2016: Backyard Bonanza

Figure 1. A snapshot of 79 exoplanetary systems located within 20 parsecs (65 light years), arranged by increasing distance from our Sun. Names in red mark planets added to the census in 2016. Spectral types are indicated by the color key at lower right. The inner circle has a radius of 5 parsecs, and each successive ring represents an increment of 5 parsecs. Stellar icons are arranged in 2 dimensions by right ascension, which is marked at the edge of the outer circle; declination is ignored. Note that this diagram shows the relative distance of planetary systems from our Sun, but not from each other.

----------------------

Without doubt, the biggest exoplanetary news of 2016 was the announcement of a small planet orbiting Proxima Centauri, a dim red star that happens to be our Sun’s closest neighbor. Not only did this story dominate headlines in the popular media: a recent query of the SAO/NASA Astrophysics Data System returned a total of 28 scientific articles about Proxima Centauri (including the discovery paper) either published or in press over the past 5 months. My blog post on the detection (The Perils of Proxima) was the biggest click magnet for Back Alley Astronomy in 2016.

No other discovery, analysis, or commentary in the field of exoplanetary astronomy rivaled the news from Proxima. Given the imbalance, it would be a stretch to concoct a “Top Ten” list of extrasolar news for the year just ended. So I’ll content myself with a Top Five: 1) the announcement of Proxima Centauri b by Guillem Anglada-Escudé & colleagues (blogged here), 2) the radial velocity detection of a sixth planet in the well-known Kepler-20 system by Lars Buchhave & colleagues (blogged here), 3) the final data dump of the Kepler Mission, which added 1,284 mostly lonely planets to the extrasolar census in one fell swoop (blogged here), 4) the return of Rho Coronae Borealis b, one of the first exoplanets ever announced, which was widely rejected as a bona fide planet a few years ago and then restored to consensual reality by Benjamin Fulton & colleagues, and 5) the discovery by Michael Endl & colleagues of a new Jupiter analog, HD 95872 b, which like Proxima Centauri b is located right in the Sun’s back yard (announced in a preprint late in 2015 but not formally published – or noticed by me – until 2016). Since I haven’t yet written about the last two items, I’ll devote some words to these less heralded new arrivals, and then assess the message their discoveries might be telling us about our immediate Galactic neighborhood.

the newest, nearest Jupiter analog

HD 95872 b is a gas giant planet in a more or less circular orbit whose estimated period of 4375 days falls within 1% of the orbital period of Jupiter. It was reported along with another cool gas giant – the latter following a notably eccentric orbit around a somewhat more distant star, Psi Draconis – by Endl et al. (2016).

The host star, HD 95872, is located just 25 light years away (7.56 parsecs) in the constellation of Crater the Wine Bowl. By any definition, it is a Sun-like star, included in the respectable Henry Draper Catalog and assigned a spectral type of K0 V in the SIMBAD database. However, Endl’s group reports a few stellar oddities. First, this object was omitted from the Hipparcos Catalog of nearby stars, from which most targets monitored by radial velocity searches have been drawn. The omission means that HD 95872 did not receive a precise distance estimate during the Hipparcos mission, a factor noted without comment by Endl & colleagues. Second, the star’s assigned spectral type seems rather late (i.e., reddish) for the mass of 0.95 ±0.4 Solar (0.95 ±0.4 Msol) determined by Endl’s group. For context, Kepler-20 has a virtually identical mass, but its spectral type is G2. Third, at an estimated age of 10 billion years, a star near Solar mass is likely to be evolving into a subgiant – an expectation contradicted by the classification of HD 95872 as a main sequence star by SIMBAD as well as Endl’s group.

HD 95872 bears a notable resemblance to 55 Cancri, another nearby star that also happens to host a gas giant in an orbit similar to Jupiter’s. Both the mass (0.90 ±0.015 Msol) and the age (10.2 billion years) of 55 Cancri are similar to those of HD 95872, and both stars are also significantly enriched in metals. According to von Braun & colleagues (2011), the metallicity of 55 Cancri is +0.31, while Endl & colleagues report +0.41 for HD 95872. Given these similarities, it’s illuminating to remember that the spectral classification of 55 Cancri is subject to disagreement, with published types ranging from G8 V to K0 IV. (Note that alternative values of 3-9 billion years are available for the age of 55 Cancri; see Teske et al. 2013.)

As substantial research has shown, metal-rich stars like 55 Cancri and HD 95872 have a high likelihood of supporting gas giant planets. 55 Cancri hosts two: planet b with an orbital radius of 0.11 astronomical units (AU) and a minimum mass 0.83 times Jupiter (0.83 Mjup), and planet d with an orbital radius of 5.76 AU and a minimum mass of 3.84 Mjup. 55 Cancri also hosts two tweens (objects intermediate in mass between Neptune and Saturn) in the gap between planets b and d, plus a dense, highly irradiated Super Earth interior to planet b with a mass of about 8 Earth units (8 Mea) and an orbital period shorter than 24 hours. These massive progeny illustrate the superior planet-forming potential of metal-rich protoplanetary disks.

Our new friend, HD 95872, has only a single reported planet, for which Endl & colleagues provide a minimum mass of 4.6 Mjup. This is similar to the estimate for 55 Cancri d, but well above the median for the full census of gas giants. For orbital period and semimajor axis, Endl’s group reports values almost identical to those of Jupiter: respectively 4375 days and 5.2 AU. In addition, they find a relatively circular orbit, although their results for eccentricity are understandably imprecise: 0.06 ±0.04. Within uncertainties, this value is consistent with the well-measured eccentricity of Jupiter: 0.048.

Endl & colleagues confidently identify both HD 95872 b and their other new planet, Psi Draconis b, as Jupiter analogs. They define such planets as “within a factor of a few Jupiter-masses and in orbits longer than 8 years.” As explained in a previous post (Almost Jupiter), I find this definition incomplete, since I’m more interested in analogs of our Solar System than in cool gas giants per se. My definition of a Jupiter analog is 1) a gas giant planet (minimum mass 0.16 Mjup/50 Mea) that is 2) located outside the system’s liquid water zone 3) with an orbit whose eccentricity is under 0.3 and 4) with a semimajor axis that permits the survival of terrestrial planets on habitable orbits but 5) without any gas giant companions on interior orbits. A Solar System analog contains a cool giant that meets all these criteria and is centered around a Sun-like star in the mass range of 0.65-1.30 Msol, corresponding to spectral types between mid K and late F.

HD 95872 nicely satisfies all these criteria and thereby assumes the status of the nearest Solar System analog, demoting HD 154345 to the second-nearest. But Psi Draconis, the other system reported by Endl et al., does not meet my standard. Despite its appealingly memorable name, this system is disqualified by the significant orbital eccentricity (0.4) of its gas giant, Psi Draconis b. It’s a disappointing result, since the host star is very similar to our Sun in age, mass, and spectral type, and it’s only 22 parsecs away.

In light of these recent discoveries, I conducted a new review of the full sample of exoplanets detected by radial velocity measurements (the only technique that has managed to characterize any Solar System analogs). I based the review on a December download of the catalog of the Extrasolar Planets Encyclopaedia (EPE), with additional revisions based on discovery papers. The results appear in Table 1. Systems are listed by increasing semimajor axis of the Jupiter analog.

Table 1. Seventeen potential analogs of our Solar System

Tags: Type = spectral type; Msol = star mass in Solar units; [Fe/H] = metallicity; Dist. = distance in parsecs (rounded); Mjup = planet mass in Jupiter units; a = semimajor axis in Earth units; e = orbital eccentricity; Period = orbital period in years. Selection criteria: star mass 0.65-1.30 Msol; a > 3 AU; e < 0.3, no interior giants perturbing the system habitable zone. Note: HD 30177 has a second planet, a massive “Saturn analog” on an orbit exterior to planet b, with an uncertain orbital period.

------------------------------------------

This is the third time I’ve searched the EPE sample for Solar System analogs during the past few years (previously blogged here and here), and each time the population has grown. HD 95872 is an especially welcome addition. Not only is it the nearest Jupiter analog – it also has the longest orbital period of the lot, making it Jupiter’s closest rival within this subset.

The 17 systems summarized in Table 1 bear a strong family resemblance, at least in terms of their gross parameters. But how much of the apparent similarity might stem from selection biases?

Distance: All but 2 are located at distances between 25 and 60 parsecs; no Solar System analogs have been reported outside that space. Their scarcity inside 25 parsecs might be an accurate reflection of the absolute rarity of such systems, but their absence beyond 60 parsecs almost certainly results from historical limits on the sensitivity of radial velocity searches.

Star mass: Even given my inclusion criterion of 0.65-1.3 Msol, the host stars fall in a narrow range of masses – 0.88-1.18 Msol – and center on a narrow range of spectral types – early to mid G. All are thus extremely similar to our Sun (type G2), while stars less massive than 0.85 Msol are conspicuously absent from the list. Since the entire population is based on continuing searches that began decades ago, this outcome might simply reflect the preference of early search programs for G-type stars. On the other hand, the non-appearance of stars in the range of 0.65-0.85 Msol might be significant. Maybe architectures like the Solar System are restricted to more massive stars.

Metallicity: Eleven out of 17 host stars have Solar metallicity or less; only 4 have [Fe/H] greater than +0.2, which would indicate a notable enhancement in heavy elements. My own (not very educated) guess is that this relative indifference to metallicity might be real. In any case, the scarcity of extremely metal-rich stars in this population supports the premise that our Sun is a typical host of Jupiter analogs. It also warrants a reminder that even the Sun is metal-rich compared to the average star in our Galactic neighborhood, where typical metallicities are about -0.10. Whether or not cool giants on circular orbits are intrinsically rare around stars impoverished in heavy elements, no extreme metallic enrichment seems necessary to form them.

Planet mass: The median gas giant mass in this sample is approximately 2 Mjup, and only 2 of these “Jupiter analogs” have masses smaller than 0.99 Mjup. This outcome might be just another reflection of the limited sensitivity of the radial velocity method, since planets of lower mass are more difficult to detect on long-period orbits. But it might instead be a clue that Jupiter is relatively small for a cool giant, and that most of its analogs are more massive.

Orbital eccentricity: Most gas giants with semimajor axes of 3 AU or more have eccentricities in excess of 0.5, and many giants with smaller eccentricities have giant companions on interior orbits that rule out Earth-like planets. Even in Table 1, which includes only unaccompanied giants with eccentricities < 0.3, the median value of 0.1 is relatively high by the standards of our Solar System. Of course, it’s possible that exoplanetary eccentricities are systematically overestimated (Shen & Turner 2008), and that the giants in Table 1 are actually less eccentric (and therefore friendlier) than they look on the screen. But it’s also possible that cool giants on orbits as circular as Jupiter’s are even rarer than Hot Jupiters. If eccentricity < 0.1 turns out to be the limiting factor for Solar System analogs, then they are much less numerous than I project here.

-------------------------------

On the other hand, if Table 1 presents a reasonable survey of systems like our own, the outlook for Earth-like planets is rosy. The available data now show that 2 out of 260 star systems (0.8%) identified within 10 parsecs – including almost 3% of the 70 FGK stars in this space – host a gas giant on a cool orbit that would permit the survival of Earth-like planets in the habitable zone. Since one of those two star systems (our own) is known to support such a world, we’re entitled to conjecture that the other one (HD 95872) does, too.

If we restrict our scope to stars other than our Sun with confirmed planets, rather than all known stars, we can say that 2% (N=2) of the 79 exoplanetary systems located within 20 parsecs qualify as Solar System analogs. Furthermore, if Jupiter analogs are at least as common as Hot Jupiters, as various analyses suggest, then 3 more systems resembling our own might be awaiting discovery within the same volume of space. That prediction rests on the fact that five Hot Jupiters are already known in this region. If we further extend this back-of-the-envelope approach to a radius of 60 parsecs, we can say that a dozen more Solar System analogs await detection in the immediate Solar neighborhood, since more than 30 Hot Jupiters systems have been reported in that space, but only 17 bona fide analogs of our system.

counting planets in the Sun’s back yard

The statistics on exoplanets within any volume-limited sample depend sensitively on how many such planets we regard as validated. Unfortunately, different exoplanetary catalogs offer different pictures even of the well-studied space within 20 parsecs. Accordingly, I have to approach this problem with a consistent set of exclusions: Alpha Centauri b, Kapteyn’s b & c, all companions identified as brown dwarfs, and all objects reported by direct imaging or astrometry, with the exception of Beta Pictoris b.

When I apply these criteria to the full census maintained by EPE, along with corrections for stellar parameters found in the literature, I get the 79 systems pictured in Figure 1. Given additional exclusions discussed in a series of older blog posts (starting here, most recently here), these 79 systems support a total of 141 planets.

However, if I apply the same criteria to the NASA Exoplanet Archive, I get a notably smaller sample of 65 systems supporting only 113 planets. Much of the mismatch can be explained by NASA’s exclusion of candidates reported in an unpublished manuscript by Michel Mayor & colleagues (2011), as well as other candidates proposed by other investigators on the strength of Bayesian reanalyses of existing radial velocity data (see list of exclusions here). Thus even my relatively skeptical approach might err on the side of optimism.

The difficulty of establishing an accurate count of the known exoplanetary systems, let alone the very nearest, is illustrated by the observational history of Rho Coronae Borealis. This Sun-like star, one of the first to be identified as an exoplanetary host, is located 17.24 parsecs (56 light years) away. In 1997, Robert Noyes & colleagues reported an object (b) with a minimum mass of 1.1 Mjup orbiting this star in a period of 39 days with an eccentricity of 0.03. Although their radial velocity measurements could not rule out much higher masses, they presented theoretical arguments in favor of a gas giant planet instead of a brown dwarf star.

Follow-up studies summarized by Fulton et al. (2016) presented additional astrometric data that, according to several astronomers, unmasked the so-called exoplanet as a very dim M dwarf or massive brown dwarf.  In this argument, the original mass value reported by Noyes & colleagues was a drastic underestimate, because we happen to observe the system from a face-on viewing angle. Such a geometry minimizes the Doppler shift detectable from Earth, whereas an edge-on angle maximizes it. According to this argument, the companion must be at least 100 times more massive than Jupiter.

Most radial velocity detections that are not supported by transit observation are vulnerable to a similar challenge, but the prevailing attitude in the exoplanet community seems to be “innocent until proven guilty.” In the case of Rho Coronae Borealis b, the skeptical argument quietly won the day, and the proposed planet was excluded from EPE sometime around 2011.

Now Fulton’s group has conducted a concentrated observing program to test the planetary hypothesis. Their findings confirm the existence of planet b while ruling out even the dimmest of M dwarfs. Thus Rho Coronae Borealis, jewel in the Northern Crown, has returned to the fold of exoplanet host stars.

Fulton & colleagues also report a second planet (c) with an orbital period of 102 days and a semimajor axis of 0.41 AU, similar to Mercury’s. Depending on our viewing angle, the planet’s minimum mass of 25 Earth units (Mea) suggests either a large low-mass planet like GJ 436 b (a “Super Neptune” or tween) or a small gas giant. In the first alternative, Rho Coronae Borealis would present a relatively rare and extremely interesting architectural feature: a pair of adjacent planets in which the inner object is a gas giant and the outer is a low-mass planet like Neptune. Apart from Rho Coronae Borealis, just five examples of this architecture have been observed: our Solar System (Saturn + Uranus), GJ 876 (planets b + e), Kepler-87 (planets b + c), Kepler-89 (planets d + e), and WASP-47 (planets b + d).

In the second alternative, Rho Coronae Borealis might a scaled-down version of 55 Cancri, which presents an adjacent pair in which the inner object is a massive gas giant (planet b) and the outer is a tween (planet c) of about 55 Mea.

-------------------------------

One of my favorite articles of 2016 was “Challenges in Planet Formation,” by Alessandro Morbidelli & Sean Raymond, two seasoned veterans of exoplanetary science. The authors frankly discuss everything we don’t really know about the evolution of planetary systems, which their opening sentence describes as “a vast, complex, and still quite mysterious subject.” The same characterization could easily apply to our understanding of exoplanetology, given the vast, mysterious, and constantly expanding nature of the extrasolar census. As with planetary evolution, when it comes to the demographics of exoplanets, “even our most successful models are built on a shaky foundation” (Morbidelli & Raymond 2016).

So here’s looking forward to the mysterious, terrifying, and inevitably fascinating events and revelations to come in 2017 . . . .

Click here for a permanent index by topic of blog posts
on Back Alley Astronomy

REFERENCES

Endl M, Brugamyer EJ, Cochran WD, MacQueen PJ, Robertson P, Meschiari S, Ramirez I, Shetrone M, Gullikson K, Johnson MC, Wittenmyer R, Horner J, Ciardi DR, Horch E, Simon AE, Howell SB, Everett M, Caldwell C, Castanheira BG. (2016) Two new long-period giant planets from the McDonald Observatory Planet Search and two stars with long-period radial velocity signals related to stellar activity cycles. Astrophysical Journal 818, 34. Abstract: 2016ApJ...818...34E
Fulton BJ, Howard AW, Weiss LM, Sinukoff E, Petigura EA, Isaacson H, Hirsch L, Marcy GW, Henry GW, Grunblatt SK, Huber D, von Braun K, Boyajian TS, Kane SR, Wittrock J, Horch E, Ciardi DR, Howell SB, Wright JT, Ford EB. (2016) Three temperate Neptunes orbiting nearby stars. Astrophysical Journal 830, 46. Abstract: 2016ApJ...830...46F
Mayor M, Marmier M, Lovis C, Udry S, Ségransan D, Pepe F, Benz W, Bertaux J-L, Bouchy F, Dumusque X, Lo Curto G, Mordasini C, Queloz D, Santos NC. (2011) The HARPS search for southern extra-solar planets XXXIV. Occurrence, mass distribution and orbital properties of super-Earths and Neptune-mass planets. Unpublished; abstract at https://arxiv.org/abs/1109.2497
Morbidelli A, Raymond S. (2016) Challenges in planet formation. Invited review; in press. Abstract: 2016arXiv161007202M
Noyes R, Jha S, Korzennik SG, Krockenberger M, Nisenson P, Brown TM, et al. (1997) A planet orbiting the star Rho Coronae Borealis. Astrophysical Journal 483, L111-L114.
Shen Y, Turner EL. (2008) On the eccentricity distribution of exoplanets from radial velocity surveys. Astrophysical Journal 685, 553-559.
Teske JK, Cunha K, Schuler SC, Griffith CA, Smith VV. (2013) Carbon and oxygen abundances in cool metal-rich exoplanet hosts: A case study of the C/O ratio of 55 Cancri. Astrophysical Journal 778, 132.
von Braun K, Boyajian TS, ten Brummelaar TA, Kane SR, van Belle GT, Ciardi DR, Raymond SN, Lopez-Morales M, McAlister HA, Schaefer G, Ridgway ST, Sturmann L, Sturmann J, White R, Turner NH, Farrington C, Goldfinger PJ. (2011) 55 Cancri: Stellar astrophysical parameters, a planet in the habitable zone, and implications for the radius of a transiting Super-Earth. Astrophysical Journal 740, 49.

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.

Click here for a permanent index by topic of blog posts
on Back Alley Astronomy

 

REFERENCES

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.
Armitage PJ. (2010) Lecture notes on the formation and early evolution of planetary systems. https://arxiv.org/abs/astro-ph/0701485
Baillie K, Charnoz S, Pantin E. (2015) Time evolution of snow regions and planet traps in an evolving protoplanetary disk. Astronomy & Astrophysics 577, A65.
Baillie K, Charnoz S, Pantin E. (2016) Trapping planets in an evolving protoplanetary disk: preferred time, locations, and planet mass. Astronomy & Astrophysics 590, A60.
Baruteau C, Bai X, Mordasini C, Molliere P. (2016) Formation, orbital and internal evolutions of young planetary systems. Space Science Reviews.
Benitez-Llambay P, Masset F, Koenigsberger G, Szulagyi J. (2015) Planet heating prevents inward migration of planetary cores. Nature 520, 63-65.
Bitsch B, Johansen A, Lambrechts M, Morbidelli A. (2015) The structure of protoplanetary discs around evolving young stars. Astronomy & Astrophysics 575, A28.
Chambers JE. (2006) Planet formation with migration. Astrophysical Journal 652, L133-L136.
Cieza LA, Casassus S, Tobin J, Bos SP, Williams JP, Perez S, et al. (2016) Imaging the water snow-line during a protostellar outburst. Nature 535, 258-261.
Cossou C, Raymond SN, Hersant F, Pierens A. (2014) Hot super-Earths and giant planet cores from different migration histories. Astronomy & Astrophysics 569, A56.
Dodson-Robinson SE, Willacy K, Bodenheimer P, Turner NJ, Beichman CA. (2009) Ice Lines, planetesimal composition and solid surface density in the Solar nebula. Icarus 200, 672-693.
Dorn C, Khan A, Heng K, Connolly JAD, Alibert Y, Benz W, Tackley P. (2015) Can we constrain the interior structure of rocky exoplanets from mass and radius measurements? Astronomy & Astrophysics 577, A83.
Ercolano B, Rosotti GP, Picogna P, Testi L. (2016) A photo-evaporative gap in the closest planet forming disc. Monthly Notices of the Royal Astronomical Society. In press. 2016arXiv160903903E
Gammie C. (1996) Layered accretion in T Tauri disks. Astrophysical Journal 457, 355-362.
Hasegawa Y, Pudritz RE. (2010) Dead zones as thermal barriers to rapid planetary migration in protoplanetary disks. Astrophysical Journal Letters 710, L167-L171.
Hasegawa Y, Pudritz RE. (2011) The origin of planetary system architectures. I. Multiple planet traps in gaseous discs. Monthly Notices of the Royal Astronomical Society 417, 1236-1259.
Hasegawa Y, Hirashita H. (2014) Planet traps and first planets: the critical metallicity for gas giant formation. Astrophysical Journal 788, 62.

Hasegawa Y. (2016) Super-Earths as failed cores in orbital migration traps. Astrophysical Journal. In press. Abstract: http://adsabs.harvard.edu/abs/2016arXiv160904798H

Ida S, Lin D. (2010) Toward a deterministic model of planetary formation. VI. Dynamical interaction and coagulation of multiple rocky embryos and Super-Earth systems around Solar-type stars. Astrophysical Journal 719, 810-830.
Ida S, Guillot T. (2016) Formation of dust-rich planetesimals from sublimated pebbles inside of the snow line. Astronomy & Astrophysics 596, L3.
Izidoro A, Raymond SN, Morbidelli A, Hersant F, Pierens A. (2015) Gas giant planets as dynamical barriers to inward-migrating Super-Earths. Astrophysical Journal Letters 800, L22.
Kennedy GM, Kenyon SJ. (2008) Planet formation around stars of various masses: the snow line and the frequency of giant planets. Astrophysical Journal 673, 502-512.
Li G, Adams FC. (2015) Cross-sections for planetary systems interacting with passing stars and binaries. Monthly Notices of the Royal Astronomical Society 448, 344-363.
Lissauer JJ (1993) Planet formation. Annual Review of Astronomy and Astrophysics 31, 129-174.
Lopez ED, Fortney JJ. (2014) Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition. Astrophysical Journal 792, 1. Abstract: 2014ApJ...792....1L
Lyra W, Johansen A, Klahr H, Piskunov N. (2008) Embryos grown in the dead zone: Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids. Astronomy & Astrophysics 491, L41-L44.
Malmberg D, Davies MB, Heggie DC. (2011) The effects of fly-bys on planetary systems. Monthly Notices of the Royal Astronomical Society 411, 859-877.
Martin R, Livio M (2012) On the evolution of the snow line in protoplanetary discs. Monthly Notices of the Royal Astronomical Society 425, L6-L9.
Masset FS, Morbidelli A, Crida A, Ferreira J. (2006) Disk surface density transitions as protoplanet traps. Astrophysical Journal 642, 478–487.
Matsumura S, Pudritz R, Thommes E. (2007) Saving planetary systems: Dead zones and planetary migration. Astrophysical Journal 660, 1609-1623.
Matsumura S, Ida S, Nagasawa M. (2013) Effects of dynamical evolution of giant planets on survival of terrestrial planets. Astrophysical Journal 767, 129.
Morbidelli A, Bitsch B, Crida A, Gounelle M, Guillot T, Jacobson S, Johansen A, Lambrechts M, Lega E. (2016) Fossilized condensation lines in the Solar System protoplanetary disk. Icarus 267, 368-376.
Morbidelli A, Raymond S. (2016) Challenges in planet formation. In press. Abstract: 2016arXiv161007202M
Mulders GD, Ciesla FJ, Min M, Pascucci I. (2015) The snow line in viscous disks around low-mass stars: Implications for water delivery to terrestrial planets in the habitable zone. Astrophysical Journal 807, 9.
Mustill AJ, Davies MB, Johansen A. (2016) The effects of external planets on inner systems: multiplicities, inclinations, and pathways to eccentric warm Jupiters. Monthly Notices of the Royal Astronomical Society. In press. Abstract: 2016arXiv160908058M
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.
Qi C, Oberg KI, Wilner DJ, D’Alessio P, Bergin E, Andrews SM, Blake GA, Hogerheijde MR, van Dishoeck EF. (2013) Imaging of the CO snow line in a solar nebula analog. Science 341, 630-632.
Raymond SN, Quinn T, Lunine JI. (2006) High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics. Icarus 183, 265-282.
Raymond SN, Kokubo E, Morbidelli A, Morishima R, Walsh KJ. (2014) Terrestrial planet formation at home and abroad. In Protostars and Planets VI, pages 595-618. Edited by Beuther H, Klessen RS, Dullemond CP, Henning T. Tucson: University of Arizona Press.
Rogers L. (2015) Most 1.6 Earth-radius planets are not rocky. Astrophysical Journal 801, 41
Weidenschilling JS. (1977) The distribution of mass in the planetary system and solar nebula. Astrophysics and Space Science 51, 153-158.
Wolfgang A, Rogers LA, Ford EB. (2016) Probabilistic mass-radius relationship for sub-Neptune-sized planets. Astrophysical Journal 825, 19.