How Weird Is Our Solar System?

Figure 1.  Io & Europa transit Jupiter. Image credit: NASA/Michael Benson

From the start, the search for extrasolar planets has been motivated by one central desire: to find other worlds like Earth. For just as long, that desire has been thwarted by the absence of any techniques with enough sensitivity to detect them.

The most consistently successful search method – radial velocity observations, which track stellar wobbles induced by gravitational perturbations of orbiting planets – still lacks the precision needed to identify an Earth-mass world on an Earthlike orbit. The other reliably fruitful approach – photometric surveys, which record the slight dimming of starlight caused by a planet transiting the face of its host – is best suited to finding big planets on orbits much shorter than 365 days. Only space-based telescopes are sensitive enough to detect transiting planets as small as Earth, and to date only the Kepler Mission has demonstrated the ability to do so. Whether Kepler will actually find an Earth-size planet on a habitable orbit remains to be seen.

To date, our most prolific techniques have returned a large census of planets, of which 90% are at least as massive as Uranus and 75% orbit their host stars closer than Mars orbits our Sun. Given these parameters, the orbital dynamics of most known extrasolar systems would prevent the survival of an Earth twin.

In other words, 20 years of exoplanet searches have been very successful at identifying planetary systems where Earthlike planets can’t possibly exist. It seems only fair to ask just how weird our Solar System really is.

solar power couple

The defining structural characteristic of our system is evidently the orbital configuration of Jupiter and Saturn. From a Galactic perspective, these are two small gas giant planets traveling on circular orbits with semimajor axes between 5 AU and 10 AU, without any massive planets on interior orbits. Since the 18th century, astronomers have recognized that the ratio of the two giants’ orbital periods (almost but not exactly 5:2) plays a key role in the dynamical architecture of our system.

Figure 2. If Jupiter & Saturn were skyscrapers in midtown Manhattan. . .

  

Of the two giant planets, nevertheless, Jupiter has played the dominant role in creating and maintaining Earth’s life-bearing environment. With a mass more than 300 times larger than Earth’s, and an orbital period more than 12 times longer, Jupiter has affected our existence in the following ways:

1. By stirring collisions among rocky planetesimals at primordial times and driving their accretion into an ensemble of full-grown telluric worlds, including Earth (Thommes et al. 2008, Raymond et al. 2009).
2. By diverting icy planetesimals from outside the region of telluric planet formation into mergers with the inner-system planets, creating Earth’s global ocean (Raymond et al. 2009).
3. By acting as a gravitational shield at later times and preventing life-destroying impacts by asteroids and comets (Horner & Jones 2008).

 A Jupiter-like planet would be a signpost for a system like our own, and potentially a biomarker for alien life. How, then, can we generalize from the Solar System to define such concepts as “Jupiter-like,” “Jupiter analog,” and “Jupiter twin?”

Figure 3. Simulated view of our Solar System from 10 parsecs, through a hypothetical 4-meter spaceborne telescope with a sunshade to block the central star’s light. Counterclockwise from upper left, the visible planets are Saturn, Venus, Earth, and Jupiter. Credit: Turnbull et al. 2012

reading the right signs

In the strictest terms, a Jupiter twin would be a planet more than 300 times as massive as Earth with a deep hydrogen-helium atmosphere, orbiting a G-type star at a semimajor axis of 5.2 AU and an eccentricity smaller than 10%, without any planets larger than Earth on smaller orbits. These characteristics find a near match in just one of the 770 exoplanets currently listed in the Extrasolar Planets Encyclopaedia.

That planet is HD 13931 b, a gas giant twice as massive as Jupiter announced in 2010 (Howard et al. 2010). Its parent star, located about 44 parsecs (144 light years) away, has a spectral type of G0 and a mass and metallicity almost identical to our Sun’s. The planet has a semimajor axis of 5.15 AU and an estimated orbital eccentricity of 0.02, even lower than Jupiter’s. In the discovery paper, the planet is variously described as “a Jupiter analog” and “reminiscent of Jupiter,” implying that Earthlike planets might have formed on warmer orbits. Despite the system’s unparalleled resemblance to our own, however, no media fanfare accompanied its announcement. Even the Facebook page for HD 13931 b (whichever vigilant machine of loving grace may have created it!) had 0 Likes until I gave it a sympathy click last Thursday.

It’s hard for me to understand the manifest lack of interest in this unique planetary system. The only explanation I can think of involves the host star’s evolutionary state. Although HD 13931 is still burning on the main sequence, Howard and colleagues report a luminosity and radius of 1.57 Solar and 1.23 Solar, respectively, implying evolutionary progress toward the subgiant phase. They also estimate a stellar age of 8.4 billion years. According to James Kasting, a noted geoscientist, the oceans of our own middle-aged Earth will be lost to evaporation by the time our Sun reaches its 6 billionth birthday. Thus, even if an Earth twin initially formed around HD 13931, it would have suffered total desiccation a few billion years ago, ending all prospects for hydrophilic life (the only kind we know of).

So vanishes our first great hope for a New Earth. Liberalizing the inclusion criteria, of course, can enlarge our sample of potential Jupiter lookalikes.

In 2011, Robert Wittenmyer and colleagues published a study with an especially alluring title: “On the frequency of Jupiter analogs.” They used data from the Anglo-American Planet Search to calculate the occurrence rate of “so-called Jupiter analogs” in the program’s list of target stars. Limiting their analysis to stars with at least 30 radial velocity observations recorded over a period of at least 8 years, they assembled a final sample of 123 relatively nearby stars. From this sample they estimated that a minimum of 3.3% of (Sun-like) stars harbor a Jupiter analog. Since a few hundred G- and K-type stars are located within a radius of only 20 parsecs, we might interpret these results to mean that a dozen or more Solar System analogs await discovery just in the Sun’s back yard.

However, that frequency of 3.3% depends sensitively on the definition of a “so-called Jupiter analog,” which for Wittenmyer at al. is as follows: “a planet with a small eccentricity (e < 0.2) and a long period (P ≥ 8 years),” to ensure that the object “plays a dynamical role similar to that of our own Jupiter, with a period long enough to imply in situ formation, and an eccentricity low enough to suggest a benign dynamical history.”

This definition, oddly enough, says nothing about the host star’s spectral type or the presence or absence of giant planets on interior orbits. In fact, of the three planets identified by Wittenmyer’s group as fulfilling their requirements, one (GJ 832 b) orbits an M dwarf and the other two (Mu Arae c and HD 134987 c) have at least one gas giant each on an interior orbit. The systems where these so-called Jupiter analogs reside bear little resemblance to our own. 

Figure 4. Goldilocks finds the one that’s just right.

Fortunately, the patron saint of exoplanetary science is Goldilocks. Between the strict demand that Jupiter analogs resemble Jupiter in every particular (too hard), and the permissive approach that assesses length of orbit rather than large-scale system architecture (too soft), an eminently useful compromise is available.

In 2006, Sean Raymond published a letter to The Astrophysical Journal whose subtitle, “Limits on the giant planet orbits that allow habitable terrestrial planets to form,” says it all. Raymond ran 460 numerical simulations of rocky planet formation around a Sun-like star accompanied by a single gas giant corresponding to Jupiter. The orbital configuration of this planet varied systematically from simulation to simulation, with semimajor axes ranging from 1.6 AU to 6 AU and eccentricities from 0 to 0.4. Raymond found that Jupiter analogs on circular orbits were best suited to the formation of planets at least 30% as massive as Earth (the minimum for long-term habitability). At an eccentricity of zero, a Jupiter-mass planet with a minimum semimajor axis of 2.6 AU permits the formation of large rocky planets. At an eccentricity of 0.4, however, its semimajor axis must increase to at least 5 AU for a similar outcome (Raymond 2006).

Using these results, Raymond identified a sample of seven planetary systems (then about 5% of the total) with the potential to form “habitable-mass planets.” In a telling example of the rapid yet uncertain progress of exoplanetary science, only two of those seven systems still meet his criteria, despite the passage of only six years. For one proposed host, HD 149221, the candidate Jupiter analog has never been confirmed; for two other systems, additional planets have been identified, altering the overall system architecture; and for two more, values for semimajor axis or eccentricity or both have been revised. Only HD 70642 and HD 89307 remain viable.

Nevertheless, Raymond’s method remains robust, and both his solo article and a related publication the next year (Mandell et al. 2007) continue to be cited in studies of system architectures. Raymond’s delineation of the orbital parameters that permit habitable rocky planets can be considered a touchstone in the field.

A more recent study of long-period planets by Claire Moutou and colleagues notes the unique difficulties presented by searching for such objects:

Finding long-period, massive planets in volume-limited surveys is of prime importance to get the complete picture of extrasolar system architectures, despite the natural biases towards short-period planets of the radial-velocity method.

However, when searching for best-fit solutions of planetary orbits with periods larger than the time span of the observations, one meets the degeneracy of several types of solutions, with or without linear drifts, additional components in the system, or accounting for degeneracies in the fitted parameters. One expects long-period planets to be part of systems, because inward migration should not have blown out the inner planets, and series of giant planets may exist as in the solar system.

Orbital fitting for long-period planets is thus more uncertain than for shorter-period planets. The significance of periods, masses, and eccentricities of known radial-velocity long-distance planets should then be taken with some care, as the best-fit solution is likely to evolve when more data are available. (Moutou et al. 2011)

This “evolutionary” tendency of the data requires iterative scrutiny of the exoplanet census if we want to keep any potential Solar System analogs in focus.

reading the signs right

The earliest radial velocity search programs, back in the 1980s, were designed to find Jupiter twins (Marcy & Butler 1992, Walker 2012). In hindsight it is clear that their observations were too infrequent, their time baselines too short, and their instrumental precision too coarse to yield robust detections. As a result, the first several years of exoplanet discoveries were dominated by Hot Jupiters and by warm gas giants on relatively short-period, eccentric orbits.

Even now, with the census hurtling toward 800 extrasolar planets, Jupiter-like objects remain in short supply:

• Only 2% of exoplanets have semimajor axes of 5 AU or more.
• The median eccentricity of exoplanets orbiting beyond 1 AU is about 0.2.
• The median mass of known gas giant planets is about 1.5 times Jupiter, with two-thirds of extrasolar giants exceeding Jupiter’s endowment.
• 69% of exoplanets orbiting at 5 AU or more have inner companions at least twice as massive as Neptune.

This sample of overwhelmingly massive objects on close orbits is certainly the outcome of detection bias. If an exact duplicate of our Solar System were located 20 parsecs (65 light years) away, and if astronomers had been measuring the radial velocity of its host star regularly and carefully since the 1990s, the only planet that they could have detected would be the Jupiter analog. Saturn’s counterpart would remain elusive, since Saturn’s mass is less than one-third of Jupiter’s, and its orbital period is more than twice as long. Analogs of Earth and Uranus would be completely out of reach. These stubborn facts provide at least a partial explanation for the seeming oddness of our system.

Odd it may be, but perhaps not unique.

If we apply the criteria of Wittenmyer and colleagues (2011) to currently available data, we find no fewer than 15 “so-called Jupiter analogs.” Unfortunately, as we have seen, these criteria tell us nothing about the potential presence of Earthlike companions. One such “analog” orbits a red giant that was formerly an A-type star, whose short lifetime rules out sustained habitability; two others orbit M dwarfs, whose narrow habitable zones translate into tidally locked and potentially desiccated planets; and eight more reside in multiple planet systems, whose orbital dynamics would prevent the survival of Earthlike objects. Just four bona fide Jupiter analogs survive scrutiny: HD 13931 b (see above), HD 154345 b, HD 24040 b, and HD 222155 b.

Sean Raymond’s approach yields a richer harvest: 10 systems whose architectures meet the Goldilocks test. Joining the six candidates already noted in passing (HD 13931, HD 70642, HD 89307, HD 154345, HD 24040, and HD 222155) are HD 6718, HD 72659, HD 117207, and HD 290327. This planetary decade was assembled through a two-step process. First, the current list of radial velocity planets in the Extrasolar Planets Encyclopaedia was pruned of all multiplanet systems, all host stars less massive than 0.5 Msol, all planets with eccentricities of 0.4 or more, and all planets with semimajor axes smaller than 2 AU. Then, the criteria presented in Raymond 2006 were applied planet by planet to the resulting sample, accounting for host star mass individually. (This reckoning excludes HD 150706, a newly announced exoplanetary system whose Jupiter analog has incomplete orbital data (Boisse et al. 2012), and three other systems – HD 25171, HD 50499, and HD 73534 –  that are outliers in terms of stellar mass or planetary semimajor axis.)

Figure 5. Ten Solar System analogs

Distance is expressed in parsecs (1 parsec = 3.26 light years); star mass in Solar units (Msol); planet mass in Jupiter units (Mjup); and period in days. [Fe/H] is metallicity; a is semimajor axis in astronomical units (AU); and e is eccentricity.

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The final candidate selection amounts to fewer than 2% of all systems discovered by radial velocity surveys (the only method currently capable of detecting Jupiter twins). It includes host stars ranging in mass from 0.88 to 1.18 Msol (median 1 Msol), in metallicity from -0.14 to +0.27 (median -0.04), and in distance from 18 to 60 parsecs (median 45). It includes planets ranging in mass from 0.95 to 4 Mjup (median 1.95), in semimajor axis from 3.27 to 5.15 AU (median 4 AU), and in eccentricity from 0.02 to 0.24 (median 0.1). According to these numbers, our Sun is typical of stars that host Jupiter analogs, whereas Jupiter itself is more distant, more lightweight, and less eccentric than most of its counterparts.

To put these results in context: our Sun is also similar in mass and metallicity to stars that host Hot Jupiters (median 1.08 Msol and +0.08, respectively), even though it hosts none. Hot Jupiters themselves are found in 33% of all announced exoplanetary systems, in stark contrast to the ~2% with passable analogs of the original Jupiter. Of course, like other exoplanet data, the apparent frequency of Hot Jupiters is an illusion resulting from detection bias. A series of careful analyses has established that their true frequency must be less than 1% of all Sun-like stars (Wright et al. 2012, Steffen et al. 2012). What the true frequency of Jupiter analogs might be remains a mystery.

theoretical excursions

The data considered so far derive from radial velocity and transit searches, which have yielded the vast majority of announced planets. Astronomers in the microlensing community offer a valuable alternative view, since the randomness of microlensing events provides a sample of planetary systems that is more typical of the Galactic rank and file. In addition, the sensitivity of microlensing observations to orbits wider than 2 AU helps to counterbalance the short-period bias of the more prolific techniques. 

A series of publications in 2010 used microlensing data to estimate the relative distribution of system architectures in our neighborhood of the Milky Way. Sumi et al. (2010) concluded that Neptune-mass planets are substantially more common than gas giants like Jupiter in orbits outside the ice lines of low-mass stars (2.7 AU for our Sun; less for smaller stars). The frequency of these cool Neptunes is at least three times, and probably seven times, that of cool gas giants, with the likelihood of Jupiter-like planets decreasing along with stellar mass (Sumi et al. 2010).

An overlapping group of researchers produced a more extensive statistical analysis of the microlensing data, again finding that gas dwarfs like Uranus and Neptune are more common than gas giants outside system ice lines (Gould et al. 2010). They also reached the interesting conclusion that “our Solar System appears to be three times richer in planets than other stars along the line of sight toward the Galactic Bulge.” They further calculated that “Solar-like systems,” defined as those with two or more gas giants orbiting outside the ice line (like Jupiter and Saturn), accompany about 17% of stars. Their study received a favorable review in Nature (Chambers 2010), and has often been cited since.

A third study, whose senior author collaborated on the previous two, presented a large suite of numerical simulations based on the findings of Sumi et al. 2010 and Gould et al. 2010. Andrew Mann and colleagues Eric Gaidos and B. Scott Gaudi began by assuming that “a substantial fraction, and probably the majority of stars do not host giant planets” on orbits smaller than Saturn’s. In this “invisible majority” of planetary systems, the most massive planet to evolve will be in the range of Earth to Neptune (see Between Earth and Uranus). Mann and colleagues simulated the outcome of planet formation in systems where such an object accreted near the system ice line and never underwent Type I migration (i.e., migration to a short-period orbit in response to tidal interactions with the primordial nebula of hydrogen and helium before it dissipated). Typical outcomes of their simulations were systems with two to four planets about as massive as Uranus (i.e., gas dwarfs) on low-eccentricity orbits between 2 and 20 AU. The innermost planet tended to be the most massive, and most planets orbited within 10 AU.

Notably, this giant-free architecture was intolerant of terrestrial planets resembling those in the inner Solar System. Perturbations from the innermost gas dwarf drove collisions among rocky planetesimals close to the star, resulting in a single rocky planet about twice as massive as Earth (Mann et al. 2010).

Mann and colleagues presented their work as complementary rather than contradictory to the simulations of Kennedy & Kenyon (2008) and Thommes et al. (2008). The first of these also studied systems without gas giants, assuming (unlike Mann et al. 2010) that Type I migration tended to move objects quite rapidly from the ice line to short-period orbits. The resulting simulations produced compact systems of icy Super Earths, much like Kepler-11 or GJ 581 (Kennedy & Kenyon 2008). The second study focused on systems with gas giants, finding a wide range of potential system architectures resulting from a combination of smooth migration through the gas disk and violent episodes of planet-planet scattering (Thommes et al. 2008). The simulated systems of Mann et al. recall those of Kennedy & Kenyon, except that the planets travel on much more widely spaced orbits. Given the inspiration for their work, it’s no surprise that their synthetic planets most closely resemble the systems detected by microlensing.

Figure 6. According to CBS News, 7% of Americans believe they have been abducted by aliens.

just how weird?

Taken together, this body of research finds that systems containing gas giants (like our Solar System) represent a minority within the Milky Way – perhaps one-sixth of all planetary systems. Within this minority, systems with two gas giants traveling on circular orbits outside the ice line (true Solar System analogs) are a still smaller subset, although the frequency of this architecture has not yet been quantified. The “invisible majority” of planetary systems are predicted to be more or less compact collections of low-mass planets: 61 Virginis and HD 69830 are typical examples. Systems like our own are far less common.

I always like to consider exoplanet data in the context of the volume of space within 20 parsecs of our Sun, where statistics are least affected by selection bias. This volume-limited sphere contains 60 confirmed exoplanetary systems, including 5 (8%) with Hot Jupiters, 6 (10%) with multiple low-mass planets on compact orbits, 16 (27%) centered on M dwarfs, and exactly one (1.6%) with a Jupiter analog (HD 154345). This volume also contains one transiting gas giant (HD 189733 b), one transiting gas dwarf or “Hot Neptune” (GJ 436 b), and two transiting Super Earths (GJ 1214 b and 55 Cancri e).

Careful statistical analyses have shown that Hot Jupiters occur in fewer than 1% of planetary systems, whereas transiting Super Earths outnumber transiting gas giants by much more than a factor of 2. Meanwhile, M dwarfs account for some 75% of all stars in the Galaxy. Clearly, certain system architectures are underrepresented in available data, while Hot Jupiters in particular are hugely overrepresented.

But if you’re a glass-half-full type, systems with Jupiter twins aren’t especially rare. Even if they accompany only 1% of Sun-like stars, several dozen might exist within a few hundred parsecs (since 10 are already known within 60 parsecs). That’s enough potential Earth twins to populate an imposing Galactic Empire, in case anyone out there plans to build one.

Whether all these numbers indicate that our Solar System is kinda weird, very weird, or just a bit eccentric is ultimately a subjective judgment.

In 1999, a Gallup poll found that 18% of Americans thought the Sun orbits the Earth. In 2007, CBS News reported that 7% of Americans believed they had been abducted by aliens. For me, those are pretty weird fractions. Right now, sadly, it looks like alien planets with craggy mountains wreathed in fluffy white clouds with waves crashing on rocky shores may be even rarer across our Galaxy than self-described alien abductees north of the Rio Grande.

REFERENCES

Boisse I, Pepe F, Perrier C, Queloz D, Bonfils X, Bouchy F, et al. (2012) The SOPHIE search for northern extrasolar planets. V. Follow-up of ELODIE candidates: Jupiter-analogues around Sun-like stars. Astronomy & Astrophysics, in press. Abstract: http://adsabs.harvard.edu/abs/2012arXiv1205.5835B

Chambers J. (2010) More giants in focus. Nature 467, 405-406.

Gould A, Dong S, Gaudi BS, Udalski A, Bond IA, Greenhill J, and 148 others, including T. Sumi and D.P. Bennett. (2010) Frequency of Solar-like systems and of ice and gas giants beyond the snow line from high-magnification microlensing events in 2005-2008. Astrophysical Journal 720, 1073–1089. Abstract: http://adsabs.harvard.edu/abs/2010ApJ...720.1073G

Kennedy GM, Kenyon SJ. (2008) Planet formation around stars of various masses: Hot super-Earths. Astrophysical Journal 682, 1264-1276. Abstract: http://adsabs.harvard.edu/abs/2008ApJ...682.1264K

Mandell A, Raymond S, Sigurdsson S. (2007) Formation of Earth-like planets during and after giant planet migration. Astrophysical Journal 660, 823-844.

Mann AW, Gaidos E, Gaudi BS. The invisible majority? Evolution and detection of outer planetary systems without gas giants. (2010) Astrophysical Journal 719, 1454–1469. Abstract: http://adsabs.harvard.edu/abs/2010ApJ...719.1454M

Marcy GW, Butler RP. (1992) Precision radial velocities with an iodine absorption cell. Publications of the Astronomical Society of the Pacific 104, 270-277. Abstract: http://adsabs.harvard.edu/abs/1992PASP..104..270M

Moutou C, Mayor M, Lo Curto G, Ségransan D, Udry U, Bouchy F, et al. (2011) The HARPS search for southern extra-solar planets. XXVII. Seven new planetary systems. Astronomy & Astrophysics 527, A63. Abstract: http://adsabs.harvard.edu/abs/2011A%26A...527A..63M

Raymond SN. (2006) The search for other Earths: Limits on the giant planet orbits that allow habitable terrestrial planets to form. Astrophysical Journal 643, L131–L134. Abstract: http://adsabs.harvard.edu/abs/2006ApJ...643L.131R

Raymond SN, O’Brien DP, Morbidelli A, Kaib NA. (2009) Building the terrestrial planets: Constrained accretion in the inner Solar System. Icarus 203, 644-662. Abstract: http://adsabs.harvard.edu/abs/2009Icar..203..644R

Steffen JH, Ragozzine D, Fabrycky DC, Carter JA, Ford EB, Holman MJ, Rowe JF, Welsh WF, Borucki WJ, Boss AP, Ciardi DR, Quinn SN. (2012) Kepler constraints on planets near hot Jupiters. In press; abstract: http://adsabs.harvard.edu/abs/2012arXiv1205.2309S

Sumi T, Bennett DP, Bond IA, Udalski A, Batista V, Dominik M, and 97 others, including A. Gould and B.S. Gaudi. (2010) A cold Neptune-mass planet OGLE-2007-BLG-368Lb: Cold Neptunes are common. Astrophysical Journal, 710:1641–1653. Abstract: http://adsabs.harvard.edu/abs/2010ApJ...710.1641S

Thommes EW, Nagasawa M, Lin DNC. (2008) Dynamical shakeup of planetary systems II: N-body simulations of Solar System terrestrial planet formation induced by secular resonance sweeping. Astrophysical Journal 676, 728-739. Abstract: http://adsabs.harvard.edu/abs/2008ApJ...676..728T

Thommes EW, Matsumura S, Rasio FA. (2008c) Gas disks to gas giants: Simulating the birth of planetary systems. Science, 321: 814-817. Abstract: http://adsabs.harvard.edu/abs/2008arXiv0808.1439T

Turnbull MC, Glassman T, Roberge A, Cash W, Noecker C, Lo A, Mason B, Oakley P, Bally J. (2012) The search for habitable worlds: 1. The viability of a starshade mission. Publications of the Astronomical Society of the Pacific 124, 418-447. Abstract: http://adsabs.harvard.edu/abs/2012arXiv1204.6063T

Walker G. (2012) The first high-precision radial velocity search for extra-solar planets. New Astronomy Reviews 56, 9-15. Abstract: http://adsabs.harvard.edu/abs/2012NewAR..56....9W

Wittenmyer R, Tinney CG, O’Toole SJ, Jones HRA, Butler RP, Carter BD, Bailey J. (2011) On the frequency of Jupiter analogs. Astrophysical Journal 727, 102. Abstract: http://adsabs.harvard.edu/abs/2011ApJ...727..102W

Wright JT, Marcy GW, Howard AW, Johnson JA, Morton T, Fischer DA. (2012) The frequency of hot jupiters orbiting nearby solar-type stars. In press; abstract: http://adsabs.harvard.edu/abs/2012arXiv1205.2273W

Kepler-11 As Testbed

Six low-mass planets orbit Kepler-11; masses are constrained only for the inner five (b-f)

No sooner did I post my critical review of the hoopla surrounding Super Earths when two directly relevant preprints appeared in the astrosphere: “In situ accretion of hydrogen-rich atmospheres on short-period super-Earths: Implications for the Kepler-11 planets,” by Masahiro Ikoma and Yasunori Hori (linked here), and “How thermal evolution and mass loss sculpt populations of super-Earths and sub-Neptunes: Application to the Kepler-11 system and beyond,” by Eric Lopez, Jonathan Fortney, and Neil Miller (linked here).

As you can guess from the titles, both articles investigate the structure and composition of exoplanets less massive than Uranus (14.5 Earth masses/Mea), and both use the Kepler-11 system as a testbed for their theoretical excursions. The same system has already been highlighted in this blog (Between Earth & Uranus, Parts I and II).

Kepler-11 is a G-type star much like our Sun, except that it is older (~8 billion years), a little less massive (0.95 Msol), and located about 2000 light years away. The star harbors at least 6 transiting planets, 5 of which orbit within 0.25 astronomical units (AU) with periods between 10 and 47 days. Because their orbital configuration is so compact, the 5 inner planets exert mutual gravitational perturbations that cause variations in the timing of their transits. These transit timing variations (TTV) enable estimates of each planet’s mass. Such data represent a huge bonus for extrasolar astronomers, since the small planetary candidates in most Kepler systems lack firm constraints on their potential masses. For Kepler-11, only the mass of the sixth planet (g) remains uncertain, since its wider orbit (0.46 AU, 118 days) prevents interactions with its neighbors.

Although the orbital space occupied by Kepler-11b-f is much hotter than the environment of Mercury in our Solar System, each of these planets is more than an order of magnitude more massive than Mercury, ranging roughly from 2 to 14 Mea. Thus their aggregate mass is similar to the sum of Uranus and Neptune. At least 3 and probably 4 of these planets have radii so large that they can be explained only by the presence of lightweight hydrogen envelopes (Lissauer et al. 2011). Since the radius of the sixth planet (3.66 Rea) falls in the same range as those of the second through fourth (3.15-4.52 Rea), its mass is probably comparable to theirs (6-14 Mea), and its composition is likely similar.

Comparative orbital architectures of Kepler-11 and the Solar System. Credit: NASA/Tim Pyle

Using this fascinating system as their point of reference, the two teams of astronomers take different approaches to the problem of planetary structure and reach distinct but non-contradictory conclusions.

Ikoma and Hori conduct a narrowly defined inquiry. They ask whether the 5 inner planets of Kepler-11 could have acquired substantial hydrogen-helium atmospheres while orbiting in their present configuration. Their answer is a qualified yes, as long as the following conditions are met:

1.    Five rocky cores, with masses in the approximate range of 2-4 Mea, form very rapidly in the first few million years after stellar ignition.

2.    Before the protoplanetary nebula disperses, all 5 achieve orbits inside 0.25 AU and accrete substantial hydrogen envelopes.

3.    The nebula then dissipates slowly enough to avoid significant erosion of the newly accreted atmospheres.

4.    Atmospheric loss over the next 8 billion years is insufficient to strip the envelopes from these sweltering planets, with the possible exception of the closest and hottest, Kepler-11b, whose radius can be explained either by a steam atmosphere, a mixture of water vapor and hydrogen, or a tenuous surviving envelope of hydrogen around a rocky core.

However, some of these conditions (1 and 2) seem highly unlikely, while another (3) depends critically on fine-tuning the process of nebular dissipation.

The least likely assumption is probably the first: the assembly of 5 purely rocky objects more massive than Earth in the span of just a few million years. The Solar System, by contrast, required 30 million years to build Earth, which achieved its final mass only after a long series of violent impacts within a squabbling family of protoplanets. Today, inside a semimajor axis of 2 AU (8 times larger than the orbit of Kepler-11f), only 2 Earth masses of rocky material orbit our Sun, in the form of 4 low-mass, high-density planets. Objects as massive as the cores proposed for the inner Kepler planets appear able to assemble only on wider orbits, in the so-called “sweet spot” of planet formation, just outside the system ice line (Thommes et al. 2008, Mordasini et al. 2012). What makes this region so sweet is the presence of frozen volatiles, which significantly enhance the mass available for planetary accretion while ensuring that any resulting cores will be rich in water and other ices. Given the close similarities between our Sun and Kepler-11, such an extraordinary difference in their histories of core accretion would require extraordinary supporting evidence, theoretical or otherwise; the authors offer none.

To be fair, Ikoma and Hori make no grand claims, and state their conclusions in the most measured terms: “The in situ formation of the relatively thick H/He atmospheres inferred by structure modeling is possible only under restricted conditions; namely, relatively slow disk dissipation and/or cool environments.”

Lopez and colleagues take a larger perspective that leads to results with broader applicability. Their stated goal is to constrain the structure and history of a class of planets that they call “low-mass low-density (LMLD),” which are assumed to consist of some combination of rock, water, and hydrogen/helium (H/He). First they model the formation and evolution of a range of such objects. Then they test their models against the 5 inner planets of Kepler-11, with helpful results for low-mass exoplanets in general.

Their theoretical approach encompasses three planetary types, for which they supply their own terminology: [1] “super-Earths,” with rocky cores surrounded by a H/He envelope; [2] “water-worlds,” with rocky cores surrounded by a layer of pure H₂O; and [3] “sub-Neptunes,” with rocky cores surrounded by a water layer of equal mass and a H/He layer on top. In the terminology I’ve used in previous posts, the second and third of these types correspond to “icy telluric planets” and “gas dwarfs,” respectively (although I’m beginning to like plain old “water planets” as an alternative for the second type). For me the first type, which is theoretically suspect and not attested by observations, shall remain nameless. 

A key feature of the approach of Lopez and colleagues is their attention to mass loss driven by extreme ultraviolet (XUV) irradiation, whose effects will be powerful in the near vicinity of Sun-like stars. Also notable is the comprehensiveness of their methodology. They return several robust conclusions with wide relevance to exoplanetary studies:

• It is unlikely that the planets around Kepler-11 could have formed in situ.

• More likely, they were originally “water-rich sub-Neptunes” that formed beyond the system ice line (about 2.7 AU for a Sun-like star) and then migrated into their present orbits.

• They originated as massive cores with bulk compositions approximately 50% rock and 50% ice, then accreted substantial H/He atmospheres before converging on short-period orbits near the central star, where they lost much of their primordial atmospheres.

• The hottest and closest planet, Kepler-11b, retains no H/He, consisting of 40% water and 60% rock and metal. The other four planets retain small quantities of H/He around rock/ice cores. The likely proportion of lightweight gases is 3%-8% for Kepler-11e, at 8.4 Mea; 0.5%-2% for Kepler-11-d, at 6 Mea; and less than 1% for Kepler-11c (13.5 Mea) and Kepler-11f (2.3 Mea). 

• Generally speaking, low-mass planets with H/He envelopes that achieve orbits in hot environments will suffer mass loss and evolve into either “water-dominated worlds with steam atmospheres” or “rocky super-Earths.”

Thus most or all of the short-period Kepler planets with radii of about 1.5-5 Rea probably originated as gas dwarfs on cold orbits and then metamorphosed into the range of low-mass types that are increasingly announced under a growing lexicon of nicknames.

Lopez and colleagues identify a threshold for XUV-driven mass loss that can be used to estimate minimum masses for Kepler planets with measured radii but no other mass constraints, and maximum radii for low-mass planets found by radial velocity searches, which measure only minimum masses. Given the frequent occurrence of compact systems of low-mass planets, both in the immediate Solar neighborhood and in the Galactic region probed by the Kepler mission, the modeling undertaken by Lopez and colleagues has wide applicability.

Limiting ourselves to radial velocity detections, 6 similar systems are known within 20 parsecs (65 light years) of Earth:

• 82 Eridani: 3 planets < 5 Mea orbiting within 0.35 AU
• GJ 581: 4 planets < 16 Mea orbiting within 0.22 AU
• 61 Virginis: 3 planets < 23 Mea orbiting within 0.48 AU
• HD 69830: 3 planets < 19 Mea orbiting within 0.63 AU
• HD 40307: 3 planets < 10 Mea orbiting within 0.13 AU
• HD 136352: 3 planets < 12 Mea orbiting within 0.41 AU

Since such systems are relatively difficult to detect with the radial velocity method, their frequency in near space suggests that they are common throughout the Milky Way.

Michael Whiting used a Meccano set to build a hand-cranked orrery of the Kepler-11 system

Postscript: As I was finishing up this posting today, I checked the Extrasolar Planets Encyclopaedia and saw another brand-new preprint about Kepler-11: “A dynamical analysis of the Kepler-11 planetary system,” by Cesary Migaszewski, Mariusz Slonina, and Krzysztof Gozdziewski (linked here). That makes three studies from three different continents within a span of three weeks on this single high-profile system. Migaszewski and colleagues focus on orbital dynamics instead of planetary structure, returning results that generally agree with the findings of the original discovery paper by Jack Lissauer’s group. However, their approach offers a way to constrain the mass of the sixth planet, Kepler-11g. They find that its mass is most likely under 30 Mea, confirming its status as a gas dwarf like four out of five of its companions.

REFERENCES

Ikoma M, Hori Y. (2012) In situ accretion of hydrogen-rich atmospheres on short-period super-Earths: Implications for the Kepler-11 planets. In press; abstract: http://adsabs.harvard.edu/abs/2012arXiv1204.5302I

Lissauer JJ, Fabrycky DC, Ford EB, Borucki WJ, Fressin F, Marcy GW, et al. (2011) A closely packed system of low-mass, low-density planets transiting Kepler-11. Nature 470, 53-58. Abstract: http://adsabs.harvard.edu/abs/2011Natur.470...53L

Lopez E, Fortney J, Miller N. (2012) How thermal evolution and mass loss sculpt populations of super-Earths and sub-Neptunes: Application to the Kepler-11 system and beyond. In press; abstract: http://adsabs.harvard.edu/abs/2012arXiv1205.0010L

Migaszewski C, Slonina M, Gozdziewski K. (2012) A dynamical analysis of the Kepler-11 planetary system. In press; abstract: http://adsabs.harvard.edu/abs/2012arXiv1205.0822M

Mordasini C, Alibert Y, Benz W, Klahr H, Henning T. (2012) Extrasolar planet population synthesis. IV. Correlations with disk metallicity, mass, and lifetime. Astronomy & Astrophysics, 541, A97. Abstract: http://adsabs.harvard.edu/abs/2012arXiv1201.1036M

Thommes EW, Matsumura S, Rasio FA. (2008) Gas disks to gas giants: Simulating the birth of planetary systems. Science, 321: 814-817. Abstract: http://adsabs.harvard.edu/abs/2008arXiv0808.1439T