown dwarfs andgiantplanets areall roughly the same size, while theSun andthe MV star Gliese229A differ radically in size andeffective temperature, despite having masses of thesameorderof magnitude.These most basiccharacteristics arisebecause of thephysics operatingtosupport thesevariousobjects againstself-gravity,someofwhich we will explore in Chapter 4ofthisbook. When discussing exoplanets, astronomersuse themassofJupiter,MJ,orthe mass of theEarth, M⊕,asa convenient mass unit, just as the mass of theSun is used as aconvenientunit in discussing stars. Thevalues of theseunits aregiven in the Appendix. (Table 4.1 in Chapter 4gives conversion factorsbetween the units.) Figure 1.5bshows part of theSun andthe Solar System planets,immediately revealing the huge difference in size between thegiantplanets andthe terrestrial planets.Itisbecause giantplanets aresomuchbiggerthan terrestrial planets that almostall thetransitingexoplanets discoveredsofar (Dec.2009) aregiantplanets.Aswewill seeinChapter 4, giantplanets are

18 Introduction

(a)

(b) (c)

Figure1.5 Comparisonsofstars, brown dwarfs andplanets.(a) Twomain sequencestars, twobrown dwarfs,and twoobjects of planetarymass, arranged in asequenceofdecliningmass. Neither theradius nor thesurface temperature followsthe mass sequenceexactly.(b) TheSun andits planets.The giantplanets are much largerthanthe terrestrial planets.(c) TheSolar System’s terrestrial planets in order of distance from the Sun: Mercury,Venus,Earth andMars, from toptobottom. formed predominantly of gasorice, i.e. low-density material. Theterrestrial planets,asweknowfrom ourintimate experienceofthe Earth, have solid surfaces composed of rock, andare denserthangiantplanets by about afactor of three. Jupiter is over 300 times more massivethanthe Earth, andhas aradius about 10 times bigger, i.e. avolume 1000 times bigger. Generally,terrestrial planets arethought to have lowermassthangiantplanets:thisiscertainly true in theSolar System.There may, however, be mini-Neptune ice giant exoplanets with lowermassesthan super-Earth terrestrial exoplanets.Since fewtransitingexoplanets with masses below 10 M⊕ areyet known (Dec. 2009), this remainsanopenquestion, though one that we will explore later.

19 Chapter 1Our Solar System from afar

Could extraterrestrial astronomers detect the Solar System planets?

So far, in this Introductionand in theboxes entitled ‘The neareststarsand planets’ and‘Stars, planets andbrown dwarfs’, we have setour ownSolar System in the contextofits place in our Milky WayGalaxy,and briefly compared main sequence stars with brown dwarfs andplanets.The subject of the book is transitingexoplanets,but to interpret our findings about exoplanets,weneed first to understandthe variousmethods that have been or couldbeusedtofind them. To this end, in theremainder of this chapter we will usethe familiar Solar System planets to illustrate the variousexoplanet detectionmethods.Wewill examine the question: If theGalaxyharboursintelligentlife outside our own Solar System, couldthese hypotheticalextraterrestrialsdetect the Solar System planets? Each of theexoplanet detectionmethods will be applied to theSolar System,and through this thelimitations for each method will be explored.

1.1Directimaging

TheSolar System planets were all, of course, detected from Earthusing direct imaging(Figure 1.6).Obviously,direct imagingworks best for nearby objects, andbecomesmore difficult as the distance, d,toanobject increases,asFigure 1.7 demonstrates.

(a) (b) (c)

Figure1.6 NASA images of Saturn andJupiter.(a) Theback-lit ringsof Saturn observed by Cassini.(b) Saturn’smoon Tethys andaclose-up of therings. (c) Jupiter,the largest planet in the Solar System.

This is particularly true if theobject to be imaged is close to abrighter object. Sincethe optical light from theSolar System’s planets is overwhelmingly reflected sunlight,thisisclearly thecasefor them.The biggest andmostluminous planet in the Solar System,Jupiter,reflects about 70%ofthe sunlight that it −9 intercepts,and consequently hasaluminosity of ∼10 L%. ● Compare thepositionofVoyager 1whenthe images in Figure 1.7 were taken, with thedistance to thenearestknown exoplanetarysystem.How many times furtherawayisthe nearestknown exoplanet? ❍ Voyager1was 6.4 × 1012 mfrom theEarth, while thedistance to thenearest known exoplanetarysystem, ε Eri, is 9.96 ± 0.02 × 1016 m. Theratio of these twodistances is 15 560:the nearestknown exoplanetarysystem is over 15 000 times furtheraway. 20 1.1 Direct imaging

Venus Earth Jupiter

Saturn Uranus Neptune

Figure1.7 Theseimagesshowsix of theSolar System’s planets.Theywere taken by Voyager1from apositionsimilar to whereitisshown in Figure 1.1, more than 6.4 × 1012 mfrom Earthand about 32 degreesabove the eclipticplane. Mercury wastoo closetothe Suntobeseen;Marswas not detectable by the Voyagercameras due to scattered sunlight in theoptics.Top row, lefttoright,are Venus,Earth andJupiter;the bottomrow showsSaturn, Uranus andNeptune. The background featuresinthe images areartefacts resultingfrom themagnification. Jupiter andSaturnwereresolvedbythe camera, butUranusand Neptune appear largerthantheyshouldbecause of spacecraftmotionduring the 15 sexposure. Earthappearsinthe centreofthe scattered lightraysresultingfrom theSun. Earth wasacrescentonly 0.12 pixels in size. Venus was 0.11 pixels in diameter. Jupiter is aprominentobject in our ownnight sky, butviewedfrom ε Eriitis very closetothe Sun, which outshines it by afactor of 109.Jupiter’s orbital 11 semi-majoraxis,aJ,is7.784 × 10 m. Using the smallangle formula,the angularseparation between theSun andJupiter as viewed at the distance of ε Eri is a θ = J radians dε Eri 7.784 × 1011 m = rad 9.96 × 1016 m =7.815 × 10−6 rad 360 × 60 × 60 =7.815 × 10−6 × 2π arcsec =1.61 arcsec.

21 Chapter 1Our Solar System from afar

● Does the angular separationofJupiter andthe Sunatthe distance of ε Eri depend on thedirectionfrom which the Solar System is viewed? ❍ Yes. Theangular separationcalculated above is themaximum value, which wouldbeattained onlyifthe system were viewed from above so that theplane of Jupiter’s orbit coincides with the planeofthe sky.Evenfor edge-on systems, though, thefullseparation can be observedattwo positions on the orbit. Thus detectingJupiter from thedistance of ε Eribydirect imagingwouldbe extremely challenging, as thereisanobject ∼109 times brighter within 2 arcsec. If Jupiter were brighter andthe Sunwerefainter this wouldhelp, andone wayto achieve this is to observe in theinfrared.Atthese wavelengths Jupiter’s thermal emission peaksbut theSun’semissionpeaksatmuchshorterwavelengths,sothe contrastratio between theSun andJupiter is lessextreme. Figure 1.8 showsthe spectralenergydistributions of theSun andfour of theSolar System planets as theywouldbeobservedatadistance of 10 pc.Thisfigure showsthatthe contrast ratio between theSun andthe planets becomesgenerally more favourableat longerwavelengths.

10−6 10−7 10−8 10−9 Sun 10−10 10−11 25 mag, 10 billion −12 units 10 10−13 rary Jupiter 17.5mag, it 10 million 10−14 Venus arb

/ Earth

λ −15 I 10 Mars 10−16 10−17 10−18 10−19 10−20 0.1 1 10 100 λ/µm

Figure1.8 Thespectral energy distributions of theSun, Jupiter,Mars, Earth andVenus.The curvefor theEarth is farmore detailed than thecurves for the otherobjects because empirical data have been included. Foreach of theplanets, thespectral energy distributioniscomposed of twobroadcomponents: peaking at around 0.5 µmisthe reflected solar spectrum,while thethermal emission of the planet itself peaksat9–20 µm.

22 1.1 Direct imaging

● Jupiter is thebiggest planet in the Solar System,yet at wavelengths around 10 µmthe Earthemits more light.Why is this? ❍ TheEarth is closer to the Sun, andconsequently it receivesmore insolation, i.e. more sunlight falls perunitsurface area. Thus theEarth is heated to a highertemperature than Jupiter,and theEarth’sthermal emission peaksat around 10 µm. Theamount of light emitted is the surface area multiplied by theflux perunitarea. Thelatter depends stronglyontemperature, thus the Earthisbrighter at 10 µmdespite having approximately 100 times less emittingarea. Planets can have internalsourcesofenergyinadditiontothe insolationthatthey receive;for example, radioactive decay of unstable elements generates energy within theEarth. Radioactive decay is generally thought to be insignificantin giantplanets as their compositionispredominantly Hand He.More important for theplanets that we will discussinthisbook is internalheating generated by gravitationalcontraction, which is known as Kelvin–Helmholtz contraction. Jupiter emits almosttwice as much heat as it absorbs from theSun, andall fourgiantplanets in theSolar System radiate some powergenerated by Kelvin–Helmholtz contraction.

Exercise 1.2 Figure 1.8 showsthe spectral energy distributions for theSun andfour of our Solar System’s planets.Consider thefollowing with referenceto this figure. (a) State what wavelengthgives the most favourablecontrastratio with theSun for thedetection of Jupiter.Whatisthe approximate valueofthismostfavourable contrastratio? (b) At whatwavelength doesthe spectral energy distributionofJupiter peak?Is this thesamewavelength as you stated in part (a)? Explain your answer. (c)Whatadvantages arethere to usingawavelengthofaround 20 µmfor direct imagingobservations of Jupiter from interstellar distances? ■ In fact, infraredimaging hasdetected an exoplanet directly.Agiantexoplanet wasdiscoveredatanangular distance of 0.78 arcsec from thebrown dwarf 2MASSWJ1207334-393254 by infraredimaging, as showninFigure 1.9. Direct imaging is most effective for brightplanets in distantorbits around nearby faint stars. Theserequirements mean that directimaging haslimited applicability in the search for exoplanets.Returning to our hypothetical extraterrestrial astronomers, even if theywerelocated on one of thenearestknown exoplanets,theywouldface problems in detectingeventhe most favourableofthe Solar System’s planets by directimaging. Theangular separationofJupiter from theSun is lessthan 2 arcsec, andthe Sunisone of thebrighter starsinthe solar neighbourhood, with thecontrastratio between theSun andJupiter beingover 104 even at the most favourablewavelength. Thus it seemsunlikely that hypothetical extraterrestrials wouldfirstdetect the Solar System planets through directimaging. Despite thedifficulties,astronomersare designing instruments specifically to detect exoplanets by directimaging. Theseinstruments employ sophisticated techniquestoovercomethe overwhelminglight from theplanets’hoststars. The Gemini Planet Imager (GPI) is designedtodetect planets with contrastratios as

23 Chapter 1Our Solar System from afar

Figure 1.9 False-colour imageofthe brown dwarf 2MASSWJ1207334-393254 usingH,KandLband infraredfilters. Blue indicates pixelsbrightestinH,while redindicates pixels brightest in L. Thecompanion exoplanet is relatively bright in theLband andthus appearsred.The exoplanet hasaneffective temperature of 1250 ± 200 K.

extremeas108 usingadevice called a coronagraph.Aspectacular recentresult usingthismethodissummarized in Subsection 1.1.1below. As Figure 1.8 shows, this technology couldinprinciple render the Earthdetectable. In practice, to detect theEarth, the extraterrestrials’telescope wouldneed to be implausibly closetothe Solar System. ● If thecontrastratio of theEarth andthe Sunislessthanthe thresholdfor planet detectionwith theGPI, whatlimits thedetectability of theEarth with such an instrumentatlarge distances? ❍ Thereare twolimitingfactors. First, theangular separationofthe Earthand theSun decreases with distance; at large distances the twoobjects arenot spatiallyresolved. Theangular separationdiminishesas1/d.Second, the telescope needstohavesufficientEarthlight fallingonittopermitdetection of theEarth. Thenumberofphotons reaching the telescope diminishes as 1/d2. TheSPHERE instrument is scheduled to be deployed on theVeryLarge Telescope (VLT)in2010, andaimstodetect some nearby young giantexoplanets at large separations from their hoststar.Giantplanets arebrightestearly in their life, when theyare contractingrelatively quickly.The Kelvin–Helmholtz powered luminosity diminishes as agiantplanet contracts andcoolswith age, as we will seeinSubsection 4.4.3.

1.1.1Coronagraphy

As thenameimplies,coronagraphs were invented to study thesolar coronaby blocking thelight from thedisc(i.e. thephotosphere) of theSun. An occulting elementisincludedwithin theinstrument, andisusedtoblock thebrightobject, allowing fainter features to be detected.Ifanexoplanetarysystem is close enough for thestar andexoplanet to be resolved, then acoronagraph maypermitdetection of an exoplanet wherewithout it thedetector wouldbefloodedwith light from the central star. Fomalhaut(αPsA)isone of the 20 brighteststarsinthe sky; some of its characteristics were listed in Table1.1. It is surrounded by adustdiscthatappears 24 1.1 Direct imaging elliptical andhas asharp inneredge.Thisled to speculation that theremight be a planet orbitingFomalhautjustinsidethe dustring, andcreating the sharpinner edge of theringrather as the moons of Saturn shepherd its rings(cf.Figure 1.6). Figure 1.10 wascreated usingthe HubbleSpace Telescope’s coronagraph, combiningtwo images taken in 2004 and2006. In this figure theorbital motionof theplanet Fomalhautbis clearly revealed. Fomalhautbis ∼109 times fainter than Fomalhaut, andis∼100 AU from thecentral star.

Figure1.10 False-colour imageshowing theregionsurrounding Fomalhaut. Theblack shapeprotruding downwards from 11 o’clock is thecoronagraph mask,which hasbeen used to blockthe light from thestar located as indicated at the centreofthe image. Thesquare box is theregionsurrounding theplanet, which hasbeen blown up andinset. Themotionofthe planet, called Fomalhautb,along its elliptical orbit between 2004 and2006 is clearly seen.Atthe distance of Fomalhaut 13!! corresponds to 100 AU. Thereare designs (though not necessarily thefunding) for aspace telescope with acoronagraph optimized to detect terrestrial exoplanets:Fomalhautbmaybethe first of asignificantnumberofexoplanets detected in this way. Ourhypothetical extraterrestrial astronomerscouldpossiblydetect the Solar System’s planets using coronagraphy, providedthattheyare closeenough to theSun to be able to block its light without alsoobscuring thelocationsofthe Sun’splanets.

1.1.2Angular differenceimaging

Another spectacular recentresult, showninFigure 1.11, uses some otherclever techniquestoovercomethe adverseplanet to star contrastratio. Figure 1.11 reveals three giantplanets around theA5V star HR 8799. Thetechnique employed is called angular difference imaging,anoptimal wayofcombining many short exposures to reveal faintfeatures.HR8799’sage is between 30 Myr and 160 Myr,Myr indicates 106 yr,ora i.e. it is ayoung star.Because this planetarysystem is young, thegiantplanets are megayear. relatively bright,making their detectionbydirect imagingpossible. Thethree 25 Chapter 1Our Solar System from afar

planets have angular separations of 0.63, 0.95 and 1.73 arcsec from thecentral star,corresponding to projected separations of 24, 38 and 68 AU.The orbital motion, counter-clockwise in Figure 1.11, wasdetected by comparing images taken in 2004, 2007 and2008. Themassesofthese threebodies areestimated to be between 5 MJ and 13 MJ.

Figure1.11 Thethree planets around HR 8799. Thecentral star is overwhelminglybright andhas been digitally removed from theimages, causing the featurelessormottled round central region in each panel. The threeplanets,whosenames are HR 8799 b, cand d, arelabelled b, cand d. At thedistance of HR 8799, 0.5!! corresponds to 20 AU.

1.2Astrometry

Astrometryisthe science of accurately measuring thepositions of stars. The Hipparcos wasanESA satellite Hipparcos satellite measured thepositions of over 100 000 starstoaprecisionof that operated between 1989 and 1 milliarcsec, andthe Gaia satellite, due for launchbythe European Space Agency 1993. (ESA)inspring 2012, will measure positions to aprecision of 10 microarcsec (µarcsec).Astrometryoffersawaytoindirectly detect thepresenceofplanets. Though we oftencasually refertoplanets orbitingaround stars, in fact planets andstarsbothpossess mass, andconsequently all thebodies in aplanetary system orbit around the barycentre,orcommoncentreofmassofthe system. Figure 1.12 illustrates this.

26 1.2 Astrometry

2aP foci star foci star

v∗

v v P,bary centre planet of mass planet

2a∗ 2aP (a) (b)

Figure1.12 (a)The elliptical orbitsofaplanet andits hoststar about thebarycentre(or centreofmass) of the system.(b) In astrocentric coordinates,i.e.coordinates centred on thestar,the planet executes an elliptical orbit with thestar at one focus.The semi-major axis of this astrocentric orbit, a,isthe sumofthe semi-major axes of the star’s orbit andthe planet’sorbitinthe barycentric coordinates shownhere. In general, orbitsunderthe inversesquare force laware conicsections, the loci obtained by intersecting acone with aplane. Forplanets,the orbitsmustThere is no physical significance be closed,i.e.theyare either circular or,more generally,elliptical, with the to the cone or theplane; it eccentricity of theellipse increasingasthe misalignmentofthe normal to the simply happens that thereisa planewith theaxisofthe cone increases.Ofcourse, acircle is simply an ellipse mathematical coincidence. with an eccentricity, e,of0. Theorbital period, P ,the semi-major axis, a,and thestar andplanet masses are related by (the generalizationof) Kepler’sthird law: a3 G(M + M ) = ∗ P , P 2 4π2 (1.1) where a = a∗ + aP as indicated in Figure 1.12. TheSun constitutes over 99.8%ofthe Solar System’s mass,sothe barycentre of theSolar System is closeto, butnot exactly at, the Sun’sown centreofmass. As theplanets orbit around thebarycentre, the Sunexecutes asmaller reflexorbit, keeping the centreofmassofthe system fixed at the barycentre. In general,the motionofastar in areflex orbit hasasemi-major axis, a∗,thatcan, in principle, be detected as an angular displacement, β,whenthe star is viewed from distance d.Thisangleofthe astrometric wobble, β,isproportionaltothe semi-major axis of thestar’s reflexorbit: a β = ∗ . d However, since MP a∗ = aP, M∗ we have M a β = P P , (1.2) M∗d andwesee from Equation1.2 that theastrometric wobblemethodismost effective for findinghigh-massplanets in wide orbitsaround nearby relatively low-mass stars. 27 Chapter 1Our Solar System from afar

Worked Example 1.1

(a) Calculate theorbital semi-major axis,a%,ofthe Sun’sreflex orbit in responsetoJupiter’s orbital motion. ThemassofJupiter,MJ,is 1.90 × 1027 kg, themassofthe Sunis1.99 × 1030 kg, andJupiter’s orbital 11 semi-major axis,aJ,is7.784 × 10 m. Jupiter constitutes about 70%ofthe mass in theSolar System apartfrom theSun, so you mayignore theother lesserbodies in the system.

(b) Hencecalculate the distance, dGaia,atwhich the astrometric wobble angle, β,due to theSun’sreflex orbit is greater than βGaia =10µarcsec. (c)State whether aGaia satellite positionedanywherewithin thesphere of radius dGaia wouldbeabletodetect the astrometric wobbledue to theSun’s reflexorbit, explainingyour reasoning. (d) Comment on thefraction of theGalaxy’s volume overwhich a hypothetical extraterrestrial Gaia coulddetect Jupiter’s presence by the astrometrymethod. Solution (a) Thebarycentreofthe Sun–Jupiter system is such that

MJaJ = a%M%, (1.3) so 1.90 × 1027 = MJ = × 7.784 × 1011 a% aJ 30 m M% 1.99 × 10 =7.432 × 108 m. Thesemi-majoraxisofthe Sun’sreflex orbit is 7.43 × 108 m.

(b) Thedistance dGaia is givenbythe small angleformula. To usethis formula we must first convertthe angle βGaia to radians: 2 × π 1 × 10−5 =1×10−5 × arcsec 360 × 60 × 60 rad =4.85 × 10−11 rad. Here we have multiplied by the 2π radiansinafullcircle anddivided by the 360 × 60 × 60 arcseconds in afullcircle, thus converting our angular units. Here π is not theparallax. −11 So βGaia =10µarcsec =4.85 × 10 rad. Theastrometric wobbleangleof theSun’sreflex orbit is givenby β=a%, d (1.4)

so dGaia is givenby a% dGaia = . (1.5) βGaia Substitutingvalues, 7.43 × 108 d = a% = =1.532 × 1019 . Gaia 4.85 × 10−11 4.85 × 10−11 m m

28 1.2 Astrometry

Clearly the SI unitofmetres is not agood choice for expressing interstellar distances,sowewill expressthisdistance in parsecs: 1.532 × 1019 m d = =4.96 × 102 pc =496 pc. Gaia 3.086 × 1016 mpc−1 Hencethe limitingdistance is around 500 pc,tothe one significantfigure of thestated angular precision(10 µarcsec). (c)Ifthe extraterrestrials’Gaia satellite is ideally positionedsothat Jupiter’s orbit is viewed face on, then thesatellite will seethe true elliptical shapeofthe Sun’sreflex orbit.Atany otherorientation,the satellite will see aforeshortenedshape;but even in the leastfavourableorientation,with orbitalinclination i =90◦,asinFigure 1.13a, thesatellite will seethe Sun move back andforth alongalinewhoselengthisgiven by thesize of the orbit.Onlyinthe extremely unlucky caseofahighlyeccentric orbit,viewed from theleastfavourableinclination and azimuth, will theangular deviation Theazimuthisthe anglearound be substantially lessthanthatcorresponding to thesemi-majoraxis. Since theorbit: for ahighlyeccentric Jupiter hasaloworbital eccentricity,the extraterrestrial Gaia coulddetect orbit,the projection on thesky d the Sun’sreflex wobblefrom anywhere within thesphere of radius Gaia. will vary with azimuth, being smallestwhenthe orbit is star’sorbit normal viewed from an extension of the semi-major axis. i =90◦ star

centreofmass (a)

normal

i

(b)

i =0◦ normal

(c)

Figure1.13 Theshape of theorbitthatthe Gaia satellite sees is a function of theorbital inclination, i.Inpanel (a), i =90◦andthe orbit appearsasalinetraced on thesky.Panel (b) showsanintermediate value of i,and theorbitappearselliptical, with thetrue orbital shapebeing foreshortened. Panel(c) showsthe situationwhere i =0◦;onlyinthiscase doesthe observersee the true shapeofthe orbit.

29 Chapter 1Our Solar System from afar

(d) Thedistance dGaia is about 500 pc,i.e.about 1500 ly.Comparing this with Figure 1.3a, we can seethatthislengthscale is comparable to the width of thespiral armstructure in theGalaxy.The astrometric wobbleofthe Sun due to Jupiter’s pullcouldbedetected by advanced,spacecraft-building extraterrestrial civilizations in thesameregionofthe Orion Arm as the Sun. Theastrometric wobblewouldbetoo small to be detected by aGaia-like satellite built by more remote extraterrestrials.

● Howdoesthe semi-major axis of theSun’sreflex orbit in responsetoJupiter, a%,compare with thesolar radius, R%?Whatdoesthisimply for theposition of thebarycentreofthe Solar System? 8 ❍ Thevalue of R% is 6.96 × 10 m, which is onlyjustsmaller than thevalue 8 that we calculated for a%,namely 7.43 × 10 m. This meansthatthe barycentre of theSolar System is justoutside thesurface of theSun. ● Will thebarycentreofthe Solar System remain at thesamedistance from the centreofthe Sunasthe eightplanets in theSolar System all orbit around the barycentre? Explain your answer. ❍ No,the eightplanets all have differentorbital periods,sosometimes theywill all be located on thesamesideofthe Sun. When this happens,the barycentre will be pulled furtherfrom thecentreofthe Sunthanthe valuethatwe calculated usingJupiter alone.Atsomeother times most of theseven lesser planets will be on theopposite side of theSun from Jupiter,inwhich case theywill pullthe barycentre closer to the centreofthe Sunthanimplied by our calculations usingJupiter alone. ● Forastrometric discovery prospects,isthere anydisadvantageinherent in a planet having awideorbit? ❍ While thesize of theastrometric wobbleincreasesasthe planet’ssemi-major axis increases,sotoo doesthe orbital period (i.e.the planet’s‘year’). Kepler’s thirdlaw tells us that P ∝ a3/2,soasthe orbital size increases,the lengthof timerequired to measure awholeorbitincreasesevenfaster. Ourcalculations show that our hypothetical extraterrestrial astronomerswouldbe able to detect Jupiter’s presence so long as theywerewithin about 500 pc of the Sunand were able to constructaninstrumentwith Gaia’scapabilities.Wedonot yetknowhow commonplanetarysystemslikeour ownare,but onceGaia is launched we will begintofind out!

1.3Radialvelocitymeasurements

Like theastrometric method, theradial velocity method of planet detectionrelies on detectingthe hoststar’s reflexorbit. In this case, rather than detectingthe change in positionofthe hoststar as it progressesaround its orbit,wedetect the change in velocity of thehoststar.The radial velocity,i.e.the velocity of an object directly towards or away from theobserver, can be sensitively measured usingthe Doppler shiftofthe emitted light. This hasbeen apowerful technique in many areas of astrophysics andwas adopted in the 1980s by astronomers searching for Jupiter-likeplanets around nearby Sun-like stars. 30 1.3 Radial velocity measurements

1.3.1The stellar reflexorbitwithasingle planet

Themotionofaplanet is most simply analyzed in therestframe of thehoststar, i.e. the astrocentric frame.Inthisframe theplanet executes an orbit with semi-major axis a,period P andeccentricity e,asshown in Figures 1.12b and1.14.

Figure1.14 x z Theastrocentric periapsis orbit of aplanet. Theobserveris planet positionedinthe directionofthe γ bottomofthe page,and is viewing thesystem along thedirectionof θ the z-axis. The x-axisisinthe y planeofthe skyand is oriented so ω OP that it intersects the planet’sorbit ω − π OP i sky at the point wherethe z-component of theplanet’svelocity is towards

to theobserver. Finally,the y-axis

ob is thethird directionmaking orbital plane se up aright-handedCartesian rv

er coordinate system.The planet is closesttothe star at the pericentre, whosepositionisdefinedbythe angle ωOP.

Thepoint at which theplanet is closest to thestar is called the pericentre,and the star is positionedatone focus of theelliptical orbit.Wewill adopt aCartesian coordinate system,centred on thehoststar,oriented as showninFigure 1.14. Theanglebetween the planeofthe skyand theplaneofthe orbit is theorbital inclination, i.The x-axisisdefinedbythe intersection of theorbitwith theplane of thesky as seen by theobserver. Positive x is on thesideofthe orbit wherethe planet movestowards theobserver. Thepoint labelled γ is theintersection of the orbit with thepositive x-axis. Theangle θ is the true anomaly,which measures howfar around theorbitfrom thepericentrethe planet hastravelled.Thisangleis measured at the positionofthe hoststar.The angle ωOP measures theorientation of thepericentrewith respect to γ.The velocity, v,has componentsinthe x-, y- and z-directionsthatare givenby 2πa vx=− √ (sin(θ + ω )+esin ω ) , P 1 − e2 OP OP 2πacos i vy = − √ (cos(θ + ω )+ecos ω ) , (1.6) P 1 − e2 OP OP 2πasin i vz = − √ (cos(θ + ω )+ecos ω ) . P 1 − e2 OP OP What astronomerscan actually observe is thestar,not theplanet, so we need the analogous equations for thereflex orbit of thestar.Sofar we’veconsidered the orbit of theplanet around thestar,i.e.inan‘astrocentric’ frame.The star is actually moving too, executing its reflexorbitaround thebarycentre, as illustrated in Figure 1.12a.

31 Chapter 1Our Solar System from afar

Thevelocity, v,ofthe planet in the astrocentric frame (Figure 1.12b)isgiven by simple vector subtraction:

v = vP,bary − v∗, (1.7)

where v is theastrocentric velocity giveninEquation1.6, and v∗ is the velocity of thestar in thebarycentric frame,i.e.the velocity of thestar as it performsits reflexorbitabout thebarycentreasshown in Figure 1.12a. Equation1.3 gave us theratio of thesemi-majoraxesofthe orbit of aplanet andthe reflexorbitofits star.The relationship is much more generalthanour useofitinSection 1.2: for anyplanetarysystem,the barycentre remains fixed in its owninertial frame,soat all times the distances of thestar andthe planet from thebarycentrewill vary proportionately:

M∗r∗ = −MPrP. (1.8) Here we have used vector notation,and sincethe planet andthe star arein opposite directions from thebarycentre, this equationintroducesaminus sign into Equation1.3, which used the (scalar)distance rather than thevector displacement. Differentiating with respect to time, we then obtain the general relationship,inthe barycentric frame, between thevelocities of theplanet andthe star’s reflexorbit:

M∗v∗ = −MP vP,bary. (1.9) ● What do Equations 1.8 and1.9 implyfor theshapesofthe twoellipsesin Figure 1.12a? ❍ Theellipsesare thesameshape,and differ onlyinsize.

Consequently,using Equation1.9 to substitute for vP,bary in Equation1.7, and making thebarycentric velocity of thestar thesubject of theresultingequation, Thefraction multiplying v is we obtain known as the reduced mass of MP theplanet, andisanalogous to v∗ = − v, (1.10) MP + M∗ that quantity in simple two-body v problems in otherareas of where is theastrocentric orbital velocity of theplanet, as giveninEquations 1.6. physics. Finally,weshouldnotethatingeneral the barycentre of theplanetarysystem beingobservedwill have anon-zero velocity, V 0,with respect to the observer. V 0 changesonthe timescale of thestar’s orbit around thecentreofthe Galaxy, i.e. hundreds of Myr.Thus we can regard it as aconstantasthistimescale is much longerthanthe timescale for theorbits of planets around stars. From thepoint of view of an observerinaninertial frame,therefore, the reflexvelocity of thestar is V = v∗ + V 0.Sowenow have acompletely general expression, in theframe of an inertial observer, for thereflex velocity of astar in responsetothe motionofa planet around it:

2πaMP Vx = V0,x + √ (sin(θ + ω )+esin ω ) , 2 OP OP (MP + M∗)P 1 − e 2πaMP cos i Vy = V0,y + √ (cos(θ + ω )+ecos ω ) , 2 OP OP (1.11) (MP + M∗)P 1 − e 2πaMP sin i Vz = V0,z + √ (cos(θ + ω )+ecos ω ) . 2 OP OP (MP + M∗)P 1 − e

32 1.3 Radial velocity measurements

● Howdothe threecomponentsofV contributetothe observedstellar radial velocity? ❍ Theradial velocity is themotiondirectly towards or away from theobserver. Thecoordinate system that we adopted hasthe z-axisdirected away from the observer, while the x-and y-axes areinthe planeofthe sky. Theradial velocity is givenbyVz.The othertwo componentsdonot contributetothe radial velocity. ● Which of theterms in theexpression for thestellar radial velocity are time-dependent?Describe in simple physical terms howthe time-dependence arises.

❍ Theonlytime-dependent terminthe expression for Vz is thetrue anomaly, i.e. the angle θ(t),which changescontinuously as theplanet andstar proceed alongtheir orbitsaround thebarycentre.

Exercise 1.3 Use Kepler’s thirdlaw to estimate thetimefor theSun to orbit 12 around theGalaxy.You mayassume themassofthe Galaxyis10 M% andmay be approximated as apoint mass at the centreofthe Galaxy, andthatthe distance of theSun from thecentreofthe Galaxy(known as the Galactocentric distance) is 8 kpc. ■ Theradial velocity,which we will henceforth simply call V ,ofastar executing a reflexmotionasaresult of asingleplanet in an elliptical orbit is givenby

2πaMP sin i V(t)=V0,z + √ (cos(θ(t)+ω )+ecos ω ) . 2 OP OP (1.12) (MP + M∗)P 1 − e

θ(t) completes afullcycle of 360◦ (or 2π radians) each orbit.Unlessthe orbit is circular, θ doesnot change linearly with time; instead,itobeys Kepler’s second law, or equivalently the lawofconservation of angularmomentum.

Exercise 1.4 Use Equation1.12 for theradial velocity to answerthe following. (a) What is the dependenceofthe observedradial velocity variation on theorbital inclination, i?State this dependenceasaproportionality,and drawdiagrams illustratingthe values of i for themaximum,the minimumand an intermediate valueofthe observedradial velocity.You mayassume that all thecharacteristics of theobservedplanetarysystem,exceptfor its orientation,remain constant. (b) Forfixedvalues of all parametersexceptthe orbital eccentricity, e,how does theamplitude of theobservedradial velocity variation change as the eccentricity varies?(By definition,the eccentricity of an ellipselies in therange 0 ≤ e ≤ 1.) Explain your answerfully,with referencetothe behaviour of therelevant terms in Equation1.12. (c)Adoptingthe approximation that Jupiter is theonlyplanet in theSolar System,calculate the observedradial velocity amplitude, ARV ,for theSun’sreflex orbit.Expressyour answerasafunction of theunknown orbital inclination, i. Use thefollowing (approximate) values of constants to evaluate your answer: 27 30 11 MJ =2×10 kg, M% =2×10 kg, aJ =8×10 m; Jupiter’s orbital period is PJ =12years, andits orbital eccentricity is eJ =0.05. ■

33 Chapter 1Our Solar System from afar

An important resultfrom Exercise1.4 is that theamplitude of thereflex radial velocity variationspredicted by Equation1.12 is 2πaM sin i A = P √ . RV 2 (1.13) (MP + M∗)P 1 − e Applying this to theSun’sreflex orbit due to Jupiter,wefind aradial velocity −1 amplitude of ARV ≤ 13 ms . Astronomersmeasure radial velocities usingthe Doppler shiftofthe featuresin thestellar spectrum.The wavelengthchange, Δλ,due to theDoppler shiftis givenby Δλ V = , λ c (1.14) so to detect thereflex orbit of theSun due to Jupiter’s presence, our hypothetical extraterrestrial astronomerswouldneed to measure thewavelength shifts of featuresinthe solar spectrum to aprecision of Δλ 13 −1 = ms =4.2×10−8, λ 3.0×108 ms−1 wherewehavesubstituted thevalue for thespeed of light, c,inSIunits.This sounds challenging,but it is possiblewith current technology; terrestrial astronomershaveaspired to this sincethe 1980s.For bright starswith prominent spectral features it is nowpossibletomeasure radial velocities to precisions of better than 1 ms−1,i.e.motions slower than walkingspeed can be detected! Figure 1.15 showsthe radial velocity measurements used to infer the presence of GJ 832 is one of the 100 nearest theplanet around GJ 832 (also known as HD 204691); this planet hasalower known starslisted Table1.1. mass than Jupiter andhas P =9.4years. GJ 832’sreflex radial velocity amplitude slightly exceedsthatofJupiter because,aswesaw in Table1.1, thestar has mass lessthanhalf that of theSun, andthe planet hasashorterorbital period than Jupiter.Our Sunhappens to have aspectral type(G2V) that makesit particularly suitable for radial velocity measurements:ithas ahostofsharp, well-defined photospheric absorptionlines.Bymeasuring theshifts in the observedwavelengths of theselines,our hypothetical extraterrestrial astronomers wouldbeabletodetect the presence of Jupiter unlesstheyhappentobeunlucky andviewthe Sun–Jupiter system from an orbital inclination, i,close to 0◦.The otherlimitingfactor,assuming that they have technology comparable to ours,is their distance from theSun. To make radial velocity measurements of therequired precision, astronomersneed to collect alot of light,and as noted previously the fluxofphotons from theSun drops offas1/d2.

Exoplanet naming convention Theplanet discoveredaround thestar GJ 832 is called GJ 832 b. This is the general convention:the first exoplanet discoveredaround anystar is given its hoststar’s name with ‘b’ appended. Thesecond planet discoveredinthe system is labelled ‘c’, andsoon. This distinguishes planets from stellar companions, which have capital lettersappended: for example, the stars α Cen Aand α CenB.The planets in amultiple planet system arealways labelled b, c, d, ... in theorder of discovery;the distances of theseplanets from thehoststar can consequently be in anyorder.

34 1.3 Radial velocity measurements

● If aplanet were discoveredorbitingaround thestar α CenA,whatwoulditbe called? ❍ Assuming that it wasthe first planet discoveredorbitingaround thestar,it wouldhavethe star’s name with ‘b’ appended: α CenAb.

30 P =9.4yr e =0.12 M =0.64 MJ 20 1 − 10 /m s ty

ci 0 lo ve −10

−20 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 year 20 1 − 10

/m s 0 ty

ci −10 lo

ve −20 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 year

Figure1.15 Upperpanel: radial velocity measurements revealing the presence of theplanet around GJ 832, with thebest-fittingsolutionofthe formof Equation1.12 overplotted as adashedline. Theparameterscorresponding to this fit forthe planet GJ 832 bare indicated. This planet’sorbithas similarities to that of Jupiter.Lower panel: thedeviations of themeasured data pointsfrom the best-fittingsolution. Figure 1.15 showsradial velocity measurements as afunctionoftime. Thebest-fittingmodelsolution, which is overplotted,was generated using Equation1.12.Ifweexamine Equation1.12,wesee that it predicts the same valuefor V (t) everytime θ(t) completes afullcycle, i.e. everytimethe star returns to thesamepositiononits orbit.Inthe caseofGJ832 b, theorbital period is long, anditiseasytomakeobservations samplingeach part of theorbit. For shorterorbital periods,sometimes onlyasinglemeasurementismadeduring a particular orbit;tomakeagraph likeFigure 1.15, many orbitswouldneed to be plotted on thehorizontal axis,and theplotted pointswouldbeverythinlyspread out.Amore efficientway of presenting such data is to phase-fold,sothatinstead of plottingtimeonthe horizontal axis,one plots orbitalphase, φ: Thetimetable giving orbital t − T0 phase for anyvalue of time, t, is φ = − N , (1.15) P orb known as an ephemeris. where t is time; T0 is a fiducial time, for example, T0 couldbefixedatthe first observedtimeatwhich the star is farthest from theobserver; P is theorbital 35 Chapter 1Our Solar System from afar

period; and Norb is an integersuchthat 0 ≤ φ ≤ 1.Asthe star proceedsaround a fullorbit, t increases by an amount equaltothe orbital period, P ,and φ covers the fullrange of values 0 ≤ φ ≤ 1.Onceper orbit,whenthe star crossesthe fiducial point corresponding to T0,the integer Norb increments its count: Norb is known as the orbitnumber. At first glance the curveshown in Figure 1.15 looks very much likethe familiar sinusoidalcurvethatone expects to seewheneverthere is motioninacircle. If youlook carefully,however,you shouldsee that the curvedoesnot have theperfect symmetries of asinecurve: it corresponds to an orbit with finite eccentricity, e =0.12.For more extremevalues of theeccentricity, the deviations from asinecurvebecome more pronounced,asshown in Figure 1.16. The eccentricities of thesolutions showninFigure 1.16 range from e =0.17 for HD 6434 to e =0.41 for HD 65216.

Exercise 1.5 In Exercise1.4 we found that theamplitude of thestellar reflex orbit’sradial velocity is 2πaM sin i A = P √ . RV 2 (Eqn 1.13) (MP + M∗)P 1 − e

(a)Thisequationhas the orbital semi-major axis in the numerator,soatfirst glance it appearsthatthe radial velocity amplitude increases as theplanet’s orbital semi-major axis increases.Does ARV in fact increaseasaplanet’sorbital semi-major axis increases?Explain your reasoning. (b) State, with reasoning, howthe radial velocity amplitude depends on planet mass,star mass,semi-majoraxisand eccentricity. ■

1.3.2Reflex radial velocityfor many non-interacting planets

So farwehaveonlyconsidered asingleplanet. Formore than one planet, so long as the planets do not significantly perturb each other’selliptical orbits, we can simply combineall of theelliptical reflexorbits about thebarycentre. The observedradial velocity will be 7n V = V0,z + Ak (cos(θk + ωOP,k)+ekcos ωOP,k) , (1.16) k=1

where thereare n planets,each with their ownmass, Mk,and instantaneous orbitalparameters ak, ek, θk and ωOP,k,and their owninstantaneous valueofAk givenby

2πakMk sin i Ak= ; , (1.17) 2 MtotalPk 1 − ek

where Mtotal is thesum of themassesofthe n planets andthe star.Generally, Equation1.16 is an approximation.The instantaneous orbital parameterswill evolve overseveral cycles of thelongest planet’speriod because of the gravitationalinteractionsbetween the planets. 36 1.3 Radial velocity measurements

HD 6434 HD 19994 − 1 − 1

23.05 19.35 y/km s y/km s it it oc oc el el 23 19.3 lv lv ia ia rad rad 22.95 0 0.5 1 0 0.5 1 1 orbital phase, φ orbital phase, φ 1 − − ms 0.04 0.02 ms /k 0 0 /k C) −0.04 −0.02 C) − 51 500 52 000 52 500 51 500 52 000 52 500 − (O (JD − 2400 000)/days (JD − 2400 000)/days (O HD 65216 HD 92788 − 1 42.70 − 1 −4.4 42.68 y/km s y/km s it it oc 42.66 oc el −4.5 el lv 42.64 lv ia ia rad 42.62 rad −4.6 0 0.5 1 0 0.5 1 1 1 orbital phase, φ orbital phase, φ − − 0.04 0.02 ms ms /k /k 0 0 C) C) −0.02 − − −0.04 51 500 52 000 52 500 51 500 52 000 52 500 (O (O (JD − 2400 000)/days (JD − 2400 000)/days HD 111232 HD 114386 − 1 − 1 104.5 33.4 y/km s y/km s it 104.4 it oc oc el 33.35 el lv lv

ia 104.3 ia rad rad 0 0.5 1 0 0.5 1 1 1 orbital phase, φ orbital phase, φ − − 0.02 ms ms 0.02 /k /k 0 0 C) C) −0.02 −0.02 − − 52 000 52 500 51 500 52 000 52 500 (O (O (JD − 2400 000)/days (JD − 2400 000)/days

Figure1.16 Radialvelocity measurements andbest-fittingsolutions of theform of Equation1.12.Upper panels:radial velocity measurements andsolutions foldedand plotted as afunctionoforbital phase.Lower panels: thedeviations of themeasured data pointsfrom thebest-fittingsolution, plotted as afunctionoftime. Data are shownfor sixdifferent stars, illustratingsomeofthe many diversecurves that aredescribed by Equation1.12. ‘(O − C)’denotes ‘observed’minus ‘calculated’and indicates howwell the modelfits themeasurements.

37 Chapter 1Our Solar System from afar

● What conditions arerequired for Equation1.16 to be valid? ❍ Theplanets’mutualgravitationalattractionatall times must be negligible compared to the gravitationalforce exerted by thecentral star on each planet. This requires theplanets to all be of small mass compared to the star,and to have large orbital separations.Ifthisisnot thecase, the simple two-body solutionfor theastrocentric orbit of theplanet will not be valid. Figure 1.17 showstwo examples of two-planetfits usingEquation1.16.In thecaseofHD82943, theplanet inducingthe larger-amplitude reflexmotion hasapproximately twice the orbital period of thesecond planet, so apattern of alternatingextremeand lessextremenegative radial velocity variationsis produced. In thecaseofHD169830, theshorter-period planet completes about sevenorbits for oneorbitofthe longer-period planet. This figure demonstrates howcontinuedmonitoring of theradial velocities of known planet hosts can reveal the existence of additionalplanets.

HD 82943 HD 169830 −17.10 8.20 − 1 − 1

8.15 −17.20 y/km s y/km s it it oc oc el el 8.10 lv lv

ia −17.30 ia rad rad 8.05 1 1 − 0.02 −

ms 0.02 ms

/k 0 0 /k

C) −0.02 C)

− −0.02 −

(O 51 500 52 000 52 500 51 500 52 000 52 500 (O (JD − 2400 000)/days (JD − 2400 000)/days

Figure1.17 Radialvelocity measurements andbest-fittingsolutions of theform of Equation1.16 for two planets overplotted.Upperpanels:radial velocity measurements andsolutions plotted as afunctionoftime. Lower panels:the deviationsofthe measured data pointsfrom thebest-fittingsolution, plotted as afunctionoftime. Data areshown fortwo differentstars, illustratingtwo of themanydiverse curves that aredescribed by Equation1.16.

Theradial velocity technique hasbeen extremely successful in detectingplanets around nearby stars. Themajority of known exoplanets (October2009) were detected usingit. Thetechnique is limited in its applicability in twosignificant ways:itcan measure theradial velocity precisely onlyifthe stellar spectrum contains suitable features,and onlyifthe star appearsbrightenough. Even for the brightestofplanet hoststars, current telescopescan onlymakepreciseenough velocity measurements for starswithin ∼2000 pc (or ∼6000 light-years). Finally, theresults from radial velocity measurements all carry theunknown factor sin i, unlessthe orbital inclination, i,can be determinedusing some othermethod. 38 1.4 Transits

1.4Transits

Thetransittechnique is second onlytodirect imaginginits simplicity.Figure 1.18 showstransits of Venus andMercury: whenaplanet passesinfrontofthe disc of astar,itblockssomeofthe light that theobserverwouldnormally receive.

(a) (b)

Figure1.18 Photographs of transits of (a) Venus and(b) Mercury as observed from Earthonpartiallycloudy days. Thus thepresenceofanopaque object orbitingaround astar maybeinferred if the star is seen to dipinbrightnessperiodically.The size of thedip in brightness expected during thetransitcan be estimated simply from thefraction of thestellar disc coveredbythe planet: ΔF R2 = P . 2 (1.18) F R∗

Here F is theflux measured from thestar,and ΔF is theobservedchange in this fluxduring thetransit. Theright-hand side is simply theratio of theareas of the planet’sand star’s discs. Equation1.18 givesusastraightforward andjoyous result: if aplanet transits its hoststar,weimmediately have an estimate of thesize of theplanet, in terms of thesize of its hoststar.Equation1.18 applies when the hoststar is viewed from an interstellar distance. Thegeometryfor transits of Solar System planets viewed from Earthisslightly more complicated. ● Generally,the fraction of abackground object obscuredbyasmaller foregroundobject depends on therelative distances of thetwo objects from theobserver; for example, it is easytoobscure theMoon with your fist.Why doesEquation1.18 notneed to account for therelative distances of thestar andplanet from theobserver? ❍ As we noted in theIntroduction, thedistances between starsare very much largerthanthe typical sizes of planetaryorbits.Thus thedistance between any observerand an exoplanet is identical to high precisiontothe distance between thesameobserverand thehoststar.Expressedgeometrically,the rays of light reaching the observerfrom theexoplanet hoststar areparallel, so Equation1.18 holds.

39 Chapter 1Our Solar System from afar

1.4.1Transit depth forterrestrial andgiantplanets

Equation1.18 allows us to calculate thedepth of thetransitlight curvethatwould be observedbyour hypothetical extraterrestrial astronomersfor anyofthe Solar System planets.For example, the Earthtransitingthe Sunwouldcause adip 5 6 ΔF 2 6.4 × 103 2 E = R⊕ = km 2 5 F R% 7.0 × 10 km =8×10−5,

wherewehavesubstituted in thevalues of theradius of theEarth, R⊕,and the radius of theSun, R%,totwo significantfigures,and reported the result to one significantfigure. Similarly,atransitbyJupiter wouldcause adip of 5 6 ΔF 2 7.0 × 104 2 J = RJ = km 2 5 F R% 7.0 × 10 km =1×10−2.

As a‘ruleofthumb’, agiantplanet transitwill cause adip of ∼1%inthe light curveofthe hoststar,while aterrestrial planet transitwill cause adip of ∼10−2%. Thefirstofthese figures is easily within theprecision of ground-based photometric instruments.Infact, in the 1950s Otto Struve predicted that transits of Jupiter-likeexoplanets couldbedetected if such planets were orbitingat favourableorbital inclinations.The transitdepth for aterrestrial planet is 100 times smaller,and requires aphotometric precisionofbetter than 10−4.This is impossibletoobtain reliably from Earth-bound telescopesbecause of the constantly changing transparency of theEarth’satmosphere. Forthisreason, while thereare scores of known transitinggiantexoplanets,weknowofonlyone transitingterrestrial planet, CoRoT-7b,though we believe that thediscovery of anotherisabout to be announced (December2009). Furtherdiscoveries are anticipated imminently as theFrench/ESAsatellite CoRoTcontinuesits mission, theNASA Kepler satellite begins announcingresults,and thefirsttransitsurveys optimized for Mdwarf starsproduceresults.Furtherspace missions arebeing designedspecifically to findterrestrial planets;wewill discusstheminChapter 8. ● If an astronomer detects aregular 1%dip in thelight from astar,can they immediately conclude that they have detected atransitingJupiter-sized planet orbitingaround that star? ❍ No.The conclusion can onlybethatthere is aJupiter-sized opaque body orbitingthe star.Toprove that this body is aplanet, rather than,for example, abrown dwarfstar,the mass of thetransitingbody needstobeascertained. ● Howcan the astronomer ascertain the mass of theobject that is transitingthe star? ❍ By usingthe radial velocity technique describedinSection 1.3. ● Whyare Mdwarf starsparticularly promisingfor thediscovery of terrestrial planet transits? ❍ Mdwarfs arethe smalleststars, so asmall planet producesarelatively large transitsignalinanMdwarf, as Equation1.18 shows.

40 1.4 Transits

Thetransittechnique is extremely powerful;however,radial velocity confirmation of planet status is vital for transitcandidates.The transitingextrasolar planets are the only planets outside our ownSolar System with directly measured sizes. Fortunately,the transittechnique andthe radial velocity technique arebeautifully complementary: radial velocity measurements allowthe mass of thetransiting body to be deduced,while thepresenceoftransits immediately constrainsthe valueofthe orbital inclination, i,thus removingthe majoruncertainty in the interpretation of radial velocity measurements.For thetransitingextrasolar planets,therefore, it is possibletodeduceaccurate andprecisemasses, radiiand a wholehostofother quantities.Thiswealth of empirical information makesthe transitingplanets invaluable, andunderpins our choice of subjects for this book.

1.4.2Geometricprobabilityofatransit

Howlikely areour hypothetical extraterrestrial astronomerstodiscovertransits of theSolar System planets?Atransitwill be seen if the orbital planeissufficiently close to theobserver’slineofsight.Figure 1.19 illustrates thegeometryofthis situation; for thepurposeofthisdiscussion we will assume acircular orbit.

a i

i

(a)

a cos i

d(t)

R∗ (b) a

Figure1.19 (a)The geometryofatransitasviewedfrom theside. Thedistant observer(not seen)views thesystem with orbital inclination i.(b) Thegeometry of thesystem from theobserver’sviewing direction. Note that theobserverdoes not ‘see’ this geometry: thestar is an unresolvedpoint source. Foratransittobeseen,the disc of theplanet must pass acrossthe disc of thestar. Referring to Figure 1.19b, theclosest approachofthe centreofthe planet’sdiscto thecentreofthe star’s disc occurs at inferior conjunction, when the planet is closesttothe observer. At this orbital phase,byconventionreferredtoasphase φ =0.0,the distance between thecentres of thetwo discsisNote: the right-hand side of Equation1.19 is not the d(φ =0.0) = a cos i. (1.19) arccosine function(which is Notethathereand throughoutthisbook, a is thesemi-majoraxisofthe orbit; sometimes typesetasacos). in this caseweare assuming acircular orbit,soais simply theradius of the transitingplanet’sorbit. 41 Chapter 1Our Solar System from afar

Forthe planet’sdisctooccult the star’s disc,therefore, the orbital inclination, i, must satisfy

a cos i ≤ R∗ + RP. (1.20)

● What happens if R∗ − RP

❍ For R∗ − RP ≤ a cos i ≤ R∗ + RP,wehaveagrazing transit: thediscofthe planet onlypartiallyfalls in frontofthe disc of thestar,soatransitis observed, butits depthislessthanthatgivebyEquation1.18 because a smaller area of thestellar disc is occulted. Theprojection of theunitvector normal to the orbital planeontothe planeofthe skyiscos i,and is equally likely to takeonany random valuebetween 0 and 1.To simplifynotation below, we temporarily replace the variable cos i with x.For the purposes of our discussion we will assume that our extraterrestrial astronomers have thenecessary technology andare located in arandom direction. Thus the probability of our extraterrestrials detectingatransitofaparticular Solar System planet is the probability that therandom inclinationsatisfiesEquation1.20: numberoforbits transiting geometric transitprobability = ( all orbits (R∗+RP)/a 0 dx = ( 1 , 0 dx so R + R R = ∗ P ≈ ∗ . geometric transitprobability a a (1.21)

Equation1.21 showsthattransits aremostprobable for planets with small orbits andlarge parent stars. Theprobabilityfor transits beingobservableissmall; as Figure 1.20 shows, it is lessthan 1%for all of theSolar System’s planets exceptMercury.Itisrather unlikely that our hypothetical extraterrestrial astronomerswouldbefortunate enough to observe transits for anyofthe Solar System’s planets.

1.5Microlensing

Gravitationalmicrolensing exploits thelensing effect of thegeneral relativistic curvatureofspacetimetodetect planets.For theeffect to occur, achance alignment of starsfrom thepoint of view of theobserverisrequired. These alignmentsdooccurfrom timetotime, andare most frequentifone looks at regionsofthe Galaxythatare densely populated with stars. Terrestrial astronomersworking on microlensing observe in thedirections of regions that are densely populated with stars. Themostobvious andbest-studied of theseisthe Galactic bulge:the denseregionofstarsaround thecentreofour Galaxy. The bulgeofthe nearestexternalspiral galaxy, M31,has alsobeen targeted,ashave theMagellanic Clouds.Over 2000 microlensing events have been observedinthe Galactic bulgestudies,and in ahandful of theseevents, planets have been detected around theforeground, lensing star. 42 1.5 Microlensing

0.015

Mercury

ility 0.01

robab Venus tp 0.005 si Earth an

tr Mars Jupiter Uranus Neptune Pluto 0 Saturn 0 10 20 30 40 (a) a/AU

) Figure1.20 −2 Mercury Theprobability lity Venus of transits of each of theSolar

babi Earth Mars System planets beingobservable ro for randomly positioned

tp −3 Jupiter

si extraterrestrials.(a) The

an Saturn Uranus a−1

tr probability drops offas ,and (

10 Neptune Pluto even for Mercury is onlyjust −4 1 log over %. (b) Plotted on a log( ) log(a) −1 0 1 2 probability versus graph, therelationship is a (b) log10 a straight lineofgradient −1.

Figure 1.21 showsour positionrelative to theGalactic bulge. Theplanets detected by microlensing arepositionedjustonour side of theGalactic bulge. Sincethe Sunispositionedtowards theedge of theMilkyWay Galaxy, as shownin Figure 1.21, to view it against thedense stellar background of theGalactic bulge, an observerwouldneed to be situated in thesparsely populated regionsatthe edge of theGalaxy.

ourSun 26 000 light-years Milky WayGalaxy 100 000 000 000 stars

Figure1.21 Aside-on view of our Galaxyproduced from acomposite of 2MASS photometry, our Sun’s distance from thecentreisindicated. Thedotsschematicallyindicate the locations of exoplanets discoveredby threeprimary methods of exoplanet discovery: yellowdots, radial velocity method; red dots, transits;bluedots, microlensing. Theplanets discoveredbydirect imagingare all very closetoour Sun.

Sincethese regionshavelow abundances of elements heavier than He,and the density of starsthere is low, this part of theGalaxy is apriori not themostlikely to contain technological extraterrestrial civilizations.Inaddition, theprobability of anygiven star becoming aligned with abackground star andacting as a microlensisvanishinglysmall; this is aconsequenceofthe very small size of

43 Chapter 1Our Solar System from afar

starscompared to interstellar distances.Einstein realized this,and predicted in 1936 that microlensing wouldoccur, though notingthat‘thereisnogreat chance of observing this phenomenon’. Thereason whywehavedetected microlensing events is that modern technology permits continuous monitoring of millions of stars, to outweighthe vanishinglysmall probability (∼10−6)ofany individual star participatinginamicrolensing alignment at anyparticular time. Even Einstein couldnot have begun to anticipate thepowerful technologies that have revolutionized astrophysics within thelasthalf century. Puttingthe two factorstogether,i.e.the improbability of theSun participatinginamicrolensing alignment andthe expected dearth of technological extraterrestrials on theedges of theMilkyWay,wecan conclude that it is highlyunlikely that Solar System planets wouldbedetected by hypothetical extraterrestrial astronomersvia the microlensing method. Though it hasdetected onlyten planets (December2009), gravitational microlensing is important because it is themethodthathas found themajority of terrestrial exoplanets;recently,however,terrestrial mass planets have been discoveredbybothtransitand radial velocity techniques(December2009). Notably,gravitationalmicrolensing mayalsohavedetected aplanet in the galaxyM31; it is probablythe onlymethodthatcouldconceivablydetect planets outside theMilkyWay.Tooffsetthese advantages,microlensing hasthe serious disadvantage that the lensing eventisaone-offoccurrence: thereisnoopportunity for confirmingand refining theobservations.Thismeansthatthe parametersare rather ill-constrained,and can be meaningfully discussedonlyinastatistical sense. Thestatistical analysisofmicrolensing results implies that no more than a thirdofsolar-typestarshostgiantplanets.The topicofexoplanet detectionby microlensing couldeasily fillanentirebook; sinceweare focusing on transiting exoplanets,weexhort theinterested reader to lookelsewhere for thesedetails.

Summary of Chapter 1

1. TheSun is one of themore luminous starsinthe solar neighbourhood. The majority of objects within 10 parsecs areisolated Mdwarf stars. Sixofthe nearest 100 stars(including theSun) harbour known planets (October2009). 2. Theexoplanets in amultiple planet system arelabelled b, c, d, ... in the orderofdiscovery. 3. Direct imaging as amethodfor exoplanet detectionislimited to bright planets in distantorbits around nearby faintstars. It is most effective in the infraredwhere thecontrastratio is favourable. Agiantexoplanet hasbeen discoveredorbitingabrown dwarfusing thedirect imagingmethod. 4. Aplanet’slight is composed of reflected starlight, which hasaspectral energy distributionclose to that of thehoststar,and athermal emission component peaking at longerwavelengths. 5. Thethermal emission from giantplanets is partially poweredby gravitational(Kelvin–Helmholtz) contraction. This emission is brightestfor young giantplanets. 6. Ayoung planet hasbeen detected around Fomalhautusing coronagraphy, andthree young planets have been discoveredaround HD 8799.Exoplanet 44 SummaryofChapter 1

imaginginstruments likeSPHERE and GPI shouldmakefurtherdiscoveries soon (October 2009). 7. Theorbits of planets areelliptical. In astrocentric coordinates,the hoststar is at one focus of theellipse.The orbital period, thesemi-majoraxis, andthe masses arerelated by Kepler’s thirdlaw: a3 G(M + M ) = ∗ P . P 2 4π2 (Eqn 1.1) Thepericentreisthe point on theplanet’sorbitthatisclosest to thestar.The motionofthe planet around theelliptical orbit is measured by thetrue anomaly, θ(t).The true anomaly is measured at the star,and is zerowhen theplanet crossesthe pericentre. 8. Boththe hoststar andits planet(s) move about thebarycentre(thecentreof mass)ofthe system.For asingle-planet system,

M∗r∗ = −MPrP. (Eqn 1.8) Thereflex orbit of thestar is,therefore, ascaled-down ellipseofthe same eccentricity as the planet’sorbit. 9. Thereflex motionofthe stellar orbit can be detected by astrometry. The Gaia satellite coulddetect the Sun’sreflex orbital motionfrom adistance of about 500 pc,which is roughly thewidth of aspiral arm. Astrometryismost effective for massiveplanets in wide orbitsaround low-mass stars, but long-term monitoring is required to detect planets with large semi-major axes. 10. Theorbital positions of thestar andplanet areuniquely defined by the orbital phase t − T φ = 0 − N , P orb (Eqn 1.15)

where t is time, T0 is afiducial time, and Norb is theorbitnumber. 11. Forasingleplanet, theamplitude of thestellar reflexradial velocity variation is 2πaM sin i A = P √ . RV 2 (Eqn 1.13) (MP + M∗)P 1 − e Thelargest radial velocity amplitudesare exhibited by low-mass hoststars with massiveclose-inplanets in eccentric orbits. 12. Theradial velocity, V ,ofastar is givenby 7n V =V0,z + Ak (cos(θk + ωOP,k)+ekcos ωOP,k) , (Eqn 1.16) k=1

where thereare n planets,each with their owninstantaneous parameters Mk, ak, ek, θk, ωOP,k,and Ak givenby

2πakMk sin i Ak= ; , (Eqn 1.17) 2 MtotalPk 1 − ek

where Mtotal is thesum of themassesofthe n planets andthe star. 45 Chapter 1Our Solar System from afar

13. Radialvelocity measurements usingthe Doppler shiftoffeatures in stellar spectracan be made to aprecision lessthan 1 ms−1.The majority of known exoplanets (December2009) were detected by theradial velocity method. This is themostlikely method by which hypothetical extraterrestrials might detect theexistence of theSun’splanets. 14. Thedepth of an exoplanet transitis ΔF R2 = P. 2 (Eqn 1.18) F R∗ ForJupiter-sized andEarth-sized planets around asolar-typestar,thisdepth is ∼1%and ∼10−2%, respectively. 15. Thegeometric transitprobabilityisgiven by R ≈ ∗ . geometric transitprobability a (Eqn 1.21) Transits aremostlikely for large planets in close-in orbits. If theSolar System were viewed from arandom orientation,onlyMercury,with a =0.4AU,has atransitprobabilityexceeding 1%. 16. Terrestrial exoplanets have so farbeen detected primarily viathe microlensing method, though they arenow beingdiscoveredbythe transit andradial velocity techniques(December2009).

46 Acknowledgements

Grateful acknowledgement is made to thefollowing sources: Figures Coverimage:Anartist’simpression of the‘hot Jupiter’exoplanet HD 189733 b transitingacrossthe face of its star (ESA,C.Carreau); Figure 1: *c Lynette R. Cook; Figure 1.1: NASA Ames Research Center (NASA-ARC);Figures 1.2 and 1.3: RichardPowell, www.atlasoftheuniverse.com, used underaCreative Commons Attribution-ShareAlike2.5 License;Figure 1.4; generated by the author from RECONsdata; Figure 1.5a: adapted from aEuropeanSpace Agency image; Figure 1.5b: TheInternationalAstronomical Union/Martin Kornmesser; Figure 1.5c: Lunarand PlanetaryInstitute/NASA; Figures 1.6a &band1.7: NASA JetPropulsion Laboratory (NASA-JPL); Figure 1.6c: NASA/Goddard Space Center;Figures 1.8 &8.12:adapted from Kaltenegger, L. (2008)‘Assemblingthe Puzzle —EvolutionofanEarth-Like Planet’, Harvard–Smithsonian Center for Astrophysics;Figure 1.9: ESA; Figure 1.10: NASA/ESA, P. Kalas &J.Graham(UC Berkeley), M. Clampin(NASA/GSFC); Figure 1.11: Marois, C. et al.(2008) ‘Direct imagingofmultiple planets orbiting thestar HR8799’, Science, 322,1348, American Associationfor theAdvancement of Science; Figure 1.14: adapted from Beauge,´ C.,Ferraz-Mello,S.and Michtchenko,T.A.inExtrasolar Planets:Formation, Detectionand Dynamics, Dvorak (ed.), Wiley, (2008); Figure 1.15: adapted from Bailey, J. et al. (2009)‘A Jupiter-likeplanet orbitingthe nearby Mdwarf GJ 832’, The Astrophysical Journal, 690,743, TheAmerican Astronomical Society; Figures 1.16 &1.17: adapted from Mayor, M. et al. (2004)‘TheCORALIE survey for southern-solar planets’, Astronomyand Astrophysics, 415,391, EDPSciences;Figure 1.18: Photos by DavidCortner; Figures 1.19 &1.20:adapted from Sackett, P. D. (1998) ‘Searching for unseen planets viaoccultation andmicrolensing’, Mariotti, J. and Alloin,D.M.(eds.), ‘Planets outside thesolar system:theory andobservations’ (NATOScience series C).Springer; Figure 1.21: Atlas Imageobtained as part of theTwo Micron AllSky Survey (2MASS), ajoint project of theUniversity of Massachusetts andthe InfraredProcessing andAnalysisCenter/CalTech,funded by theNational Aeronautics andSpace Administrationand theNational Science Foundation, annotationsdue to K. D. Horneand C. A. Haswell; Figure 2.1: *c University Corporationfor Atmospheric Research;Figure 2.2a: ObservatoiredeHaute Provence; Figure 2.2b: Gdgourou, used underaCreative Commons Attribution-ShareAlike3.0 Licence; Figure 2.3: adapted from Mazeh, T. et al. (2000), ‘The SpectroscopicOrbitofthe PlanetaryCompanion transiting HD209458’, TheAstrophysicalJournal, 532,55, TheAmerican Astronomical Society; Figure 2.4: adapted from Charbonneau, D., et al. (2000), ‘Detectionof planetarytransits acrossasun-like star’, The AstrophysicalJournal, 529,45, The American Astronomical Society; Figure 2.6: *c Franc¸ois du Toit; Figure 2.7 adapted from Charbonneau, D., Brown, T. M., Latham,D.W.and Mayor,M. (2000) The AstrophysicalJournal Letters, 529,L45; Figure 2.9(a):NASA Jet Propulsion Laboratory (NASA-JPL); Figures 2.10 &2.11:The SuperWASP Consortium; Figure 2.12(a) adapted from SuperWASP archivebyA.J.Norton; Figures 2.12b &2.20:adapted from Pollacco,D.L., et al. (2006), ‘The WASP 324 Acknowledgements

Project andthe SuperWASP Cameras’, Publications of theAstronomicalSociety of thePacific, 118,1407, Astronomical Society of thePacific; Figure 2.14: adapted from SuperWASP archivebythe author; Figure 2.15adapted from a WASP consortium powerpoint;Figure 2.16: adapted from Collier-Cameron, A., et al. (2007), ‘Efficient identification of exoplanetarytransitcandidates from SuperWASP light curves’, MonthlyNotices of theRoyal Astronomical Society, 380,1230, TheRoyal Astronomical Society; Figure 2.17: produced usingsoftwarewritten by Rob Hynes; Figure 2.18: adapted from Exoplanet Encyclopedia data by A. J. Norton, A. Dackombe andthe author; Figure 2.19: Parley,N.R., (2008) Serendipitous AsteroidSurveyUsing SuperWASP,PhD thesis,The Open University; Figures 3.1, 3.5 &3.17:adapted from Brown, T. M. et al. (2001), ‘Hubble Space Telescope Time-Series Photometryofthe TransitingPlanet of HD209458’, TheAstrophysicalJournal, 552,699, TheAmerican Astronomical Society; Figure 3.3: adapted from Sackett, P. D. arXiv:astro-ph/9811269; Figure 3.6: SOHO/ESA/NASA; Figure 3.9a: adapted from VanHamme,W.(1993), ‘New Limb-Darkening Coefficients for modellingBinaryStar Light Curves’, The AstronomicalJournal, 106,Number5,2096, TheAmerican Astronomical Society; Figure 3.9b: adapted from Morrill J. S. andKorendykeC.M., (2008), ‘High-ResolutionCenter-to-limbvariation of thequiet solar spectrum near MgII’, The AstrophysicalJournal, 687,646, TheAmerican Astronomical Society; Figures 3.10 &3.11:adapted from KnutsonH.A.etal. (2007), ‘UsingStellar Limb-Darkening to Refine theProperties of HD 209458 b’, TheAstrophysical Journal, 655,564, TheAmerican Astronomical Society; Figures 3.16 &3.18: adapted from Charbonneau, D. et al. (2000), ‘DetectionofPlanetaryTransits acrossaSun-like Star’, The AstrophysicalJournal, 529,45, TheAmerican Astronomical Society; Figures 4.1 &4.10:adapted from Udry,S.(2008) Extrasolar planets:XVI Canary Islands Winter School of Astrophysics,CUP; Figure 4.2: CNES; Figures 4.3, 4.4, 4.5, 4.6, 4.7 &4.9: adapted from Exoplanet Encyclopedia data by A. J. Norton, A. Dackombe andthe author; Figures4.8b &c:adapted from Johnson, J. A. (2009), Draft versionofsubmission International Year of Astronomy Invited ReviewonExoplanets, *c John Asher Johnson; Figure 4.11: adapted from Leger, A. et al. (2009), ‘Transitingexoplanets from theCoRoT space mission: VIII. CoRoT-7b: thefirstsuper-Earthwith measured radius’, Astronomy and Astrophysics, 506,287, ESO; Figures 4.12, 4.13 &4.15:adapted from Guillot, T. (2005)‘TheInteriorsofGiantPlanets:Models andOutstanding Questions’, Annual ReviewofEarth and Planetary Sciences, 33,493, *c Annual Reviews; Figures 4.14 &4.17:adapted from Liu, X., Burrows,A.and Igbui,L. (2008)‘Theoretical RadiiofExtrasolar GiantPlanets:the cases of TrES-4, XO-3b andHAT-P-1b’, The AstrophysicalJournal, 687,1191, TheAmerican Astronomical Society; Figure 4.16: adapted from Arras, P. andBildsten,L., (2006), ‘Thermal Structureand Radius EvolutionofIrradiated GasGiantPlanets’, The AstrophysicalJournal, 650,394, TheAmerican Astronomical Society; Figure 4.19: adapted from Sasselov, D. (2008) ‘Astronomy: Extrasolar Planets’, Nature, 451,29; Figure 4.20: adapted from Charbonneau, D. et al. (2006), ‘When Extrasolar Planets TransitTheir Parent Stars’ review chapter in Protostars and Planets V (Space Science Series), Jewitt, D. andReipurth, B. (eds.) University of Arizona Press;Figure 4.21: adapted from Southworth, J. (2008), ‘Homogeneous 325 Acknowledgements

studies of transitingextrasolar planets -I.Light-curveanalyses’,MonthlyNotices of theRoyal Astronomical Society, 386,1644, TheRoyal Astronomical Society; Figure 5.1: adapted from adrawing of Frances Bagenal, University of Colorado; Figure 5.2: adapted from Brown, T. M. (2001)‘Transmission spectraas diagnostics of extrasolar giantplanet atmospheres’, TheAstrophysicalJournal, 553,1006, TheAmerican Astronomical Society; Figure 5.4: adapted from Marley,M.S.(2009) ‘The atmospheres of extrasolar planets’, Physics and Astrophysics of Planetary Systems,EDP Sciences;Figure 5.5a: *c 2009 Astrobio.net;Figures 5.5b &cand5.6: adapted from Charbonneau, D. et al. (2002)‘Detectionofanextrasolar planet atmosphere’, TheAstrophysicalJournal, 568,377, TheAmerican Astronomical Society; Figure 5.7: adapted from Vidal-Madjar,A.etal. (2003)‘An extendedupperatmosphere around the extrasolar planet HD209458b’, Nature, 422,143, Nature Publishing Group; Figure 5.8: adapted from Charbonneau, D. (2003) ‘Atmosphere out of that world’, Nature, 422,124, Nature Publishing Group; Figures 5.9 &5.10a: adapted from Vidal-Madjar,A.etal. (2004)‘Detectionofoxygenand carbon in the hydrodynamically escapingatmosphere of theextrasolar planet HD 209458 B’, TheAstrophysicalJournal, 604,69, TheAmerican Astronomical Society; Figure 5.10b: NASA/MSSTA; Figure 5.11: adapted from Sing,D.K.etal. (2009) ‘Transitspectrophotometryofthe exoplanet HD189733 b. I. Searching for water butfinding haze with HST NICMOS’, Astronomy&Astrophysics, 505,819, European Southern Observatory; Figure 5.12: adapted from Desert,´ J. et al. (2009)‘Search for carbon monoxide in theatmosphere of thetransitingexoplanet HD 189733b’, TheAstrophysicalJournal, 699,478, TheAmerican Astronomical Society; Figure 5.13: adapted from Redfield, S. et al. (2008)‘Sodium Absorption from theexoplanetaryatmosphere of HD 189733 Bdetected in the optical transmission spectrum’, TheAstrophysicalJournal, 673,87, TheAmerican Astronomical Society; Figure 5.14: adapted from ScottGaudi,B.and Winn, J. N. (2007)‘Prospects for thecharacterizationand confirmation of transiting exoplanets viathe Rossiter–McLaughlin effect’, TheAstrophysicalJournal, 655,550, American Astronomical Society; Figures 5.15 &5.16:adapted from Winn, J. N. (2007)‘Exoplanets andthe Rossiter–McLaughlin Effect’, Transiting Extrasolar Planets Workshop,ASP ConferenceSeries, 336,170, Astronomical Society of thePacific; Figures 5.19a &b:adapted from Triaud, A. H. M. J. et al. (2009)‘TheRossiter–McLaughlin Effect of CoRoT-3b &HD189733b’, Astronomyand Astrophysics, 506,377, European Space OperationsCentreESOC; Figure 5.19c: adapted from Bouchy, F. et al. (2008)‘Transitingexoplanets from theCoRoT space missionIII. ThespectroscopictransitofCoRoT-Exo-2b’, Astronomyand Astrophysics, 482,25, European Space OperationsCentre; Figures 5.19d &e:adapted from Narita, N. et al. (2009)‘ImprovedMeasurement of theRossiter–McLaughlin effect in the ExoplanetarySystem HD 17156’, Publications of theAstronomicalSociety of Japan, 61,991, Astronomical Society of Japan; Figure 5.19f:adapted from Heb´ rard, G. et al. (2009)‘Misaligned spin-orbit in theXO-3 planetarysystem?’, Astronomyand Astrophysics, 488,763, European Southern Observatory; Figure 5.20: adapted from Fabrycky, D. C. and Winn, J. N. (2009)‘ExoplanetarySpin-Orbit Alignment: results from the ensemble of Rossiter–McLaughlin observations’, TheAstrophysicalJournal, 696, 1230, TheAmerican Astronomical Society;

326 Acknowledgements

Figure 6.1 adapted from Seager,S., Deming, D. andValenti, J. A. (2008) in Astrophysics in the Next Decade:The JamesWebbSpaceTelescope and Concurrent Facilities,Thronson, H. A., Stiavelli, M., Tielens,A. (eds.); Figure 6.3:NASA/JPL-Caltech/R. Hurt (SSC); Figure 6.4: adapted from NASA/JPL-Caltech/D.Charbonneau(Harvard–Smithsonian CfA) and NASA/JPL-Caltech/D.Deming (GoddardSpace Flight Center); Figure 6.5: adapted from Deming, D. et al. (2006)‘Strong infraredemissionfrom the extrasolar planet HD 189733b’, TheAstrophysicalJournal, 644,560, The American Astronomical Society; Figure 6.6: adapted from Borucki, W. J. et al. (2009)‘Kepler’s optical phase curveofthe exoplanet HAT-P-7b’, Science, 325,709, American Associationfor theAdvancementofScience; Figure 6.7: adapted from Charbonneau, D. et al. (2008)‘Thebroadbandinfrared emission spectrum of theexoplanet HD 189733b’, TheAstrophysicalJournal, 686, 1341, American Associationfor theAdvancementofScience; Figure 6.8a: adapted from Showman,A.P.etal. (2009)‘Atmospheric circulation of hot jupiters: coupled radiative-dynamical general circulation modelsimulations of HD189733b andHD209458b’, TheAstrophysicalJournal, 699,564, The American Astronomical Society; Figure 6.8b: adapted from Knutson, H. A. et al. (2008)‘The 3.6–8.0 µmBroadbandEmissionSpectrum of HD 209458 b: Evidence for an Atmospheric TemperatureInversion’ TheAstrophysicalJournal, 673,526, IOPPublishing; Figure 6.8c: adapted from Machalek, P. et al. (2008) ‘Thermal emission of exoplanet XO-1b’, TheAstrophysicalJournal, 684,1427, TheAmerican Astronomical Society; Figure 6.8d: adapted from Knutson, H. A. et al. (2009)‘Detectionofatemperature inversioninthe broadband infraredemissionspectrum of TrES-4’, The AstrophysicalJournal, 691,866, The American Astronomical Society; Figures 6.8e &6.9: adapted from Machalek, P. et al. (2008)‘Detectionofthermal emission of XO-2b: evidence for aweak temperature inversion’, TheAstrophysicalJournal, 701,514, TheAmerican Astronomical Society; Figure 6.10: adapted from Deming, D. (2008) ‘Emergent exoplanet flux: review of theSpitzer results’, TransitingPlanets —Proceedings of theIAU Symposium, 253,197, InternationalAstronomical Union; Figures 6.11 &6.12:adapted from Harrington, J. et al. (2006)‘Thephase-dependentinfrared brightness of theextrasolar planet υ Andromedae b’, Science, 314,623, American Associationfor theAdvancementofScience; Figures 6.13 &6.14:adapted from Knutson, H. A. et al. (2007)‘Amap of theday-nightcontrastofthe extrasolar planet HD 189733b’, Nature, 447,183, Nature Publishing Group; Figure 7.1: adapted by A. J. Norton from Exoplanet Encyclopaedia; Figure 7.3: adapted from Jones, B. W.,Sleep,P.N.and Underwood, D. R. (2006)‘Which exoplanetarysystemscouldharbour habitable planets?’, International Journal of Astrobiology, 5(3), 251, CUP; Figure 7.5: NASA/JPL-Caltech/T.Pyle(SSC); Figure 7.6: adapted from Agol,E.etal. (2005)‘On detectingterrestrial planets with timingofgiantplanet transits’, MonthlyNotices of theRoyal Astronomical Society, 359,567, TheRoyal Astronomical Society; Figure 8.2: adapted from ESA/SRE(2009) PLATO-Next GenerationPlanet Finder-AssessmentStudy Report 4, December2009. ESA; Figure 8.3: MEarth Project; Figure 8.4: adapted from Palle E. et al. (2009)‘Earth’sTransmission spectrum from lunareclipseobservations’, Nature, 459,814, Nature Publishing Group; Figures 8.5 &8.6: adapted from Miller-Ricci, E. andFortney, J. J. (2010) ‘The Nature of theAtmosphere of theTransitingSuper-EarthGJ1214b’, The 327 Acknowledgements

AstrophysicalJournal Letters, 716,L74, TheAmerican Astronomical Society; Figure 8.7: adapted from Seager,S., Deming, D. andValenti, J. A. (2008) ‘Transitingexoplanets with JWST’, Thronson, H. A., Tielens,A., Stiavelli, M., (eds.) Astrophysics in the Next Decade:JWST and Concurrent Facilities,123, Astrophysics &Space Science Library.Springer; Figure 8.8: Lahav, N. (1999) Biogenesis,courtesy of Noam Lahav; Figure 8.10: Woods Hole Oceanographic Institute, Deep SubmergenceOperations Group, DanFornari. Everyeffort hasbeen made to contact copyrightholders.Ifany have been inadvertently overlookedthe publishers will be pleased to make thenecessary arrangements at the first opportunity.

328 Acknowledgements

Grateful acknowledgement is made to thefollowing sources: Figures Coverimage:Anartist’simpression of the‘hot Jupiter’exoplanet HD 189733 b transitingacrossthe face of its star (ESA,C.Carreau); Figure 1: *c Lynette R. Cook; Figure 1.1: NASA Ames Research Center (NASA-ARC);Figures 1.2 and 1.3: RichardPowell, www.atlasoftheuniverse.com, used underaCreative Commons Attribution-ShareAlike2.5 License;Figure 1.4; generated by the author from RECONsdata; Figure 1.5a: adapted from aEuropeanSpace Agency image; Figure 1.5b: TheInternationalAstronomical Union/Martin Kornmesser; Figure 1.5c: Lunarand PlanetaryInstitute/NASA; Figures 1.6a &band1.7: NASA JetPropulsion Laboratory (NASA-JPL); Figure 1.6c: NASA/Goddard Space Center;Figures 1.8 &8.12:adapted from Kaltenegger, L. (2008)‘Assemblingthe Puzzle —EvolutionofanEarth-Like Planet’, Harvard–Smithsonian Center for Astrophysics;Figure 1.9: ESA; Figure 1.10: NASA/ESA, P. Kalas &J.Graham(UC Berkeley), M. Clampin(NASA/GSFC); Figure 1.11: Marois, C. et al.(2008) ‘Direct imagingofmultiple planets orbiting thestar HR8799’, Science, 322,1348, American Associationfor theAdvancement of Science; Figure 1.14: adapted from Beauge,´ C.,Ferraz-Mello,S.and Michtchenko,T.A.inExtrasolar Planets:Formation, Detectionand Dynamics, Dvorak (ed.), Wiley, (2008); Figure 1.15: adapted from Bailey, J. et al. (2009)‘A Jupiter-likeplanet orbitingthe nearby Mdwarf GJ 832’, The Astrophysical Journal, 690,743, TheAmerican Astronomical Society; Figures 1.16 &1.17: adapted from Mayor, M. et al. (2004)‘TheCORALIE survey for southern-solar planets’, Astronomyand Astrophysics, 415,391, EDPSciences;Figure 1.18: Photos by DavidCortner; Figures 1.19 &1.20:adapted from Sackett, P. D. (1998) ‘Searching for unseen planets viaoccultation andmicrolensing’, Mariotti, J. and Alloin,D.M.(eds.), ‘Planets outside thesolar system:theory andobservations’ (NATOScience series C).Springer; Figure 1.21: Atlas Imageobtained as part of theTwo Micron AllSky Survey (2MASS), ajoint project of theUniversity of Massachusetts andthe InfraredProcessing andAnalysisCenter/CalTech,funded by theNational Aeronautics andSpace Administrationand theNational Science Foundation, annotationsdue to K. D. Horneand C. A. Haswell; Figure 2.1: *c University Corporationfor Atmospheric Research;Figure 2.2a: ObservatoiredeHaute Provence; Figure 2.2b: Gdgourou, used underaCreative Commons Attribution-ShareAlike3.0 Licence; Figure 2.3: adapted from Mazeh, T. et al. (2000), ‘The SpectroscopicOrbitofthe PlanetaryCompanion transiting HD209458’, TheAstrophysicalJournal, 532,55, TheAmerican Astronomical Society; Figure 2.4: adapted from Charbonneau, D., et al. (2000), ‘Detectionof planetarytransits acrossasun-like star’, The AstrophysicalJournal, 529,45, The American Astronomical Society; Figure 2.6: *c Franc¸ois du Toit; Figure 2.7 adapted from Charbonneau, D., Brown, T. M., Latham,D.W.and Mayor,M. (2000) The AstrophysicalJournal Letters, 529,L45; Figure 2.9(a):NASA Jet Propulsion Laboratory (NASA-JPL); Figures 2.10 &2.11:The SuperWASP Consortium; Figure 2.12(a) adapted from SuperWASP archivebyA.J.Norton; Figures 2.12b &2.20:adapted from Pollacco,D.L., et al. (2006), ‘The WASP 324 Acknowledgements

Project andthe SuperWASP Cameras’, Publications of theAstronomicalSociety of thePacific, 118,1407, Astronomical Society of thePacific; Figure 2.14: adapted from SuperWASP archivebythe author; Figure 2.15adapted from a WASP consortium powerpoint;Figure 2.16: adapted from Collier-Cameron, A., et al. (2007), ‘Efficient identification of exoplanetarytransitcandidates from SuperWASP light curves’, MonthlyNotices of theRoyal Astronomical Society, 380,1230, TheRoyal Astronomical Society; Figure 2.17: produced usingsoftwarewritten by Rob Hynes; Figure 2.18: adapted from Exoplanet Encyclopedia data by A. J. Norton, A. Dackombe andthe author; Figure 2.19: Parley,N.R., (2008) Serendipitous AsteroidSurveyUsing SuperWASP,PhD thesis,The Open University; Figures 3.1, 3.5 &3.17:adapted from Brown, T. M. et al. (2001), ‘Hubble Space Telescope Time-Series Photometryofthe TransitingPlanet of HD209458’, TheAstrophysicalJournal, 552,699, TheAmerican Astronomical Society; Figure 3.3: adapted from Sackett, P. D. arXiv:astro-ph/9811269; Figure 3.6: SOHO/ESA/NASA; Figure 3.9a: adapted from VanHamme,W.(1993), ‘New Limb-Darkening Coefficients for modellingBinaryStar Light Curves’, The AstronomicalJournal, 106,Number5,2096, TheAmerican Astronomical Society; Figure 3.9b: adapted from Morrill J. S. andKorendykeC.M., (2008), ‘High-ResolutionCenter-to-limbvariation of thequiet solar spectrum near MgII’, The AstrophysicalJournal, 687,646, TheAmerican Astronomical Society; Figures 3.10 &3.11:adapted from KnutsonH.A.etal. (2007), ‘UsingStellar Limb-Darkening to Refine theProperties of HD 209458 b’, TheAstrophysical Journal, 655,564, TheAmerican Astronomical Society; Figures 3.16 &3.18: adapted from Charbonneau, D. et al. (2000), ‘DetectionofPlanetaryTransits acrossaSun-like Star’, The AstrophysicalJournal, 529,45, TheAmerican Astronomical Society; Figures 4.1 &4.10:adapted from Udry,S.(2008) Extrasolar planets:XVI Canary Islands Winter School of Astrophysics,CUP; Figure 4.2: CNES; Figures 4.3, 4.4, 4.5, 4.6, 4.7 &4.9: adapted from Exoplanet Encyclopedia data by A. J. Norton, A. Dackombe andthe author; Figures4.8b &c:adapted from Johnson, J. A. (2009), Draft versionofsubmission International Year of Astronomy Invited ReviewonExoplanets, *c John Asher Johnson; Figure 4.11: adapted from Leger, A. et al. (2009), ‘Transitingexoplanets from theCoRoT space mission: VIII. CoRoT-7b: thefirstsuper-Earthwith measured radius’, Astronomy and Astrophysics, 506,287, ESO; Figures 4.12, 4.13 &4.15:adapted from Guillot, T. (2005)‘TheInteriorsofGiantPlanets:Models andOutstanding Questions’, Annual ReviewofEarth and Planetary Sciences, 33,493, *c Annual Reviews; Figures 4.14 &4.17:adapted from Liu, X., Burrows,A.and Igbui,L. (2008)‘Theoretical RadiiofExtrasolar GiantPlanets:the cases of TrES-4, XO-3b andHAT-P-1b’, The AstrophysicalJournal, 687,1191, TheAmerican Astronomical Society; Figure 4.16: adapted from Arras, P. andBildsten,L., (2006), ‘Thermal Structureand Radius EvolutionofIrradiated GasGiantPlanets’, The AstrophysicalJournal, 650,394, TheAmerican Astronomical Society; Figure 4.19: adapted from Sasselov, D. (2008) ‘Astronomy: Extrasolar Planets’, Nature, 451,29; Figure 4.20: adapted from Charbonneau, D. et al. (2006), ‘When Extrasolar Planets TransitTheir Parent Stars’ review chapter in Protostars and Planets V (Space Science Series), Jewitt, D. andReipurth, B. (eds.) University of Arizona Press;Figure 4.21: adapted from Southworth, J. (2008), ‘Homogeneous 325 Acknowledgements

studies of transitingextrasolar planets -I.Light-curveanalyses’,MonthlyNotices of theRoyal Astronomical Society, 386,1644, TheRoyal Astronomical Society; Figure 5.1: adapted from adrawing of Frances Bagenal, University of Colorado; Figure 5.2: adapted from Brown, T. M. (2001)‘Transmission spectraas diagnostics of extrasolar giantplanet atmospheres’, TheAstrophysicalJournal, 553,1006, TheAmerican Astronomical Society; Figure 5.4: adapted from Marley,M.S.(2009) ‘The atmospheres of extrasolar planets’, Physics and Astrophysics of Planetary Systems,EDP Sciences;Figure 5.5a: *c 2009 Astrobio.net;Figures 5.5b &cand5.6: adapted from Charbonneau, D. et al. (2002)‘Detectionofanextrasolar planet atmosphere’, TheAstrophysicalJournal, 568,377, TheAmerican Astronomical Society; Figure 5.7: adapted from Vidal-Madjar,A.etal. (2003)‘An extendedupperatmosphere around the extrasolar planet HD209458b’, Nature, 422,143, Nature Publishing Group; Figure 5.8: adapted from Charbonneau, D. (2003) ‘Atmosphere out of that world’, Nature, 422,124, Nature Publishing Group; Figures 5.9 &5.10a: adapted from Vidal-Madjar,A.etal. (2004)‘Detectionofoxygenand carbon in the hydrodynamically escapingatmosphere of theextrasolar planet HD 209458 B’, TheAstrophysicalJournal, 604,69, TheAmerican Astronomical Society; Figure 5.10b: NASA/MSSTA; Figure 5.11: adapted from Sing,D.K.etal. (2009) ‘Transitspectrophotometryofthe exoplanet HD189733 b. I. Searching for water butfinding haze with HST NICMOS’, Astronomy&Astrophysics, 505,819, European Southern Observatory; Figure 5.12: adapted from Desert,´ J. et al. (2009)‘Search for carbon monoxide in theatmosphere of thetransitingexoplanet HD 189733b’, TheAstrophysicalJournal, 699,478, TheAmerican Astronomical Society; Figure 5.13: adapted from Redfield, S. et al. (2008)‘Sodium Absorption from theexoplanetaryatmosphere of HD 189733 Bdetected in the optical transmission spectrum’, TheAstrophysicalJournal, 673,87, TheAmerican Astronomical Society; Figure 5.14: adapted from ScottGaudi,B.and Winn, J. N. (2007)‘Prospects for thecharacterizationand confirmation of transiting exoplanets viathe Rossiter–McLaughlin effect’, TheAstrophysicalJournal, 655,550, American Astronomical Society; Figures 5.15 &5.16:adapted from Winn, J. N. (2007)‘Exoplanets andthe Rossiter–McLaughlin Effect’, Transiting Extrasolar Planets Workshop,ASP ConferenceSeries, 336,170, Astronomical Society of thePacific; Figures 5.19a &b:adapted from Triaud, A. H. M. J. et al. (2009)‘TheRossiter–McLaughlin Effect of CoRoT-3b &HD189733b’, Astronomyand Astrophysics, 506,377, European Space OperationsCentreESOC; Figure 5.19c: adapted from Bouchy, F. et al. (2008)‘Transitingexoplanets from theCoRoT space missionIII. ThespectroscopictransitofCoRoT-Exo-2b’, Astronomyand Astrophysics, 482,25, European Space OperationsCentre; Figures 5.19d &e:adapted from Narita, N. et al. (2009)‘ImprovedMeasurement of theRossiter–McLaughlin effect in the ExoplanetarySystem HD 17156’, Publications of theAstronomicalSociety of Japan, 61,991, Astronomical Society of Japan; Figure 5.19f:adapted from Heb´ rard, G. et al. (2009)‘Misaligned spin-orbit in theXO-3 planetarysystem?’, Astronomyand Astrophysics, 488,763, European Southern Observatory; Figure 5.20: adapted from Fabrycky, D. C. and Winn, J. N. (2009)‘ExoplanetarySpin-Orbit Alignment: results from the ensemble of Rossiter–McLaughlin observations’, TheAstrophysicalJournal, 696, 1230, TheAmerican Astronomical Society;

326 Acknowledgements

Figure 6.1 adapted from Seager,S., Deming, D. andValenti, J. A. (2008) in Astrophysics in the Next Decade:The JamesWebbSpaceTelescope and Concurrent Facilities,Thronson, H. A., Stiavelli, M., Tielens,A. (eds.); Figure 6.3:NASA/JPL-Caltech/R. Hurt (SSC); Figure 6.4: adapted from NASA/JPL-Caltech/D.Charbonneau(Harvard–Smithsonian CfA) and NASA/JPL-Caltech/D.Deming (GoddardSpace Flight Center); Figure 6.5: adapted from Deming, D. et al. (2006)‘Strong infraredemissionfrom the extrasolar planet HD 189733b’, TheAstrophysicalJournal, 644,560, The American Astronomical Society; Figure 6.6: adapted from Borucki, W. J. et al. (2009)‘Kepler’s optical phase curveofthe exoplanet HAT-P-7b’, Science, 325,709, American Associationfor theAdvancementofScience; Figure 6.7: adapted from Charbonneau, D. et al. (2008)‘Thebroadbandinfrared emission spectrum of theexoplanet HD 189733b’, TheAstrophysicalJournal, 686, 1341, American Associationfor theAdvancementofScience; Figure 6.8a: adapted from Showman,A.P.etal. (2009)‘Atmospheric circulation of hot jupiters: coupled radiative-dynamical general circulation modelsimulations of HD189733b andHD209458b’, TheAstrophysicalJournal, 699,564, The American Astronomical Society; Figure 6.8b: adapted from Knutson, H. A. et al. (2008)‘The 3.6–8.0 µmBroadbandEmissionSpectrum of HD 209458 b: Evidence for an Atmospheric TemperatureInversion’ TheAstrophysicalJournal, 673,526, IOPPublishing; Figure 6.8c: adapted from Machalek, P. et al. (2008) ‘Thermal emission of exoplanet XO-1b’, TheAstrophysicalJournal, 684,1427, TheAmerican Astronomical Society; Figure 6.8d: adapted from Knutson, H. A. et al. (2009)‘Detectionofatemperature inversioninthe broadband infraredemissionspectrum of TrES-4’, The AstrophysicalJournal, 691,866, The American Astronomical Society; Figures 6.8e &6.9: adapted from Machalek, P. et al. (2008)‘Detectionofthermal emission of XO-2b: evidence for aweak temperature inversion’, TheAstrophysicalJournal, 701,514, TheAmerican Astronomical Society; Figure 6.10: adapted from Deming, D. (2008) ‘Emergent exoplanet flux: review of theSpitzer results’, TransitingPlanets —Proceedings of theIAU Symposium, 253,197, InternationalAstronomical Union; Figures 6.11 &6.12:adapted from Harrington, J. et al. (2006)‘Thephase-dependentinfrared brightness of theextrasolar planet υ Andromedae b’, Science, 314,623, American Associationfor theAdvancementofScience; Figures 6.13 &6.14:adapted from Knutson, H. A. et al. (2007)‘Amap of theday-nightcontrastofthe extrasolar planet HD 189733b’, Nature, 447,183, Nature Publishing Group; Figure 7.1: adapted by A. J. Norton from Exoplanet Encyclopaedia; Figure 7.3: adapted from Jones, B. W.,Sleep,P.N.and Underwood, D. R. (2006)‘Which exoplanetarysystemscouldharbour habitable planets?’, International Journal of Astrobiology, 5(3), 251, CUP; Figure 7.5: NASA/JPL-Caltech/T.Pyle(SSC); Figure 7.6: adapted from Agol,E.etal. (2005)‘On detectingterrestrial planets with timingofgiantplanet transits’, MonthlyNotices of theRoyal Astronomical Society, 359,567, TheRoyal Astronomical Society; Figure 8.2: adapted from ESA/SRE(2009) PLATO-Next GenerationPlanet Finder-AssessmentStudy Report 4, December2009. ESA; Figure 8.3: MEarth Project; Figure 8.4: adapted from Palle E. et al. (2009)‘Earth’sTransmission spectrum from lunareclipseobservations’, Nature, 459,814, Nature Publishing Group; Figures 8.5 &8.6: adapted from Miller-Ricci, E. andFortney, J. J. (2010) ‘The Nature of theAtmosphere of theTransitingSuper-EarthGJ1214b’, The 327 Acknowledgements

AstrophysicalJournal Letters, 716,L74, TheAmerican Astronomical Society; Figure 8.7: adapted from Seager,S., Deming, D. andValenti, J. A. (2008) ‘Transitingexoplanets with JWST’, Thronson, H. A., Tielens,A., Stiavelli, M., (eds.) Astrophysics in the Next Decade:JWST and Concurrent Facilities,123, Astrophysics &Space Science Library.Springer; Figure 8.8: Lahav, N. (1999) Biogenesis,courtesy of Noam Lahav; Figure 8.10: Woods Hole Oceanographic Institute, Deep SubmergenceOperations Group, DanFornari. Everyeffort hasbeen made to contact copyrightholders.Ifany have been inadvertently overlookedthe publishers will be pleased to make thenecessary arrangements at the first opportunity.

328