Friday, February 28, 2014

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).

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: [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: [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: 
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: [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: [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: [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: [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: [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: 
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.


  1. Nice discussion!

    There's an interesting paper on planetary formation models out today on arXiv:

    This seems to agree that in-situ formation doesn't fully explain things (nor does the planetesimal migration model) and that migration is still needed to explain these compact systems:

    "migration is still a necessary step in the formation of systems of close-in low-mass planets"

    Another VERY interesting finding (though *highly* speculative, it isn't that far from your 1.5%):

    "true Solar System analogs with both a terrestrial planet in the habitable zone and a long-period giant planet companion to protect it occur around only 0.06% of solar-type stars"

    ... but this still means 4 million solar system analogues

    --- Tony Jebson

  2. Yes, I like that study by Kevin Schlaufman - "Tests of In-Situ Formation Scenarios for Compact Multiplanet Systems." The 0.06% estimate is interesting. There's another similar article on planet formation by Sean Raymond and Christophe Cossou -- "No universal minimum-mass extrasolar nebula: evidence against in situ accretion of systems of hot super-Earths" (