Sunday, November 8, 2015

Jupiter Descending

Figure 1. “Jupiter rules all things in heaven with his brilliant light, and with his warmth he caresses all creatures. With his mighty hand that God scatters cruel missiles, flashing fire as he hurls thunderbolts from his high citadel.” Image credit: The Warburg Institute
As the extrasolar census approaches 2000 confirmed planets located in more than 1200 different systems, its no longer possible to ignore the oddity of our Solar System. About half of all stars like our Sun host planets a few times the mass of Earth orbiting inside circumstellar radii of 0.5 astronomical units (AU). A smaller fraction support one or more gas giant planets on eccentric orbits substantially shorter than Jupiter’s period of 12 years. One percent or less have gas giants (“Hot Jupiters”) roasting inside 0.1 AU on orbits of just a few days.

Yet here at home, the Sun’s closest offspring, Mercury, maintains an average separation of about 36 million miles (0.39 AU) from our parent star, and masses less than quintuple our Moon. The bulk of the Solar System’s mass is located quite far from the Sun, outside a radius of 5 AU. In that cool region our two giants, Jupiter and Saturn, glide along slow, circular orbits with few parallels in the extrasolar catalog.

Why are the innermost regions of the Solar System empty of planets, when so many other stars, near and far, support either tightly packed families of low-mass planets or smaller collections of gas giants in the same orbital space? Two studies published earlier this year offer clever explanations. For different reasons, both propose that our system once had additional short-period planets that were destroyed by an inner-system catastrophe shortly after they formed. Both also assume that the formation of low-mass planets on hot orbits is robust even in the presence of gas giants. Subsequent evolution can then produce a variety of system architectures. 

a grand attack 

From Konstantin Batygin and Greg Laughlin, via Publications of the National Academy of Science, came a scenario based on recent models of the evolution of our system’s four inner planets. In the traditional picture, these objects condensed near their present locations out of a broad field of planetesimals extending outward from 0.4 AU. Recent theoretical work, however, demonstrates that the terrestrial planets must have accreted within a narrow ring between 0.7 and 1 AU (Hansen 2009). During their formative years, Venus and Earth scattered Mercury inward and Mars outward. Although the widely endorsed Grand Tack scenario explains the outer edge of the birth ring by evoking perturbations by migrating Jupiter, Batygin & Laughlin noted that no rationale had yet been presented for its inner edge. Hence their study.

Figure 2. The Grand Tack as Grand Attack
This figure combines the scenarios of Walsh et al. 2011 and Batygin & Laughlin 2015. Panel a shows the beginning of the Grand Tack at a system age of ~1-2 million years. The gas nebula is still present and accretion has progressed throughout the system, with several low-mass planets already formed on inner orbits and two gas giants growing in the “snow region” beyond 3 AU where water freezes. (Note: BL15 place Jupiter’s starting point at 6 AU.) Panel b shows the maximum incursion of the two gas giants into the inner system, where they scatter planets and planetesimals as they establish an orbital resonance. Some of the original low-mass planets have already been engulfed by the Sun. In the outer system, two or more additional low-mass planets are growing interior to a massive planetesimal belt. Panel c shows the retreat of proto-Jupiter and proto-Saturn as their resonant orbits carry them back into the snow region, just as the gas nebula begins to dissipate. Meanwhile, the planetesimals scattered inward by proto-Jupiter have already crowded all the original low-mass planets into the Sun, leaving a ring of colliding planetesimals and debris near the present orbit of the Earth. Panel d shows the final stable configuration of the Solar System at an age of about 1 billion years. The collisional assembly of the four terrestrial planets has scattered residual debris into a “garbage orbit” beyond Mars, creating the ancestral Asteroid Belt, while the outward migration of Saturn has pushed Uranus and Neptune onto wide orbits, outside the scale of this diagram.
They begin by proposing that proto-Jupiter originally assembled somewhere between 3 and 10 AU (Figure 2a). Once it reached a threshold mass, tidal interactions with the primordial gas nebula caused its orbit to shrink in a process known as Type II migration. Simultaneously, proto-Saturn began accreting in proto-Jupiter’s wake, following its big nursery-mate on an inbound voyage. Jupiter’s passage into the inner Solar System scattered a substantial existing population of planetesimals and protoplanets even farther inward, pitching most of them into the Sun.

Eventually, tagalong Saturn was embraced by Jupiter in a 3:2 mean motion resonance, such that Jupiter completed three orbits for every two of Saturn. Their planetary hook-up occurred at Jupiter’s maximum incursion into the inner system (Figure 2b), at a proposed radius of 1.5 AU, the present orbit of Mars. The marriage of Jupiter and Saturn initiated a kind of honeymoon cruise that carried them back into the outer system on ebbing tides of nebular gas (or in more astronomical lingo, this pair of gap-opening planets underwent resonant migration reversal). 

Meanwhile, in the inner system, a nascent family of Super Earths and assorted rocky planetesimals were being overwhelmed by hordes of planetesimals displaced inward by Jupiter’s aborted invasion. Batygin & Laughlin suggest that the mass scattered by the marauding giant exceeded 10 Earth masses (10 Mea) and might have been as much as 20 Mea. As soon as Jupiter began migrating outward again, these scattered objects spiraled rapidly into the Sun. Unfortunately for the existing Super Earths, the wave of annihilation swept them along with it. As the authors argue, “Provided that the cumulative mass of the resonant planetesimal population is not negligible compared with the mass of the close-in planets, the planetesimals will gravitationally shepherd the close-in planets into the Sun.” All that remained after their engulfment was about 2 Mea of debris, left like a cosmic bathtub ring around a radius of 1 AU (Figure 2c). These leftovers were the substrate of the four terrestrial planets (Figure 2d).

The scenario of Batygin & Laughlin blends smoothly into the Grand Tack and provides an apparently self-consistent model of Solar System evolution. Its mechanism is the forward scattering of a massive population of planetesimals by Jupiter’s inward-then-outward migration, a process that swept the inner system clean within a radius of about 0.7 AU. The authors emphasize that their results “imply a strong anti-correlation between the existence of multiple close-in planets and giant planets at orbital periods exceeding ~100 days within the same system,” an anti-correlation supported by much – but hardly all – existing exoplanetary data. (Current exceptions are HD 219134, HD 10180, Kepler-48, Kepler-68, Kepler-87, Kepler-90, and WASP-47.)

Batygin & Laughlin also draw a second and grimmer inference from their work: “the majority of Earth-mass planets are strongly enriched in volatile elements and are uninhabitable.” Although they don’t pause to detail the rationale behind that conclusion, I believe they mean something like this: Absent dynamic instabilities caused by migrating or scattered gas giants, inner system evolution is likely to produce several planets of a few Mea, all of which can accrete hydrogen atmospheres as long as they assemble before the gas nebula dissipates Although stellar irradiation can strip this hydrogen layer from small planets on hot orbits, planets of Earth mass or more in the system habitable zone will potentially retain their primordial envelopes indefinitely, causing an intense greenhouse effect that rules out surface water.

consolidation & crushing

Just two months after the publication of this widely praised work came a preprint by Kathryn Volk and Brett Gladman addressing the same problem from a different angle. Their study has since been published in the Astrophysical Journal Letters. The title itself is a great hook: “Consolidating and crushing exoplanets: Did it happen here?” Like Batygin & Laughlin (hereafter BL15), Volk & Gladman argue that most stars originally form compact systems of low-mass planets like Kepler-11 and Kepler-62, but then lose those planets in later stages of system evolution. Our Solar System is just one member of the dispossessed majority. Unlike BL15, Volk & Gladman do not make their scenario contingent on the Grand Tack. Without explicitly saying so, they offer an alternative model whose outcome would pre-empt the Nice model as an explanation for the Late Heavy Bombardment and replace the Grant Tack as an account of the sculpting of the inner Solar System. 

Volk & Gladman introduce their study by referring to the anomaly of our system’s mass cut-off inward of 0.4 AU. But their explanation is unrelated to a putative incursion by Jupiter and Saturn. Instead, they argue that all compact low-mass systems persist on the brink of chaos, and that the sample observed today represents only the survivors of an endogenous wave of orbital disaster that destroys most such systems. As Volk & Gladman describe it, their scenario “fits our solar system into a framework where dynamical instability mercilessly consolidates or degrades close-in planets.”

They begin with the construct of the minimum mass Solar nebula, which is based on the present-day masses of the eight surviving planets. As long as we extend that construct beyond its traditional but unmotivated inner limit, “several Earth masses of material [would be] available” between 0.05 AU and 0.7 AU, the present semimajor axis of Venus.

Volk & Gladman propose that, during primordial times, at least three rocky planets with a collective mass of 4 Mea coalesced inside Venus’ orbit. These worlds coexisted with Venus, Earth, and Mars for many millions of orbits, making the ancient Solar System an analog of those crowded Kepler systems. Then, at some point between system ages of 50 million and 500 million years or more, the innermost planets experienced a dynamical upset. The result was a cascade of orbit crossings and high-speed, shattering collisions that disintegrated 90% of their collective mass. Much of that mass was ground into fine dust that simply blew away, leaving battered Mercury as “the last remaining relic” of our inner system apocalypse.

To test their hypothesis of a primordial inner system of packed planets, Volk & Gladman numerically simulated analogs of 13 Kepler systems with 5 or more low-mass planets, eventually generating about 600 synthetic systems that they integrated for at least 100 million years. In half of the simulated systems, two planets eventually collided. On this evidence Volk & Gladman concluded that 90% to 95% of all tightly packed low-mass systems experience similar dynamic instabilities. The result is either “consolidation,” where smaller planets collide and coalesce to form larger planets, or “destruction,” where shattering destroys colliding planets. In their view, the low-mass, high-multiplicity systems observed by Kepler represent the 5% to 10% that avoided such an instability, whereas our Solar System is one of the more common cases in which destruction outpaced consolidation.

In their preferred model, four Earth-mass planets formed inside 0.5 AU. The model appears to be agnostic regarding the origin of Venus, Earth, and Mars, since it doesn’t address their accretion. Volk & Gladman conducted test integrations indicating that those three planets could coexist for at least half a billion years with a hypothetical packed inner system, and would remain unaffected by the furious collisions that eventually consumed their inner companions.

Volk & Gladman also suggest that the destruction of the inner planets could have caused the storm of asteroidal and cometary collisions variously known as the Lunar Cataclysm and the Late Heavy Bombardment. This hypothesis appears to contradict the Nice Model, which proposes that Neptune’s migration into the Solar System’s outer debris disk (now known as the Kuiper Belt) scattered comets inward among the planets and their moons, leaving the cratered landscapes we see today.

more different than not

The models of BL15 and Volk & Gladman 2015 (hereafter VG15) share important similarities. Both assume that the infant Solar System contained a compact family of short-period planets, and both argue that this ensemble was annihilated, leaving a void inside Mercury’s present orbit. But they differ on significant points, including the amount of mass originally available for planet formation inside 0.5 AU, the mechanism of the dynamical instability, and the timing of the resulting cataclysm, which has important implications for the terrestrial planets we know today.

Regarding mass, VG15 suggest about 4 Mea, while BL15 go an order of magnitude higher. BL15’s assumptions depend critically on recent models of in situ formation, which are discussed below, whereas VG15 use the traditional model of the minimum mass Solar nebula. They simply extend the nebula’s inner edge, as in many other recent studies.

Regarding mechanism, VG15 propose an internal trigger, while BL15 appeal to gravitational perturbations by wandering Jupiter. For VG15, the original planets simply self-destruct in an epoch of shattering collisions. For BL15, they are shepherded into the Sun by the swarm of planetesimals kicked into motion by Jupiter’s tacking maneuver.

As for timing, BL15’s scenario is constrained to play out within the first 10 million years of system evolution, possibly within the first 2 million. This hard limit derives from the observed lifetimes of protoplanetary nebulae around Sun-like stars, which have a median of 2 to 3 million years (Williams & Cieza 2011). The proposed tacking of Jupiter and Saturn from narrower to wider orbits could be sustained only by their interaction with the nebular gas, whose dissipation closed the window on such activity. None of this contradicts the established Grand Tack/Nice model, which has been developed over more than a decade of theoretical testing. Thereafter, the formation of the terrestrial planets proceeds along accepted lines, by giant impacts among protoplanets.

VG15 suggest a more leisurely schedule for their catastrophe. After the initial clutch of hot planets formed, they survived for hundreds of millions years before an instability developed. In fact, VL15 propose that the catastrophe coincided with the Lunar Cataclysm. Considerable evidence dates this event (or series of events) to an approximate system age of 800 million years. In other words, the Lunar Cataclysm is the same system-wide upheaval that the Nice model was developed to explain. Thus, while BL15 explicitly fold their scenario into the Nice/Grand Tack framework, VG15 appear to ignore or even oppose it. Their results, therefore, seem to conflict with what we know about the assembly of the existing terrestrial planets.

questions for volk & gladman

I find it hard to accept that the massive catastrophe described by VG15 would leave Venus, Earth, and Mars largely untouched. Maybe my instincts have been shaped more by science fiction than by astrophysics, but wouldn’t an instability on the scale they envision propagate throughout the system, destroying the three cool terrestrials along with the hotter hypothetical planets?

In addition, VG15 appear to neglect the evidence for the formation history of Earth and Mars. Radiogenic isotopes indicate that Mars formed about 10 million years after the Sun’s ignition, while the Earth-Moon system required 30 to 50 million years. Since VG15 suggest that all three terrestrials had already formed when the innermost planets disintegrated, something other than the birth ring presented by Hansen (2009) is needed to explain their assembly. VG15 never mention the well-known mass deficit in the space between present-day Earth and Jupiter – i.e., the “small Mars” problem and the presence of an attenuated debris field instead of a Super Earth inside Jupiter’s orbit. To my knowledge, the Grand Tack is the only plausible explanation offered to date for these architectural features (Walsh et al. 2011, Pierens & Raymond 2011). Since VG15 implicitly reject both the Nice model and the Grand Tack, accepting their scenario means we would need to find a new explanation for the architecture of the Solar System between 2 and 5 AU.

It looks like VG15 raise more questions than they answer. Among them is the very plausibility of consolidation and crushing as a mechanism for annihilation. A similar hypothesis was explored by Anders Johansen and colleagues in 2012 to explain the observed “Kepler dichotomy” between systems with a single transiting planet and those with several. Like VG15, Johansen and colleagues (hereafter J12) tested dynamical instability as an explanation for planetary depletion, and they did so by integrating a set of synthetic planetary systems based on real Kepler systems. Despite these similarities, the results of J13 directly contradict those of VG15. Most salient is their finding that the synthetic systems, containing planets on circular orbits with small mutual inclinations, were extremely stable over billions of years. Instances of planetary collision and consolidation were too rare to explain the observed system architectures. To assess this question in more detail, J12 integrated successively mass-boosted versions of their sample until collisions became significant. They found that smash-ups tended to happen only when the synthetic planets were boosted into the gas giant range, and even then, instabilities required more than a billion years to develop. On this and related evidence, J12 concluded that dynamical instabilities were not a significant factor in the evolution of compact Kepler systems. [Note: another recent simulation study by Hansen & Murray (2014) also found that, in compact systems of planets less massive than 10 Mea, “significant dynamical instability may not occur because, in most cases, orbit crossing cannot be achieved.”]

As a fan instead of an astronomer, I can’t authoritatively measure VG15 and J12 against each other. I can only note some of the ways in which they differ. One is their choice of simulated system architectures. J12 restricted their selection to systems of exactly three planets orbiting inside 0.5 AU, observing that the Kepler sample of higher-order multiples available in 2012 was too small to provide a statistically significant template for constructing synthetic systems. VG15 limited their simulations to systems with at least five planets – a surprising choice, since they also argued that a maximum of four hot planets formed in the primordial Solar System. In addition, one of their 13 systems (Kepler-90) appears to include a gas giant. Still worse, all 13 systems support planets substantially more massive than Earth, whereas VG15 propose only planets of approximately Earth-mass for their hypothetical Solar System ensemble. I have to wonder whether VG15 chose the most appropriate sample to investigate their study question.

Another difference between the two is that J12 addressed only ejections and collisional consolidations, without considering collisions that cause shattering. Yet the latter type was the explicit focus of VG15. Of course, without collisions, nothing shatters, so J12 cannot be faulted for omitting any mention of this outcome. In this regard it seems significant that VG15 kept their investigation of shattering collisions separate from their simulation study. They tested shattering only in analytic terms, and noted that these results were independent of the findings from the simulations. Yet without a high frequency of shattering, those findings would have no bearing on the emptiness of the inner Solar System.

Remarkably, VG15 never comment on the major findings of J12, even though they cite that study to support a statement about orbital inclinations. Why didn't they discuss its conclusions?

questions for batygin & laughlin 

So I have to favor BL15 over VG15. Nevertheless, despite my great respect for the work of Batygin and Laughlin, both separately and in collaboration, I find several nits to pick. These fall under three headings (with some overlap): their handling of Jupiter’s original birthplace, their choice of Kepler-11 as a model for the hypothetical inner Solar System, and their adherence to the theory of in situ formation.

For the Grand Tack, BL15 state that the exact starting point of Jupiter’s inward migration is unimportant. I believe that’s debatable, and I note that they actually model it as 6 AU. That semimajor axis is not only wider than Jupiter’s present orbit, but also wider than previous proposals for the Grand Tack, which placed the starting point between 2 and 5 AU (Walsh et al. 2011, Pierens & Raymond 2011). I can’t argue that 6 AU is implausible (in fact, it would make sense as long as the snow region commenced at a wider semimajor axis than it does today, as implied by theories of viscous heating), but I have to ask why BL15 chose that location in particular.

Since the mechanism underlying the inner system cataclysm in BL15’s model is a horde of scattered planetesimals, the hordes aggregate mass is a critical factor. The wider Jupiter’s original orbit, the larger the available mass. BL15 note that 20 Mea in planetesimals would be available inside 6 AU, while stating vaguely that the mass in planetesimals must be “not negligible” in comparison with the aggregate mass of the inner planets. But what does that mean? At least 10%, more than 50%, even 100% of the total mass? It would be helpful to know both the approximate fraction as well as the approximate mass against which it was estimated. For example, VG15 set a low bar by positing an aggregate mass of 4 Mea for their hypothetical planets, whereas 20 Mea would be another story entirely.

Another issue raised by Jupiter’s birthplace is the nature of the region through which proto-Jupiter and Saturn migrated on their way to sunnier orbits. If the early Solar System had several planets inside 0.5 AU and several more outside 6 AU, what was going on in the vast region between those endpoints? Core accretion theory says that coagulation of solids progressed throughout the Solar nebula. I would expect more planets to have formed in the space between, and that one or more of them would have complicated Jupiter’s inward passage. This doesn’t seem to be a fatal flaw in the theory, but it’s worth looking into.

Regarding the primordial family of planets doomed by Jupiter, BL15 mention the likelihood that they were “multi-Earth-mass” objects, as in so many Kepler systems. Three paragraphs later, they offer an illustration of the potential mass involved by referring to their simulation of the dynamical evolution of the Kepler-11 planets. In so doing they express appropriate caution: “We are not suggesting that a primordial population of the Solar Systems close-in planets would have necessarily borne any similarity to the Kepler-11 system.” Nevertheless, their previous mention of “multi-Earth-mass” planets implies a considerable aggregate mass. For the Kepler-11 system in particular, their opening paragraph cites Lissauer et al. 2011 to define a total in excess of 40 Mea. (That total was later revised downward to about 30 Mea by Lissauer et al. 2013.) In context, then, their “not negligible” mass in planetesimals would be 50% of the aggregated planetary masses (20 Mea of planetesimals/40 Mea of planets).

But how could our Solar System get 30 to 40 Mea worth of planets inside 0.5 AU?

the problem with in situ formation

While conceding that the theory is controversial, BL15 assume that their hypothetical family of Super Earths arose by in situ formation. In this model, planets of several Earth masses readily form in place on short-period orbits, tracing the primordial distribution of solids in the protoplanetary disk. Apart from a few earlier inquiries of limited scope (Raymond et al. 2008, Montgomery & Laughlin 2009), this theory emerged in 2012-2013 as a fully-fledged paradigm with various instantiations, some strict and some less so.

Chiang & Laughlin (2013) presented the “strict” version (their word). They argued that “disk-driven migration seems too poorly understood to connect meaningfully with observations,” and deprecated models that require this mechanism as both “premature” and “na├»ve.” In their place they proposed a minimum mass extrasolar nebula (MMEN). They obtained this construct by plotting the masses and orbits of all small Kepler planets then known, an exercise that highlights the pile-up of mass inside 0.25 AU. They explained this pile-up by arguing that the MMEN supports a much larger concentration of solids at small semimajor axes than previous models. Such a large mass, they argued, readily congeals into several Super Earths, as they illustrated with reference to the Kepler-11 system.

Brad Hansen & Norm Murray (2012) presented a “less strict” variation on the model (according to Chiang & Laughlin). They proposed that 30-100 Mea of solids could migrate from the outer regions of the protoplanetary disk to clump within 1 AU, where the planetesimals would stop migrating and rapidly condense into an ensemble of Super Earths (which I would call gas dwarfs). In a subsequent publication (Hansen & Murray 2013), the authors reduced the aggregate mass required to 20 Mea, while arguing that migration might not be necessary after all to account for such a concentration of solids. (Presumably their revision upped the strictness factor.)

Critiques of in situ theory came pretty quickly. The principal objection was that MMEN and similar models require protoplanetary disk masses much larger than those actually observed (Raymond et al. 2014) – so large that they would be gravitationally unstable (Schlichting 2014). Another objection was that MMEN implies a universal disk structure that is incompatible with the diversity of known multiplanet system architectures (Raymond & Cossou 2014). Still another was that “strict” in situ models rule out disk-driven migration. Yet as Izidoro et al. (2014) argued, “Assuming that no migration occurs essentially ignores 30 years of disk-planet studies that show the inevitability of orbital migration.” Indeed, Schlaufman (2014) found that without migration, the observed Kepler system architectures would be impossible. Additional research (Inamdar & Schlichting 2015) argued that planets forming on short-period orbits, even by condensation of solids originating in the outer system, could not accrete the substantial hydrogen envelopes observed in the Kepler sample.

According to the Astrophysical Data System, Greg Laughlin hasnt published anything theoretical on in situ formation since 2013. However, his colleague Eugene Chiang has continued to expand on this approach. Chiang’s recent work makes notable concessions to migration theory. He and his collaborators acknowledge that strict in situ approaches make the formation of gas giants at least as likely as Super Earths, possibly requiring some fine-tuning in the time scale for nebular dissipation (Lee et al. 2014). A brand-new study (Lee & Chiang 2015) even concedes that in situ models are insufficient to explain the diversity of the existing population of low-mass planets. Dividing the sample into two groups – “Super-Earths, which they define as planets between 1 and 4 Rea, and “Super-Puffs,” which have radii between 4 and 10 Rea but remain in the mass range of gas dwarfs – they offer this remarkable conclusion: “Unlike Super-Earths, which can form in situ, Super-Puffs probably migrated in to their current orbits.”

Apparently the strict in situ paradigm is stalled for now, leaving us with many fluid variations on the theme of disk-driven migration.

still looking pretty shiny

From my back alley perspective, the essential feature of Batygin & Laughlin’s scenario is its appeal to Jupiter’s migration as the source of the catastrophe. The giant’s inward passage was the mechanism that scattered forward a huge mass in planetesimals, which then efficiently herded all the baby planets in the inner nebula into the Sun. Although Batygin & Laughlin assume the existence of a system of compact Super Earths (which I would call gas dwarfs) inside 0.7 AU, their scenario doesn’t seem to require such a configuration, especially not one with an aggregate mass of 20 to 40 Mea. Any collection of protoplanets would do, including the modest system of terrestrial objects proposed by Volk & Gladman.

By now the limitations of the MMEN and similar in situ models have been discussed by numerous peer-reviewed studies, while a major proponent of the early model (Chiang) has since revised his approach. Simultaneously, increasingly sophisticated theories based on migration continue to proliferate. My hunch is that the latest migratory models are largely consistent with Batygin & Laughlin’s scenario, especially since it depends so critically on Type II migration. Kepler-11 aside, their comprehensive approach provides the best explanation yet for the strange things that must have happened before our world could be born.

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