Between Earth and Uranus: Part II

Figure 1. Exoplanets between Earth & Uranus in radius (R) and mass (M)

The media market for Super Earths remains robust. Two months back, MSNBC noted the discovery of a steamy new breed of alien planet (actually GJ 1214 b, discovered almost three years ago and long since characterized as a Super Earth). A few weeks ago, BBC News reported that our galaxy contains billions of habitable Super Earths. And in a seductive press release, the European Southern Observatory presented the nearby system of GJ 667 C as the home of a balmy Super Earth with glinting seas and weathered mountains and canyons that bear a remarkable resemblance to the landforms of the American Southwest. Clearly, Super Earths are the planetary flavor of the year. As with any food fad, however, it is imperative for potential consumers to investigate the ingredients before they tuck in.

The term super-Earth or Super Earth entered astronomical parlance around 2005 to describe the first confirmed exoplanet with a minimum mass lower than 10 times Earth (GJ 876 d; Marcy et al. 2005). Just a year earlier, the French astronomer Alain Leger resorted to the cumbersome term “Earth-Uranus class planet” to describe objects with radii between 1.5 and 4 times Earth, without reference to their mass (Leger et al. 2004a).

From Marcy’s publication until the present day, Super Earths have generally been understood as objects in the range of 2 to 10 Earth masses (2-10 Mea). Since language is powerful, they have also been interpreted as primarily rocky in composition, like Earth. According to theoretical arguments, they have been considered unlikely to harbor significant hydrogen/helium atmospheres (Adams et al. 2008 and references therein). These structural features distinguish them from planets of Uranus mass and above (see Between Earth & Uranus, Part I).

early theoretical discussions

From the start it was expected that such planets would come in two different varieties with two distinct formation histories:

1. Rocky Super Earths would be scaled-up versions of our home planet, which is about one-third iron and two-thirds silicates, with a thin envelope of heavy gases. Such planets form along warm, ice-free orbits. These are located within a few astronomical units (AU) of a Sun-like star, and within a few tenths of an AU around M dwarfs.

a.    Out of a primordial nebula of hydrogen and dust, rocky protoplanets like Vesta coagulate and then collide until they assemble objects similar to Mars, whose mass is 11% of Earth’s and whose radius is 53% of Earth’s.

b.   Within 10 million years after the parent star’s ignition, the hydrogen cloud dissipates, removing a major “buffer” that previously helped to damp orbital eccentricities and prevent orbit crossings during protoplanetary accretion. For several million years longer, the remaining rocky embryos undergo giant impacts until objects in the mass range of Earth and Venus – and potentially at least a few times heavier – remain as the final population. Subsequent impacts by asteroids and comets might bring enough ice to create planetary oceans, as they are believed to have done on Earth.

2. Icy Super Earths would be scaled-up versions of Ganymede and Titan, with rock/metal cores surrounded by thick layers of ice amounting to 25%-75% of their total mass. This planetary species was formally proposed by Marc Kuchner and then discussed in detail by Alain Leger and colleagues (Kuchner 2003, Leger et al. 2004b).

a.   Both studies argued that these icy worlds (or Ocean Planets, in Leger’s terminology) would assemble rapidly, within several million years of stellar ignition, either at or beyond the ice line of a given planetary system. This is the circumstellar radius outside which icy particles remain frozen on astronomical time scales, corresponding to about 3 AU from a Sun-like star and about 1 AU from an M dwarf. Inside this radius, rocky protoplanets would probably be insufficient to build objects more massive than about 4 Mea, according to the results of numerical simulations of planet formation (Raymond et al. 2004, Kenyon & Bromley 2006).

b.   Both also assumed that objects less massive than 10 Mea could not accrete or retain significant hydrogen envelopes. This feature would distinguish icy Super Earths from the so-called ice giants, Uranus and Neptune, which exceed 10 Mea and are 10%-20% hydrogen by mass. Leger and colleagues focused on a model planet of 6 Mea with a radius of 2 Mea, a bulk composition about 50% ice, and an atmosphere dominated by water vapor, nitrogen, and carbon dioxide.

c.   Both discussions proposed mechanisms by which icy planets might travel from their birth region to warmer, inner orbits. Migration through interaction with the protoplanetary nebula, also known as Type I migration, received the most attention. This process necessarily occurs in the earliest phase of planetary evolution, before the hydrogen cloud dissipates. Kuchner also proposed planet scattering, which would occur after the nebula dispersed, at about the same time as giant impacts were occurring in the inner system.

d.   Although neither article mentions it, such a formation scenario assumes that no gas giants emerge from the protoplanetary nebula. If one or more gas giants assembled in the “sweet spot” of the cloud – between about 3 and 10 AU from a Sun-like star – they would likely prevent the accretion of icy Super Earths. In our Solar System, for example, the evolution of Jupiter around 5.2 AU prevented the birth of any additional planets between 2 and 5 AU.

One loophole to such a restriction would require Type II migration by a gas giant planet at primordial times. This process involves dynamical interaction between the hydrogen cloud and a forming gas giant, generally of Saturn mass or above. As the giant spirals into the inner system, it can shepherd icy and rocky planetesimals inside its shrinking orbit. By the time the protoplanetary nebula disperses and migration ends, these assorted scraps might coalesce into a Super Earth with a short-period orbit. Both GJ 876 and 55 Cancri do in fact harbor Super Earths with periods shorter than 2 days, orbiting just interior to a gas giant planet. Nevertheless, objects in this mass range are much more common in multiple systems that contain other rocky and icy planets, without any nearby gas giants to explain their formation.

Figure 2. Hypothetical rocky and icy telluric planets (“Super Earths”). The icy planet is assumed to contain 25% water.

Under such nicknames as Ocean Planets, Water Worlds, and Sauna Planets – along with the catch-all designation of Super Earths – these theory-inspired candidates entered exoplanetary consciousness just as the first objects with minimum masses smaller than 10 Mea began to appear in radial velocity searches. By the autumn of 2009, more than a dozen such exoplanets had been announced, all orbiting stars less massive than our Sun, and all but two on orbits shorter than 20 days.

At the same time, theoretical studies of the potential bulk composition and even habitability of individual candidates began to accumulate. For example, much discussion has centered on the nearby system of GJ 581, a modest M dwarf harboring at least four low-mass planets within a circumstellar radius of 0.22 AU. Many such studies rest on two unlikely assumptions: that the actual masses of Super Earths are identical to their minimum masses, and that they are all rocky planets like Earth (e.g., von Bloh et al. 2007, Wordsworth et al. 2010, von Paris et al. 2011). Thus GJ 581 d, with a minimum mass of 7 Mea and an orbit largely confined to the system’s liquid water zone, has been proposed repeatedly as a potentially habitable Super Earth – always on the shaky assumption that it is a rocky planet half as massive as Uranus.

Yet the vast majority of planets whose radial velocity signals place their minimum masses between Earth and Uranus are likely to be at least 15% heavier (and potentially several hundred percent heavier) than those minimum values. As evidence from transiting planets accumulates, it is also apparent that objects of more than a few Earth masses may have substantial ice content and perhaps even hydrogen atmospheres. A planet whose bulk composition is approximately 1% hydrogen or more will likely support a deep atmosphere. Such a structure resembles a lightweight version of Neptune or Uranus rather than a Big Venus or a Super Earth.

Transit observations are the key to measuring the radii of exoplanets. Without data on radius as well as mass, estimates of bulk composition are impossible. The first transiting Super Earth candidate was CoRoT-7b, announced in 2009. Unfortunately, this object orbits a stormy star whose activity reduces the effectiveness of radial velocity observations, so that exact measurements of its mass have been impossible. Reliable estimates of its radius (1.58 Rea) nevertheless indicate that CoRoT-7 is a big airless rock – a literally hellish place that orbits a Sun-like star in a period shorter than 21 hours. This Hadean environment corresponds to dayside temperatures above 2000 K: hot enough to sustain a magma ocean (Leger et al. 2011).

CoRoT-7b has been followed by a few dozen more transiting Super Earth candidates, whose numbers increase with every new release of Kepler data. Although all of them have well-constrained radii, relatively few have robust mass determinations obtained through measured radial velocities or transit timing variations (TTV). At the time of this posting, the elite subset of Super Earth candidates with both measured masses and measured radii includes just eight members: GJ 1214 b, 55 Cancri e, Kepler-11b, Kepler-11d through f, Kepler-18b, and Kepler-20b. For two other candidates (CoRoT-7b and Kepler-10b), masses can be reliably constrained if the data on radii are interpreted in light of the objects’ thermal environment.

Several more telluric or gas dwarf candidates have been announced with radii measured by the Kepler telescope but few or no constraints on mass. Above and beyond this population looms a backlog of several hundred similar Kepler candidates awaiting confirmation and publication.

Much theoretical work over the past few years, conducted by such investigators as Jonathan Fortney, Jack Lissauer, Leslie Rogers, Sara Seager, Diana Valencia, and their collaborators, has helped to establish the potential bulk compositions that correspond to each pairing of mass and radius. Figure 3 is based on the model presented by Fressin et al. (2012) to assess the structure of planets discovered by the Kepler Mission.

Figure 3. Mass/radius curves for telluric and gas dwarf planets of 11 Mea or less

In this figure, the three solid lines represent pure compositions, with blue = water, violet = perovskite (MgSiO₃), and red = iron. Dashed blue is 75% water, 22% silicates, 3% iron; dot-dashed blue is 45% water, 48% silicates, 7% iron; dotted blue is 25% water, 52% silicates, 23% iron; dashed red is 68% silicates, 32% iron; and dotted red is 30% silicates and 79% iron. Radii increase slowly among the most metallic planets, so that an object with the same composition as Earth and a mass 30 times greater would have a radius only 2.2 times greater. According to Figure 3, the likeliest radii for telluric planets of 2-10 Mea fall between the dotted red line for Mercury-like compositions and the dashed blue line for extreme water worlds, with a corresponding span of 1-2.5 Rea. Any radius above the blue line is likely to require a hydrogen-rich atmosphere, making the object a candidate gas dwarf (“Mini Neptune”) rather than a Super Earth.

confronting theory with observation

Figure 4 shows what happens when we insert likely mass and radius values for a sample of the most reliably constrained planets between 2 and 10 Mea. (Note that large uncertainties surround all values; Figure 4 does not attempt to express these uncertainties, but Figure 5 does so for a subset of the Kepler planets.) Colored curves have the same values as in Figure 3.

Figure 4. Approximate masses and radii of selected exoplanets

At first glance Figure 4 suggests, contrary to pre-2009 expectations, that this mass range includes not two but three planetary subspecies: [1] the true Super Earths, with radii of 2 Rea or less; [2] the “ice dwarfs” or Ocean Planets, with radii between 1.3 Rea and 2.6 Rea; and [3] the “gas dwarfs,” with radii starting around 1.5 Rea and ranging above 4 Rea (i.e., the radius of Uranus and Neptune).

Figure 5 gives a fuller picture of two key systems with multiple low-mass planets: Kepler-11 and Kepler-20. Both are G-type stars like our Sun with masses between 90% and 95% Solar. All seven planets in this figure have semimajor axes of 0.25 AU or less and periods shorter than 50 days, making them hotter than Mercury.

Figure 5. Shadowy dwarfs: low-mass planets orbiting Kepler-11 and Kepler-20

Colored curves have the same values as in Figure 3. The dashed green line marks the radius of Uranus. Boxes delineate uncertainties. Planets of Kepler-11 are turquoise; planets of Kepler-20 are purple.

Even given the large uncertainties in parameters, we can recognize at least two populations orbiting these Sun-like stars: objects with substantial hydrogen content and objects consisting only of rock, metal, and ices. A further division might be drawn between purely rocky planets and those with a significant percentage of ice, as recommended by Kuchner and Leger. The result would again be three distinct planetary types for the mass range between 1 and 10 Mea.

It is possible, nevertheless, that we are seeing successive developmental phases of a single planetary species. Theoretical studies have already shown that objects under 10 Mea – perhaps even as lightweight as 2.5 Mea – can capture substantial hydrogen atmospheres from the primordial nebula (Adams et al. 2008, Rogers et al. 2011). The resulting planets can grow to dimensions in excess of 6 Rea (literally off the charts according to the schema of Figure 5). If they remain on cool orbits, these gas dwarfs can retain their hydrogen envelopes, but if they migrate into hot, short-period orbits – like Kepler-10b, Kepler-11b, Kepler-20b, CoRoT-7b, or 55 Cancri e – they will be subject to mass loss through stellar irradiation, and likely lose their hydrogen, their ices, and eventually their surface layers of rock (Jackson et al. 2010, Poppenhaeger et al. 2012).

Thus it may turn out that most or all of the candidates represented in Figures 4 and 5 formed near their systems’ ice line through a process involving coagulation of refractory and icy particles and subsequent capture of hydrogen envelopes. Type I migration then carried them into the inner system, perhaps in “convoys” of low-mass objects. In their new hot orbits, these planets experienced greater or lesser degrees of mass loss. This history might explain the system architecture of Kepler-11 and Kepler-20, and perhaps of other non-transiting systems containing multiple low-mass objects, such as GJ 581, HD 69830, and HD 10180.

Indeed, given current theories of planet formation, it is difficult to understand how an object more than a few time as massive as Earth could form beyond the ice line without accreting a hydrogen envelope. Once we acknowledge this difficulty, the status of Leger’s Ocean Planets becomes debatable, on the following rationale: Any object with a primordial hydrogen atmosphere that achieves an orbit with the insolation appropriate to sustain liquid water would still be cool enough to retain its gaseous hydrogen. Yet a hydrogen-rich atmosphere apparently makes watery oceans impossible, except perhaps under finely-tuned conditions (Wiktorowicz et al. 2007, Rogers et al. 2011).

between Earth and Uranus: alien worlds

So where are we now in our quest to identify and understand extrasolar planets whose masses place them within an order of magnitude of Earth? The next two figures summarize currently available data on low-mass planets with measured or estimated masses (Figure 6) and those with measured radii (Figure 7). Data were retrieved from the Extrasolar Planets Encyclopaedia (http://exoplanet.eu/catalog.php) in mid-February, 2012, and remain largely up-to-date at the time of this posting. Note that there is little overlap between these two populations – planets with measured masses vs. planets with measured radii – in the ranges of interest here (less than 10 Mea and 4 Rea).

Figure 6. Radial velocity and TTV planets less massive than 32 Mea

Radial velocity observations return only minimum masses, so that actual masses may be 10% to a few hundred percent larger than the ones represented in Figure 6. Transit timing variations (TTV) can be observed only in systems with multiple transiting planets that interact dynamically, so the existing sample is small and limited to planets detected by the Kepler mission.

Figure 7. Transiting planets with radii smaller than 6 Rea

The range of radii shown in Figure 7 spans a great variety of planetary masses, structures, and types, from true terrestrial planets like Kepler-20f, to rocky Super Earths like Kepler 10-b, to gas dwarfs like Kepler-11d, to Hot Neptunes like GJ 436 b. The most massive planet represented in Figure 7 is about 26 Mea, while the least massive is under 1 Mea.

Figures 6 and 7 use the general term “telluric” to refer to planets composed entirely of heavy elements – metal, rock, and ices – without reference to their formation history. Among objects detected by radial velocities only, the upper limit for telluric planets is probably in the range of 4-8 Mea rather than 8-12 Mea, because mass estimates provide minimum values only. Among planets detected by transits only, the upper limit is about 2 Rea, as detailed in Figure 3.

The term “gas dwarf” refers to any planet less massive than about 65 Mea (0.2 Jupiter masses, the lower limit for gas giants) with a significant hydrogen content – i.e., about 1% or more. This definition applies equally to Neptune, at 17.2 Mea, and to Kepler-11f, at about 3 Mea. According to the models presented here, it also applies to GJ 1214 b, despite the frequent use of the term Super Earth to describe this nearby exoplanet. (Nevertheless, some recent studies argue that GJ 1214 b is a telluric planet, without any significant fraction of hydrogen; see, e.g., Berta et al. 2012.)

In Figures 6 and 7, telluric and gas dwarf planets less massive than 10 Mea are not clearly demarcated from more massive planets like Uranus. Indeed, if we had to rely on radius measurements alone, lightweight gas dwarfs would be largely indistinguishable from their higher-mass siblings. If we look at a larger sample of radii, extending into the realm of the inflated Hot Jupiters, we do see two distinct populations – but the dividing line appears well above the mass range of telluric planets:

Figure 8. Confirmed transiting planets with radii < 15 Rea, as of mid-February 2012

In Figure 8, initial letters indicate the approximate radii of Earth, Uranus, Saturn, and Jupiter. We can plainly distinguish a class of low-mass planets (those with radii smaller than 6 Rea) from the class of gas giants (those with radii of 8 Rea and above). Since Figure 8 is limited to confirmed exoplanets listed in the Extrasolar Planets Encyclopaedia, the apparent preponderance of gas giants is an illusion created by detection bias: larger planets are much easier to observe and characterize than smaller, less massive objects, so they continue to dominate the exoplanetary census as they have done since the 1990s. Kepler data nevertheless indicate that low-mass planets dramatically outnumber gas giants, at least in the orbital space probed by transit searches. Similarly, the apparent drop-off in numbers below 2 Rea is another result of detection bias, again because smaller planets are much harder to identify than larger ones.

For the same reason, however, the pronounced gap between 5 Rea and 8 Rea must be real, since a planet of 7 Rea is much easier to detect than a planet of 3 Rea. Thus we see compelling observational evidence for at least part of the toy model of planetology described in Part I of this discussion. Contrary to the understanding of an earlier generation of astronomers, massive planets like Saturn and Jupiter – the bona fide gas giants – are quite distinct from lower-mass planets like Uranus, Neptune, and GJ 436, even though all these objects harbor substantial hydrogen atmospheres. Thus “gas dwarf” seems a more appropriate descriptor for this class of lower-mass objects, which as Kepler demonstrates is extremely common in our Galaxy. Despite its current popularity, “ice giant” seems less suitable, since it seems to exclude smaller, more lightweight icy planets like Kepler-11d and 11f.

our telluric future

Scaled-up versions of our homeworld remain rare to nonexistent within the current sample of extrasolar planets. Candidates breathlessly described as habitable Super Earths on the “science” or “space” pages of major media outlets – GJ 667Cc, Kepler-22b – most likely represent the low-mass tail of the population of gas dwarfs, and are more soberly nicknamed Mini Neptunes. Even reliably rocky objects like CoRoT-7b and Kepler-10b may have had non-terrestrial origins, forming as lightweight gas dwarfs and then suffering complete evacuation of volatiles through thermal evolution.

Given the recent extension of funding for the Kepler mission, we can expect many more planets with radii smaller than 2 Rea to appear in the catalogs of the Extrasolar Planets Encyclopaedia over the next few years. Nevertheless, it will be problematic to determine the masses and bulk compositions of these objects, and our understanding of their formation histories will remain speculative.

Much of the excitement around Super Earths stems from the hope that some of them may support life. By contrast, no gas giant or gas dwarf, regardless of its orbital configuration, is considered capable of biogenesis (Deming 2008). Despite this inherent interest, no consensus has developed regarding surface conditions on a hypothetical telluric planet of 3 to 5 Mea traveling on an Earthlike orbit.

The universal view is that a planet must reach some minimum mass (probably 0.3 to 0.5 Mea) in order to generate a magnetic field, retain a substantial atmosphere, and sustain plate tectonics – all of which seem to be prerequisites for habitability as we know it (Williams 1997, Raymond et al. 2007). Whether there is a maximum mass for habitability, and what it might be, are still matters for debate. Notable studies have argued that the internal structures of rock/metal planets of 2 Mea or more will be incompatible with plate tectonics and planetary magnetic fields (O’Neill & Lenardic 2007, Morard et al. 2011). Under the circumstances, we must admit that the potential habitability of massive telluric planets has not yet been established.

Once again, exoplanetary science brings us to a familiar conclusion: there’s no place like home.

Figure 9. Lunar transit of Earth: photo by Deep Impact/EPOXI, 2008

REFERENCES

Adams ER, Seager S, Elkins-Tanton L. (2008) Ocean planet or thick atmosphere? On the mass-radius relationship for solid exoplanets with massive atmospheres. Astrophysical Journal 673, 1160.

Berta ZK, Charbonneau D, Desert J-M, Miller-Ricci Kempton E, McCullough PR, Burke CJ, Fortney JJ, Irwin J, Nutzman P, Homeier D. (2012) The flat transmission spectrum of the Super-Earth GJ 1214 b from Wide Field Camera 3 on the Hubble Space Telescope. Astrophysical Journal 747, 35.

Deming D. (2008) Quest for a habitable world. Nature 456, 714-715.

Fortney J, Nettelmann N. (2010) The interior structure, composition, and evolution of giant planets. Springer Space Science Reviews 152, 423-447.

Fressin F, Torres G, Rowe JF, Charbonneau D, Rogers LA, Ballard S, et al. (2012) Two Earth-sized planets orbiting Kepler-20. Nature 482, 195-198. Abstract: http://adsabs.harvard.edu/abs/2012Natur.482..195F

Gautier TN, Charbonneau D, Rowe JF, Marcy GW, Isaacson H, Torres G, Fressin F, Rogers LA, et al. (2012) Kepler-20: A Sun-like star with three sub-Neptune exoplanets and two Earth-size candidates. Astrophysical Journal 749, 15. Abstract: http://adsabs.harvard.edu/abs/2012ApJ...749...15G

Hand E. (2011) Super-Earths give theorists a super headache. Nature 480, 302.

Jackson B, Miller N, Barnes R, Raymond SN, Fortney JJ, Greenberg R. (2010) The roles of tidal evolution and evaporative mass loss in the origin of CoRoT-7 b. Monthly Notices of the Royal Astronomical Society 407, 910-922.

Kenyon SJ, Bromley BC. (2006) Terrestrial Planet Formation. I. The transition from oligarchic growth to chaotic growth. Astronomical Journal 131, 1837-1850. Abstract: http://adsabs.harvard.edu/abs/2006AJ....131.1837K

Kuchner MJ. (2003) Volatile-rich Earth-mass planets in the habitable zone. Astrophysical Journal 596, L105-L108.

Leger A, Baglin A, Barge P, Borde P, Defay C, Deleuil M, Rouan D, Schneider J, Vuillemin A. (2004a) Detecting Earth-Uranus Class Planets with the Space Mission COROT. In Penny A, Artymowicz P, Lagrange A-M, Russell S. Planetary Systems in the Universe: Proceedings of the IAU Symposium No. 202.

Leger A, Selsis F, Sotin C, et al. (2004b) A new family of planets? “Ocean Planets.” Icarus 169, 499-504. Abstract: http://adsabs.harvard.edu/abs/2003ESASP.539..253L

Leger A, Grasset O, Fegley B, Codron F, Albarede AF, Barge P, et al. (2011) The extreme physical properties of the CoRoT-7b super-Earth. Icarus 213, 1-11. Abstract: http://adsabs.harvard.edu/abs/2011Icar..213....1L

Marcy GW, Butler RP, Fischer D, Vogt S, Wright JT, Tinney CG, Jones HR. (2005) Observed properties of exoplanets: masses, orbits, and metallicities. Progress of Theoretical Physics Supplement 158.

Morard G, Bouchet J, Valencia D, Mazevet S, Guyot F. (2011) The melting curve of iron at extreme pressures: implications for planetary cores. High Energy Density Physics 7, 141-144.

O’Neill C, Lenardic A. (2007) Geological consequences of super-sized Earths. Geophysical Research Letters 34, L19204.

Poppenhaeger K, Czesla S, Schroter S, Lalitha S, Kashyap V, Schmitt J. (2012) The high-energy environment in the super-earth system CoRoT-7. Astronomy & Astrophysics 541, A26. Abstract: http://adsabs.harvard.edu/abs/2012A%26A...541A..26P 

Raymond SN, Quinn T, Lunine JI. (2004) Making other earths: dynamical simulations of terrestrial planet formation and water delivery. Icarus, 168: 1-17. Abstract: http://adsabs.harvard.edu/abs/2004Icar..168....1R

Raymond SN, Scalo J, Meadows VS. (2007) A decreased probability of habitable planet formation around low-mass stars. Astrophysical Journal, 669: 606-614. Abstract: http://adsabs.harvard.edu/abs/2007ApJ...669..606R

Rogers L, Bodenheimer P, Lissauer JJ, Seager S. (2011) Formation and structure of low-density exo-Neptunes. Astrophysical Journal 738, 59. Abstract: http://adsabs.harvard.edu/abs/2011ApJ...738...59R

von Bloh W, Bounama C, Cuntz M, Franck S. (2007) The habitability of super-Earths in Gliese 581. Astronomy & Astrophysics, 476: 1365-1371.

von Paris P, Gebauer S, Godolt M, Rauer H, Stracke B. (2011) Atmospheric studies of habitability in the Gliese 581 system. Astronomy & Astrophysics 532, A58.

Wiktorowicz S, Ingersoll A. (2007) Liquid water oceans in ice giants. Icarus, 186: 436-447. Abstract: http://adsabs.harvard.edu/abs/2006astro.ph..9723W

Williams DM, Kasting JF, Wade RA. (1997) Habitable moons around extrasolar giant planets. Nature 385, 234-236. Abstract: http://adsabs.harvard.edu/abs/1997Natur.385..234W

Wordsworth R, Forget F, Selsis F, Madeleine J-B, Millour E, Eymet V. (2010) Is Gliese 581d habitable? Some constraints from radiative-convective climate modeling. Astronomy & Astrophysics 522, A22.