arXiv:1409.7245v1 [astro-ph.EP] 25 Sep 2014 assadrdii trpae-onsse ( system star-planet-moon a absolute 2010 in the radii reveal and could masses observation exomoon an tions, 2006 Hamilton system, Uranian misaligned the (see the record (see bardment history collision binary, system’s Earth-Moon the constrain disks also accretion can circumplanetary early compositional ( the and satellites in thermal planet the properties giant about as information carry perspective, formation planet exist. worlds such if have exomoons for hunts ( initiated dedicated been first now The detected. t nteselrhbtbezns( zones habitable stellar the in ets ( planets giant in in exomoons ( large curves find light may stellar the telescopes space PLATO or obdlie l 2012 al. et Morbidelli 2013 al. Szab´o et ones(e rtnscpueaon Neptune, around capture Triton’s (see counters ae aebe on,sm ssala h Earth’s the as small as some found, ( Moon been have dates au ad2006 Ward & Canup Program h eeto feoon ol epeiu rma from precious be would exomoons of detection The rpittpstuigL using 2018 typeset 30, Preprint July version Draft lhuhtosnso xrslrpaesadcandi- and planets extrasolar of thousands Although 2 1 .Wa smr,mosmyotubrrcyplan- rocky outnumber may moons more, is What ). tla srpyisCnr,Dprmn fPyisadAst and Physics of Department Centre, Astrophysics Stellar ototrlflo fteCnda srbooyTraining Astrobiology Canadian the of fellow University McMaster Postdoctoral Astronomy, and Physics of Department aca ta.2013 al. et Barclay bylremo rniigadrcl mgdpae like planet to imaged respect directly with a s m SOM transiting 100 Rossiter-McL moon’s moon This the equa large unveils planetary moon. ably therefore the its and between by plane, m angle transited orbital distor the such is reveals measures enable it spectrum method will when planetary E-ELT dich second t planet The timing The the giant For “transit s. stars. tating 12 This nearby motion. and circumstellar around 2 light. wit the between moons (early) of to range late speed respect TTDs be with system, finite will SOM the planet exomoon’s the to an of) due du front events period (in Europ planet planet-moon orbital behind the mutual the passing with on to moon possible relies the respect method be with first will The one measurements (E-ELT). required and orbita the of orbit that sense circumstellar show exomoon’s planet’s an the determine to to methods two present We ehd a eue opoeteoii feoon,ta s whet is, that exomoons, of origin the Keywords: probe to nature. used in be can methods ,adee h irto itr fclose- of history migration the even and ), − rgn nttt,MMse nvriy aitn NLS4 L8S ON Hamilton, University, McMaster Institute, Origins ,adi a ensonta h Kepler the that shown been has it and ), 1 aon 2010 Namouni bu wc h tla M mltd ftetastn xpae HD exoplanet transiting the of amplitude RME stellar the twice about , O ODTRIEA XMO’ ES FOBTLMOTION ORBITAL OF SENSE EXOMOON’S AN DETERMINE TO HOW ciss—mtos aaaayi ehd:osrainl—plane — observational methods: — analysis data methods: — eclipses ote l 2007 al. et Pont niiul( individual atan&Dvs1975 Davis & Hartmann A 1. ,te a rc lntpae en- planet-planet trace can they ), T ; E ipn ta.2009 al. et Kipping elr&Pdiz2014 Pudritz & Heller tl mltajv 04/17/13 v. emulateapj style X CONTEXT ,n xrslrmo a been has moon extrasolar no ), β .Udrsial condi- suitable Under ). i )—tcnqe:pooerc—tcnqe:rda velocities radial techniques: — photometric techniques: — b) Pic elr&Bre 2014 Barnes & Heller ; ipn ta.2012 al. et Kipping ; elr2014 Heller Denmark; n bom- and ) .Moons ). rf eso uy3,2018 30, July version Draft go & Agnor Kipping io Albrecht Simon Ren ABSTRACT [email protected] ), Heller e ´ ) ; ooy ahsUiest,N ukgd 2,D-00Aarhu DK-8000 120, Munkegade Ny University, Aarhus ronomy, and ucetylw ocueadrc rni intr nthe ( in signature curve variability transit light direct photometric a stellar star’s cause the to low) (and sufficiently enough large be hl ea nJn 04 ihfis ih niiae n2024 in anticipated light first with 2014, June in began Chile ( 2011a Kipping around axis semi-major orbital ( planet moon’s the the on pending built. Ex- being European now ELTs the several use of we of Telescope direction simulations, Large planet’s our tremely the In circum- to the respect rotation. to with relative and orbit SOM stellar exomoon’s equip- an technical determine current to with a ( SOM extra- ment About exomoon’s an an find history. mine to ( proposed orbital moon been and solar have origin techniques its dozen determine to ulpae-onelpe.Teeeet aebe sim- been mu- have show events then ( These will ulated pair eclipses. planet-moon planet-moon the tual of transits lar n hrfr ol etems bnatseiso hab- of species ( abundant worlds most the itable be could therefore and 2.1. iaoe l 2012 al. et Hirano 3 o u rtnwmto owr,temo ed to needs moon the work, to method new first our For onssneo ria oin(O)i crucial is (SOM) motion orbital of sense moon’s A 1,2 osrcino h -L ertePrnlOsraoyin Observatory Paranal the near E-ELT the of Construction β nEoonsTastTmn ihtm (TTD) Dichotomy Timing Transit Exomoon’s An i assa M mltd falmost of amplitude RME an causes b Pic 1 Canada; M1, ei ui 2014 Fujii & Lewis arr cnie 2007 Schneider & Cabrera a o n h onscircumplanetary moon’s the and tor in nteI pcrmo h ro- the of spectrum IR the in tions ps elr2014 Heller igselrtast.Elpe with Eclipses transits. stellar ring oin(O) n ihrespect with one (SOM), motion l ilase l 1997 al. et Williams n nteobtlainet oestel- some alignment, orbital the on and ) ; e hyaerglro irregular or regular are they her h lntsrtto.Areason- A rotation. planet’s the P´al 2012 a xrml ag Telescope Large Extremely ean r oain u simulations Our rotation. ary [email protected] nlretmosi h solar the in moons largest en eadt h onsmean moon’s the to regard h swl smta vnsi stel- a in events mutual as well as ) uhi ffc RE nthe in (RME) effect aughlin aueet o Earth-sized for easurements atrti&Shedr1999 Schneider & Sartoretti tm”(T)determines (TTD) otomy” 2. 3 ,btnn fte a deter- can them of none but ), METHODS ,adapae-lnteclipse planet-planet a and ), EET sa xml o one for example an as (E-ELT) .W eeietf w means two identify here We ). 048b ohnew Both b. 209458 sadsatellites: and ts ; ; elre l 2014 al. et Heller ao&Aaa2009 Asada & Sato .De- ). C, s . ). ; 2 Rene´ Heller & Simon Albrecht

(a) prograde orbit (b) retrograde orbit guished from events III and IV, simply by determining ! ! whether the moon enters the stellar disk first and then performs a mutual event with the planet (III and IV) or the planet enters the stellar disk first before a mutual ● ● event (I and II). However, this inspection cannot discern event I from II or event III from IV. Therefore, prograde and retrograde orbits cannot be distinguished from each (c) top view (d) edge view other. I IV Figure 1 (e) illustrates how the I/II and III/IV ambi- guities can be solved. Due to the finite speed of light, there will be a time delay between events I and II, and between events III and IV. It will show up as a transit could be timing dichotomy (TTD) between mutual events where II III I - II - III - IV (pro) the moon moves in front of the planetary disk (early mu- or tual events) or behind it (late mutual events). Events I IV - III - II - I (retro) and IV will be late by ∆t = 2aps/c compared to events

to Earth to II and III, respectively. Imagine that two mutual events, either I and [II or III] or IV and [III or II]), are observed during two different stellar transits and that the moon ! star has completed n circumplanetary orbits between the two ● planet mutual events. Then it is possible to determine the se- moon orbital motion quence of late and early eclipses, and therefore the SOM (e) with respect to the circumstellar movement, if (1) the orbital period of the planetary satellite (P ) can be de- late eclipses ps δΔt termined independently with an accuracy δPps < Pps/n, I (zoom) and if (2) the event mid-times can be measured with a I IV precision < ∆t. As a byproduct, measurements of ∆t yield an estimate for aps = ∆t × c. Concerning (1), the planet’s transit timing variation (TTV) and transit duration variation (TDV) due to the α moon combined may constrain the satellite mass (Ms) and Pps (Kipping 2011b). As an example, if two mutual 2 aps Δt = c events of a Jupiter-Ganymede system at 0.5 AU around a Sun-like star were observed after 10 stellar transits (or 3.5 yr), the moon (Pps ≈ 0.02 yr) would have completed n ≈ 175 circumplanetary orbits. Hence, δPps . 1 hr would be required. A combination of TTV and TDV measurements might be able to deliver such an accuracy II III (Section 6.5.1 in Kipping 2011b). For our estimates of ∆t, we can safely approximate to Earth to early eclipses that a moon enters a mutual event at a radial distance aps to the planet, because Figure 1. Orbital geometry of a star-planet-moon system in circu- lar orbits. (a) Top view of the system’s orbital motion. The moon’s circumplanetary orbit is prograde with respect to the circumstellar a orbit. (b) Similar to (a), but now the moon is retrograde. (c) Top δ∆t = ps 1 − cos(α) view of the moon’s orbit around the planet. Roman numbers I to c IV denote the ingress and egress of mutual planet-moon eclipses.   (d) Edge view (as seen from Earth) of a circumplanetary moon or- aps Rp bit. (e) Transit timing dichotomy of mutual planet-moon events. = 1 − cos arcsin Due to the finite speed of light, an Earth-bound observer witnesses c aps ! events I and IV with a positive time delay ∆t compared to events n  o II and III, respectively. ≪ ∆t , (1)

with c being the speed of light, Rp the planetary ra- lar triple system (Carter et al. 2011) have already been dius, and α defined by sin(α)= Rp/aps as shown in Fig- found in the Kepler data. ure 1(e). For a moon at 15 Rp from its planet, such as Figure 1 illustrates the difficulty in determining a Ganymede around Jupiter, α ≈ 3.8◦ and δ∆t ≈ 0.005 s, moon’s SOM. Panels (a) and (b) visualize the two possi- which is completely negligible. Orbital eccentricities ble scenarios of a prograde and a retrograde SOM with could also cause light travel times different from the one respect to the circumstellar motion. Panel (c) presents shown in Figure 1. But even for eccentricities comparable the four possible ingress and egress locations (arbitrarily to Titan’s value around Saturn, with 0.0288 the largest labelled I, II, III, and IV) for a mutual planet-moon event among the major moons in the solar system, TTDs would during a stellar transit. Panel (d) shows the projection of be affected by < 5%, or fractions of a second. Signifi- the three-dimensional moon orbit on the two-dimensional cantly larger eccentricities are unlikely, as they will be celestial plane. If the moon transit is directly visible in tidally eroded within a million years (Porter & Grundy the stellar light curve, then events I and II can be distin- 2011; Heller & Barnes 2013). How to determine an exomoon’s sense of orbital motion 3

Figure 3. Transit timing dichotomies of the ten largest moons Figure 2. Theoretical emission spectra of a hot, Jupiter-sized in the solar system. Moon radii are symbolized by circle sizes. planet (orange, upper) and a Sun-like star as reflected by the planet The host planets Jupiter, Saturn, Neptune, Uranus, and Earth are at 10 AU (blue, middle) and 100 AU (light blue, lower). For the indicated with their initials. Note that the largest moons, causing planet, a Jupiter-like bond albedo of 0.3 is assumed. the deepest solar transits, induce the highest TTDs. 2.2. The Rossiter-McLaughlin effect (RME) in the which are hot (> 1000 K), and young (< 100 Myr). Up- Planetary Emission Spectrum coming instruments like SPHERE (Beuzit et al. 2006) In the solar system, all planets except Venus (Gold & and GPI (McBride et al. 2011) promise a rapid increase Soter 1969) and Uranus rotate in the same direction as of this number. Stellar and planetary spectra can also they orbit the Sun. One would expect that the orbital be separated in velocity space without the need of spatial motion of a moon is aligned with the rotation of the separation (Brogi et al. 2012; de Kok et al. 2013; Birkby planet. However, collisions, gravitational perturbations, et al. 2013), but for β Pic-like systems, instruments like capture scenarios etc. can substantially alter a satel- CRIRES can also separate stellar and planetary spectra lite’s orbital plane (Heller et al. 2014). Hence, knowl- spatially. Snellen et al. (2014) determined the rotation period of β Pic b to be 8.1 ± 1.0 hours. The high rotation edge about the spin-orbit misalignment, or obliquity, in −1 a planet-exomoon system would be helpful in inferring velocity (≈ 25kms ) favors a large RME amplitude, its formation and evolution. but makes RV measurements more difficult. One such method to constrain obliquities is the Contamination of the planetary spectrum by the star Rossiter-McLaughlin effect (RME), a distortion in the ro- via direct stellar light on the detector and stellar reflec- tationally broadened absorption lines caused by the par- tions from the planet might pose a challenge. Conse- tial occultation of the rotating sphere (typically a star) quently, observations need to be carried out in the near- by a transiting body (usually another star or a planet). IR, where the planet is relatively bright and presents a rich forest of spectral absorption lines. Figure 2 This distortion can either be measured directly (Albrecht 5 et al. 2007; Collier Cameron et al. 2010) or be picked up shows that contamination of the planetary spectrum as an RV shift during transit. The shape of this anoma- by reflected star light becomes negligible beyond several lous RV curve reveals the projection of the angle between 10 AU, with no need for additional cleaning. the orbital normal of the occulting body (in our case 3. RESULTS AND PREDICTIONS the moon) and the rotation axis of the occulted body 3.1. (here the planet). Originally observed in stellar binaries Transit Timing Dichotomies (Rossiter 1924; McLaughlin 1924), this technique experi- We computed the TTDs of the ten largest moons in enced a renaissance in the age of extrasolar planets, with the solar system, yielding values between about 2 and the first measurement taken by Queloz et al. (2000) for 12 s (Figure 3). Most intriguingly, the largest moons the transiting hot Jupiter HD209458 b. Numerous mea- (Ganymede, Titan, and Callisto), which have the deep- surements4 revealed planets in aligned, misaligned, and est solar transit signatures, also have the largest TTDs. even retrograde orbits – strongly contrasting the archi- This is owed to the location of the water ice line in the tecture of the solar system (e.g. Albrecht et al. 2012). accretion disks around Jovian planets, which causes the The stellar RME of exomoons has been studied before most massive icy satellites to form beyond about 15 RJup (Simon et al. 2010; Zhuang et al. 2012), but here we refer (Heller & Pudritz 2014). Figure 3 indicates that timing to the RME in the planetary infrared spectrum caused precisions of 1 - 6s need to be achieved on transit events by the moon transiting a hot, young giant planet. with depths of only about 10−4, corresponding to the For this method to be effective, a giant planet’s light transit depth of an Earth-sized moon transiting a Sun- needs to be measured directly. Starting with the plan- like star. etary system around HR8799 (Marois et al. 2008) and Precisions of 6 s in exoplanet transit mid-times have the planet candidate Fomalhaut b (Kalas et al. 2008), 18 been achieved from the ground using the Baade 6.5 m giant exoplanets have now been directly imaged, most of telescope at Las Campanas Observatory in Chile (Winn

4 So far, 79 exoplanet have had their spin-orbit alignment mea- 5 Models were provided by T.-O. Husser (priv. comm.), based sured via the RME, see R. Heller’s Holt-Rossiter-McLaughlin En- on the spectral library by Husser et al. (2013) available at cyclopaedia (www.physics.mcmaster.ca/∼rheller). http://phoenix.astro.physik.uni-goettingen.de.

4 Rene´ Heller & Simon Albrecht

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❚✂✄☎ ✆✝✞✄ ✄ ✂✟ ✠ ✝✡☛☞ ✂✠ ✌✍ ✝✎ Figure 4. Probability of mutual planet-moon events as a func- ✲ tion of the moon’s planetary distance around a Jupiter-like planet, which is assumed to orbit a Sun-like star at 1 AU. The five curves Figure 5. Simulated Rossiter-McLaughlin effect of a giant moon indicate the frequency of 0, 1, 2, 3, or 4 mutual events during stellar (0.7 R⊕) transiting a hot, Jupiter-sized planet similar to β Pic b. stellar transits as measured in our transit simulations. The orbits Solid and dashed lines correspond to a prograde and a retrograde of Io, Europa, Ganymede, and Callisto are indicated with symbols coplanar orbit, respectively. Full and open circles indicate simu- along each curve. lated E-ELT observations. A single stellar transit with ≥ 3 mutual events con- et al. 2009). On the one hand, the planet in these obser- tains TTD information on its own. A two-event stellar vations (WASP-4b) was comparatively large to its host transit only delivers TTD information if the events are star with a transit depth of about 2.4%. On the other either a combination of I and II or of III and IV. Moons hand, the star was not particularly bright, with an appar- in wide orbits cannot proceed from one conjunction to the other during one stellar transit. Hence, the contribu- ent visual magnitude mV ≈ 12.6. The photon collecting power of the E-ELT will be (39.3 m/6.5 m)2 ≈ 37 times tion of TTD-containing events along P2 is zero beyond about 106 km. In close orbits, the fraction of two-event that of the Baade telescope. And with improved data −1 cases with TTD information is P2,TTD≈Rp(apsπ) . For reduction methods, timing precisions of the order of sec- −1 onds should be obtainable for transit depths of 10−4 with Io, as an example, P2,TTD = (6.1 × π) ≈ 5 %. So even the E-ELT for very nearby transiting systems. for very close-in moons, two-event cases with TTD infor- We calculate the probabilities of one to four mutual mation are rare. events (Pi, i ∈ {1, 2, 3, 4}) during a stellar transit of a 3.2. coplanar planet-moon system. The distance of the moon The Planetary Rossiter-McLaughlin Effect due to travelled on its circumplanetary orbit during the stel- an Exomoon lar transit s = 2R⋆P⋆baps/(Ppsa⋆b), with a⋆b denoting We simulated the RME in the near-IR spectrum of the circumstellar orbital semi-major axis of the planet- a planet similar to β Pic b assuming a planetary rota- −1 moon barycenter and P⋆b being its circumstellar orbital tion speed of 25kms (Snellen et al. 2014) and a Jo- period. We analyze a Jupiter-like planet at 1 AU from vian planetary radius (RJup). The moon was placed in 6 a Sun-like star and simulate 10 transits for a range of a Ganymede-like orbit (aps = 15 RJup) and assumed to possible moon semi-major axes, respectively, where the belong to the population of giant moons that form at moon’s initial orbital position during the stellar transit the water ice lines around super-Jovian planets, with is randomized. As the stellar transit occurs, we follow a radius of up to about 0.7 Earth radii (R⊕) (Heller the moon’s circumplanetary orbit and measure the num- & Pudritz 2014). Using the code of Albrecht et al. ber of mutual events (of type I, II, III, or IV) during the (2007, 2013), we simulated absorption lines of the ro- transit, which can be 0, 1, 2, 3, or even 4. tating planet as distorted during the moon’s transit with For siblings of Io, Europa, Ganymede, and Callisto we a cadence of 15min. Focusing on the same spectral win- find P1 = 21, 13, 8, and 5% as well as P2 = 50, 24, dow (2.304 − 2.332 µm) as Snellen et al. (2014), we then 11, and 5 %, respectively (Figure 4). Notably, the prob- convolved the planetary spectrum (Figure 2) with these abilities for two mutual events (purple long-dashed line) distorted absorption lines. Employing the CRIRES Ex- are higher than the likelihoods for only one (red solid posure Time Calculator and incorporating the increase of 6 2 line) if aps . 1.6 × 10 km. For moons inside about half- (39.3 m/8.2 m) ≈ 23 in collecting area for the E-ELT, we way between Io and Europa, the probability of having no obtain a S/N of 75 per pixel for a 15min exposure – the event (black solid line) is < 50 %, so it is more likely to same values as obtained by Snellen et al. (2014) for a sim- have at least one mutual event during any transit than ilar calculation. The resulting pseudo-observed spectra having none. Moons inside 200,000 km (half the semi- are finally cross-correlated with the template spectrum, major axis of Io) can even have three or more events, and a Gaussian is fitted to the cross-correlation functions allowing the TTD method to work with only one stellar to obtain RVs. transit. Deviations from well-aligned orbits due to high Pro- and retrograde coplanar orbits are clearly dis- transit impact parameters or tilted moon orbits would tinguishable in the resulting RME curve (Figure 5). naturally reduce the shown probabilities. Nevertheless, In particular, the RME amplitude of ≈ 100ms−1 is mutual events could obviously be common during tran- quite substantial. In comparison, the RME amplitude of sits. HD209458b is ≈ 40ms−1 (Queloz et al. 2000), and re- How to determine an exomoon’s sense of orbital motion 5 cent RME detections probe down to 1 m s−1 (Winn et al. manent, highly-accurate IR photometric monitoring of a 2010). few dozen directly imaged giant exoplanets thus has a high probability of finding an extrasolar moon. 4. DISCUSSION AND CONCLUSION We present two new methods to determine an exo- moon’s sense of orbital motion. One method, which we The report of an anonymous referee was very helpful in refer to as the transit timing dichotomy, is based on a clarifying several passages in this letter. We thank Tim- light travelling effect that occurs in subsequent mutual Oliver Husser for providing us with the PHOENIX mod- planet-moon eclipses during stellar transits. For the ten els. Ren´eHeller is supported by the Origins Institute at largest moons in the solar system, TTDs range between McMaster University and by the Canadian Astrobiology 2 and 12s. If the planet-moon orbital period can be Program, a Collaborative Research and Training Experi- determined independently (e.g. via TTV and TDV mea- ence Program funded by the Natural Sciences and Engi- surements) and with an accuracy of . 1hr, or if a very neering Research Council of Canada (NSERC). Funding close-in moon shows at least three mutual events during for the Stellar Astrophysics Centre is provided by The one stellar transit, then TTD can uniquely determine the Danish National Research Foundation (Grant agreement sequence of planet-moon eclipses. To resolve the TTD ef- no.: DNRF106). fect, photometric accuracies of 10−4 need to be obtained along with mid-event precisions . 6 s, which should be REFERENCES possible with the E-ELT. If an exomoon is self-luminous, e.g. due to extreme tidal heating (Peters & Turner 2013), Agnor, C. B., & Hamilton, D. 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