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arXiv:1603.00174v1 [astro-ph.EP] 1 Mar 2016 ulte eurdfreoondtcin ( detections for required qualities o wet for 2014 al. et Heller ( capacities TMT IR unprecedented with scopes more and ( more habitats coming potential now as focus are into exoplanets around but endtce,msl yNASA’s by mostly detected, been 2014 ( systems - 2014 resolved of analyses 1999 1997 al. et 2000 al. et neau et fsc on(10 moon a such of depth predicted been ( have super-Jovian such around few form a to as heavy as su is star host its ( from K tamination 700 1 about is tive ne planets These planets. su be host luminous young, their siting ( spectroscopy transit t transit planetary via ( accuraci variations e.g., duration observational transit detection, extreme plus variations a the both in for are required habitab inhabited is even exomoon an or whether determining in challenges Key 2014 al. et Rsetocp with spectroscopy IR n tla pcrltp rmAt tr,ms fte at them of most super-Jovia young stars, The star. M their to from planet AU A of from hundreds or type around tens discovered spectral been have stellar them any of dozen two About imaged. ic h icvr fapae rniigishs tr( star host its transiting planet a of discovery the Since Introduction 1. a 1 2021 31, May eeIivsiaetepsiiiyo eetn xmostr exomoons detecting of possibility the investigate I Here s ih 2022; light 1st , evsa ecmr o hs osdrtos t e Its considerations. these for benchmark a as serves ) ; ; ffi luiainwl ewa eod5A,teeatraieene alternative t these AU, from 5 radiation beyond by weak heated be be will will illumination moons The imaged. directly a lnkIsiuefrSlrSse eerh Justus-von Research, System Solar for Institute Planck Max bnat on oinpaescnb shta aeMsas w stars, M late as e hot as No be too. can habitable, planets be Jovian Young can abundant. moons planets, -like Beyond 2016 1, February Accepted 2015; 2, October Received ih edtcal nterifae htmti ih cur light photometric infrared their in detectable be might y.AMr-asH Mars- A Myr. e words. Key nrrd lntr systems planetary Infrared: gle l 2015 al. et Agol ipn 2009 Kipping β rniso xrslrmosaon uiosgatplanets giant luminous around moons extrasolar of Transits inl a wyfo hi tr ( stars their from away far ciently / c opsto ( composition icy i (11 b Pic ; .Paesaentrlpae olo o xrslrlife, extrasolar for look to places natural are Planets ). caf2006 Scharf & Astrophysics ,tosnso xpaesadcniae have candidates and exoplanets of thousands ), ,adte ih ea ag s07Erhradii Earth 0.7 as large as be might they and ), ± srbooy–Mtos bevtoa ehius photo Techniques: – observational Methods: – Astrobiology ie smsiea , as massive as times 5 ,adflo-pcaatrzto,eg,by e.g., characterization, follow-up and ), atnge 2010 Kaltenegger E-ELT CRIRES .Nweteeylregon-ae tele- ground-based large extremely New ). ; 2 elre l 2014 al. et Heller -ihmo around moon O-rich elr&Pdiz2015b Pudritz & Heller − 3 s ih 04 ol civ data achieve could 2024) light 1st , aucitn.ms no. manuscript ol emr hna re of order an than more be would ) tthe at enlse l 1987 al. et Reynolds ffi Kepler adn ta.2014 al. et Baudino inl o oalwfrdirect for allow to low ciently VLT rifae I)spectral (IR) infrared or ) & pc eecp ( telescope space atrti&Schneider & Sartoretti ; GTM au ad2006 Ward & Canup ( 0A)t edirectly be to AU) 10 un ta.2015 al. et Quanz amre l 2014 al. et Lammer nle ta.2014 al. et Snellen β elr&Albrecht & Heller i ol aeatastdpho 1 of depth transit a have would b Pic s ih 2021; light 1st , Rsac Note) (Research .Tetransit The ). nle tal. et Snellen ,adcon- and ), ; Charbon- Williams iming e ftepaesaesu are planets the if ves Rowe dto ed ff Lei-e ,307Gtign Germany; Göttingen, 37077 3, -Liebig-Weg ABSTRACT .Heller R. ). an- ec- g ore ol iuf ufc ae neoon o hund for exomoons on water surface liquify could sources rgy es le ). ). n oon aebe eueydtce,btte ol eextre be could they but detected, securely been have xomoons eryugpaesadptnilyb ia rcin Altho friction. tidal by potentially and planets young heir ; t e ith hssget a suggests This rto ikta nteJva ik With disk. Jovian the in than disk cretion r h e the iesa.Pooercacrce ont aenwbeen now have % 1 using to IR the down in achieved accuracies Photometric a around star. planet Earth-sized like an of that than larger magnitude hs fayug uie-iepae ( planet Jupiter-like young, a of those h tr elcigtecmlxoaiyvrain nboth in ( variations disks opacity circumplanetary and complex cumstellar the neglecting star, the uaa crto rgesfraino in lnt nth ( in disk planets giant toplanetary of formation triggers accretion runaway eudrtn hsrlto ycmaigtepoete fa of properties the comparing ( by star -like relation young this understand we ( et( ject nteslrsse omd a nweebtenteorbits the between ( anywhere icy was and formed, rocky system of solar the in t1 n 5Jptrrdi( radii Jupiter 15 and 10 at gi- local the of H formation ( the planets during Sun ant the from AU 2.7 about H The planets). (transiting moons di and transits depths transit transit on probabilities, and transit cies, geometric formation that di expect on moon thus form and moons and Planets planet of Effects 2.1. transits planet-moon versus Star-planet 2. compellin moons. a extrasolar are detecting planets for possibility giant new young around exomoons large of r ff ice 2 c ie eodwihsm ftems asv moons massive most the of some which beyond line, ice O 1 cietmeaue fu o20 .Tast ftermoons their of Transits K. 2000 to up of ective ∝ ,wihi omlzdt h hsclrdu ftehs ob- host the of radius physical the to normalized is which ), ff R cietmeaue( temperature ective q ,ws2 was ), erc–Elpe lnt n aelts eeto – detection satellites: and Planets – Eclipses – metric R 2 T . 5 ffi aah 1981 Hayashi e 4 ff × inl eaae ( separated ciently . AU 7 10 , √ isur1987 Lissauer − 10 3 nraho erftr technology. near-future of reach in , / 2 R 12 × = . 5 5 HST 4 R T ff R .I oprsn h circum-Jovian the comparison, In ). R ⊙ e rbtenpaes(rniigstars) (transiting planets between er = J ff J slrradius], [solar ≈ ,rsetvl.Teieln radius line ice The respectively. ), ftehs beta per as object host the of ) ( 5 ie ie H wider times 250 ff hue l 2015 al. et Zhou & 8 ie agri h oa ac- solar the in larger times 480 rn ptoeprlsae.We scales. spatiotemporal erent [email protected] ; 0A)fo h tr obe to stars the from AU) 10 rte&Ln2007 Lin & Kretke olc enls1974 Reynolds & Pollack 2 R ishe l 2015 al. et Bitsch c ie eodwhich beyond line, ice O ril ubr ae1of 1 page number, Article r = ice T R eedn on depending e J ff , .Hne transits Hence, ). T = g stellar ugh 2 e ff c iefor line ice O

00K with K) 5000 c esof reds = S 2021 ESO mely ,wsat was ), 00K). 1000 frequen- ). pro- e R Sun- and cir- (1) g 4 ) A&A proofs: manuscript no. ms

The mean geometric transit probabilities (P¯) of the most massive moons should thus be larger than P¯ of the most massive planets. Because of their shorter orbital periods, planet-moon transits of big moons should also occur more often than stel- lar transits of giant planets. In other words, big moons should exhibit higher transit frequencies ( f¯) around planets than giant planets around stars, on average. However, Eq. (1) does not give us a direct clue as to the mean relative transit depths (D¯ ).

2.2. Geometric transit probabilities, transit frequencies, and transit depths I exclude moons around the local terrestrial planets (most no- tably the Earth’s moon) and focus on large moons around the so- lar system giant planets to construct an empirical moon sample representative of moons forming in the accretion disks around Fig. 1. Dependence of (a) the mean geometric transit probability, (b) giant planets. This family of natural satellites has been suggested mean transit frequency, and (c) mean transit depth of the largest solar to follow a universal formation law (Canup & Ward 2006). We system moons on the number of moons considered. The abscissa refers to the ranking (N ) of the moon among the largest moons. need to keep in mind, though,that these planetsorbitthe outer re- s gions of the solar system, where stellar illumination is negligible for moon formation (Heller & Pudritz 2015a). However, many cies. For comparison, f¯ of the 20 largest moons of the solar sys- giant exoplanets are found in extremely short-period (the tem giant planets is 0.170(+0.111, 0.030)/. “hot ”); and stellar radial velocity (RV) measurements Stellar limb darkening, star spots,− partial transits, etc. aside, suggest that giant planets around Sun-like stars can migrate to the maximum transit depth depends only on R and on the ra- 1AU, where we observe them today. Moreover,at least one large dius of the transiting object (r) as per D = (r/R)2. In my cal- moon, , has probably been formed through a capture rather culations of D, I resort to the transiting exoplanet data because than in-situ accretion (Agnor & Hamilton 2006). r is not known for most RV planets. For the transiting plan- 3 3 For the planet sample, I first use all RV planets confirmed as ets, D¯ = 3.00(+4.69, 2.40) 10− . It is not clear whether of the day of writing. I exclude transiting exoplanets from my a debiased D¯ value would− be× larger or smaller than that. This analysis as these objects are subject to detection biases. RV ob- depends on whether long-period planets usually have larger or servations are also heavily biased (Cumming 2004),butwe know smaller radii than those used for this analysis. For comparison, that they are most sensitive to close-in planets because of the de- D¯ of the 20 largest moons of the solar system giant planets is 4 creasing RV amplitude and longer orbital periods in wider orbits. 6.319(+3.416, 4.543) 10− . Thus, planets in wide orbits are statistically underrepresented in The choice of− the 20× largest local moons for comparisonwith the RV planet sample, but these planets are not equally underrep- the exoplanet data is arbitrary and motivated by the number of resented as planets in transit surveys. Transit surveys also prefer digiti manus. Figure 1(a)-(c) shows P¯, f¯, and D¯ as functions of close-in planets, as the photometric signal-to-noise ratio scales the number of natural satellites (Ns) taken into account. Solid as ntr (ntr the number of transits, Howard et al. 2012). lines denote mean values, shaded fields standard deviations. The ∝ Mean values of P¯ (similarly of f¯ and D¯ ) are calculated as first moon is the largest moon, Ganymede, the second moon Ti- ¯ Np tan, etc., and the 20th moon . The trends toward higher P = ( i Pi)/Np, where Pi is the geometric transit probability of each individualP RV planet and Np is the total number of RV plan- transit probabilities (a), higher transit frequencies (b) and lower ets. Standard deviations are measured by identifying two bins transit depths (c) are due to the increasing amount of smaller around P¯: one in negative and one in positive direction, each of moons in short-period orbits. The negative slope at moons 19 1 and 20 in (a) and (b) is due to and Hyperion, which are which contains 2 68 % = 34 % of all the planets in the distribu- tion. The widths of these two bins are equivalent to asymmetric in wide orbits around and , respectively. 1 σ intervals of a skewed normal distribution. The key message of this plot is that P¯(Ns = 20), f¯(Ns = 20), The geometric transit probability P = R/a, with a as the or- and D¯ (Ns = 20) used above for comparison with the exoplanet bital semimajor axis of the companion. For the RV planets, P¯ = data serve as adequate approximations for any sample of solar 0.028(+0.026, 0.019).1 The P¯ value of an unbiased exoplanet system moons that would have been smaller because variations population would− be smaller as it would contain more long- in those quantities are limited to a factor of a few. period planets. On the contrary, no additional detection of a large ¯ = + solar system moon is expected, and P 0.114( 0.080, 0.045), 2.3. Evolution of exomoon habitability for the 20 largest moons of the solar system giant planets,− likely reflects their formation scenarios. An exomoon hosting planet needs to be sufficiently far from its The transit frequency f 1/(2π) (GM)/a3, where G is star to enable direct imaging and to reduce contamination from Newton’s gravitational constant≈ and Mpthe mass of the central IR stellar reflection. This planet needs to the star beyond object, assuming that M is muchlargerthan the mass of the com- several AU, where alternative energy sources are required on panion. For the RV planets, f¯ = 0.040(+0.052, 0.037)/day.2 its putative moons to keep their surfaces habitable, i.e., to pre- − The value of f¯, which would be corrected for detection biases, vent freezing of H2O. This heat could be generated by (1) tides would be smaller with long-periodplanets having lower frequen- (Reynolds et al. 1987; Scharf 2006; Cassidy et al. 2009; Heller & Barnes 2013), (2) planetary illumination (Heller & Barnes 1 Information for both R and a was given for 398 RV planets listed on 2015), (3) release of primordial heat from the moon’s accretion http://www.exoplanet.eu as of 1 October 2015. 2 The was given for 612 RV planets 3 Information for both r and R was given for 1202 transiting planets.

Article number, page 2 of 4 R. Heller: Transits of extrasolar moons around luminous giant planets (RN)

Fig. 2. Habitable zone (HZ) of a Mars-sized moon around a Jupiter-mass (light green) and a β Pic b-like 11 MJ-mass (dark green) planet at & 5 AU from a Sun-like star. Inside the green areas, tidal heating plus planetary illumination can liquify water on the moon surface. Values of the are denoted by their initials. Left: Both HZs refer to a planet at an age of 10 Myr, where planetary illumination is significant. Right: Both HZs refer to a planet at an age of 1 Gyr, where planetary illumination is weak and tidal heating is the dominant energy source on the moon.

(Kirk & Stevenson 1987), or (4) radiogenic decay in its mantle hot and inflated; and one, in which the system has evolved to an and/or core (Mueller & McKinnon 1988). All of these sources age of 1Gyr and the planet is hardly releasing any thermal heat. tend to subside on a Myr timescale, but (1) and (2) can compete Planetary luminosities are taken from evolution models with stellar illumination over hundreds of Myr in extreme, yet (Mordasini 2013), which suggest that the Jupiter-mass planet 2 plausible, cases. (3) and (4) usually contribute 1Wm− at the evolves from R = 1.28 R and T ff = 536K to R = 1.03 R and ≪ J e J surface even in very early stages. Earth’s globally averaged in- Teff = 162K over the said period. For the young 11 MJ-mass 2 ternal heat flux, for example, is 86mWm− (Zahnle et al. 2007), planet, I take R = 1.65 RJ (Snellen et al. 2014)and Teff = 1700K which is mostly fed by radiogenic decay in the Earth’s interior. (Baudino et al. 2014). For the 1Gyr version, I resort to the Mor- The globally averaged absorption of sunlight on Earth is dasini (2013) tracks, predicting R = 1.09 RJ and Teff = 480K. 2 239Wm− . If an Earth-like object (planet or moon) absorbs Tidal heating is computed as by Heller & Barnes (2013), follow- 2 more than 295Wm− , it will enter a runaway greenhouse ef- ing an earlier work on tidal theory by Hut (1981). fect (Kasting 1988). In this state, the atmosphere is opaque in Figure 2 shows the HZ for exomoons around a Jupiter-like the IR because of its high water vapor content and high IR opac- (dark green areas) and a β Picb-like planet (light green areas) ity. The surface of the object heats up beyond 1000K until the at ages of 10Myr (left) and 1Gyr (right). Planet-moon orbital globe starts to radiate in the visible. Water cannot be liquid un- eccentricities (e, abscissa) are plotted versus planet-moon dis- der these conditions and the object is uninhabitableby definition. tances (ordinate). In both panels, the HZ around the more mas- For a Mars-sized moon, which I consider as a reference case, the sive planet is farther out for any given e, which is mostly due 2 runaway greenhouse limit is at 266Wm− , following a semian- to the strong dependence of tidal heating on Mp. Most notably, alytic model (Eq. 4.94 in Pierrehumbert 2010). If the combined the planetary luminosity evolution is almost negligible in the HZ illumination plus tidal heating (or any alternative energy source) around the 1 MJ planet. In both panels, the corresponding dark exceed this limit, then the moon is uninhabitable. green strip has a width of just 1 RJ, details depending on e. On the otherhand,there is a minim energyflux fora moonto The HZ around the young β Picb, on the other hand, spans prevent a global snowball state that is estimated to be 0.35 times from 18 RJ to 33 RJ for e . 0.1 (left panel). This wide range 2 the solar illumination absorbed by Earth (83Wm− , Kopparapu is due to the large amount of absorbed planetary thermal illu- et al. 2013), which is only weakly dependent on the object’s mination, which is the main heat source on the moon in these mass. I use the terms global snowball and runaway greenhouse early stages. Planetary radiation scales as a 2, causing a much ∝ − limits to identify orbits in which a Mars-sized moon would be smoother transition from a runaway greenhouse (at 18 RJ) to a habitable, which is similar to an approach presented by Heller & snowball state (at 33 RJ) than on a moonthat is fed by tidal heat- 9 Armstrong (2014). A snowball moon might still have subsurface ing alone, which scales as a− . In the right panel, planetary il- oceans, but because of the challenges of even detecting life on lumination has vanished and∝ tides have become the principal en- the surface of an exomoon, I here neglect subsurface habitabil- ergy source around an evolved β Pic b. However, the HZ around ity. I calculate the total energy flux by adding the stellar visual the evolved β Pic b is still a few times wider (for any given e) illumination and the planetary thermal IR radiation absorbed by than that around a Jupiter-like planet; note the logarithmic scale. the moon to the tidal heating within the moon. Illumination is computed as by Heller & Barnes (2015), and I neglect both stel- 3. Discussion lar reflected light from the planet and the release of primordial and radiogenic heat. Assuming an of 0.3, similar to the A major challenge for exomoon transit observations around lu- Martian and terrestrial values, the absorbed stellar illumination minous giant planets is in the required photometric accuracy. Al- 2 by the moon at 5.2AU from a Sun-like star is 9Wm− . I con- though E-ELT will have a collecting area 1600 times the size of sider a Jupiter-mass planet and a β Pic b-like 11 MJ-mass planet, Kepler’s, it will have to deal with scintillation. The IR flux of both in two states of planetary evolution; one, in which the sys- an extrasolar Jupiter-sized planet is intrinsically low and comes tem is 10 Myr old (similar to β Pic b) and the planet is still very with substantial white and red noise components. Photometric

Article number, page 3 of 4 A&A proofs: manuscript no. ms exomoon detections will thus depend on whether E-ELT can the local giant planets. However, each solar system 3 3 achieve photometric accuracies of 10− with exposures of a few has at least one moon with a transit depth of 10− . Following the minutes.4 Adaptive optics and the availability of a close-by ref- gas-starved accretion disk model for moon formation (Canup & erence object, e.g., a low-mass star with an apparent IR bright- Ward 2006; Heller & Pudritz 2015b), a super-Ganymede around ness similar to the target, will be essential. Alternatively, sys- the young super-Jovian exoplanet β Pic b could have a transit 3 tems with multiple directly imaged giant planets would provide depth of 1.5 10− , which is 18 times as deep as the tran- particularly advantageous opportunities, both in terms of reli- sit of the Earth≈ around× the Sun. able flux calibrations and increased transit detection probabili- Beyond the stellar HZ, more massive planets have wider ties. Systems akin to the HR8799 four-planet system (Marois circumplanetary HZs. The HZ for a Mars-sized moon around et al. 2008, 2010) will be ideal targets. β Picb is between 18 RJ and 33 RJ for moon eccentricities e . Transiting moons could also impose RV anomalies on the 0.1. As the planet ages, the HZ narrows and moves in. After a planetary IR spectrum, known as the Rossiter-McLaughlin (RM) few hundred Myr, tidal heating may become the moon’s major effect (McLaughlin 1924; Rossiter 1924). The RM reveals the energy source. Owing to the strong dependence of tidal heating sky-projected angle between the orbital plane of transiting object on the planet-moon distance, the HZ around β Picb narrows to a and the rotational axis of its host, which has now been measured few RJ within 1Gyr from now, details depending on e. An exo- for 87 extrasolar transiting planets5. E-ELT might be capable of moonwould haveto reside in a veryspecific part of the e-a space RM measurements for large exomoons transiting giant exoplan- to be continuously habitable over a Gyr. ets that can be directly imaged (Heller & Albrecht 2014). The high geometric transit probabilities of moons around gi- Even nontransiting exomoons might be detectable in the IR ant planets, their higher transit frequencies, and the possibility of RV data of young giant planets. The estimated RV 1σ confi- transit signals that are one order of magnitude deeper than that dence achievable on a β Pic b-like giant exoplanet with a high- of the Earth around the Sun, make transit observations of moons resolution (λ/∆λ 100 000, λ being the wavelength of the ob- around young giant planets a compelling science case for the served light) near-IR≈ spectrograph mounted to the E-ELT could upcoming GMT, TMT, and E-ELT extremely large telescopes. 1 be as low as 70ms− in reasonable cases (Heller & Al- Most intriguingly, these exomoons could orbit their young plan- brecht 2014). The≈ RV amplitude of an Earth-mass exomoon in ets in the circumplanetary HZ and therefore be cradles of life. a Europa-wide (a 10 RJ) orbit around a Jupiter-mass planet Acknowledgements. This study has been inspired by discussions with Rory 1 ≈ wouldbe43ms− with a period of 3.7d. RV detections of super- Barnes, to whom I express my sincere gratitude. The reports of an anonymous massive moons, if they exist, would thus barely be possible even referee helped to clarify several passages of this paper. I have been supported by with E-ELT IR spectroscopy. We should nevertheless recall that the German Academic Exchange Service, the Institute for Astrophysics Göttin- gen, and the Origins Institute at McMaster University, Canada. This work made “hot Jupiters” had not been predicted prior to their detection use of NASA’s ADS Bibliographic Services. (Mayor & Queloz 1995). In analogy, observational constraints could still allow for detections of a so-far unpredicted class of hot super-Ganymedes; they might indeed be hot due to enhanced tidal heating (Peters & Turner 2013)and/or illumination from the References young planet (Heller & Barnes 2015). Agnor, C. B. & Hamilton, D. 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