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