A New Design for Planetary Systems

Planetary systems across the Milky Way. Credit: M. Kornmesser, ESO

(full-size image available here)

Two decades of exoplanetary astronomy have shown that system evolution tends to produce two kinds of planets: high-mass objects like Jupiter and Saturn, whose bulk composition is dominated by hydrogen, and low-mass objects like Uranus and Earth, which consist mostly of heavy elements. Observations suggest that individual systems might feature one species to the exclusion of the other: gas giants only, as in Upsilon Andromedae and HIP 14180, or low-mass planets only, as in HD 40307 and HD 69830.

It looks like dwarfs are common, while giants are less so, and the two species are often in conflict.

Yet about 20% of all exoplanetary systems with at least two planets contain examples of both species. Within this group (which has seen considerable growth in the past few years, thanks to the Kepler Mission) just under half contain exactly two planets. In every one of these, the low-mass planet has the inner orbit, and the gas giant has the outer orbit. Among the remainder – i.e., mixed-mass systems with at least three planets – just under half contain exactly one low-mass planet, again as the innermost planet in every case.

At the current reckoning, we have found only 10 systems with at least two low-mass planets and at least one gas giant. That amounts to 1.5% of all exoplanetary systems detected by transit and radial velocity searches. While the percentage is small, it represents an integrated architectural design that happens to characterize our own Solar System. We Earthlings were fortunate enough to evolve in the presence of two reasonably congenial gas giants flanked by a half-dozen low-mass planets in various flavors and sizes.

This unique architectural type was unknown in the extrasolar universe before 2010, when a second low-mass planet was reported in orbit around GJ 876. It remained rare enough to seem anomalous until 2012, when Kepler-25 and Kepler-30 (each containing two low-mass planets and one gas giant) were confirmed, joining GJ 876 and HD 10180. Several more such systems have been announced in the past 12 months, all thanks to Kepler data. The species of gas giants, which I’ve characterized in the past as aloof and predatory, now reveals a fuzzier, more gregarious side, while the clannish low-mass types are proving more accommodating to massive outsiders.  

This post describes four newly confirmed Kepler systems that present a set of variations on the theme of compact, mixed-mass design. All have at least one gas giant and one low-mass planet, and three out of four have at least two low-mass planets. The four host stars range from about 0.96 Solar masses (0.96 Msol) to 1.25 Msol. The corresponding range in spectral types is early G to late F. Although stellar enrichment in metals is significantly associated with the presence of gas giant planets, only one of the four stars is metal-rich (Kepler-88 at +0.20). Among the other three, one has Solar metallicity (Kepler-89) and the other two are sub-Solar (Kepler-87 at -0.17 and Kepler-90 at -0.12).

Notably, the gas giants in all four of these systems occupy the orbital space known as the period valley (Wittenmyer et al. 2010). This is the region between 0.1 and 1 AU, where known extrasolar giants are much less abundant than they are in the hot zone inside 0.1 AU (the range of Hot Jupiters) and somewhat less abundant than in the temperate region between 1 and 1.5 AU (where Earth and Mars orbit in our Solar System). 

In three of these systems, transit timing variations (TTV) permit an estimate of planetary masses, and in two of them, at least one planet has been confirmed by radial velocity (RV) observations. The availability of data on mass through two different observational methods makes these systems unusually valuable for the study of planetary structure, system architecture, and system evolution.

Figure 1. Kepler-88 system architecture (also known as KOI-142)

Kepler-88 is the scene of an exoplanetary trifecta. Its architecture has been revealed by three different channels: transit light curves, TTV, and RV. The resulting numbers provide evidence for two planets: a low-mass object on a short-period orbit and a gas giant on a slightly wider orbit, whose period is exactly double that of the inner planet. This configuration is known as a mean motion resonance, an orbital relationship that links a small fraction of known planet pairs (Goldreich & Schlichting 2014). The most common mean motion resonance is 2:1, which is the type observed here.

Kepler-88b is a puffy gas dwarf, similar in size to Uranus and Neptune (but probably less massive), while Kepler-88c is a gas giant somewhere between Saturn and Jupiter in mass. Both are locked in a precise spin near the brink of their host star’s gravity well.

Table 1. Kepler 88 system parameters (also known as KOI-142)

Column 2 gives the mass in Earth units (two different values are available for Kepler-88c); Column 3 gives the radius in Earth units; Column 4 gives the semimajor axis in astronomical units (AU); Column 5 gives the orbital eccentricity; Column 6 gives the period in days; and Column 7 gives an estimate of the equilibrium temperature (Teq) provided by the Kepler site.

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Kepler-88b orbits very close to its host star, in a period of about 11 days. Because the star is only 60% as luminous as our Sun, the planet’s equilibrium temperature is just 12% higher than that of Mercury. Since the early Kepler results became available, it has been apparent that this object (originally known as KOI-142.01) experiences large TTVs – indeed, their amplitude is the largest ever recorded among Kepler candidates. Given the absence of other transiting planets in this system, at least on periods shorter than a few hundred days, it has long been evident that one or more non-transiting companions must be responsible for these TTVs.

David Nesvorny and colleagues used the Kepler-88 transit data to calculate the characteristics of the implied planetary system. They found a mass about 8.7 times Earth (8.7 Mea) for Kepler-88b, equivalent to half the mass of Neptune. They also confirmed the presence of a second planet, Kepler-88c, with a mass about 0.63 times Jupiter (0.63 Mjup, equivalent to 199 Mea) and an orbital period just over 22 days.

At the same time, S.C. Barros and colleagues conducted RV observations of Kepler-88 that also confirmed the presence of Kepler-88c, finding an orbital period identical to that returned by Nesvorny’s group. However, their estimate of the object’s minimum mass (0.76 Mjup / 242 Mea) was notably larger than the mass calculated with TTVs. Nevertheless, Barros’ group presented their estimate with very generous error margins, which permit a range of masses between 200 and 343 Mea for Kepler-88c. Thus the findings of the two studies are marginally consistent.

The tendency for mass values determined by RVs to be systematically larger than those determined by TTVs has been discussed in a recent study by Lauren Weiss and Geoff Marcy (Weiss & Marcy 2014). They argue that the discrepancy is unlikely to result from a bias in the RV data. They suggest two possibilities: 1) TTV-derived masses are low because other, undetected planets in the same system are “damping” the TTVs, or 2) systems with the compact architecture that is most likely to produce TTVs (e.g., Kepler-11) have “lower-density planets than non-compact systems.” Whatever the explanation may be, it remains true that we have only TTV data to characterize the masses of the small planets detected by Kepler. Sadly, such data are available only for a small fraction of systems. Nor can we hope to obtain RV data on any of these planets, since they are so distant that no existing instrument can measure the minuscule variations that they induce in their host stars’ motion. If the TTV data are wrong, then our current understanding of planet structure loses much of its support.

For Kepler-88c, at least, the discrepancy between the two mass determinations does not substantially change our picture of the system. We see an architecture somewhat reminiscent of a few other exoplanetary systems near and far: 55 Cancri, HD 3651, and Kepler-30. Each of them contains a planet about the mass of Uranus on a short-period orbit, plus one or more gas giants in the period valley.

Neither photometric nor RV data provide evidence of any other planets around Kepler-88, but it seems unlikely that the orbital space is simply empty outside 0.15 AU. Additional low-mass planets that (like Kepler-88c) are non-coplanar with Kepler-88b would be invisible to both search methods.

Also open are questions about the origins of this system: how did the known planets form and become entangled in their present relationship? With luck, some investigators will address this problem soon.

Figure 2. Kepler-89 system architecture (also known as KOI-94)

Kepler-89 looks like an augmentation or upgrade of Kepler-88. Instead of two planets we have four, all transiting and all on orbits smaller than Mercury’s. As in Kepler-88, we see a low-mass planet with a puffy radius, Kepler-89c, completing an orbit in just over 10 days. Immediately outside is Kepler-89d, a gas giant the same size as Jupiter on an orbit of about 22 days. But there’s more. Immediately inside planet c is an even smaller object, Kepler-89b, which is small enough to be rocky and close enough to its host to sustain a lava ocean. Many similar Hellworlds have been reported. Immediately outside planet d, the gas giant, is another puffy dwarf, Kepler-89e: a familiar planetary type in a configuration almost unknown outside our Solar System.

By this I mean an arrangement in which one or more low-mass planets orbit exterior to one or more gas giants. The Solar System exemplifies this architecture in the nested orbits of Jupiter, Saturn, Uranus, and Neptune – two gas giants encircled by two low-mass planets. To date, however, out of several hundred exoplanetary systems, only four offer scaled-down analogs: Kepler-30, Kepler-87, Kepler-89, and GJ 876. Space-based transit surveys have clearly been more effective than RV in exposing this rare design.

Table 2. Kepler-89 system parameters (also known as KOI-94)

Column 2 gives the mass in Earth units; Column 3 gives the radius in Earth units; Column 4 gives the semimajor axis in astronomical units (AU); Column 5 gives the period in days; and Column 6 gives an estimate of the equilibrium temperature (Teq) in Kelvin. Most of the quantities in Column 2, and all in Column 3, have two alternative estimates. M indicates values from Masuda et al. (2013). W indicates values from Weiss et al. (2013).

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Two different studies have tried to define the masses of these planets, as shown in Table 2. Their results are even less consistent than the conflicting values for Kepler-88, providing another example of the mismatch between TTV and RV results. In this case, the two groups also worked from slightly different values for stellar mass and (apparently) radius, but this disparity cannot explain the wide divergence of their findings.

Using TTVs and a stellar mass of 1.25 Msol, Masuda and colleagues estimated Kepler-89d at about 52 Earth masses (52 Mea). This measurement places it right on the threshold of the gas giant population, within a sparsely attested mass range. For Kepler-89c and 89-e, which flank the orbit of 89-d, they found masses in the range of Uranus and Neptune.

Using RV data and a stellar mass of 1.28 Msol, Weiss and colleagues found that Kepler-89d was heavier than Saturn, at about 106 Mea: this is more than double the result from the other study. They also found larger masses for the two adjacent planets, in particular 89-e, which in their analysis would be double the mass of Neptune.  

As with Kepler-88, the discrepancy between these studies does not change our overall picture of the system. Both models of Kepler-89d present a planet whose bulk composition is dominated by hydrogen, consistent with a gas giant like Saturn rather than a more metallic planet like Neptune. The two adjacent companions also remain more or less consistent with our understanding of gas dwarfs, even if the high-mass model of Kepler-89e stretches the limits.

Masuda et al. did not estimate a mass for the innermost planet, which does not participate in the TTVs. Although Weiss et al. present a mass range centered on 10 Mea, they concede its unreliability. We are better informed by the radius measurement: whether at 1.6 or 1.7 Rea, the tight orbit and hot primary star of Kepler-89b point to a bare rock of about 7 to 10 Mea – a Super Hellworld.  

We also have an excellent understanding of the relative orbital alignment of the four known planets. Because all four are observed in transit, Kepler-89 must be a very “flat” system, with its planets sharing the same orbital plane (see Mass Matters). In addition, a mutual eclipse of two planets has been observed, and the Rossiter-McLaughin effect has been measured during a transit of the largest planet (Masuda et al. 2013). All evidence agrees that Kepler-89 is a placid, well-aligned system. A history of major dynamic instabilities seems unlikely.

Figure 3. Kepler-87 system architecture

Kepler-87 is a sibling of Kepler-89. Again we see four planets, with one low-mass planet near 0.1 AU and another, smaller companion orbiting inside. In this system, however, neither of the inner planets (d, e) is large enough to accommodate a substantial hydrogen envelope. Both must be rocky Hellworlds. As in Kepler-89, the third planet is a gas giant, though it is much farther from the star and not engaged in a mean motion resonance. With a period of about 115 days, this planet (b) has a semimajor axis wider than Mercury’s. The fourth planet (c) is a puffy low-mass object with a semimajor axis within 10% of that of Venus.

Table 3. Kepler 87 system parameters

 

Column 2 gives the mass in Earth units; Column 3 gives the radius in Earth units; Column 4 gives the semimajor axis in astronomical units (AU); Column 5 gives the orbital eccentricity; Column 6 gives the period in days; and Column 7 gives an estimate of the equilibrium temperature (Teq) in Kelvin provided by the Kepler site.

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Ofir and colleagues (2014) confirmed that the two outer planets experience TTVs, which permit calculation of their masses. They found that Kepler-87b is slightly more massive than Jupiter, as well as slightly larger. Kepler-87c, however, appears unusually puffy for its mass, which is only half that of Uranus. Although no RV studies have been attempted (and thus no competing data are involved), it is impossible not to consider these findings in light of Weiss and Marcy 2014. Perhaps the TTVs are providing a lower mass boundary rather than a precise figure.

As Ofir’s group observes, “The relatively high multiplicity of this system [is] notable against the general paucity of multiple systems in the presence of giant planets like Kepler-87 b.”

Figure 4. Kepler-90 system architecture (also known as KOI-351 / KIC 11442793)

In many ways, Kepler 90 is the most remarkable of this quartet of variegated systems, since it offers the jaw-dropping prospect of seven transiting planets within a period of 332 days. Still better, Kepler 90 presents diverse radii, from an Earth-size planet (c) to rivals of Saturn (g) and Jupiter (h). If only Pythagoras, or for that matter Johannes Kepler himself, could have glimpsed this array!

Table 4. Kepler 90 system parameters (also known as KOI-351 / KIC 11442793)

Column 3 gives the radius in Earth units; Column 4 gives the semimajor axis in astronomical units (AU); Column 5 gives the orbital period in days; and Column 6 gives an estimate of the equilibrium temperature (Teq) in Kelvin. All values were retrieved from the Kepler site in December 2013.

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Yet we have no information on any of the planets’ masses, except for hints provided by radius and estimated equilibrium temperatures. Large TTVs have been reported for planet g, indicating strong gravitational interactions with planet h, but so far these data have not yielded any mass estimates for either planet (Cabrera et al. 2014). Nor have any RV studies been reported. Fortunately, the latest article by Jack Lissauer’s group offers the news that a detailed analysis of the system is in preparation by Eric Agol and colleagues. We’ll wait in anticipatory ignorance until it appears.

Meanwhile, we can contemplate the picture of a strange sibling to our own Solar System, with seven planets instead of eight, and all of them packed within a space equivalent to the Earth’s orbit around the Sun. The two candidate gas giants may be similar in mass to our own pair, but they are just as likely to be less massive. Cabrera and colleagues found that both planets would be dynamically stable as long as they follow circular orbits and are less than 5 Mjup. The same group also suggested that planet g is significantly less massive than planet h, perhaps close to Neptune's mass (Cabrera et al. 2014). Among the low-mass planets, the three largest (d, e, f) are almost certainly less massive than Uranus and Neptune, and the remaining two are probably similar in mass to Earth and Venus. Again we glimpse the presence of truly cosmic themes and variations.

Cabrera and colleagues explored the possibility that Kepler-90g has a moon, given some blips in the light curves, but they found this prospect unlikely. At least theoretically, the outermost planet, Kepler-90h, is capable of hosting a satellite system comparable to those of Jupiter and Saturn, as it is far enough from the host star to retain moons over the system’s lifetime. Any such moons, however, would be unlikely to sustain Earthlike conditions, even if they were big enough to sustain an atmosphere. The reason is that the host star is hotter, bigger, and more massive than our Sun (5994 K, 1.166 Rsol, 1.118 Msol), guaranteeing a thermal environment inconsistent with liquid water even under appropriate atmospheric pressure.  

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The four systems discussed here call for a new look at theories of planet formation and secular evolution. All four systems are closely packed, and three out of four are co-planar, arguing against a history of planet scattering. Despite the current popularity of theories of in situ formation for low-mass planets, the close proximity of the gas giants to their low-mass companions in these systems is – as far as my limited understanding can tell me – inconsistent with in situ models. That leaves us with the now old-fashioned scenario of accretion followed by migration. I’m eager to see a big-picture analysis of multiplanet system architectures and their likely origins, something along the lines of the work by Edward Thommes a few years back (2008a, 2008b).

REFERENCES

Barros SCC, Díaz RF, Santerne A, Bruno G, Deleuil M, Almenara J-M, Bonomo AS, Bouchy F, Damiani C, Hébrard G, Montagnier G, Moutou C. (2014) SOPHIE velocimetry of Kepler transit candidates XI. KOI-142 c: first radial velocity confirmation of a non-transiting exoplanet discovered by transit timing. Astronomy & Astrophysics 561, L1. Abstract: http://adsabs.harvard.edu/abs/2014A%26A...561L...1B [Kepler-88] 
Cabrera J, Csizmadia S, Lehmann H, Dvorak R, Gandolfi D, Rauer H, Erikson A, Dreyer C, Eigmüller P, Hatzes A. (2014) The Planetary System to KIC 11442793: A Compact Analogue to the Solar System. Astrophysical Journal 781, 18. Abstract: http://adsabs.harvard.edu/abs/2013arXiv1310.6248C [Kepler-90] 
Goldreich P, Schlichting HE. (2014). Overstable librations can account for the paucity of mean motion resonances among exoplanet pairs. Astronomical Journal 147, 32. 
Lissauer JJ, Marcy GW, Bryson ST, Rowe JF, Jontof-Hutter D, Agol A, Borucki WJ, Carter JA, Ford EB, Gilliland RL, Kolbl R, Star KM, Steffen JH, Torres G. (2014) Validation of Kepler’s multiple planet candidates. II: Refined statistical framework and descriptions of systems of special interest. Astrophysical Journal, in press. Abstract: http://adsabs.harvard.edu/abs/2014arXiv1402.6534R. 
Masuda K, Hirano T, Taruya A, Nagasawa M, Suto Y. (2013) Characterization of the KOI-94 system with transit timing variation analysis: Implication for the planet-planet eclipse. Astrophysical Journal 778, 185. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...778..185M [Kepler-89] 
Nesvorny D, Kipping D, Terrell D, Hartman J, Bakos GA, Buchhave LA. (2013) KOI-142, the king of transit variations, is a pair of planets near the 2:1 resonance. Astrophysical Journal 777, 3. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...777....3N [Kepler-88] 
Ofir A, Dreizler S, Zechmeister M, Husser TO. (2014) An independent planet search in the Kepler dataset II. An extremely low-density super-Earth mass planet around Kepler-87. Astronomy & Astrophysics 561, A103. Abstract: http://adsabs.harvard.edu/abs/2013arXiv1310.2064O [Kepler-87] 
Pierens A, Nelson RP. (2008) Constraints on resonant-trapping for two planets embedded in a protoplanetary disc .Astronomy & Astrophysics 482, 333-340. 
Schmitt JR, Wang J, Fischer DA, Jek KJ, Moriarty JC, Boyajian TS, Megan E. Schwamb, Chris Lintott, Smith AS, Parrish M, Schawinski K, Lynn S, Simpson R, Omohundro M, Winarski T, Goodman SJ, Jebson T, Lacourse D. (2013) Planet Hunters VI: The first Kepler seven-planet candidate system and 13 other planet candidates from the Kepler archival data. Astrophysical Journal, in press. Abstract: http://adsabs.harvard.edu/abs/2013arXiv1310.5912S [Kepler-90] 
Thommes EW, Bryden G, Wu Y, Rasio FA. (2008a) From mean-motion resonances to scattered planets: Producing the Solar System, eccentric exoplanets and Late Heavy Bombardments. Astrophysical Journal 675, 1538-1548. Abstract. 
Thommes EW, Matsumura S, Rasio FA. (2008b) Gas disks to gas giants: Simulating the birth of planetary systems. Science 321, 814-817. Abstract; additional content. 
Weiss LM, Marcy GW, Rowe JF, Howard AW, Isaacson H, Fortney JJ, Miller N, Demory BO, Fischer DA, Adams ER, Dupree AK, Howell SB, Kolbl R, Johnson JA, Horch EP, Everett ME, Fabrycky DC, Seager S. (2013) The mass of KOI-94d and a relation for planet radius, mass, and incident flux. Astrophysical Journal 768, 14. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...768...14W [Kepler-89] 
Weiss LM, Marcy GW. (2014) The mass-radius relation between 63 exoplanets smaller than 4 Earth radii. Astrophysical Journal Letters 783, L6. Abstract: http://arxiv.org/abs/1312.0936 
Wittenmyer RA, Simon J. O’Toole, H. R. A. Jones, C. G. Tinney, R. P. Butler, B. D. Carter, and J. Bailey. (2010) The frequency of low-mass exoplanets. II. The “Period Valley.” Astrophysical Journal, 722:1854–1863.
 

The Year Kepler Climaxed

“The diversity of the phenomena of nature is so great, and the treasures
hidden in the heavens so rich, precisely in order that the human mind
shall never be lacking in fresh enrichment.” Johannes Kepler

Apart from a few peaks and one big valley, the past year in exoplanets continued the momentum built by the Kepler Mission over the past three years. These were among the major developments of exoplanetary astronomy in 2013:

• Kepler Mission scientists finally reported a plausibly terrestrial planet orbiting in the classical habitable zone of a Sun-like star. In fact, over the course of the year they reported three such planets, each transiting and each with a distinct claim to the title of Most Earthlike Exoplanet: Kepler-62e (Kaltenegger et al. 2013), Kepler-62f (Borucki et al. 2013), and Kepler-69c (Barclay et al. 2013). With these discoveries, Kepler can justly say “mission accomplished.”
• The best candidate of the lot is Kepler-62f, a probable rocky object whose radius is just 1.41 times that of Earth (1.41 Rea). Its host is an orange star of spectral type K2, about 69% as massive as our Sun (0.69 Msol). With an orbital period of 267 days, Kepler-62f traces the outer edge of the system habitable zone. Four more transiting planets, all smaller than 2 Rea, orbit closer to the star. There’s one drawback, though. It hinges on the argument that only rocky objects with a minimal percentage of ices can sustain a carbon cycle or plate tectonics (Alibert 2013). A purely rocky object with the same radius as Kepler-62f will be about 3.5 times as massive as Earth (3.5 Mea). Much research cautions that such a massive object might be unlikely to support plate tectonics, potentially ruling out seas as well as a carbon cycle. Despite its small radius, then, Kepler-62f may still be too big to sustain life. The other two candidates are even worse: Kepler-62e (which orbits just inside Kepler-62f) has a radius of 1.61 Rea, implying a rocky mass of 6 Mea, while Kepler-69c has a radius of 1.70 Rea, implying 8 Mea.
• Just one month after breaking the happy news about Kepler-62, the Kepler crew reported disaster: the space observatory itself suffered catastrophic equipment failure, ending the mission. The exoplanet community found consolation by reflecting that Kepler managed to complete its originally scheduled scientific mission and has been, by any measure, a revelatory success.
• And those Kepler discoveries keep rolling in, since the available data are so rich that they will continue to yield new planets for months, if not years, to come. Among the most striking publications of the past few months are a group of mixed-mass systems numbered Kepler-87 through Kepler-90, which collectively illustrate a system architecture barely attested in the past: a closely packed assemblage of low-mass planets with one or more gas giants tucked in their midst. With luck I’ll write about them in 2014.
• As predicted, the census maintained by the Extrasolar Planets Encyclopaedia surged past 1000 in 2013, and is on course to reach 1100 during 2014. Along with this burgeoning census, the tendency for data to outrun theory continues apace.
• The general consensus that planets form by accretion and subsequent migration, such that the local ice line plays a major role in system architectures, has been shaken by the Kepler data on compact multiplanet systems. Doubts had been rumbling for the past few years, and in 2013, thanks to some widely discussed publications, the rumbles got louder. The most popular alternative scenario for forming an inner system full of low-mass planets is now in situ assembly (Hansen & Murray 2012, Chiang & Laughlin 2013, Hansen & Murray 2013). More exotic solutions have also been proposed, such as a combination of gravitational instability, “tidal downsizing,” and core accretion (Galvagni & Mayer 2013, Ogihara et al. 2013). But the “classic migrationists” (my neologism) have already begun to strike back (Alibert et al. 2013, Hasegawa & Pudritz 2013) by producing new models that seem capable of accounting for the architectures discovered by Kepler. This clash of theories should provide interesting blog fodder in 2014.
• Finally, the many controversies surrounding proposed planetary systems in the Sun’s back yard are no nearer to resolution than they were last year. My annual round-up for 2012 noted doubts and arguments about GJ 667C, GJ 676A, and Tau Ceti; later posts discussed Fomalhaut, Epsilon Eridani, and Alpha Centauri B. All the question marks and asterisks remain in place.

National Geographic led its review of the year in science with this artist’s view of Kepler-62f

So then! As the new year begins, we can point to 1055 confirmed exoplanets, including one or two that may have a slim chance of supporting environments that resemble certain places on Earth or Mars. Talk about wow!

Will the coming year be mostly about consolidating the evidence and revising the theories, or will we have pleasant surprises that compare with the circumbinary planets of 2011-2012 or the bona fide Super Earths of 2013? Stay tuned.

Kepler-69c was also proposed as a habitable Super Earth, but it’s probably too hot, too big,
and nowhere near as seductive as this artist’s view.

REFERENCES

Alibert Y. (2013) On the radius of habitable planets. Astronomy & Astrophysics, in press.
Alibert Y, Carron F, Fortier A, Pfyffer S, Benz W, Mordasini C, Swoboda D. (2013) Theoretical models of planetary system formation: mass vs semi-major axis. Astronomy & Astrophysics 558, A109. Abstract: http://adsabs.harvard.edu/abs/2013A%26A...558A.109A

Barclay T, Burke CJ, Howell SB, Rowe JF, Huber D, Isaacson H, et al. (2013) A Super-Earth-sized planet orbiting in or near the habitable zone around a Sun-like star. Astrophysical Journal 768, 101.

Borucki WJ, Agol E, Fressin F, Kaltenegger L, Rowe J, Isaacson H, et al. (2013) Kepler-62: A Five-Planet System with Planets of 1.4 and 1.6 Earth Radii in the Habitable Zone. Science Express 18 April 2013. 10.1126/science.1234702 http://www.sciencemag.org/content/early/recent.

Chiang E, Laughlin G. (2013) The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths. Monthly Notices of the Royal Astronomical Society 431, 3444-3455. Abstract: http://adsabs.harvard.edu/abs/2013MNRAS.431.3444C

Galvagni M, Mayer L. (2013) Early evolution of clumps formed via gravitational instability in protoplanetary discs: precursors of Hot Jupiters? Monthly Notices of the Royal Astronomical Society, in press.

Hansen BM, Murray N. (2012) Migration then assembly: Formation of Neptune-mass planets inside 1 AU. Astrophysical Journal 751, 158. Abstract: http://adsabs.harvard.edu/abs/2012ApJ...751..158H 

Hansen BM, Murray N. (2013) Testing in situ assembly with the Kepler planet candidate sample. Astrophysical Journal 775, 53. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...775...53H

Hasegawa Y, Pudritz RE. (2013) Planetary populations in the mass-period diagram: A statistical treatment of exoplanet formation and the role of planet traps. Astrophysical Journal 778, 78. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...778...78H

Kaltenegger L, Sasselov D, Rugheimer S. (2013) Water-planets in the habitable zone: Atmospheric chemistry, observable features, and the case of Kepler-62e and -62f. Astrophysical Journal Letters 775, L47.

Ogihara M, Inutsuka S, Kobayashi H. (2013) Crowding out of giants by dwarfs: An origin for the lack of companion planets in Hot Jupiter systems. Astrophysical Journal Letters 778, L9.

 

 

Puffy Planets

Hot air balloons over Malqata, Egypt, site of the jubilee palace of Amenhotep III (ca. 1350 BC)

Recent work by Eric Lopez and Jonathan Fortney brings welcome clarity to the bewildering array of Kepler transit data on small planets. These esteemed planetologists just circulated a preprint entitled “Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition” (hereafter LF13). It addresses questions that have surfaced several times in this blog: How can we distinguish Super Earths from Neptune-like exoplanets? And what is the likely composition of each species? That topic is explored here, here, here, here, and most recently here.

puff threshold

Using the results from a large ensemble of thermal evolution models, LF13 draw a physically motivated boundary between true Super Earths (which are scaled-up versions of Earth, consisting only of heavy elements) and planets like Uranus and Neptune (which maintain at least a small percentage of their mass in a hydrogen/helium (H/He) envelope).

As Lopez and Fortney conclude, “for most of Kepler’s Neptune and sub-Neptune sized planets, radius is quite independent of planet mass and is instead a direct measure of bulk H/He envelope fraction.” They offer a method to estimate the likely composition of low-mass transiting planets simply on the basis of radius. This is an extremely useful contribution, because for the vast majority of Kepler candidates, radius and orbital period are the only reliable information we have.

LF13 find that the maximum size for a typical rocky planet is 1.75 Earth radii (Rea). Although some planets more massive than 5 Earth masses (Mea) may have radii larger than 2 Rea because they consist primarily of ices, with no appreciable contribution from H/He, the vast majority of planets with a substantial rocky component must be smaller than 1.75 Rea. It follows that most planets larger than 2 Rea must have some percentage of H/He in their atmospheres. A well-known example is Kepler-22b, announced in 2011 and sometimes described as a “habitable Super Earth.” According to LF13, however, this object would be a miniature version of Uranus, given its radius of 2.2 Rea.

LF13 describe a hypothetical planet with a radius of 2 Rea and an orbit within its system’s classical habitable zone. Assuming a rocky core and an overall mass of 5 Mea, 0.5% of the planet’s total mass must be H/He. This tiny fraction creates an atmospheric pressure of about 20 kilobars of H/He, which as LF13 say is 20 times higher than the pressure at the bottom of the Marianas Trench, the deepest fissure in Earth’s global ocean. In the habitable zone, such an atmosphere will produce surface temperatures around 3000 K, more than 10 times higher than the mean surface temperature on Earth (288 K). This environment is hostile to liquid water and carbon-based life.

Figure 1. Puffy Planets. Selected transiting planets between 3 and 7 Earth radii, with estimated fractions of hydrogen/helium (H/He). All values except for Neptune are taken from Lopez & Fortney 2013. The approximate H/He fraction for Neptune is inferred from their Table 3. 

The astronomer Robin Wordsworth has presented a sceario in which a rocky planet of 5 Mea with a dissipating hydrogen atmosphere, orbiting a Sun-like star at a distance of 2.5 AU (i.e., well outside the classical habitable zone, near the system ice line), will experience a transient but potentially significant epoch during which it might sustain liquid water. However, this optimistic model seems to suffer from fine-tuning. As even Wordsworth concludes, when it comes to hydrogen, “usually, either far too much or too little of it is present” (Wordsworth 2012). For Kepler planets larger than 2 Rea, it’s “far too much.”

degeneracy on ice

A few years ago, virtually everyone assumed that some subset – maybe the majority – of Super Earths would be “Water Planets” or “Ocean Planets.” The consensus has changed dramatically since the discovery of the Kepler-11 system in 2011. Now investigators routinely model rocky planets with H/He envelopes, while the likelihood of Water Planets is questioned. Nevertheless, LF13 accept the possibility of rock/ice planets, noting that a planet of 10 Mea consisting of 20% rock/metal and 80% water would have a radius of 2.7 Rea. They concede that their model suffers from the same “degeneracy” as previous efforts when it comes to distinguishing icy planets from gassy planets. In other words, the same radius could correspond to very different compositions.

For example, 55 Cancri e has a measured mass and radius of 8.3 Mea and 1.99 Rea, respectively, and is sometimes proposed as a Water Planet (Dragomir et al. 2013). Since its temperature is about 2000 K and its age is around twice that of the Solar System, Diana Dragomir and colleagues argue that a trace hydrogen envelope would have dissipated eons ago, while a substantial fraction of ices might remain.

Without providing a rationale, LF13 model 55 Cancri e as a rocky object instead, proposing a modest H/He envelope amounting to only 0.14% of its bulk composition. However, they leave open the possibility that other planets between 2 and 3 Rea might qualify as Water Planets (and thus Super Earths), as long as they have a large enough fraction of ices in their composition.

If they exist, planets that contain a significant fraction of water or high-pressure ices, but lack a H/He envelope, are of great scientific interest. Nevertheless, they appear to have little relevance for astrobiology. A growing consensus holds that, in order to maintain bodies of liquid water, a rocky planet requires both plate tectonics and a carbon cycle. Neither is possible on the Water Planets proposed by contemporary theorists. An object of 5 Mea whose bulk composition is 25% water will have a differentiated structure, with a rock/metal core surrounded by a layer of high-pressure ice thousands of kilometers thick. This layer would block chemical interactions between atmospheric gases and heavy elements in deeper strata, preventing the development of a carbon cycle (Lammer et al. 2010, Alibert 2013). Yann Alibert finds that a planet of Earth mass and composition can maintain both a global ocean and a carbon cycle only if its water content is 2% or less, with the maximum percentage decreasing with increasing mass (Alibert 2013).

In addition, many astrobiologists assume that plate tectonics requires liquid water rather than ice to lubricate continental plates (Korenaga 2010, Lammer et al. 2010). Also widely endorsed is the argument that solid objects above a few times the mass of the Earth, even if they somehow retained thin envelopes of water, cannot support plate tectonics at all (O’Neill & Lenardic 2007, Morard et al. 2011, Stein et al. 2013). Ocean Planets look less and less attractive than they used to.

low-mass cousins

To illustrate their model, LF13 present a table summarizing all confirmed exoplanets smaller than Saturn with reliably measured masses and radii. Although this sample is too small to yield robust statistics, suggestive trends are evident. The six planets with radii between 1 and 2 Rea (where LF13 place the transition from Super Earths to Neptune-like planets) range in mass from 1.9 to 8.45 Mea, with a mean of 5.8 Mea and a median of 6 Mea. The corresponding mass values are remarkably similar for the six planets between 2 and 3 Rea, which LF13 call “sub-Neptunes” and which others have shown to represent the most numerous population of Kepler planets (Petigura et al. 2013). For these planets, the range in mass is 2 to 7.86 Mea, the mean is 5.6 Mea, and the median is 6.7 Mea. According to LF13, objects in this group have mass fractions of H/He ranging from 0.31% to 5%, substantially smaller than the fractions for Uranus and Neptune.

For the 12 planets between 3 and 7 Rea, which by all agreement have H/He envelopes, masses range widely, rising from 7.3 Mea to 68.6 Mea, with a mean of 20.6 Mea and a median of 16.8 Mea. However, confirmed exoplanets are sparse between 25 and 60 Mea; LF13 offer only three examples, none of them between 27 and 40 Mea. Such a gap in the distribution justifies removal of the most obvious outlier, CoRoT-8b. With a mass of almost 70 Mea, CoRoT-8b resembles a gas giant, but its unexpectedly small radius of 6.38 Rea implies a composition dominated by heavy elements. LH13 list its bulk composition as only one-third H/He. If we eliminate CoRoT-8b from the sample of Neptune-like objects, the mass range becomes 7.3 to 26.2 Mea and the mean becomes 14.9 Mea, while the median remains almost the same at 16.3 Mea. A representative sample of this group is illustrated above in Figure 1.

inner system regulars

The latest Kepler data show that puffy planets of 3 to 7 Rea are common within 1 astronomical unit (AU) of Sun-like stars. Objects in this range of radii, as we just saw, have a median mass very similar to Neptune’s. A number of recent studies have calculated the distribution of these planets and their smaller, lower-mass siblings.

Andrew Youdin found that 3 Rea marks a clear divide in the distribution of low-mass planets on short-period orbits (< 50 days) around Sun-like stars (Youdin 2011). Planets of this approximate radius are extremely rare on periods shorter than 7 days, whereas both smaller and larger planets are plentiful in the same orbital space. Youdin interpreted this distribution as a probable result of the thermal evolution of H/He envelopes around low-mass planets that migrate to the immediate vicinity of their host stars. Planets of the lowest mass (less than about 8 Mea) will lose their envelopes completely, leaving bare rocky spheres smaller than 2 Rea. More massive planets with more substantial cores can sustain lightweight atmospheres against stripping, resulting in final radii larger than 3 Rea.

In a more recent analysis using a larger set of Kepler data, Subo Dong and Zhaohuan Zhu characterize the planet population within 0.75 AU of Sun-like stars. This boundary corresponds to an orbit of about 250 days, similar to the orbit of Venus (225 days). They find that planets smaller than 4 Rea have a relatively flat distribution at periods longer than 10 days, whereas planets of 4-8 Rea have a steadily increasing distribution at longer periods (Dong & Zhu 2013). In general, they observe, the relative fraction of “big planets” (those of 3 Rea or more) increases with increasing period, but the increase is most pronounced for planets smaller than 10 Rea (i.e., Saturn-size or less).

Dong and Zhu provide an illuminating overview of the cumulative frequencies of planets of all sizes in the Kepler sample. Within 0.75 AU, planets of 1-2 Rea (which they call “Earth-size”) have a frequency of 28%; those of 2-4 Rea (“super-Earth-size”) have a very similar frequency, at 25%; those of 4-8 Rea (“Neptune-size”) are far less common, at 7%; while those larger than 8 Rea (“Jupiter-size”) are the least common of all, at only 3%.

The relative abundance of dwarfs and rarity of giants has been widely observed. It is rapidly becoming a cornerstone of exoplanetary science, analogous to the abundance of lower-mass stars (M dwarfs) versus their higher-mass (O and B-type) siblings.

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