Water Planets in the Habitable Zone: Atmospheric Chemistry,Observable Features, and the case of Kepler-62e and -62fL. Kaltenegger1,2*, D. Sasselov2, S. Rugheimer21Max Planck Institute of Astronomy, Koenigstuhl 17, 69115 Heidelberg, Germany, email@example.comHarvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USAAbstract: Water planets in the habitable zone are expected to have distinctgeophysics and geochemistry of their surfaces and atmospheres. We explore theseproperties motivated by two key questions: whether such planets could providehabitable conditions and whether they exhibit discernable spectral features thatdistinguish a water planet from a rocky Earth-like planet. We show that the recentlydiscovered planets Kepler-62e and -62f are the first viable candidates for habitablezone water planet. We use these planets as test cases for discussing those differencesin detail. We generate atmospheric spectral models and find that potentially habitablewater planets show a distinctive spectral fingerprint in transit depending on theirposition in the habitable zone.Subject headings: Astrobiology - atmospheric effects - methods: data analysis – Earth -planets and satellites: general – stars: individual (Kepler)1. IntroductionThe possible existence of Earth andsuper-Earths1-size planets coveredcompletely by a water envelope (waterplanets) has long fascinated scientists andthe general public alike (Kuchner 2003,Leger et al.2004). No such planets areknown in the Solar System. Sometimesreferred to as “ocean planets”, stemmingfrom the implicit assumption of HabitableZone (HZ) temperatures and a liquid watersurface, water planets constitute a muchbroader class which is now known to existin nature thanks to mean densitymeasurements of a few transitingexoplanets (see e.g. Gautier et al.2012,Cochran et al.2011, Gilliland et al.2013).Until recently all known candidates forwater planets (Borucki et al.2013) werefound orbiting very close to their stars.1 Super-‐Earth size is used here for planets with radii between 1.25 R⊕ and 2.0 R⊕. Such planets, e.g., Kepler-18b, -20b, -68b,are very hot due to the high stellar flux,which ensures a smooth transition from aninterior water envelope to a steamatmosphere with no liquid surface ocean(Rogers&Seager 2010; Valencia etal.2009). The discovery of many planetarysystems with tightly packed inner planetsby the Kepler mission has opened theprospect for getting mean densities ofEarth-size planets in the habitable zone bytransit-timing variations (TTVs) whereradial velocity amplitudes are too small tomeasure (Lissauer et al.2011). Given thevery low mean densities measured so faramong the majority of such planets, e.g.those found in Kepler-11 (Lissauer etal.2013), Kepler-20 (Gautier et al.2012),Kepler-36 (Carter et al.2012), weanticipate that the first HZ super-Earths ofradius below 2 Earth radii (RE) are morelikely to be water planets than rocky ones.The recent discovery of the multipletransiting system Kepler-62, with two
1planets in its HZ (Borucki et al.2013),illustrates this point. We are motivated bythe discovery of Kepler-62e and -62f toconsider a more general approach tocomputing surface and atmosphericconditions on water planets in the HZ.Water planets of Earth- to super-Earthsizes in the HZ fall into at least 2 types ofinterior geophysical properties, in terms ofeffect on their atmosphere: In a first Type,hereafter Type1, the core-mantle boundaryconnects silicates with high-pressurephases of water (e.g. Ice VI, VII), i.e. theliquid ocean has an icy bottom. In contrastin Type2 the liquid ocean has a rockybottom, though no silicates emerge abovethe ocean at any time. The second type isessentially a rocky planet when viewed interms of bulk composition. Both subtypescould possess a liquid ocean outer surface,a steam atmosphere, or a full cover ofsurface Ice I, depending on their orbitwithin the HZ and the magnitude of theirgreenhouse effect. Frozen water planetsshould show a subsequent increase in thesurface albedo value due to high reflectiveice covering a frozen surface and will bemost easily detected by direct imagingmissions operating in the visible, while IRimaging search will preferential detectwarm water planets.Surface and atmospheric conditions onwater planets in the HZ have not been thesubject of detailed studies. So far the workhas focused on issues of evaporation(Kuchner 2003; Valencia et al.2009;Murray-Clay et al.2010) and boundaryconditions to interior models (Valencia etal.2007, Grasset et al.2009, Fu et al.2010,Rogers&Seager 2010).In this paper we develop an initialmodel for water planet atmospheres toallow assessment of their observables withfuture telescopes. This model will bebased on many explicit and implicitassumptions using Earth as a template buttaking into account anticipated differencesin outgassing, geochemical cycling, globalcirculation, etc. to assess their observableswith future telescopes. In this paper wedescribe a set of atmospheric models andtheir underlying assumptions in section 2,how they could be applied to interpretKepler-62e and -62f as water planets insections 3 and 4, and finish in section 5with discussion and conclusions.2. Atmospheric Models for WaterPlanets – Basic AssumptionsWe assume here that the initialcomposition of icy planetesimals thatassemble into water planets is similar tothat of comets, mostly H2O, some NH3 andCO2. An initial composition of ice similarto that of comets leads to an atmosphericmodel composition of 90%H2O, 5%NH3and 5%CO2 (see also Leger et al.2004,who simplified the atmosphericphotochemistry by assuming no CO norCH4). NH3 is UV sensitive,photodissociates and is converted into N2and H2 in a very short time frame, with H2being lost to space (see e.g. Leger etal.2003, Lammer et al.2007). This showsthat water planet atmospheres will havethe same chemical constituents as ocean-land planets.The carbonate-silicate cycle thatregulates CO2 cycling on our own planet iseffective due to weathering of exposedsolid rock surface. Recent work (Abbot etal.2012) has shown that for an Earth-likeplanet, the carbonate-silicate cycle couldcontinue to function largely unchanged fora continent surface fraction as low as 10%,with mid-ocean ridges taking over some ofthe recycling processes but argued thatCO2 cannot build up in the atmosphere ofa Type2 water planet without continents.Therefore the HZ for water planets wasinferred to be narrower than for planetswith continents. Note that the arguments
2presented in that work are generally onlyapplicable to Type2 water planets, i.e.those with very low water-mass fraction.For Type1 water planets, i.e. Super-Earthswith water-mass fractions like Earth orabove, the deep oceans are separated fromthe rocky interior via a layer of high-pressure ices. Therefore an alternative CO2recycling mechanism will be required inwater planets for cycling of abundantgases, like CO2 and CH4. Such a cyclewould depend on the properties of theirclathration in water over a range of veryhigh pressures. Methane clathrates arewater molecule lattices that trap CH4molecules as guests by virtue of multiplehydrogen-bonding frameworks. Undervery high pressures, common to super-Earth-size water planets, methaneclathrates undergo a phase transition intheir structure to a form known as filledice. Levi et al (2013) studied this transitionand concluded that CH4 would betransported efficiently through the high-density water-ice mantle of water planetsin filled ice clathrates and eventuallyreleased in the atmosphere. It is wellknown that CO2 substitutes CH4 readily innormal-pressure clathrates (see e.g. Park etal.2006, Nago&Nieto 2011). We expectthat this property can be extrapolated tofilled ice, though this needs to beestablished. If so, this substitution willenable effective cycling of CO2 throughthe atmosphere in water planets residing inthe habitable zone (e.g., with water oceansat the surface) and thus provide anatmospheric feedback mechanism for CO2on water planets. As for Earth-like planetswith continents, such a cycle wouldcontrol the CO2 levels, leading to water-dominated atmospheres for strong stellarirradiation and CO2-dominated atmospherefor low stellar irradiation.This new water planet model impliesthat atmospheric model profiles for waterplanets in the HZ should not differsubstantially from atmospheric profiles forland-ocean planets, except for an increasein absorbed stellar flux due to thedecreased surface reflectivity of waterplanets (see S5).3. Habitable Zone for Water PlanetsThe “narrow” HZ is defined hereclassically as the annulus around a starwhere a rocky planet with a CO2/H2O/N2atmosphere and sufficiently large watercontent (such as on Earth) can host liquidwater on its solid surface (Kasting etal.1993). A conservative estimate of therange of the narrow HZ is derived fromatmospheric models by assuming that theplanets have a H2O– and CO2–dominatedatmosphere with no cloud feedback(Kopparapu et al.2013). In this model, thelocations of the two edges of the HZ aredetermined based on the stellar fluxintercepted by the planet, at the inner edgeby thermal run away due to saturation ofthe atmosphere by water vapor and at theouter edge by the freeze-out of CO2 for aplanets that is geologically active.Climatic stability is provided by amechanism in which atmospheric CO2concentration varies inversely withplanetary surface temperature. Cloudfeedback will widen the limits of the HZ(see e.g. Selsis et al.2007, Zsoms etal.2012), we therefore use the empiricalvalue for the HZ from our own SolarSystem as the “effective” HZ, defined bythe initial solar fluxes received at theorbits of Venus and Mars during the earlyperiod of the solar system when the Sunwas less luminous and Venus (1Gyr) andMars (3.5Gyr) did not have liquid wateron their surfaces. At that time Venusreceived an equivalent flux of 1.78Sʘ andMars of 0.32Sʘ (Kopparapu et al.2013).
3The HZ changes only slightly forwater planets compared to the HZ of aland-ocean planet because at the limits ofthe HZ the albedo is solely dominated bythe atmosphere and the surface albedoonly has a small effect (see Fig.3 forinsight on the effect of the surface albedoon the resulting atmospheric structure).But within the HZ for a given incidentstellar flux a water planet has largersurface temperature due to the low surfacereflection of water compared to land.Cloud coverage influences theatmospheric temperature structure as wellas the observability of spectral features(see e.g. Kaltenegger et al.2007, Selsis etal.2007, Kaltenegger&Traub 2009, Raueret al.2010). On Earth cloud fractions issimilar over water and land (see e.g. Zsomet al.2012). If sufficient cloudcondensation nuclei are available, cloudcoverage should be the same as for rockyplanets for the same stellar insolation, butit will vary depending on the waterplanet’s position in the HZ (Rugheimer etal.in prep). The position and pattern ofindividual cloud layers depend onunknown planetary parameters likerotation rate as well as surface topography.We mimic the effects of varying cloudcoverage by varying the initial surfacealbedo in our atmospheric model from thestandard 0.2 (see Kasting et al.1993).The atmospheric structure and theresulting HZ limits depend on the densityof a planet’s atmosphere, shifting the HZoutwards for lower mass and inwards forhigher mass planets (see Kasting etal.1993, Kopparapu et al.2013). Withoutany further information on the relation ofsurface pressure to planetary mass, wemake the first order assumption here, thatif outgassing rates per m2are held constanton a solid planet, and atmospheric lossrates decrease with planetary mass due toincreased gravity, assuming a similarstellar environment, then a more massiveplanet should have a higher surfacepressure (for similar outgassing andatmospheric loss mechanisms). We scalethe surface pressure of the planet to firstorder with its surface gravity (followinge.g. Kaltenegger et al.2011) and explorethe effect of different planetary mass inFig.3. We use EXO-P (see e.g.Kaltenegger&Sasselov 2010 for detailsand reference) to model the atmosphere ofwater planets. EXO-P consists of acoupled one-dimensional radiative-convective atmosphere code developed forrocky exoplanets based on a 1D-climate,1D-photochemistry and 1D-radiativetransfer model.4. Models for transiting Type1 Water-Planets in the HZ - the Kepler-62 and -69 systemsKepler-62 (Borucki et al.2013) andKepler-69 (Barclay et al.2013) are multi-transiting planet systems with individualplanets in or close to the HZ (Fig.1 and 2).Kepler-62b, c, d, e, and f have radii of1.31, 0.54, 1.95, 1.61 and 1.41RE with lessthan 5% errors, orbiting a K2V star of4925±70°K (0.21±0.02L0) at periods of5.7, 12.4, 18.2, 122.4 and 267.3days,respectively (Borucki et al.2013). Theoutermost planets Kepler-62e and -62f aresuper-Earth-size planets in the HZ of theirhost star, receiving 1.2±0.2 and 0.41±0.05times the solar flux at Earth’s orbit (S0).Kepler-69b, and -69c have radii of about2.2 and 1.7 (+0.34-0.29)RE orbiting a 5638 ±168°K Sun-‐like star. Kepler-‐69c has semi-‐major axis to stellar radius ratio a/RStar=148 (+20-‐14) at periods of 13.7 and 242.5days respectively (Barclay et al.2013). Due to the largeuncertainty in luminosity of the star, the outermost planet Kepler-‐69c receives 1.91 (+0.43-‐0.56)S0,
4The small radii of Kepler-62e and -62findicate that the planets should not haveretained primordial hydrogen atmospheresat their insolation and estimated ages ofabout 7Gyr (Rogers et al.2011, Lopez etal.2013, Lammer et al.2009,Gaidos&Pierrehumbert 2010), makingthem strong candidates for solid planets,and not Mini-Neptunes. Given the largeamount of solid objects already present inthe Kepler-62 system on orbits inward of -62e, and following the recent results onthe Kepler-11 cohort of 6 low-densityplanets with tightly packed close-in orbits(Lissauer et al.2013) it strongly suggeststhat -62e and -62f formed outside the iceline and are therefore our first HZ waterplanets. While other possibilities remainopen until their actual masses aremeasured, for the purposes of this paperwe’ll assume that they are indeed waterplanets on low-eccentricity orbits andmodel both biotic and abiotic atmospheres.For Kepler-62e we set the O2 mixingratio to 0.21(biotic), 0.21x10-6(abiotic).We set CO2 to 10ppm for both simulationsfor Kepler-62e at the inner part of the HZ,which corresponds to the conservativelower limit for C4 photosynthesis (Heath1969, Pearcy&Ehleringer 1984) andcalculate what levels of CO2 are neededfor Kepler-62f to maintain liquid water onits surface, which results in 5bar of CO2for the considered Albedo range. ForKepler-62f we set O2 to 0.21atm for thebiotic model. Maintaining a constantmixing ratio for the biotic case like forKepler-62e would yield unrealisticallyhigh O2 pressures. For the biotic case weuse only trace amounts of O2. The CH4flux is set to 1.31x1011(biotic)(Rugheimer et al.2013), 4x10-9molecules/cm2/s (abiotic) (see e.g.Kasting&Caitling 2003, Segura et al.2007)for both planets.5. Discussion and ConclusionsFor Kepler-62e’s radius a waterplanet’s mass would be in the range 2-4ME. Kepler-62f has a smaller radius of1.41RE, so its mass would be 1.1-2.6ME.The transition from liquid water to the firstsolid phase of Ice VI occurs at 0.63 to2.2GPa, depending on the temperature.Beyond 2.2GPa, the solid phase water isIce VII. The depth of the liquid ocean isthus in the range of 80 to 150km for thesetwo planets. The radius of Kepler-69cRp=1.7 (+0.34 -0.23)RE has very largeerror bars, therefore the mass range is ill-defined.Fig.2 shows that the stellar flux valuesat the limit are 1.66 to 0.27Sʘ for theeffective HZ and 0.95 to 0.29Sʘ for thenarrow HZ, respectively, for Kepler-62and 1.78 to 0.29Sʘ for the effective HZand 1.01 to 0.35Sʘ for the narrow HZ forKepler-69 (based on models by Kopparapuet al.2013). The intercepted flux at theorbit of Kepler-62e and -62f, make bothplanets candidates for liquid water on theirsurface. If the atmosphere of Kepler-62f isaccumulates several bar of atmosphericCO2 (1.6 to 5bar, depending on the modelplanetary mass and surface albedo) itwould be covered by liquid water on itssurface, otherwise it would be ice covered.This first possibility allows an interestingcomparison of a warm Type1 water planetin the inner and outer part of the HZ, thesecond possibility allows us to comparewarm and frozen Type1 water planets inthis system (Fig. 4). These differences aresimilar to the variations with temperaturesof rocky planet spectra, but water planetsare hotter at a given distance from theirstar.Fig.2 shows that Kepler-69c liesoutside the effective HZ corresponding tothe nominal stellar flux, but the error bar
5on the star’s flux allows the possibility thatthe planet is within the inner edge of theeffective empirical HZ. To explore theatmospheric features of transiting waterplanet, we concentrate on the Kepler-62system here, where both planets are withinthe star’s HZ. We run Exo-P models tunedto the Kepler-62 parameters and explorethe effect of changing cloud parameters byvarying the surface albedo from 0.2 to 0.3mimicing increased cloud coverage forKepler-62e, and from 0.2 to 0.1 forKepler-62f mimicing decreased cloudcoverage. Fig.3 shows the atmosphericstructure of both planets as Type1 waterplanets for the maximum and minimummass and explore their changes withsurface albedo (nominally 0.2). Interiormodels (see Zeng&Sasselov 2013) ofKepler-62e models give a scaled surfacepressure of 0.78 to 1.56 times Earth’s andsurface temperatures for the low mass caseof 303.7K and 306.8K(A=0.2) and 292.5Kand 296.9K(A=0.3) for the abiotic andbiotic cases, respectively. Models for thehigh planetary mass case result in surfacetemperatures of 308.1K and310.5K(A=0.2) and 293.1K and297.5K(A=0.3) for the abiotic and bioticcases, respectively.Atmospheric models for Kepler-62fshow that 1.6bar of CO2 is needed to warmthe surface temperature above freezing foran albedo of 0.1 and 5bar of CO2 is neededto obtain Earths global temperatureaverage of 288K for an albedo of 0.3.Models of Kepler-62f lead to a scaledsurface pressure of 0.56 to 1.32 timesEarth’s. We add 5bar of CO2 to thispressure, what results in surfacetemperatures of 288.3K and289.2K(A=0.1) and 280.5K and281.6K(A=0.2) for the abiotic and bioticcases, respectively. For the high mass caseof Kepler-62f, we obtain surfacetemperatures of 298.4K and279.7K(A=0.1) and 287.8K and280.6K(A=0.2) for the abiotic and bioticcases, respectively.We use two model calculations (thelowest surface pressure and gravityconsistent with Kepler-62e and -62f, forbiotic conditions) as example to explore iftransmission spectra show differencesbetween different planetary conditions aswell as inform future instrumentsensitivity requirements. Using the highestplanetary mass in the interior modelswould decrease the observable spectralfeatures by a factor of about two. Fig.4shows the corresponding synthetictransmission spectra of (top) a water-dominated atmosphere warm water planet(using model parameters for a lightKepler-62e) and (middle) a CO2-dominated atmosphere frozen water planet(using model parameters for a lightKepler-62f with only 100 times PresentAtmospheric Level CO2), and of a currentEarth analog (bottom). The comparisonclearly shows stronger CO2 in thetransmission spectra of a water planet onouter edge of the HZ compared to a waterplanet the inner edge of the HZ, but lowerO3 and H2O features. Therefore relativelylow resolution spectra allow such planetsto be characterized for telescopes likeJWST (see e.g. Kaltenegger&Traub 2009,Deming et al.2009, Rauer et al.2010, Beluet al.2011, van Paris et al.2013) as well ashigh resolution ground based telescopeslike E-ELT (Snellen et al.2013).We have defined two types of waterplanets, Type1, which are true waterplanets in their bulk composition andType2 which are rocky planets with watercovering all surface and postulated a newcycling mechanism for CO2 usingclathrates. A detailed atmospheric modelof the specific planets of Kepler-62e and -62f as Type1 water planets permits forliquid water on each, if -62f accumulates
6several bar of CO2 in its atmosphere. TheKepler-62e models show a warm waterplanet, between the limits of the narrowHZ and the effective HZ with increasedcloud coverage. These planets allowcomparison of water planets with warmwater- and CO2-dominated atmosphere inHZ, with discernable differences in theirtransmission spectra. Fig. 4 shows that thetransmission spectrum allows aninteresting comparison of warm water-versus CO2-dominated as well as warmand cold water planets in this system.These differences are similar to thevariations with temperatures of rockyplanet spectra, but water planets are hotterat a given distance from their star.Kepler-62e and -62f are the first viablecandidates for HZ water planets whichwould be composed of mostly solids,consisting of mostly ice (due to the highinternal pressure) surrounding a silicate-iron core. The nominal flux intercepted atKepler-69c is too high for it to be in theeffective HZ, but the large error bars on itsstar’s flux allow for this planet close to theinner edge of the empirical HZ.Water planets in the HZ arecompletely novel objects, which do notexist in our own Solar System. Theatmospheric models presented here predictdetectable features in the spectra of waterplanets in the HZ in transit. Therefore weexpect that future remote characterizationwill allow us to distinguish water planetsat different parts of their HZ.Acknowledgements:The authors Thank JonathanMcDowell comments and in depthdiscussions. LK acknowledges supportfrom DFG funding ENP Ka 3142/1-1 andNAI. DS acknowledges partial support forthis work by NASA cooperativeagreement NNX09AJ50A (Kepler Missionscience team).ReferencesAbbot, D., Cowan, N.B., Ciesla, F.J. 2012,ApJ, 756, 13Abe, Y, Abe-Ouchi, A., Sleep, N.H.,Zahnle, K.J. 2011, Astrobiology 11, 443Barclay et al. 2013, ApJ, in pressBelu, A. R., Selsis, F., Morales, J., et al.2011, A&A, 525, A83Borucki, W et al. 2013, ScienceBorucki, W. J. et al. 2011, ApJ, 736, 19Carter, J.A. et al. 2012, Science, 337, 556Cochran, W.D. et al. 2011, ApJS, 197, 19Deming, D., Seager, S., Winn, J., et al.2009, Pub. Astron. Soc. Pac., 121, 952Fu, R., OConnell, R.J., Sasselov D.D.2010, ApJ, 708, 1326Gautier, T.N. et al. 2012, ApJ, 749, 19Heath, O. V. S. The Physiological Aspectsof Photosynthesis, Stanford Univ. Press,1969.Kaltenegger, L., Sasselov D.D. 2010, ApJ.708, 1162Kaltenegger, L., Segura, A., Mohanty, S.2011, ApJ, 733, 1Kaltenegger, L., Traub, W.A. 2009, ApJ,698, 519Kaltenegger, L., Traub, W.A., Jucks, K.W.2007, ApJ, 658, 598Kasting, J. E., Whitmire, D.P. , Reynolds,R. T. 1993, Icarus, 101, 108Kasting, J. F. & Catling, D. 2003, Ann.Rev. Astron. Astrophys. 41:429–63.Kasting, J.F., Pollack, J.B., Crisp, D.1984, J. Atmos. Chem., 403Kopparapu, R.K. et al. 2013, ApJ,2013arXiv1301.6674KKuchner, M. 2003, ApJ, 596, L105Lammer, H. et al. 2009, Space ScienceReviews, 139, 399Lee, J. et al. 2010, ApJ, 716, 1208Leger, A. et al. 2004, Icarus, 169, 499Levi, A., Sasselov D.D., & Podolak, M.,2013, ApJ, acceptedLi, Z. & Sasselov, D.D. 2013, PASP,2013arXiv1301.0818ZLissauer, J., et al. 2013, arXiv:1303.0227
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1Fig.1. Mass-radius plot showing Kepler-62e and -62f as presumed water planets (bluelozenges), compared to Venus, Earth, and transiting exoplanets. Kepler-69c (Rp=1.7+0.34-0.23RE) is not shown due to its very large error bars. The curves are theoreticalmodels (Li&Sasselov 2013); the dashed line the maximum mantle stripping limit(Marcus et al.2010).
2Fig.2. Comparison of known transiting exoplanets with measured radii less than 2.5 R⊕ inthe HZ to the Solar System planets. The sizes of the circles indicate the relative sizes ofthe planets to each other. The dashed and the solid lines indicate the edges of the narrowand effective HZ, respectively (Kopparapu et al.2013).
3Fig.3. Temperature and mixing ratios for H2O, O3 and CH4 for biotic and abioticatmospheric models for water planets in the inner(top) and outer(bottom) part of the HZ(using planetary parameters for Kepler-62e and –62f).
4Fig.4. Synthetic transmission spectra of atmospheric models for a hot(top) andcold(middle) water planet, using Kepler-62e and -62f parameters (see text), and the Earthin transit(bottom) for comparison.