Sunday, November 27, 2016

Accretion with Migration in Radially Structured Disks

Figure 1. The innermost regions of the protoplanetary disk surrounding TW Hydrae are unveiled in this composite of images captured by the ALMA instrument. TW Hydrae is a newborn Sun-like star located 176 light years away. Sean Andrews & al. (2016) propose that the gap and ring structure visible in the inset image has been carved by a rocky planet accreting at a circumstellar radius of about 1 astronomical unit (1 AU), equivalent to the distance of Earth from the Sun. However, Barbara Ercolano & al. (2016) argue that the dust-free gap results from photoevaporation of the inner disk by X-ray flux from the central star. Both studies suggest that the gaps in the outer disk represent the condensation fronts of various chemical species, such as carbon monoxide and molecular nitrogen. Current theory identifies these structures as potential planet traps.

Despite recent interest in the theory of in situ assembly, most astronomers over the past two decades have relied on models involving planet migration to explain the origin of planetary systems. These models are directly informed by our understanding of the primordial nebulae that surround newborn stars. The previous installment of this three-part series offered a basic picture of protoplanetary disks (the preferred term for planet-forming nebulae) and reviewed the pros and cons of in situ formation. This installment explores the recent explosion of theoretical studies that invoke gas-driven migration in radially structured protoplanetary disks as the principal mechanism underlying planet formation and system architecture.

Intensive discussion of radially structured disks dates back at least 10 years, to the 2006 publication of a study led by Frederic Masset: “Disk surface density transitions as protoplanet traps.” Since then, the term planet trap has appeared regularly in articles on system evolution, with a currency even wider than the extended circle of researchers who collaborate with Masset. Such traps are a key example of the structures invoked in this emerging field.
A major shortcoming of existing migration models provided the jumping-off point for the current approach: growing recognition that the combined effects of aerodynamic drag and gas-driven migration, as modeled in theory, would likely sweep all solid particles in the nebula into the central star before they had time to form protoplanets. Without those building blocks, planetary systems could never evolve.
Yet obviously they do. Accordingly, theorists have searched for some mechanism that could stall migration and enable solid mass to accumulate at various radial locations. These efforts have coincided with increasingly precise measurement and imaging of nearby protoplanetary disks, which are beginning to offer evidence of disk structures that are consistent with planet traps (Figure 1).

So this posting will look at 1) the basic elements of migration theory, 2) a sample of the disk structures proposed by current scenarios, 3) condensation fronts and their evolution, 4) the formation of the first planetesimals, 5) the late stages of disk evolution, and 6) the nativity and composition of the known exoplanets.

Figure 2. Protoplanetary disk model
Schematic view of a protoplanetary disk surrounding a Sun-like star, seen edge-on. The large lavender shape represents the gas nebula, which is made of hydrogen & helium in an approximate ratio of 3:1. The vertical profile of the gas flares in the outer region of the disk, beyond 10 AU. Despite a gas-free central cavity inside 0.05 AU, gas molecules flow continually through the disk to the star and deposit mass through the stellar magnetic poles. Suspended throughout the disk are solid particles of rock and frozen volatiles, the building blocks of planets. Rocky particles dominate the hot inner disk; icy particles dominate the cold outer disk. As the disk evolves, solids settle at its midplane, which is likely aligned with the star’s rotational axis. Accumulation of solids favors the assembly of pebbles and planetesimals, which collide to form protoplanets (also known as embryos or cores).

1) migration modes

In a protoplanetary disk, nothing stands still. Gas molecules orbit the central star and dust grains are carried along with the flow of hydrogen and helium (H/He) as it streams into the gravity well created by the star’s mass (Figure 2). Current models tell us that the process of accretion is driven by turbulence within the nebula. The calmest region of the gas disk is the midplane, where dust settles and aggregates, encouraging collisions. Micron-sized grains are lightweight enough to travel at the same speed as the gas, but aggregations measurable in centimeters – that is, pebbles – experience aerodynamic drag that causes their orbits to decay.

The problem of orbital decay gets worse as aggregates grow. When a protoplanet approaches the mass of Mars (~0.1 Earth masses or Mea), it becomes subject to Type I migration. Objects ranging up to and beyond the mass of Neptune are similarly affected. Type I migration is caused by the interaction between the flow of gases and a forming protoplanet, such that the object is simultaneously subject to positive and negative torques. When the negative torque exceeds the positive torque, as is usually the case, the object migrates inward. When the reverse is true, the object migrates outward. In some models, Type I migration can deliver an Earth-mass protoplanet originally traveling on an Earth-like orbit to the threshold of its parent star in about 100,000 years (Baillie et al. 2015). More massive objects travel even faster, such that on object of 10 Mea originally orbiting at 5 astronomical units (AU) can migrate to the inner edge of the disk in less than 30,000 years (Chambers 2006).

Figure 3. Type II migration of a baby gas giant

The blob in the dark ring is the forming planet, which is being carried inward by the flow of accretion as it orbits in a dust-free lane. Spiral streams of gas link the planet to the inner and outer disk. (Source: Figure 32 of Armitage 2010)

Still larger objects can escape this process. Depending on the vertical extent of the gas disk at the site of formation, a protoplanet approaching the mass of a gas giant (e.g., 50-150 Mea) can open a gap in the disk, meaning that it clears all the gas from its vicinity and orbits alone in an empty lane around the star. The exact mass required for gap clearing depends on the scale height of the disk, which changes over time. Disks are at their thickest and most massive in extreme youth, attenuating incrementally as they age. Only a massive object can open a gap in a thick disk, whereas a protoplanet as lightweight as Neptune might be able to open a gap in a sufficiently attenuated disk. Once ensconced in its gap, the planet undergoes Type II migration (Figure 3), traveling inward with the flow of gas at a more leisurely rate than in the Type I regime. Nevertheless, it still migrates, so that the orbit of a young gas giant in this mode might shrink from 5 AU to 0.1 AU in half a million years (Chambers 2006).

2) barriers and traps
For as long as the various modes of drag, drift, and migration have been understood, astronomers have realized that some opposing mechanism must be available to ensure that pebbles don’t fall into stars before they accrete into protoplanets, and that protoplanets don’t get stranded at the inner edges of disks before they can establish cooler orbits. In recent years, theorists seem to be converging on a scenario in which the gas dynamics in specific regions of a protoplanetary disk counterbalances negative torque with positive torque, for a net of zero. In this way, solid particles can remain stranded in one place long enough to accrete into planetesimals, protoplanets, and planets. Such regions have been identified as the sites of “transitions” (Masset et al. 2006), “inhomogeneities” (Hasegawa & Pudritz 2011), or “irregularities” (Baillie et al. 2016).
Several candidates have been proposed as the agents of this trapping or focusing process. Collectively, they are known as planet traps. Among the most consistent choices are condensation fronts (or sublimation lines) in the evolving disk – locations where specific chemical species condense (or sublime) out of the disk gases (Figures 4 & 5). The most widely discussed of these fronts is the ice line or snow line: the minimum radius at which water freezes instead of sublimating. Another is the silicate condensation line, where silicate dust vaporizes, creating an inner edge for the solid component of the disk (Morbidelli et al. 2016). In many models, this edge casts a long shadow on the midplane of the disk, contributing to a reduction in temperature.
Condensation fronts act as planet traps because they create a bump in the local surface density of solids (Masset et al. 2006). However, other candidates for this role are available. In a series of publications, Yasuhiro Hasegawa and collaborators have detailed a total of three potential planet traps (2010, 2011, 2014). In addition to condensation fronts – to which they apply the generic term ice line, regardless of chemical species – they include dead zones and heat transitions.
Many theoretical treatments of planet traps specify that they are intended to apply only in cases of Type I migration, with some even defining a relatively narrow range of masses for affected objects. Others, however, discuss structures capable of capturing a broad distribution of masses, including gas giants undergoing Type II migration.

Figure 4. Water condensation front around V883 Orionis

This image by the ALMA instrument reveals a protoplanetary disk of about 0.3 Msol with a radius of about 125 AU surrounding the protostar V883 Orionis, which masses about 1.3 Msol and resides 415 parsecs (1350 light years) away in the Orion Nebula Cluster (Cieza & al. 2016). The dark ring corresponds to the system ice line or water condensation front, currently located at a circumstellar distance of about 42 AU. Normally the ice line would be much closer to a star of this age and mass (in the range of 5-10 AU), but an abrupt accretion event in which the star ingested a substantial amount of hydrogen from the disk caused an outburst. The result was a temperature spike throughout the disk that evaporated water inside a radius similar to the orbit of Pluto in our Solar System. Image credit: ALMA (ESO/NAOJ/NRAO) / L. Cieza.

2a) dead zones

A dead zone is a region in the nebula where turbulence and viscosity are suppressed and the inward flow of gases slows down. This concept has been discussed for at least 20 years as the possible source of several phenomena associated with protoplanetary disks. (I have to wonder if its coinage was related to Stephen King’s 1979 horror novel, The Dead Zone.) Dead zones have been proposed to explain outbursts like those observed in newborn stars such as FU Orionis, where the sudden accretion of a large quantity of trapped mass stimulates a burst of stellar radiation (Gammie 1996). They have been described as a mechanism for trapping dust grains at specific locations in the disk, promoting the rapid collapse of solids into planetary embryos the size of Mars (Lyra et al. 2008). They have even been anointed as the saviors of planetary systems through their ability to halt Type II migration, which would otherwise deliver forming gas giants to star-hugging orbits (Matsumura et al. 2007).

In the classic model, the magnetic field of a newborn star induces magnetorotational instability in the protoplanetary nebula. This instability creates turbulence, which drives the flow of H/ He into the central star. Although the existence of magnetorotational instability has recently been questioned (Morbidelli & Raymond 2016), theorists still seem to agree that turbulence is real, regardless of the source. Current models still indicate that its suppression – by whatever means – will reduce viscosity and halt inward migration.

Some discussions appear to confine the dead zone to the midplane of the protoplanetary disk, without emphasizing its radial location (Martin & Livio 2012). However, Hasegawa and Pudritz (2011) describe their dead zone as a high-density region confined to the inner disk, where turbulence is calmed and the accumulation of dust at the midplane is enhanced. They note that an inner dead zone can coexist with other kinds of planet traps, including ice lines (which they also describe as opacity transitions) and the heat transition. They even characterize ice lines as a species of “self-regulated, localized dead zone.”

The heat transition proposed by these authors and others refers to the radius in a protoplanetary disk where the source of heating shifts from friction caused by the flow of gases (viscous heating) to energy radiated by the central star (irradiative heating). Models of disks around Sun-like stars place this transition around 10-12 AU (Baillie et al. 2016), where the disk begins to flare. Flaring enables the outer disk to escape the shadow of the inner dust wall, so that surface gases heat up and ionize. At the midplane, however, icy solids still accumulate.

Hasegawa & Pudritz (2011) argue that the placement of the various planet traps defines the initial orbital distribution of protoplanets. Although all traps tend to move inward over time as the rate of gas flow through the disk declines, each type of trap moves differently, resulting in different outcomes for its complement of protoplanets. Hasegawa & Pudritz also argue that the positioning of planet traps depends strongly on the mass of the central star and its rate of gas accretion. Through this dependency, they conclude, “host stars establish preferred scales [for] their planetary systems.

Figure 5. Carbon monoxide condensation front around TW Hydrae

A doughnut made of carbon monoxide surrounds TW Hydrae, a young Sun-like star, as captured in this image by the ALMA instrument. Qi & al. (2013) estimate its inner radius at 30 AU. (Note that the yellow dot in the center of this figure is an artificial marker of the position of the host star – it is not present in the original image.)

2b) condensation fronts

Kevin Baillie & colleagues (2016) follow Hasegawa & Pudritz in emphasizing the role of condensation fronts (which they call sublimation lines) as well as the heat transition barrier. Although their terminology foregrounds “lines,” they explain that each line actually marks the center of a broad zone or plateau that extends over a radial distance of about 1 AU. In addition to water and silicates, they model the sublimation of volatile and refractory organic molecules, along with troilite, an iron sulfide mineral. These three types of molecules sublime at temperatures between those of silicates and water, creating a series of tightly spaced traps between 0.1 and 1 AU. However, the authors find that the traps created by troilite and volatile organics are less effective than the others, while the silicate condensation trap is less enduring than the water trap.

Like other theorists (Pollack et al. 1996, Masset et al. 2006, Hasegawa & Hirashita 2014, Bitsch et al. 2015), Baillie & colleagues also foreground the effects of opacity on disk evolution. Local opacity is determined by the size of ambient dust grains, with micron-sized particles increasing opacity and millimeter to centimeter sizes (pebbles) reducing it. They note that condensation fronts are associated with opacity transitions, since solids accrete more readily outside these fronts than inside them, causing an increase in opacity. Again, however, troilite and volatile organics make a smaller contribution to opacity than do water and silicates.

While Baillie & colleagues do not discount the potential of dead zones for trapping planets, they have not explicitly integrated this type of structure in their extant models. Instead, they focus on the behavior of migrating objects that arrive at planet traps, paying special attention to mass. They argue that condensation fronts can trap low-mass planets, but not gas giants, for which the heat transition is the only effective barrier. They also find that the condensation fronts and heat transition zone create planet deserts about 1 AU beyond the inner edge of each structure. Thus, each plateau is bounded by an outer wasteland where no worlds can grow.

2c) outward migration

Another emphasis of their work is the existence of zones of outward migration associated with the heat transition, the silicate condensation front, and the water condensation front. These structures can confer a positive torque on low-mass planets, adding further complexity to an evolving system’s orbital architecture. Nevertheless, all planet traps move inward over time with the cooling and attenuation of disk gases. Thus, even if a forming planet is stalled in a trap, its orbit will still shrink as the disk ages. 

Like Baillie’s group, Bitsch & colleagues (2016) omit dead zones from their modeling to focus on opacity transitions associated with thermal discontinuities, disk geometry, and local surface densities of solids. Similarly, they explore the zones of outward migration created by temperature changes. Unlike Baillie’s group, however, they find that more massive planets are more likely to migrate outward than low-mass planets. They are particularly interested in metallicity, which they propose as a key determinant of the temperature profile of a protoplanetary disk. They find that higher metallicity is associated with wider zones of outward migration in more distant regions of the disk. These factors can help to explain the well-known correlation between stellar metallicity and the presence of gas giant planets. (See Cossou et al. 2014 for an analogous treatment of metallicity and migration.)

2d) giants at the gate

One final, widely discussed barrier to drifting dust and migrating planets is the presence of a growing gas giant, which depletes the gas and dust from its vicinity and opens a gap in the nebula. A migrating planet that approaches such a radial gap will either stall or be scattered, usually into a wider orbit. Izidoro & colleagues (2015) argue that this behavior can explain the orbital architecture of our Solar System, where the accretion of Jupiter outside the water condensation front created a barrier to the inward migration of Saturn, Uranus, and Neptune. That may well be so: the emergence of one or more gas giants might effectively segment the disk into inner and outer domains. But the authors go on to predict an anti-correlation between systems with gas giants and those with compact collections of warm gas dwarfs. The architectures of a half-dozen systems – HD 10180, HD 219134, Kepler-48, Kepler-90, Kepler-167, and WASP-47 – demonstrate that this prediction cannot be universally valid (see Almost Jupiter).

Benitez-Llambay & colleagues (2015) use the example of Jupiter to frame a different argument about the migration of growing giants. They consider the case of a protoplanet of 3 Mea that has already formed beyond the water condensation front. This hypothetical object could easily stand in for baby Jupiter. Over a period of 100,000 years, it doubles in mass by accreting a continual flux of colliding bodies. At the same time, it responds to a negative torque that tends to shrink its orbit. But the high temperatures produced by collisional accretion induce a heating torque that “constitutes a robust trap against inward migration.” Depending on various factors, the heating torque can cause the forming planet to decelerate its inward trajectory, stall completely, or migrate outward. More massive planets are more likely to experience outward migration, with a correlation between the object’s mass and the radial distance it travels. Like Cossou’s group, Benitez-Llambay & colleagues find that outward migration and full-blown gas giants are also more likely to result from disks enhanced in metals.

Figure 6. Potential planet traps in a young protoplanetary disk
Several sources of structure have been proposed for evolving disks. A series of condensation fronts (or snow lines or sublimation zones) arises in regions where local temperatures cause common chemical species to condense. These molecules include silicates, water, and carbon monoxide. In addition, the transition from viscous heating in the inner disk to irradiative heating in the outer disk creates a discontinuity known as the heat transition. The radial location of these structures changes over time, moving from larger to smaller radii along with a general cooling trend throughout the disk.

3) condensation fronts in space & time

Again and again, theoretical models converge on condensation fronts as a primary source of disk structure as well as exemplary planet traps. Many different chemical species have been nominated for leading roles, with three standing out: silicates, water, and carbon monoxide. Each one condenses around a specific temperature: silicates below 1500 K, water below 170 K, and carbon monoxide below 70 K. However, the exact location in the disk where each temperature obtains will vary widely, not only from system to system but also from time to time within the same disk. This is because local temperatures depend on irradiation, viscosity, and opacity. All these factors vary over time, such that the location of each condensation front changes substantially during disk evolution. Although the general trend is for each front to move inward as the disk attenuates and cools, stellar flares and outbursts can cause abrupt increases in temperature that evaporate dust grains and temporarily shift all fronts outward (Cieza et al. 2016; see Figure 4).

Baillie & colleagues (2015) emphasize that condensation fronts are regions rather than sharply defined lines, preferring to describe them as plateaux. In addition, even their silicate condensation front is relatively distant from the star during the earliest evolutionary phases. Baillie’s group identifies an initial plateau extending from 0.3 to 1.3 AU, which contracts to about 0.05-0.1 AU after “a few million years.” Similarly, Morbidelli & colleagues (2016) propose that the inner edge of the silicate front in the early Solar System was located at 0.7 AU, near the present orbit of Venus. Given the extreme temperatures prevailing in the vicinity of the star, no solids can survive in the inner disk and no accretion can happen there until the silicate front shrinks substantially. Presumably this situation would complicate the models of in situ accretion discussed in the previous installment of this series, especially for exoplanets orbiting inside ~0.1-0.3 AU. It is conceivable that most objects on orbits shorter than about 100 days (i.e., the vast majority of Kepler planets) formed outside the original front and arrived at their present location by inward migration after the inner system cooled.

The plateau in surface density and pressure created by the silicate front appears to coincide or at least overlap with the dead zones proposed by Hasegawa, Lyra, and others. However, I haven’t noticed any published treatments of their resemblance or lack thereof.

The water condensation front is by far the most extensively discussed of any radial structure, typically under the name of the snow line (or recently, snow region). Since water is abundant in protoplanetary disks around Sun-like stars, the local surface density of solids increases by a factor of 2 to 4 on orbits outside the water condensation front (Kenyon & Kennedy 2008, Martin & Livio 2012). This enhancement increases the likelihood that planetesimals and protoplanets will form in this region.

The vagaries and excursions of the snow line have been traced over the past few decades. Older literature typically defined 2.7 AU as the classical snow line in our Solar System, given the sharp transition in the composition of small bodies observed at that location in the contemporary Asteroid Belt. Purely rocky objects, like Vesta (semimajor axis = 2.36 AU), orbit inside that radius, while objects that include a substantial proportion of water ice, like Ceres (semimajor axis = 2.77 AU), orbit outside it.

However, more recent research argues that this transition is simply the fossilized imprint of the position of the snow line during the first few million years of system evolution, since the present-day snow line is actually located inside Earth’s orbit (Ida & Guillot 2016, Morbidelli et al. 2016). Thus, Kennedy & Kenyon (2008) have proposed that the snow line migrates from about 6 AU to 1 AU during the first few million years of disk evolution around a G-type star. Using a different approach emphasizing dust opacity, Mulders & colleagues (2016) recently argued for a primordial dispersion in the location of the snow line, with values ranging from 1.4 AU to 8 AU for a G-type star. All these studies concur that the snow line moves inward over time, and that its radial location at early times leaves an indelible imprint on planetesimal accretion and ultimately system architecture at later times.

The carbon monoxide condensation front has received growing attention in the past few years, especially since Qi & colleagues (2013) reported the detection of this structure around TW Hydrae with the ALMA instrument (Figure 5). Since carbon monoxide freezes at much lower temperatures than water, this condensation front is located much farther from a Sun-like star than the other two major fronts. Qi & colleagues propose a radial location of about 30 AU for stars of Solar mass, making the carbon monoxide region the most accessible to direct observation. This structure might be implicated in the formation of planets on very wide orbits (Dodson-Robinson et al. 2008), and its effects might be especially significant for disks with radii substantially larger than the original Solar nebula.

4) first planetesimals

Classic studies of planet formation by accretion assume that planetesimals will congeal throughout an infant disk. Indeed, many simulation studies of system evolution have started with a numerical set-up in which protoplanets are packed in a series of concentric orbits separated by several Hill radii (e.g., Raymond et al. 2006, Ida & Lin 2010). Yet the ensemble of research discussed here supports a different picture of accretion. It seems that planetesimals, the essential precursors of protoplanets and planets, are born only in favored locations: the planet traps and filters detailed above. System architectures are thus erected on chemical and physical foundations established early in disk evolution.

Dust, defined as particles smaller than one millimeter, is evidently abundant throughout a newborn protoplanetary disk. Dust grains can settle in the midplane and clump into pebbles, defined as centimeter-sized particles. But further aggregation into planetesimals, defined as particles measured in tens of meters, appears to be possible only in refuges where gas drag and Type I migration can be overcome. Some models propose that pebbles cluster in multitudes in these refuges, eventually thronging so densely that they collapse into planetesimals 100 km in diameter – much larger than the boulder-sized constituents invoked by older models. Objects this size can readily accrete pebbles and grow even bigger.

As Alessandro Morbidelli & Sean Raymond (2016) recently observed, “All this may be suggestive that the first planetesimals formed only at select locations (near the disk’s inner edge or beyond the snowline).” In this way, they say, the first generation of planetesimals “may serve as a planetary system’s blueprint.”

5) dissipation & relaxation

A forming planetary system can be regarded as a closed system engaged in feverish, time-limited activity. The processes of accretion, migration, and orbital evolution are determined by factors originating within the system: stellar irradiation, stellar outbursts, gas flow through the disk, planetesimal/disk interactions, planetesimal/planetesimal interactions, planet/disk interactions, and eventually planet/planet interactions. All these factors are sensitive to the passage of time. For example, as gas flow slackens, migration slows, and as gas dissipates, opportunities close down for young planets to accrete H/He atmospheres. At the same time, the radial location of planet traps moves inward, while their ability to trap solids diminishes.

The emergence of a gas giant planet anywhere in the disk has far-reaching consequences. A gas giant clears gas and solids from its orbit, cutting off the flow of volatiles and the migration of planetesimals and protoplanets originating at wider radii. This development starves the inner disk of replenishment for the gases, dust, and pebbles that it continually loses to stellar accretion. The inner disk therefore drains rapidly into the star, creating a central hole. Its removal exposes the outer disk to photoevaporation by stellar flux. The process of dissipation is quite fast, measured in thousands rather than millions of years.

Although not all disks give birth to giants, most of them evidently evaporate on a similar schedule in a similar sequence: drainage of the inner disk followed by photoevaporation of the outer disk. This might be a universal process that is simply accelerated by the assembly of one or more giant planets.

Disk dispersion is a watershed moment in system evolution. Not only is gas accretion quenched for young planets; the dissipation of H/He removes the mechanism by which orbital eccentricities are damped, exposing planets to mutual perturbations. These interactions can happen even in the presence of nebular gas, but their likelihood is significantly amplified at this evolutionary phase. Orbit crossings, planetary collisions, and planetary ejections are all possible, potentially leading to major revisions in the “blueprint” created by primordial disk structures. Planet/planet interactions after gas removal probably cause the orbital eccentricities observed in multiplanet systems, while orbital sculpting and dynamical upsets are especially likely in systems with gas giants outside 1 AU (Matsumura et al. 2013, Mustill et al. 2016).

External influences on system evolution are also possible. Most stars shining today, including our Sun, formed in clusters containing thousands of protostars packed within an area just a few parsecs in radius. Under these conditions, stellar flybys are inevitable. Close encounters in stellar nurseries can strip the outer disk while a star is accreting gases, or scatter outer planets at any point during a system’s lifetime. Nevertheless, studies disagree on the frequency of flybys (e.g., Malmberg et al. 2011, Li & Adams 2015), so it is unclear how common or rare an extreme disruption might be. In any case, given the short lifetimes of protoplanetary disks, flybys are more likely to happen after the gas dissipates, when orbital architectures are beginning to stabilize.

6) where do baby planets come from?

At the beginning of this series I asked the simple question shown above. According to the body of research discussed here, the simple answer seems to be: from farther out in the protoplanetary disk. Baby planets originate in cooler zones where the preservation and accretion of solids is supported at primordial times. They achieve their mature compositions and orbits by interacting with local solids and gases, typically engaging in orbital migration over some distance and likely incorporating pebbles and planetesimals that formed in planet traps.

The disk models discussed here are unfriendly to the accretion of protoplanets on short-period orbits during the earliest phases of evolution. Instead, rocky objects assemble outside the silicate condensation front and icy objects assemble in the snow region. As these fronts move inward, their clutches of planetesimals and protoplanets are conveyed into the inner system, contributing to the composition of planets with various ratios of solids and volatiles. We can expect warm, low-mass planets that are purely rocky, like the four terrestrial planets in the Solar System; part rock and part ice, like the larger satellites of Jupiter and Saturn; or composed primarily of rock and ice but supporting H/He envelopes, like Uranus and Neptune. Gas giant planets, which seem constrained to form on still wider orbits (in the snow region, near the heat transition, or even beyond the zone where carbon monoxide freezes) often have opportunities to intrude on these families of low-mass planets, with the odds of inner-system derangement increasing along with the mass of the intruders.

Given these widely endorsed views, it surprises me that theoretical models of planet composition in Kepler systems still limit their focus to rocky objects with H/He envelopes but no water or other volatile content (e.g., Lopez & Fortney 2014, Rogers 2015, Dorn et al. 2015, Wolfgang et al. 2016). I look forward to studies that widen their scope to accommodate more diverse internal structures.


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Saturday, November 5, 2016

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.


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.


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.


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.

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


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)


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)

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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