Protoplanetary Disks and In Situ Formation

Figure 1. TW Hydrae, the nearest protoplanetary disk observed at high resolution by the Atacama Large Millimeter/submillimeter Array (ALMA). The disk has an approximate radius of 80 AU, which is twice the semimajor axis of Pluto in our Solar System. For other physical parameters of TW Hydrae, see Table 1 below.

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This is the second installment in a series about current theories of the formation of planetary systems. Part One provides background on planetology and system architecture. This installment begins with an overview of protoplanetary disks, which are the site of all planet formation, and then proceeds to outline one popular theory: in situ accretion.

Astronomical discoveries over the last two decades have established that planetary systems are an ordinary outcome of star formation. The formation process begins in the depths of dark, cold, massive clouds of gas and dust, typically located in the spiral arms of their parent galaxies. Individual clumps of gas collapse under their own gravity to fuel the ignition of stars, which are born as hot, bloated spheres. Baby stars arrive swaddled in remnants of their native cocoons: vaporous leftovers known as protoplanetary nebulae (Figures 1-4). As a star spins, its surrounding nebula flattens into a disk-like structure through which molecules of hydrogen/helium (H/He) and dust swirl in a ratio of about 100:1 (Williams & Cieza 2011, hereafter WC11). The ambient “dust” consists of ices of various compositions mixed with refractory particles of metals and silicates.

The primordial disk is a kind of pancake made of clouds, except that it puffs up around the edges and eventually evaporates instead of turning crispy. Its basic ingredients determine the nature of the planetary residue left behind when the cloud disperses. Among the most important characteristics of the protoplanetary disk are its overall mass and chemical composition, especially the proportion of heavy elements (particularly iron) to hydrogen. This proportion is known as metallicity and expressed as [Fe/H], on a scale where zero equals the metallicity of our Sun. Another potential contributor to gestating planets is the ratio of water to silicates in the composition of the ambient dust (Bitsch & Johansen 2016), although this topic has not been studied as well as metallicity and mass.

High metallicity is robustly associated with the presence of gas giant planets – that is, objects of at least 50 Earth masses (50 Mea) but less than 13 Jupiter masses (13 Mjup) – whereas low-mass planets occur around stars of all chemical compositions (Buchhave & al. 2012). Stellar mass is also a predictor of gas giant companions. At constant metallicity, stars more massive than the Sun are more likely to host gas giants than stars of Solar mass or less (Johnson & al. 2010).

Extensive observations of star-forming regions have demonstrated that the mass of a protoplanetary disk scales roughly with the mass of its parent star. This relationship suggests a further correlation between disk mass and planet mass (WC11, Andrews et al. 2013). Despite a significant dispersion at any given value, a typical disk is probably 1% or less of the mass of its parent star, possibly in the range of 0.2% to 0.6%. The median mass for disks around Sun-like stars might be as low as 5 Mjup (WC11), equivalent to 0.48% of the Sun’s mass (o.0048 Msol).

Figure 2. The ALMA Three

These spectacular photographs by the ALMA instrument captured three nearby protoplanetary disks – HL Tauri, TW Hydrae, and V883 Orionis – that differ significantly in radius, mass, and age. See Table 1 for individual parameters.

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The observed radial extent of protoplanetary disks shows at least as much variation as their masses. Disk radii in nearby star-forming regions range from about 15 to 200 astronomical units (AU), with outliers in the range of 400 to 600 AU (WC11). A survey of the Orion Nebula estimated that three-quarters of all disks have radii smaller than 75 AU (WC11). By comparison, the radius of Neptune’s orbit is about 30 AU, while the aphelion of Pluto (i.e., its widest separation from the Sun) is about 50 AU. Current theory places the outer boundary of the original Solar nebula at Neptune’s orbit. If that estimate is accurate, our system’s protoplanetary disk would fall near the low end of the distribution of disk radii.

Disk mass has no necessary correspondence with disk radius, as evidenced by the largest protoplanetary disk observed in the Orion Nebula (Bally & al. 2015). Known as 114-426, this object is observed almost edge-on, with a radius of 475 AU. Dust is concentrated inside 175 AU. Despite these impressive dimensions, the central star is evidently an early M or late K dwarf with a mass in the range of 0.4-0.7 Msol. The estimated disk mass is only 3.1 Mjup (0.003 Msol). Nevertheless, recent observations indicate that 114-426 has undergone substantial evolution, even though its age is only 1-2 million years. Much of its original solid mass has likely already congealed into planetesimals and protoplanets.

Table 1. Parameters of the ALMA Three (see Figure 2)

Abbreviations: AU = astronomical unit (93 million miles/150 million km); Msol = Solar mass; Myr = millions of years; Pc = parsec (3.26 light years). Sources: Nomura et al. 2016, Andrews et al. 2016, ALMA Partnership 2015, Cieza et al. 2016.

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The recent high-resolution imaging of three active protoplanetary disks suggests that this new sample is somewhat atypical. As summarized in Table 1, the masses of these structures exceed the proposed means. At an age of half a million years, the disk around V883 Orionis has a radius of about 125 AU and an imposing mass of 0.3 Msol, about 20% of the mass of its F-type host star. At an age of 1 million years, the HL Tauri disk is about 100 AU in extent with a poorly constrained mass of 0.03-0.14 Msol. At an age approaching 10 million years, the TW Hydrae disk has a radius of 75 AU or more and a mass of 0.05 Msol. It may be that these earliest image captures are outliers within the full sample of nearby protoplanetary disks. If so, we would have a parallel between extrasolar disks and extrasolar planets: Although Hot Jupiters dominated the exoplanetary census in the late 1990s, this planetary type comprises less than 1% of the de-biased sample (Wright et al. 2012).

In any event, the overall life expectancy of protoplanetary disks appears to be better constrained than their typical masses and radii. Disks are born at the same time as their parent stars, and few (with the notable exception of TW Hydrae) have been observed at ages of 10 million years or more. For disks around stars of Solar mass or less, surveys regularly find a median age of 2 to 3 million years. A recent theoretical study arrived at a slightly higher mean age of 3.7 million years (Kimura et al. 2016). Shorter lifetimes are observed for hotter, more massive stars, as well as for stars with binary companions (WC11).

All these data on the mass, extent, and lifespan of protoplanetary disks provide inescapable limits for theories of planet formation. Most critically, any object with an atmosphere containing more than 1%-2% of its bulk composition in H/He must have formed in the presence of a gas disk, since no other source of light gases would be available to forming planets. That bulk composition describes the vast majority of exoplanets detected by any method. In sharp contrast, Earth and Venus evidently accreted many millions of years after the dispersal of our system’s protoplanetary nebula (Hansen 2009).  

Figure 3. Protoplanetary disks in the Orion Nebula

 

With likely ages between 1 and 2 million years, all these young stellar objects are still embedded in their primordial nebulae. The five photos in the center of this selection depict systems that have evolved to the stage of flared protoplanetary disks, as revealed by their silhouettes. Image credit: NASA/ESA/Luca Ricci.
 

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minimum mass solar nebula

 

Even before the availability of instruments capable of studying nearby stellar nurseries, astronomers based inferences about the Sun’s original nebula on the structure of the present-day Solar System. The construct of the “minimum mass Solar nebula” (MMSN) was developed in the 1970s to estimate the approximate mass and density of our long-vanished native cloud. Stuart Weidenschilling (1977) provided a detailed exposition of the assumptions underlying this model. First, the area occupied by the orbits of the eight major planets (excluding Pluto, despite its recognition as a planet before 2006) and the asteroid belt was divided into nine zones. Next, the bulk mass of each governing planet or debris field was distributed evenly throughout its zone, augmented with enough H/He to bring the zonal composition in line with the ratio of elements in the Sun. Mercury’s zone was assumed to extend inward as far as 0.23 AU, while Neptune’s extended outward to 41 AU.

 

This model enabled a rough estimate of the mass of the original Solar nebula. Depending on assumptions about the quantity of solid mass in the gas giant planets, estimates of the MMSN ranged from 0.01 to 0.07 Msol (Weidenschilling 1977). The same approach also enabled an estimate of the surface density of the original nebula (i.e., its two-dimensional distribution of mass). Mercury was excluded from the latter calculation, which indicated a peak in surface density around the orbit of Venus and then a steady depletion out to the orbit of Neptune. Despite the high surface density of solids inside 1 AU, the broad radial extent of the MMSN guaranteed that most of its volatile and refractory mass lay outside 4 AU.

Weidenschilling noted that the model was intended to represent the nebula at the time of planet formation, not in its primordial state. This clarification opened the possibility that unknown evolutionary processes had transformed the original cloud. In particular, Weidenschilling emphasized the depletion of mass in Mercury’s zone (0.23-0.56 AU) as well as in the more extensive region occupied by Mars and the asteroids (1.2-4.2 AU). These notable gaps suggested a “preferential removal” of “several Earth masses of solid matter.” (For more about the missing mass problem, see Solar System Archaeology, Jupiter Descending, and Jupiter Re-Ascending.)

Four decades later, the MMSN is still regularly invoked and critiqued in theoretical studies, and investigators are still debating the mass and surface density of Solar and extrasolar nebulae. Williams & Cieza favor the low end of Weidenschilling’s mass estimate (0.01 Msol), which is equivalent to approximately 10 Mjup. They estimate that only 15% of disks around stars like our Sun harbor this much mass within radii of 50 AU, and they infer that disks harboring substantially more mass must be rare (WC11). Yet many theorists have invoked disks as much as an order of magnitude more massive than 0.01 Msol to explain specific system architectures.

As for surface density, the consensus view is that it peaks in the innermost region of the disk and trails into vacuum at the outer limits, but the shape of the slope remains controversial. Many studies have adopted a smooth power-law decline, with disagreements from author to author on the relative steepness of the slope. Meanwhile, a growing number of studies argue against a smooth slope, favoring bumps and valleys instead. This view appears to be supported by recent imaging of HL Tauri, TW Hydrae, and V883 Orionis (Figures 1 & 2).

The rings and gaps in these images, as well as the peaks and valleys in surface density predicted by theory, imply that protoplanetary disks are radially structured. Among the potential sources of this structure, two candidates are especially popular. The first is growing planets, which might carve out rings in the disk by clearing dust and potentially gas along their orbits. The second is discontinuities in heat, pressure, and density located at specific radii in the disk. These two explanations are not mutually exclusive, and indeed might be interdependent. Radial structure is the focus of Part Three in this series, which will look at such constructs as planet traps, snow lines, sublimation radii, planet deserts, sweet spots, and dead zones.

Figure 4. Artist’s view of a young protoplanetary disk

Image credit: Reported as NASA

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cloud dynamics

I’ve always preferred “nebula” over “disk” to designate the environment where baby planets are born. “Nebula” makes me think of swirling gases, whereas “disk” suggests a rigid, brittle object like a CD or an LP. Although I concede that the gaps and rings revealed by ALMA actually do resemble the tracks on a vinyl LP, I still think “disk” is a dubious metaphor for the objects pictured in Figures 1-4. These clouds are fluid and highly dynamic. Their constituent gas molecules travel inward in a continuous flow to feed the central star, carrying dust along with them. At the same time, the far reaches of the nebula spread outward, such that the cloud is attenuating simultaneously at its inner and outer boundaries. It's like a candle burning at both ends.

The steady outward diffusion of gas and dust into the interstellar medium means that protoplanetary disks lack a sharp outer edge – another way in which they differ from vinyl or plastic disks. The photograph of TW Hydrae (Figure 1) illustrates this diffuse border zone. By contrast, disks have a distinct inner cavity created by the interaction between the central star’s magnetic field and the disk’s constituent gases. While accreting H/He can jump this gap to accrete through the star’s north and south magnetic poles, the cavity creates a distinct inner wall in the nebula, inside which gas dynamics cease.

When we remember that more than half of protoplanetary disks vanish within 4 million years, we get a sense of the rapid pace of their evolution. “Feverish” seems a more appropriate descriptor than “glacial.” To put the timescale in perspective, here are some big numbers: Our Solar System orbits the core of the Milky Way Galaxy in a period of about 250 million years, known as the galactic year. By that measure, our Sun is about 18 galactic years old. The Cryogenian Glaciation on our planet, often described as Snowball Earth, lasted 85 million years (from 720 to 635 million years ago). Although it was merely a single brief winter in the galactic year, this icy interval was still much longer than the span of 7 million years needed for Pan prior, the last common ancestor of apes and humans, to evolve into Homo sapiens, our own species. The accretion of mighty Jupiter, which could swallow Earth and a convoy of planets like it, probably took only half as long as that. Planet formation is a fleeting process in which small changes have big consequences, and time is of the essence.

Figure 5. Distribution of mass in selected systems with at least 3 planets

 

in situ formation

Until a few decades ago, astronomers believed that the Sun’s eight planets formed more or less where they are now observed. Then came the first discoveries of extrasolar gas giants (so-called “Hot Jupiters”) orbiting their host stars in periods of a few days or weeks. These momentous findings coincided with a rapid expansion of our understanding of protoplanetary disks, especially those in the Orion Nebula. Theorists responded to the new extrasolar data with a steadily growing body of research on the multifarious ways in which forming planets can change their orbits. In the most popular scenarios, they do so by navigating the flux of evolving nebulae. In recent years this work has resulted in a novel explanation for the apparent anomalies in our Solar System’ architecture. Known as the Grand Tack, the new model indicates that all four of the outer planets have undergone orbital migration and scattering, sometimes inward and sometimes outward, so that none of these planets are exactly where they started.

But just as cosmologists were beginning to think that the evolution of the Solar System was more like that of a typical exoplanetary system, with various regimes of migration and numerous opportunities for planet scattering and collisions, a radical new model emerged for the genesis of low-mass planets like those on the left side of Figure 5: coalescence in place, better known as in situ formation. Apart from a few earlier, more limited inquiries (Raymond et al. 2008, Montgomery & Laughlin 2009), this theory emerged in 2012-2013 as a fully-fledged paradigm.

In this model, planets of several Earth masses readily form in place on short-period orbits, tracing the distribution of solids in the protoplanetary disk. Eugene Chiang & Greg Laughlin (2013) presented a “strict” version (their word) of this hypothesis. Arguing that “disk-driven migration seems too poorly understood to connect meaningfully with observations,” they deprecated models that require migration as both “premature” and “naïve.” In their place they proposed a minimum mass extrasolar nebula (MMEN). This construct was obtained by plotting the masses and orbits of the small Kepler planets then known and constructing a disk in which the concentration of solids matched the location of the planets. Results highlighted the pile-up of planetary mass inside 0.25 AU, which is correlated with the rapidly declining likelihood of detecting transiting planets on periods longer than 10 days.

Contrary to standard models of the MMSN, which feature a gap with a radius of about 0.5 AU at the center of the protoplanetary disk, Chiang & Laughlin preferred an inner disk edge around 0.05 AU. They associate this boundary with the dust sublimation radius around a mature Sun-like star – the radius within which silicate particles transition to gas, removing the possibility of accretion. The surface density of their MMEN peaks at this location and declines smoothly with increasing distance.

Given this structure, the MMEN could support a much larger concentration of solids at small semimajor axes than previous models. After boosting its overall mass by a factor of 5 to 10, Chiang & Laughlin proposed that the MMEN could even support an in situ origin for the planets of Kepler-11 and other high-multiplicity systems.

Meanwhile, Brad Hansen & Norm Murray (2012) had already presented a “less strict” variation on this approach (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 planetesimals would congregate and rapidly condense into an ensemble of Super Earths (which I would call gas dwarfs). Perhaps to distinguish their approach from one that relies exclusively on solids of local origin, they used the term “in situ assembly” to describe it. (The questions raised by this migration + assembly scenario differ from the ones posed by the MMEN, as we’ll see below.)

Critiques of in situ theory came pretty quickly. The principal objection was that the MMEN is inconsistent with observations of actual protoplanetary disks. The high mass required for in situ formation inside 1 AU can be obtained only with extreme fine-tuning: Either the overall disk mass must be many times larger than the MMSN, or the surface density profile of the disk must be far steeper than that of the MMSN (Raymond et al. 2014). Sean Raymond & colleagues offered the example of a disk with a radius of 50 AU and an overall mass of 0.05 Msol – that is, 5 to 25 times the typical disk mass estimated by CW11 and Andrews et al. 2013. With a slope in surface density similar to the MMSN, such a disk would harbor only 0.4 to 3 Mea inside 1 AU, hardly enough to build a system like Kepler-11 or Kepler-20 (see Figure 5). Only a substantially steeper decline in surface density would supply as much as 40 Mea in the inner region of the disk.

Now, we know that some stars harbor protoplanetary disks on the order of 0.1 to 0.3 Msol, and it’s possible that some fraction of them also support central concentrations of mass consistent with the quantities needed for in situ assembly of hot gas dwarfs. But the whole point of in situ models was to capture “a major if not the dominant mode of planet formation in the Galaxy” (Chiang & Laughlin 2013), not to showcase a rare and unlikely pathway to a widespread system architecture.

Another major objection was that the MMEN implies a universal disk structure that is incompatible with the diversity of known multiplanet systems (Raymond & Cossou 2014). Sean Raymond & Christophe Cossou attempted to construct their own version of the MMEN, following the approach of Chiang & Laughlin. They took a sample of exoplanetary systems with at least three low-mass planets inside 1 AU, smoothly distributed all masses in each system in a series of concentric rings (as Weidenschilling did to construct the MMSN), and attempted to build a single disk model that could reproduce their sample. It was an impossible task. Not only would it require an unrealistically large disk mass (two to three times larger than the value proposed by Chiang & Laughlin for their MMEN) – no single profile could accommodate the diverse sample of available systems. In some of them, the mass profile had to increase with radial distance, which is implausible. In others, the slope was so steep that it produced unphysical distributions. The authors were able to demonstrate that “a universal disc profile is statistically excluded at high confidence.”

As they concluded: “The known systems of hot super-Earths must therefore not represent the structure of their parent gas discs and cannot have predominantly formed in situ. We instead interpret the diversity of disc slopes as the imprint of a process that re-arranged the solids relative to the gas in the inner parts of protoplanetary discs.” (Raymond & Cossou 2014).

In other words, the observed architectures of planetary systems do not reflect their primordial distribution of solid mass. Yet the “strict” in situ model favored by Chiang & Laughlin ruled out migration, the likeliest mechanism for concentrating solid mass at small semimajor axes.

Other critiques focused specifically on this anti-migrationist assumption. André Izidoro & colleagues (2014) argued, “Assuming that no migration occurs essentially ignores 30 years of disk-planet studies that show the inevitability of orbital migration.” Similarly, Kevin Schlaufman (2014) found that, without migration, the observed Kepler system architectures would be impossible.

Yet another flaw in the model was identified by one of its proponents, Eugene Chiang, in collaboration with first author Eve Lee and co-author Chris Ormel. As Lee & colleagues (2014) noted, the same conditions that favor the assembly of gas dwarfs in the range of 5-10 Mea at small semimajor axes are equally favorable to the formation of gas giants at the same locations. Since the latter outcome is not observed – gas giants are much less common than low-mass planets inside 1 AU – in situ theory needs adjustment. They proposed that the formation of planets capable of accreting hydrogen atmospheres must be delayed until shortly before the dissipation of the nebular gas. Otherwise, planets of a few Earth masses would rapidly balloon into warm and hot gas giants. Although this looks like a case of fine-tuning, the authors did not suggest a mechanism to account for the delay. Thus we might have another example of a scenario that would apply only to a small fraction of extant planetary systems, rather than representing a characteristic and widely encountered mode of planet formation.

immobility versus drift

All these critiques have resulted in revisions in more recent in situ models, with some studies discarding the MMEN altogether and invoking in its place either a) drift of solids or even b) migration of fully-formed planets from cooler regions of the protoplanetary disk into short-period orbits (e.g., Lee & Chiang 2016). In fact, one of the earliest self-described in situ scenarios (Hansen & Murray 2012) conceded that locally available solids inside 1 AU would probably be insufficient to form systems like Kepler 11 or Kepler 20. Therefore, in a series of articles published 2012-2015, lead author Brad Hansen proposed either migration or radial drift to explain the accumulation of 20-100 Mea of solids in the inner regions of protoplanetary disks.

But does such an approach still qualify as an in situ model? In an extended footnote to their recent study of the formation of Jupiter, Sean Raymond & colleagues say no:

“This model should not be confused with the strict ‘in-situ accretion’ model, which conjectures that hot super-Earths form locally from locally-condensed solids (proposed and subsequently rejected by Raymond et al. 2008, then re-proposed by Chiang & Laughlin (2013)). In-situ accretion requires extremely massive disks very close to their stars (Chiang & Laughlin 2013). There are many arguments against the strict in-situ accretion model (see Raymond et al. 2008, 2014; Schlichting 2014; Schlaufman 2014; Raymond & Cossou 2014; Inamdar & Schlichting 2015; Ogihara et al. 2015). We propose that models that invoke the inward drift of solids followed by accretion at close-in orbital radii should be referred to as a separate category of ‘drift’ models rather than being lumped together with in situ accretion.” (Raymond et al. 2016)

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Indeed, Hansen himself has noted various criticisms of in situ approaches, even expressing a degree of support for models that depend heavily on migration:

“. . . the speed and even direction of migration depend on the imperfect cancellation between the torques exerted by the disk interior and exterior to the planet. One possibility, suggested by several authors (e.g., Masset et al. 2006), is that the torque may reverse sign at particular locations in the disk, leading to “planet traps”—preferred locations where planets assemble. It is possible that our power-law surface density profile may simply represent an averaged version of a disk with several such preferred locations, and that some disks may have more localized distributions which could contribute to the overabundance of low-multiplicity systems. Indeed, this might help to place our solar system in the Kepler context, as our own terrestrial planet system is potentially the outcome of a disk with a single localized planet trap.” (Hansen & Murray 2013)

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all accretion is local

From my back alley perspective it looks like the exoplanet community’s recent flirtation with in situ hypotheses has cooled off. The diverse problems with this approach have now been widely discussed. Meanwhile, no study to date has presented a planetary system whose architecture can be explained only by strict in situ assembly. Instead, any system architecture that might appear consistent with in situ formation (e.g., Proxima Centauri or Kepler-11) can be explained even more plausibly by a scenario involving migration (Coleman et al. 2016, D’Angelo & Bodenheimer 2016).

I don’t mean to suggest that in situ models have been a waste of time. Their elaboration in the literature has inspired many researchers to look more closely at the ways in which solids and gas can be incorporated by planets forming in the inner regions of a protoplanetary disk. The result has been in a net gain in our understanding of accretion. Just as important, in situ theorists have successfully retired models in which solids are necessarily depleted from protoplanetary nebulae inside 0.5 AU. This move represents a further advance in the Copernican paradigm, which displaces our Solar System from its position as the reference case for evolutionary models. We now understand that a system of four or five planets, with masses ranging from 0.5 Mea to about 2 Mea, might form in situ on orbits ranging from 10 to 500 days – without invoking some special mechanism to boost the local mass in solids. Instead, it’s clear that the depletion of mass in the ancient Solar System is the oddity that needs explanation.

Whether solids are present ab initio in the feeding zone of a protoplanet, or whether they migrate there in the form of pebbles or planetesimals from elsewhere in the disk, all accretion is local. The universe has evolved manifold pathways to move mass from one region of a dusty nebula to another. These paths will be explored in the final installment of the series, which reviews current variations on the theme of disk-driven migration.

 

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REFERENCES

ALMA Partnership, et al. (2015) First results from high angular resolution ALMA observations toward the HL Tau region. Astrophysical Journal Letters 808, L3.

Andrews SM, Rosenfeld KA, Kraus AL, Wilner DJ. (2013) The mass dependence between protoplanetary disks and their stellar hosts. Astrophysical Journal 771, 129.

Andrews SM. (2015) Observations of solids in protoplanetary disks. Publications of the Astronomical Society of Pacific 127, 961-993.

Andrews SM, Wilner DJ, Zhu Z, Birnstiel T, Carpenter JM, Perez LM, Bai XN, Oberg K, Hughes AM, Isella A, Ricci L. (2016) Ringed substructure and a gap at 1 AU in the nearest protoplanetary disk. Astrophysical Journal Letters 820, L40.

Bally J, Mann RK, Eisner J, Andrews SM, Di Francesco J, Hughes M, Johnstone D, Matthews B, Ricci L, Williams JP. (2015) ALMA observations of the largest proto-planetary disk in the Orion Nebula, 114–426: a CO silhouette. Astrophysical Journal 808, 69.

Bitsch B, Johansen A. (2016) Influence of the water content in protoplanetary discs on planet migration and formation. Astronomy & Astrophysics 590, A101.

Buchhave L, Latham DW, Johansen A, Bizzarro M, Torres G, Rowe JF, Batalha NM, Borucki WJ, et al. (2012) An abundance of small exoplanets around stars with a wide range of metallicities. Nature 486, 375-377.

Chiang E, Laughlin G. (2013) The minimum-mass extrasolar nebula: in situ formation of close-in Super-Earths. Monthly Notices of the Royal Astronomical Society 431, 3444-3455. Abstract: 2013MNRAS.431.3444C

Cieza L, Casassus S, Tobin J, Bos SP, Williams JP, Perez Z, et al. (2016) Imaging the water snow-line during a protostellar outburst. Nature 535, 258-261.

Coleman GAL, Nelson RP, Paardekooper SJ, Dreizler S, Giesers B, Anglada-Escude G. (2016) Exploring plausible formation scenarios for the planet candidate orbiting Proxima Centauri. In press. Abstract: 2016arXiv160806908C

D’Angelo G, Bodenheimer P. (2016) In situ and ex situ formation models of Kepler 11 planets. Astrophysical Journal 828, 33. Abstract: 2016ApJ...828...33D

Hansen B. (2009) Formation of the terrestrial planets from a narrow annulus. Astrophysical Journal 703, 1131-1140. Abstract: 2009ApJ...703.1131H

Hansen B, Murray N. (2012) Migration then assembly: Formation of Neptune-mass planets inside 1 AU. Astrophysical Journal 751, 158. Abstract: 2012ApJ...751..158H

Hansen B, Murray N. (2013) Testing in situ assembly with the Kepler planet candidate sample. Astrophysical Journal 775, 53. Abstract: 2013ApJ...775...53H

Hansen BMS. (2014) The circulation of dust in protoplanetary discs and the initial conditions of planet formation. Monthly Notices of the Royal Astronomical Society 440, 3545-3556. Abstract: 2014MNRAS.440.3545H

Hansen BMS. (2015) In situ models for planet assembly around cool stars. International Journal of Astrobiology 14, 267-278.

Inamdar NK, Schlichting HE. (2015) The formation of Super-Earths and Mini-Neptunes with giant impacts. Monthly Notices of the Royal Astronomical Society 448, 1751-1760.

Izidoro A, Morbidelli A, Raymond SN. (2014) Terrestrial planet formation in the presence of migrating Super-Earths. Astrophysical Journal 794, 11.

Johnson JA, Aller KM, Howard AW, Crepp JR. (2010) Giant planet occurrence in the stellar mass-metallicity plane. Publications of the Astronomical Society of the Pacific 122, 905-915.

Kimura S, Kunitomo M, Takahashi S. (2016) From birth to death of protoplanetary disks: Modeling their formation, evolution, and dispersal. Monthly Notices of the Royal Astronomical Society 461, 2257-2265.

Lee EJ, Chiang E, Ormel CW. (2014 ) Make Super-Earths, not Jupiters: Accreting nebular gas onto solid cores at 0.1 AU and beyond. Astrophysical Journal 797, 95. Abstract: 2014ApJ...797...95L

Lee EJ, Chiang E. (2016) Breeding Super-Earths and birthing Super-Puffs in transitional disks. Astrophysical Journal 817, 90. Abstract: 2016ApJ...817...90L

Lissauer JJ. (1993) Planet Formation. Annual Review of Astronomy & Astrophysics 1993, 31: 129-174.

Masset FS, Morbidelli A, Crida A, Ferreira J. (2006) Disk surface density transitions as protoplanet traps. Astrophysical Journal 642, 478–487.

Montgomery R, Laughlin G. (2009) Formation and detection of Earth mass planets around low mass stars. Icarus 202, 1-11.

Nomura H, Tsugakoshi T, Kawabe R, Ishimoto D, Okuzumi S, Muto T, et al. (2016) ALMA observations of a gap and a ring in the protoplanetary disk around TW Hya. Astrophysical Journal Letters 819, L7.

Pollack JB, Hubickyj O, Bodenheimer P, Lissauer JJ, Podolak M, Greenzweig Y. (1996) Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62-85.

Raymond SN, Barnes R, Mandell AM. (2008) Observable consequences of planet formation models in systems with close-in terrestrial planets. Monthly Notices of the Royal Astronomical Society 384, 663–674.

Raymond SN, Kokubo E, Morbidelli A, Morishima R, Walsh KJ. (2014) Terrestrial planet formation at home and abroad. In Protostars and Planets VI, eds. Beuther H, Klessen RS, Dullemond CP, Henning T. Tucson: University of Arizona Press, pp 595-618.

Raymond SN, Cossou C. (2014) No universal minimum-mass extrasolar nebula: evidence against in situ accretion of systems of hot super-Earths. Monthly Notices of the Royal Astronomical Society 440, L11-L15.

Raymond SN, Izidoro A, Bitsch B, Jacobson SA. (2016) Did Jupiter’s core form in the innermost parts of the Sun’s protoplanetary disk? Monthly Notices of the Royal Astronomical Society 458, 2962-2972.

Schlaufman KC. (2014) Tests of in situ formation scenarios for compact multiplanet systems. Astrophysical Journal 790, 91.

Schlichting HE. (2014) Formation of close in Super-Earths & Mini-Neptunes: Required disk masses & their implications. Astrophysical Journal Letters 795, L15. Abstract: 2014ApJ...795L..15S  

Swanson-Hysell NL, Rose CV, Calmet CC, Halverson GP, Hurtgen MT, Maloof AC. (2010) Cryogenian glaciation and the onset of carbon-isotope decoupling. Science 328, 608-611.

Wright JT, Marcy GW, Howard AW, Johnson JA, Morton TD, Fischer DA. (2012) The frequency of Hot Jupiters orbiting nearby Solar-type stars. Astrophysical Journal 753, 160.

Weidenschilling JS. (1977) The distribution of mass in the planetary system and solar nebula. Astrophysics and Space Science 51, 153-158.

Williams JP, Cieza LC. (2011) Protoplanetary disks and their evolution. Annual Review of Astronomy and Astrophysics 49, 67-117. Abstract: 2011ARA&A..49...67W

 

 

Where Do Baby Planets Come From?

Figure 1. A stellar nursery: IC 348, the nearest rich star cluster still embedded in its primordial cloud of gaseous hydrogen and dust. Located in the constellation Perseus at a distance of 320 parsecs (1040 light years), IC 348 occupies one end of an extensive complex of molecular hydrogen clouds that includes NGC 1333. At an age of 2 to 3 million years, IC 348 contains about 300 infant stars, ranging from dim red dwarfs to hot blue stars of spectral class B. Credit: NASA/Lucas Cieza

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Back when the only planets ever discovered were the ones in our Solar System, astronomers thought they knew how planetary systems formed. Then came the news about extrasolar planets – first a trickle of oddballs and outliers, eventually a flood of rank and file candidates from the Kepler Mission and its successors. Theoreticians are still struggling to produce models that can explain the full range of system architectures and planetary types implied by observations.

 

The most widely accepted theory of planet formation is core accretion, which descends from the so-called nebular hypothesis proposed in the 18th century by Immanuel Kant and Pierre-Simon de Laplace. In different languages, these two philosophers argued that the young Sun was surrounded by a thin cloud of dust grains, which coagulated in vortices to form larger units called planetesimals (Planetesimale, planétésimaux), which in turn collided to form the known planets.

 

The 21st century variation on this hypothesis begins with a similar circumsolar nebula, now specified as a blend of hydrogen and helium (H/He) supporting a sprinkling of dust. The ambient cloud is typically called a protoplanetary disk or primordial nebula or some variation on those terms. Figure 2 is a photograph of such a structure at an approximate age of 1 million years.

 

Inside these clouds, sticky collisions among dust grains, pebbles, and planetesimals form larger objects known as protoplanets (or planetary cores or planetary embryos). These objects have masses ranging from Moon-like to Mars-like. Under appropriate conditions, protoplanets can continue to accrete mass by colliding and merging with other protoplanets. Beyond some threshold in the range of 1 to 5 Earth masses (Mea), a growing planet will acquire a H/He envelope, forming an object like Uranus or the puffy Super Earths discovered by Kepler. If an object continues stockpiling gas until its envelope rivals the mass of its solid core, runaway accretion will ensue, resulting in a massive gas-dominated planet like Jupiter.

 

Figure 2. The protoplanetary nebula around HL Tauri

This photograph by the Atacama Large Millimeter/submillimeter Array (ALMA) captures a series of bright rings and dark gaps in the protoplanetary disk surrounding HL Tauri, a newborn Sun-like star located at a distance of about 140 parsecs (456 light years). Various sources provide radii in the range of 90-120 astronomical units (AU) for the disk, which is about 1 million years old. These values are larger by a factor of 3 to 4 than the radius proposed for our Sun’s protoplanetary disk.

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Most contemporary research on planet formation is based on the accretion scenario, which is currently available in two basic models. In one, disk-driven migration is a fundamental process governing system evolution. Pebbles, protoplanets, and planets change their radial position in the nebula over time, migrating either inward or outward by interacting with the flow of gases, and in turn interacting with each other, to produce planetary systems. The other approach favors in situ formation, arguing that growing planetary cores stay where they are and simply accrete material from their immediate surroundings. Subsequent posts in this series will explore each model.

 

the extrasolar bestiary

We know that planets come in a limited number of species, as determined by their mass and composition (Figure 3). The easiest to discover are the high-mass or gas giant planets, which are objects more massive than about 50 Mea with bulk compositions that are more than 50% H/He. Our Solar System has two beauties: Jupiter and Saturn.

Then come the low-mass planets, which can be divided into two sub-populations. Gas dwarfs are generally at least 2 Mea but less than 50 Mea. Their defining characteristic is a bulk composition that is less than 50% but at least 0.1% H/He. Terrestrial planets are devoid of gaseous H/He and generally less massive than 10 Mea. Our Solar System has two gas dwarfs (Uranus and Neptune) and four terrestrial planets (Mercury, Venus, Earth, and Mars).

Despite their diminutive size and difficulty of observation in other star systems, most humans are most interested in the terrestrials. The reason is simple. As far as anyone knows, life – or at least life that we would recognize as such – can evolve only on small rocky worlds like Earth.

Figure 3. Planets across five orders of magnitude in mass

Planets are shown at their relative sizes. All have well-measured masses and radii. The numbers above the red line indicate the objects’ approximate mass in Earth units (Mea). In more exact terms, Mars is 0.11 Mea, Uranus is 14.5 Mea, and Saturn is 95 Mea. The numbers below the red line indicate the objects’ mass in Jupiter units or Mj. The image of WASP-10b is an artist’s impression; the other images are photographs or photo composites.

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Data from the most successful search methods – radial velocity and transit observations – demonstrate that low-mass planets are the most numerous species orbiting within a few astronomical units of main sequence stars (astronomical unit = AU; 1 AU = distance between Earth and Sun). They occur preferentially in multiplanet systems and are observed in a variety of architectures. Most interesting are the high-multiplicity systems, meaning those with at least three planets. A representative sample of high-multiplicity architectures centered on Sun-like stars appears in Figure 4.

 

Figure 4. Distribution of mass in selected systems with at least 3 planets

Star masses are indicated in Solar units. Planet masses are indicated in Earth units

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Within the high-multiplicity sample, we now know well over a hundred examples of compact low-mass systems consisting of three to six low-mass planets orbiting within 1 AU of stars with spectral types ranging from M to F (e.g., Kepler-20, HD 69830, and Kepler-62 in Figure 4). We even know of several compact mixed-mass systems that include gas giants orbiting alongside two or more low-mass planets (e.g., Kepler-90, WASP-47, Kepler-48, and HD 10180 in Figure 4). Both types of systems contain a much higher concentration of mass on short-period orbits than does our Solar System. Next to these robust ensembles, the inner Solar System seems anemic, with just four pint-size spheres and a swarm of rocky debris inside 5 AU, collectively totaling only 2 Mea.

In fact, after two decades in which the extrasolar census grew from a few dozen planets to a few thousand, we can confidently assert that our system is odd. Although many systems support a clutch of small planets on short-period orbits, and many others have gas giant planets orbiting outside 1 AU, relatively few support both configurations. Virtually none of these bear a significant resemblance to the Solar System. In a recent study, Morbidelli & Raymond (2016) estimated that only 1% of G-type stars like our Sun are accompanied by a gas giant on a circular orbit outside 1 AU. Planets like our Jupiter might be as rare as Hot Jupiters.

Another remarkable feature of our system is the hierarchical distribution of planetary mass, such that each planet exceeds the sum of the masses of all smaller planets. It’s unclear how common this architecture might be, since relatively few systems with four or more planets have well-constrained masses. Although mass hierarchies analogous to the Solar System are attested for 55 Cancri and Gliese 876, many other systems have flatter mass distributions. Among them, Figure 4 depicts Kepler-20, HD 10180, and Mu Arae. Another well-known example is Kepler-11. Compact multiplanet systems in particular appear to favor collections of similar-mass planets over hierarchical arrangements.

How do all these varied system architectures arise? And almost as important, why should we care?

Before addressing the difficult question of how, here are some reasons why:

• Existing data on exoplanetary systems are sparse, incomplete, and likely to remain so for decades. If we had a working model of the conditions and processes that produce the full range of system architectures, we could use available data to predict or rule out unseen companions of known objects.

• Knowing how and especially where any given planet formed provides an invaluable clue to its likely composition. Planets assembled from material available near the central star will be rocky, while planets formed from material with a more distant origin will contain a significant fraction of volatiles.

• Composition is a critical factor in habitability, since a planet’s structure and bulk constituents are associated with atmospheric properties, surface temperatures, and the potential for open bodies of water.

In sum: knowing how and where planets of various types form will help us predict the distribution of Earth-like planets in the Solar neighborhood and throughout our Galaxy.

(This discussion will continue with Protoplanetary Disks and In Situ Formation and conclude with Accretion with Migration in Radially Structured Disks.)

 

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A New Planet for Kepler-20

Figure 1. All announced planets of Kepler-20 at their relative sizes, with colors corresponding to the densities provided by Buchhave et al. 2016 (see Figure 2 for the color key; redder hues indicate higher densities). Since planet g does not transit, the radius and composition shown here are informed guesses, as indicated by the striped fill. Planets e and f are about the same size as Earth, but none of the planets in this system are cool enough to support Earth-like conditions.

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Lars Buchhave and colleagues just reported new radial velocity data on Kepler-20, one of the best-known systems revealed by the Kepler Mission. The new results include more precise mass estimates for three of the system’s five known planets (Kepler-20b, c, d) and robust evidence for a previously unknown sixth candidate (Kepler-20g), whose orbit is apparently misaligned with the others. The new planet is notably more massive than its five companions, but despite its short orbital period (35 days), it was not observed in transit by the Kepler Telescope.

When preliminary Kepler data started circulating in 2011, we learned that a highly specific orbital architecture is more common than anyone ever dreamed: compact systems with three or more planets visible in transit (Lissauer et al. 2011b). Lissauer & colleagues reported 55 in 2011. By May 2016, the Extrasolar Planets Encyclopaedia listed 154.

Two systems have always stood out from the pack. One is Kepler-20 (Gautier et al. 2012), which harbors five transiting planets inside a semimajor axis of 0.4 astronomical units (AU). The other is Kepler-11 (Lissauer et al. 2011a), with six transiting planets inside a semimajor axis of 0.5 AU. Both systems center on mature G-type stars like our Sun, yet each one sustains a rich multiplanet architecture confined within a radius similar to the semimajor axis of Mercury (0.39 AU). The corresponding region of our Solar System, of course, is empty.

From the beginning, Kepler-11 has received the lion’s share of attention, for one simple reason. Five of its six planets exhibit transit timing variations (TTVs), such that their orbital motion periodically speeds up or slows down to avoid awkward encounters with neighboring planets. Although this behavior had previously been theorized, Kepler-11 and another early discovery, Kepler-9, were the first cases ever actually confirmed (Ford et al. 2011).

For Kepler-11, analysis of TTVs enabled estimates of the masses of the five inner planets, which presented yet another surprise (Lissauer et al. 2011a). Although their radii were originally estimated in the range of 2 to 4.5 Earth units (Rea), all five turned out to be substantially less massive than Neptune, whose radius of 3.9 Rea contains a mass of 17.2 Earth units (Mea). Like Neptune, Lissauer & colleagues concluded, the Kepler-11 planets must be enveloped in extended atmospheres of hydrogen and helium (H/He), even though their individual masses are smaller than 10 Mea. With that inference began the modern era of planetology.

The planets of Kepler-20 are packed almost as tightly as those of Kepler-11, but no TTVs are available to provide mass estimates. Fortunately, Kepler-20 is substantially closer to our Solar System than is Kepler-11. Its distance is estimated at 290 parsecs (945 light years), versus 613 parsecs (1998 light years) for Kepler-11. This proximity enabled the collection of ground-based radial velocity observations in 2009-2011 by the Keck/HIRES spectrograph, which placed rough constraints on the masses of Kepler-20b, c, and d (Gautier et al. 2012). These constraints indicated that, despite the broad similarities between Kepler-20 and Kepler-11, the planets of the former star are both denser and more massive than those of the latter.

Figure 2. Kepler-20 and Kepler-11 Compared

 

Planets are rendered at their relative sizes on the same orbital scale, with semimajor axes in astronomical units (AU). Numbers in red indicate approximate planet masses in Earth units, rounded to the nearest integer. Planet colors indicate approximate densities, with values taken from Buchhave et al. (2016) for Kepler-20 and from Lissauer et al. (2013) for Kepler-11. Buchhave et al. propose that Kepler-20e and -20f have Earth-like compositions, given their similarity in size to Venus and Earth. The radius and composition of Kepler-20g are informed guesses, as are the mass and composition of Kepler-11g.

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Observations of these two benchmark systems have continued since their discovery. A follow-up study using additional quarters of Kepler data revised the masses and radii of the Kepler-11 planets, mostly downward, resulting in even puffier planets (Lissauer et al. 2013). Another follow-up study reported radial velocity data on Kepler-11 obtained by Keck/HIRES in 2014 (Weiss et al. 2015), placing an upper limit of twice the mass values derived by Lissauer & colleagues.

Now Buchhave & colleagues (2016) have refined the masses of the known planets around Kepler-20 and validated a sixth planet by analyzing archival HIRES data and new HARPS-N data. Figure 2, above, is a graphic comparison of the two systems based on current findings; Table 1, below, provides comparative numbers.

The most striking difference between the planetary systems of Kepler-11 and Kepler-20 appears in the bulk compositions of their planets. The estimated density of Kepler-20b substantially exceeds that of Earth, the densest planet in our system. Its composition might be explained by an enhancement in iron. Likewise, despite their similarity in mass to Uranus, Kepler-20c and -20d are much denser, indicating a smaller bulk percentage of H/He and an enrichment in metal, rock, and potentially ice. Conclusive data are lacking for the other three planets of Kepler-20, but planet g is likely to be similar in composition to planets c and d, while planets e and f might resemble our system’s terrestrial planets.

All the planets of Kepler-11 are less massive than Uranus, but two of them (b, d) have densities comparable to Neptune and Uranus, respectively. The other three planets with estimated densities (c, e, f) are comparable to Saturn, the most rarefied planet in our system, despite masses in the range of 2 to 8 Mea. For context, Saturn is 95 Mea, and if our ringed planet fell into an ocean large enough, it would float. Half the Kepler-11 planets could float along with it, bobbing like rubber ducklings after a colossal rubber duck.

kepler-20: six-planet architecture

The new study by Buchhave & colleagues (hereafter B16) begins by reexamining the properties of the host star. For Kepler-20, they report a higher mass (0.948 Solar masses or Msol), a slightly higher metallicity (+0.07 ±0.08), and an earlier spectral type (G2) than did earlier sources. These new parameters imply an even closer resemblance among Kepler-20, Kepler-11, and our own Sun than previously indicated. Kepler-20 and Kepler-11 are now assigned virtually identical masses and metallicities, while both appear older and slightly less massive than our Sun.

The most significant contribution from B16 is their discovery of the new planet, Kepler-20g. Notably, Hansen & Murray (2013) previously found that a stable orbit might be available between planets f and d, and the HARPS-N radial velocity data have confirmed their hypothesis. In addition, B16 report a more precise mass for Kepler-20d, which remains the outermost of the known planets. Its new mass value (10 Mea) is just half the upper limit reported in the discovery paper (Gautier et al. 2012), although the precision of that estimate is still inferior to those for planets b and c.

Other major results from B16 support the basic picture unveiled by the discovery paper, including null results for TTVs. As before, we see a distinctive mass distribution in which smaller, more lightweight planets alternate with larger, more massive planets inside 0.25 AU. The two smallest planets (e, f) are remarkably similar in radius – and probably in mass and composition – to the terrestrial planets of our Solar System. Their diminutive profiles are inconsistent with H/He envelopes, whereas such envelopes are essential to explain the radii of the two largest planets (c, d). We are also safe in assuming an H/He atmosphere for the most massive planet (g).

The innermost planet (b), however, appears to be rocky, without any contribution from water or H/He. Kepler-20b is therefore the most massive rocky planet discovered to date. All other objects with similar radii and well-constrained masses – with the possible exception of 55 Cancri e – require substantial volatile content to explain their profiles.

Unfortunately, B16 did not present stability limits for any additional planets that might orbit outside 0.4 AU, in the cooler region where the system’s habitable zone is located. As a result, the potential of Kepler-20 to support habitable planets remains unexplored.

Table 1. Kepler-20 and Kepler-11 System Parameters

Masses and radii are expressed in Earth units. Mass is rounded to a single decimal place, with uncertainties omitted. Radius is rounded to two decimal places. a = semimajor axis, expressed in astronomical units (AU), where 1 AU = separation between Earth and Sun. Period = days. Teq = equilibrium temperature, expressed in Kelvin (K); for context, the Teq of Earth is 255 K. Density = grams/cc. Data on Kepler-20 are from Buchhave et al. 2016, except for Teq values in parentheses, which are older estimates from the Kepler Table based on a lower stellar effective temperature. Data on Kepler-11 are from Lissauer et al. 2013.

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kepler-11 and kepler-20: formation scenarios

Although they do not discuss any specific formation models for the planets of Kepler-20, B16 opine that all six planets assembled shortly before the dissipation of the primordial circumstellar nebula. This timing enabled all six to accrete small amounts of H/He from the nebula without initiating a runaway process that would turn them into gas giants. After the nebula dispersed, stellar flux likely ablated the H/He envelopes from planets b, e, and f – the former because of its star-hugging orbit, the latter two because of their small masses. The cooler and heavier planets (c, d, g) were able to retain their lightweight atmospheres, consistent with current models of atmospheric evolution (Lopez & Fortney 2014, Erkaev et al. 2016).

The release of B16 was almost simultaneous with the publication of a new study of possible evolutionary scenarios for Kepler-11 (D’Angelo & Bodenheimer 2016). Given the similarities between the two host stars, a scenario that can explain one system architecture should also tell us something about the other.

In their new study, Gennaro D’Angelo and Peter Bodenheimer (hereafter DB16) test the two most popular formation processes for close-in planets: 1) in situ accretion of solids locally available in the inner nebula, and 2) accretion of solids over a broad radial distance by a planetary core migrating from the outer nebula to the vicinity of the central star. For brevity they call the latter process “ex situ formation.” For each scenario they seek initial conditions that permit the formation of the known planets within currently observed parameters, and in both cases they achieve some degree of success. Accordingly, they conclude that “it is not possible to distinguish between the two modes of formation from [the planets’] final properties.”

However, a review of their models suggests that ex situ is more plausible than in situ, given two major flaws in the in situ scenario. First, DB16 find that a protoplanetary nebula massing 0.18 Msol inside 70 AU would be required to achieve the concentration of solid mass needed for in situ formation of the Kepler-11 planets inside 0.5 AU. This total is equivalent to the mass of a mid to late M dwarf star. Yet observations of protoplanetary nebulae in nearby star-forming regions indicate that most have masses in the range of 0.002 to 0.01 Msol (Williams & Cieza 2011, Andrews et al. 2013). Such findings argue that the in situ nebula invoked by DB16 is unrealistic.

In the second place, even assuming the existence of a protoplanetary nebula more massive than Proxima Centauri, the in situ model still could not produce a good analog of Kepler-11b. Since the inner nebula is completely dry in this model, the six planets originally form as rock/metal cores surrounded by H/He atmospheres. No water or other volatile materials are available to enhance their composition. Given the low core mass and tight semimajor axis of Kepler-11b, DB16 find that the planet’s primordial atmosphere would be stripped by stellar flux within 40 million years after the evaporation of the ambient nebula. To achieve the puffy radius observed today, some 8 billion years later, the planet would have to outgas very large quantities of H/He from its interior over a period lasting a few hundred million years – first to replace its original envelope, and later to replenish the outgassed atmosphere, which would remain vulnerable to stripping during the time it takes for a G star to settle into maturity (Erkaev et al. 2016). DB16 acknowledge the difficulties involved in this outcome.

Their ex situ or migratory model avoids both pitfalls. They begin with a protoplanetary nebula of 0.03 Msol inside a radius of 60 AU. Although this value is larger than a typical nebular mass, it still falls within an order of magnitude of observations, and is therefore substantially more realistic than the in situ nebula. Within this structure DB16 insert newly formed planetary cores of approximately Martian mass (0.1 Mea) at orbital radii ranging from 2.1 AU to 5.35 AU, in the region of the nebula where ices are abundant. All cores begin accreting mass and migrating inward. The timing of their insertion in the nebula is just as important as their radial placement, since cores that achieve smaller final masses need to begin accreting later than those that achieve larger masses in order to avoid orbit crossings during migration.

Because they originate in a well-hydrated region, all six forming planets accrete abundant water along with their H/He envelopes, and all are subject to loss of atmosphere once they reach their final destinations and the nebula dissipates. With this model, DB16 succeed in reproducing the masses and radii of all six planets of Kepler-11. In particular, they find that Kepler-11b retains a steam atmosphere after the loss of its lightweight H/He envelope, and that this heavier atmosphere can survive until the present age of the system, consistent with the planet’s current radius.

DB16 underscore the difference in planetary compositions produced by their two contrasting approaches to system evolution. Although they do not apply the term, the water-rich bodies resulting from their ex situ model are consistent with the Ocean Planets predicted by Leger et al. (2004).

The approach taken by DB16 is paralleled in some of the studies that accompanied the recent announcement of Proxima Centauri b (Barnes et al. 2016, Coleman et al. 2016), as discussed in my previous post. Like DB16, Coleman & colleagues explored several scenarios for planet formation, including in situ accretion in an implausibly massive protoplanetary disk, as well as long-distance migration in a more realistic disk. As with DB16, the migration scenario provided a better fit with observations than did in situ formation. Notably, Coleman’s group explicitly invoked Ocean Planets to describe the objects produced by migration.

I look forward to a study that applies similar models to the dual evolutionary histories of Kepler-20 and Kepler-11. I suspect that in situ scenarios will continue to face difficult challenges.

the high-multiplicity sample

With the confirmation of Kepler-20g, Kepler-20 moves from one exclusive club – systems with at least five known planets – to the even smaller elite – systems with at least six planets. The current exoplanetary census offers only four examples of this rare architecture: HD 10180, Kepler-11, Kepler-90, and now Kepler-20. Their orbital arrangements provide invaluable data that will continue to inform our understanding of planet formation and the distribution of specific planetary types (including temperate rocky planets) in our region of the Galaxy.

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REFERENCES
Andrews SM, Rosenfeld KA, Kraus AL, Wilner DJ. (2013) The mass dependence between protoplanetary disks and their stellar hosts. Astrophysical Journal 771, 129.
Barnes R, Deitrick R, Luger R, Driscoll PE, Quinn TR, Fleming DP, Guyer B, McDonald DV, Meadows VS, Arney G, Crisp D, Domagal-Goldman SD, Lincowski A, Lustig-Yaeger J, Schwieterman E. (2016) The habitability of Proxima Centauri b I: Evolutionary scenarios. In press. Abstract: 2016arXiv160806919B
Buchhave LA, Dressing CD, Dumusque X, Rice K, Vanderburg A, Mortier A, Lopez-Morales M, Lopez E, et al. (2016) A 1.9 Earth radius rocky planet and the discovery of a non-transiting planet in the Kepler-20 system. In press. 2016arXiv160806836B
Coleman GAL, Nelson RP, Paardekooper SJ, Dreizler S, Giesers B, Anglada-Escude G. (2016) Exploring plausible formation scenarios for the planet candidate orbiting Proxima Centauri. Monthly Notices of the Royal Astronomical Society, in press. Abstract: 2016arXiv160806908C
D’Angelo G, Bodenheimer P. (2016) In situ and ex situ formation models of Kepler 11 planets. Astrophysical Journal 828, 33. Abstract: 2016ApJ...828...33D
Erkaev NV, Lammer H, Odert P, Kislyakova KG, Johnstone CP, Gudel M, Khodachenko ML. (2016) Thermal mass loss of protoplanetary cores with hydrogen-dominated atmospheres: The influences of ionization and orbital distance. Monthly Notices of the Royal Astronomical Society 460, 1300-1309.
Ford EB, Rowe JF, Fabrycky DC, Carter JA, Holman MJ, Lissauer JJ, et al. (2011) Transit timing observations from Kepler. I. Statistical analysis of the first four months. Astrophysical Journal Supplement Series 197, 2.
Fressin F, Torres G, Rowe JF, Charbonneau D, Rogers LA, Ballard S, Batalha NM, Borucki WJ, Bryson ST, Buchhave LA, et al. (2012) Two Earth-sized planets orbiting Kepler-20. Nature 482, 195-198. Abstract: 2012Natur.482..195F
Gautier TN, Charbonneau D, Rowe JF, Marcy GW, Isaacson H, Torres G, Fressin F, Rogers LA, Desert J-M, Buchhave LA, et al. (2012) Kepler-20: A Sun-like star with three sub-Neptune exoplanets and two Earth-size candidates. Astrophysical Journal 749, 15. Abstract: 2012ApJ...749...15G
Hansen B, Murray N. (2013) Testing in situ assembly with the Kepler planet candidate sample. Astrophysical Journal 775, 53. Abstract: 2013ApJ...775...53H
Leger A, Selsis F, Sotin C,  Guillot T, Despois D, Mawet D, Ollivier M, Labeque A, Valette C, Brachet F, Chazelas B, Lammer H. (2004b) A new family of planets? “Ocean Planets.” Icarus 169, 499-504.
Lissauer JJ, Fabrycky DC, Ford EB, Borucki WJ, Fressin F, Marcy GW, et al. (2011a) A closely packed system of low-mass, low-density planets transiting Kepler-11. Nature 470, 53-58. Abstract: 2011Natur.470...53L
Lissauer JJ, Ragozzine D, Fabrycky DC, Steffen JH, Ford EB, Jenkins JM, et al. (2011b) Architecture and dynamics of Kepler’s candidate multiple transiting planet systems. Astrophysical Journal Supplement Series 197, 8.
Lissauer JJ, Jontof-Hutter D, Rowe JF, Fabrycky DC, Lopez ED, Agol E, et al. (2013) All six planets known to orbit Kepler-11 have low densities. Astrophysical Journal 770, 131. Abstract: 2013ApJ...770..131L
Lopez E, Fortney J. (2014) Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition. Astrophysical Journal 792, 1.
Weiss LM, Marcy GW, Isaacson H, Deck KM, Lissauer JJ, Jontof-Hutter D. (2015) Constraining the masses of the Kepler-11 planets with radial velocities. Abstract presented at Physics of Exoplanets: From Earth-sized to Mini-Neptunes, February 23-27, 2015.
Williams JP, Cieza LC. (2011) Protoplanetary disks and their evolution. Annual Review of Astronomy and Astrophysics 49, 67-117. Abstract: 2011ARA&A..49...67W