Saturday, December 19, 2015

Evolutionary Twist

Figure 1. The Sun-like star WASP-47 hosts a transiting Hot Jupiter flanked by two low-mass planets, and all three have periods shorter than 10 days. This was the first and so far the only detection of such a configuration. Above, an artist’s rendering shows a Hot Jupiter in transit across the face of its star. Credit: European Southern Observatory
A few months back I wrote about WASP-47b, the first Hot Jupiter ever found with low-mass planets on nearby orbits. I noted my eagerness to see a theoretical study of the possible formation mechanisms behind this unusual system, while venturing that the orbital architecture of WASP-47 could not have resulted from in situ accretion.

Then last month I took a close look at a study by Konstantin Batygin & Greg Laughlin (2015), who offered a novel explanation for the formation of the inner planets of the Solar System. Their approach folds the evolutionary history of the four terrestrial planets into the Nice Model and the Grand Tack. I observed in passing that, although Laughlin was one of the earliest proponents of in situ theory (which underlies the scenario that he and Batygin proposed), he hadn’t written anything purely theoretical on this topic for quite a while.

Two new preprints respond serendipitously to those conjectures and observations. One is a theoretical study by Batygin, Bodenheimer & Laughlin (2015) on the potential for Hot Jupiters – Hot Jupiters, no less! – to form in situ. The authors develop a new formation scenario for star-hugging gas giants and use numerical simulations to test it. Then they appeal to the WASP-47 system as possible evidence that this mechanism really works.

The second preprint is also highly theoretical. Nathan Kaib and John Chambers (2015) tersely present the results of a large ensemble of numerical simulations designed to test the Nice Model of Solar System evolution. Their findings question the utility of this approach as an explanation for the Late Heavy Bombardment. They can also be interpreted as evidence that our four terrestrial planets formed after, not before, the dynamical instability addressed by the Nice model. Although Kaib & Chambers don’t mention the recent articles by Batygin & Laughlin or Volk & Gladman on the inner Solar System, their conclusions call for rethinking both the Nice model and the Grand Tack.

a burning cradle for baby giants?

The new study by Batygin & colleagues (hereafter B15) is called “In situ formation and dynamical evolution of Hot Jupiter systems.” The title is a misnomer, however, as they don’t actually model the in situ accretion of solids on orbits where Hot Jupiters are observed. Instead, as often happens in simulation studies, they use simplified initial conditions to examine a narrowly defined question: Can a dense planet of sufficient mass, orbiting at or near the inner edge of a protoplanetary nebula, accrete enough ambient hydrogen to balloon into a gas giant?

B15 offer four representative evolutionary sequences in which solid planetary cores at a range of masses follow circular orbits around a Sun-like star at a semimajor axis of 0.05 AU. They “purposely adopted an agnostic viewpoint” regarding formation mechanisms, explaining that their results “are largely independent of how the solid core arises.” The simulations seem equally friendly to x) strict in situ formation involving the accretion of local mass only; y) migration of solids from cooler orbits into the hot inner nebula and subsequent accretion at the new location; or z) migration of fully-formed cores from cooler orbits.

In units of Earth mass (Mea), the core masses they select are 4 Mea, 10 Mea, and 15 Mea. The object of 15 Mea is used in two different set-ups, one with low ambient gas density and the other with higher density. As a reality check, I note that atmosphere-free planets of 10 Mea or more are not attested (Jontof-Hutter et al. 2015), while realistic models of planet formation have great difficulty forming an object of 4 Mea or more at 0.05 AU, where silicate dust sublimates (Dullemond & Monnier 2010).

Regarding gas accretion, B15 concede that insufficient mass in ambient gas would be available in the local feeding zone to build a gas giant at 0.05 AU. Therefore, they assume that the local supply of hydrogen/helium is constantly replenished by the regular flow of gas through the nebula onto the infant star. Their model seems to hinge on the capacity of the short-period planet to capture this inrushing gas.

Across simulations, objects of 15 Mea were the only ones that managed to accrete gas envelopes equal in mass to their solid cores and thereby trigger runaway gas accretion. Thus, they find that the minimum core mass capable of growing into a gas giant in the vicinity of a Sun-like star is 15 Mea.

Figure 2. Light curves of the three inner planets of WASP-47
Phase-folded light curves of the three transiting planets detected by the K2 mission: Becker et al. 2015

B15 conclude that their scenario will regularly produce gas giants, so that in situ formation might “represent the dominant channel for hot Jupiter generation.” They proceed to a discussion of WASP-47b as an example of what this channel might bring.

But I’m not convinced. The likeliest origin for an object of 15 Mea with a semimajor axis around 0.05 AU is migration from a wider orbit where accretion can more readily produce such massive objects. As far as I know, a gas giant can migrate into a hot orbit just as easily as a Neptune-mass object can. So why resort to a two-step process – first migrate the core, then capture the atmosphere – when a well-theorized one-step process (Type II migration) works even better? B15 appear to be offering a solution in search of a problem.

They cite WASP-47 as a rare system in which a compact family of Super Earths somehow managed to promote one of their number to giant status without changing any semimajor axes or otherwise disrupting the rest of the family. But it seems that considerable acrobatics would be needed to achieve this remarkable outcome. For example, how did only one planet get pumped up? What kept the others down?

I suggest that, along with exploring novel in situ explanations for the evolution of WASP-47, the exoplanet community should test whether migration scenarios could explain this architecture with fewer contortions.

Figure 3. The wreck of the Kronan
In 1676, the Swedish warship Kronan capsized while trying to execute a sharp turn under too much sail, causing an explosion in the gunpowder magazine. Few survived. Illustrated is an imaginative (and historically inaccurate) rendering of the disaster by Claus Moinichen in 1686.

does the sailing master have no clothes?

The study by Kaib & Chambers is conducted on a grander scale than B15. They ran almost 300 high-resolution simulations of Solar System evolution to test three different versions of the Nice model and explore the effects of the resulting dynamical instability on the four terrestrial planets. A simulation was considered successful if the final system met three criteria after the instability concluded: A) all four outer planets from Jupiter to Neptune survived, with the orbits of Saturn and Jupiter lying between a 2:1 and 3:1 mean motion resonance; B) all four inner planets also survived on stable orbits; and C) the angular motion deficit of the four inner planets was less than or equal to its present value after their orbits were integrated for an additional billion years.

In all three versions of the initial set-up, the four terrestrial planets were assigned their present masses and orbits. In two versions, the outer system contained Jupiter, Saturn, and three Neptune-like planets. In the third, it contained Jupiter, Saturn, two Neptune-like planets, and two “Super Earths” of 8 Mea each. Among all iterations of these set-ups, the success rate according to Criterion A was 13% to 16%. However, the set-up with six outer planets failed both of the other criteria, while the other two models produced just 1 and 2 systems, respectively, that met Criterion B. Only one iteration of one of these models also met Criterion C. All other iterations lost at least one terrestrial planet (usually Mercury), and many lost two (usually Mercury and Mars).

These results are very likely to inform future discussions of the Nice Model. As Kaib & Chambers conclude:

[W]e find a probability of 1% or less that the orbital architectures of the inner and outer planets are simultaneously reproduced in the same system. These small probabilities raise the prospect that the giant planet instability occurred before the terrestrial planets had formed. This scenario implies that the giant planet instability is not the source of the Late Heavy Bombardment and that terrestrial planet formation finished with the giant planets in their modern configuration.

Notably, the recent study by Volk & Gladman (2015) proposed an approach to the evolution of the four terrestrial planets that dispensed with the Nice Model altogether, suggesting an alternative explanation for the Late Heavy Bombardment. Although I don’t find their alternative persuasive, I hope these efforts inspire further evolutionary studies to address the problem of our denuded inner system.

In the meantime, the findings of Kaib & Chambers might benefit from reframing. As discussed in earlier blog posts, the phenomenon known as the Late Heavy Bombardment or Lunar Cataclysm can be understood in different ways. In one view, it was a self-contained period of heavy cometary impacts that were preceded and followed by long stretches of relative calm; its peak came about 3.8 billion years ago (Gya), at a system age of ~800 million years (Gomes et al. 2005). In another, it was simply one episode in a long, saw-toothed series of bombardments that began with Earth’s accretion and subsided only toward the end of the Archean period, about 2.5 – 3 Gya (Morbidelli et al. 2012, Marchi et al. 2014). Instead of triggering a late and relatively short-lived catastrophe, maybe the dynamic instability happened in the first 100 million years of Solar System history and inaugurated that long and violent epoch of bombardments. The Nice Model would still explain how the massive outer planets nudged and jostled one another into their mature (and usually wider) orbits.

Figure 4. Overview of Earth history

Again, maybe the failure of a single model to explain the final architecture of the inner as well as the outer Solar System is another clue that we need a new picture of inner system evolution. What if the Grand Tack triggered an inner system catastrophe, as modeled by Batygin & Laughlin (2015), but the resulting mess did not immediately resolve into a four-planet system? Maybe the battle of oligarchs that followed Jupiter’s retreat from the Sun’s inner territories was still raging while Neptune was decimating the outer realms. Maybe lasting peace in the inner system was contingent on resolving tensions among the outer worlds, a resolution that evidently hinged on the exile of a Uranus-type planet. Maybe the final detente between Jupiter and Saturn was what enabled Earth to dominate its three smaller siblings.


Batygin K, Laughlin G. (2015) Jupiter’s decisive role in the inner Solar System’s early evolution. Proceedings of the National Academy of Sciences 112, 4214-4217. Abstract: 2015PNAS..112.4214B
Batygin K, Bodenheimer P, Laughlin G. (2015) In situ formation and dynamical evolution of Hot Jupiter systems. In press. Abstract: 2015arXiv151109157B
Becker J, Vanderburg A, Adams F, Rappaport S, Schwengler H. (2015) WASP-47: A Hot Jupiter system with two additional planets discovered by K2. Astrophysical Journal Letters 812, L18. Abstract: 2015ApJ...812L..18B
Dullemond CP, Monnier JD. (2010). The inner regions of protoplanetary disks. Annual Review of Astronomy & Astrophysics 48, 205-239.
Gomes R, Levison HF, Tsiganis K, Morbidelli A. (2005) Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets. Nature, 435: 466-469. Abstract: 2005Natur.435..466G
Jontof-Hutter D, Ford EB, Rowe JF, Lissauer JJ, Fabrycky DC, Christa Van Laerhoven5, Agol E, Deck KM, Holczer T, Mazeh T. (2015) Robust TTV mass measurements: Ten Kepler exoplanets between 3 and 8 Mearth with diverse densities and incident fluxes. In press.
Kaib NA, Chambers JE. (2015) The fragility of the terrestrial planets during a giant planet instability. Monthly Notices of the Royal Astronomical Society. In press. Abstract:
Marchi S, Bottke WF, Elkins-Tanton LT, Bierhaus M, Wuennemann K, Morbidelli A, Kring DA. (2014) Widespread mixing and burial of Earth’s Hadean crust by asteroid impacts. Nature 511, 578-582. 2014Natur.511..578M
Morbidelli A, Marchi S, Bottke WF, Kring DA. (2012) A sawtooth-like timeline for the first billion years of lunar bombardment. Earth and Planetary Science Letters 355, 144-151. Abstract:
Volk K, Gladman B. (2015) Consolidating and crushing exoplanets: Did it happen here? Astrophysical Journal Letters, 806: L26. Abstract: 2015ApJ...806L..26V

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