Saturday, July 30, 2016

Jupiter Re-Ascending

Figure 1. Les Grands Zig-zags. The assembly and migration of Jupiter and Saturn through the primordial Solar nebula, according to a scenario presented by Sean Raymond & colleagues (2016).Numbers alongside the concentric semicircles indicate radii in astronomical units (AU), where 1 AU equals the radius of Earth’s present orbit and 5.2 AU equals the radius of Jupiter’s present orbit.

This one slipped past me during the excitement of the spring music festivals: a new contribution by Sean Raymond & colleagues to the ongoing debate over the history of the inner Solar System. Here’s the background:
Our Solar System is weird. Among its most notable oddities is the dearth of mass inside a radius of one astronomical unit (AU, where 1 AU equals the average separation between Earth and Sun). Outside our system, the nearest G-type star known to harbor planets is 82 Eridani, at a distance of 20 light years. This metal-poor G8 star supports three planets with an aggregate mass at least 10 times Earth (10 Mea) inside an area equivalent to the orbit of Mercury. The next-nearest G-type host is 61 Virginis, located about 28 light years away. This G5 star hosts three planets with an aggregate mass in excess of 46 Mea inside the equivalent of the orbit of Venus. Both of these architectures are typical of multiplanet systems discovered by radial velocity and transit searches.
By contrast, the three planets closest to our Sun – Mercury, Venus, and Earth – have an aggregate mass smaller than 2 Mea.
Last year, two studies tried to find an explanation for the missing mass. Batygin & Laughlin (2015), hereafter BL15, proposed a solution that extends the popular scenario of the Grand Tack, which has been advocated by Pierens & Raymond (2011) and is discussed here and here. BL15 hypothesized that several Super Earth-type planets formed inside the present orbit of Mercury during the first few million years after the birth of our Sun, when it was still surrounded by an extensive nebula. (In this context, Super Earths should be understood as rocky or gassy planets of a few Earth masses.) No sooner had these objects assembled than the growing core of Jupiter began migrating from the outer Solar nebula to the vicinity of the present orbit of Mars. Young Jupiter’s inward passage swept a huge swarm of planetesimals into the inner system, causing perturbations that destabilized the orbits of the Super Earths. As a result, both the planets and the planetesimals were engulfed by the Sun. At this point, Jupiter executed a dramatic course change (the Grand Tack itself) which carried it back into the outer system on the nebular tides, courtesy of an intimate connection with its smaller and chillier sidekick, Saturn. Meanwhile, the inner system catastrophe left behind a ring of debris that coalesced into the four terrestrial planets we know today.
Volk & Gladman (2015), hereafter VG15, also proposed that our system originally harbored a cluster of planets inside the present orbit of Mercury (“intra-Mercurians”). In all other ways, however, their model differs markedly from BL15. To start with, their intra-Mercurian objects are similar in mass to Earth and Venus, not to Super Earths like 82 Eridani b or 61 Virginis b. A more striking difference is that VG15 implicitly reject both the Nice Model and the Grand Tack, since their scenario does not involve the outer Solar System at all. Instead, VG15 suggest that the four terrestrial planets assembled exactly where we see them today, outside the orbits of the intra-Mercurian planets, with which they peacefully coexisted for tens of millions of years. Then, one bright millennium, an abrupt dynamical instability upset the apple cart. The intra-Mercurians devolved into a donnybrook of orbit crossings and collisions that rapidly ground them into dust. The dust itself was then engulfed by our Sun, while the four terrestrial planets continued circling the scene of the catastrophe like horrified onlookers. The only remaining evidence of those disintegrated inner planets can be found in the cratered surfaces of Mercury, the Moon, and Mars, which were pelted by fragments during the period of annihilation. In sharp contrast, the Nice Model argues that these rocky worlds were etched by a storm of asteroids that originated in a dynamic instability among the four outer planets – Jupiter, Saturn, Uranus, and Neptune.
Figure 2. Inside-out planet formation

This image appears as Figure 1 of Chatterjee & Tan 2014. (i) The magnetic field of the young star creates a cavity in the center of the gaseous protoplanetary disk. Immediately outside the cavity is a “dead zone” through which pebbles drift. (ii) Pebbles accumulate in a ring around the edge of the cavity, where the gas pressure is at its maximum. (iii) The pebble ring coalesces into an Earth-size planet. (iv) The dead zone retreats from the star, creating a new pressure maximum at a larger radius where new pebbles accumulate and potentially form a new planet. Abbreviations: MRI = magnetorotational instability; P max = pressure maximum.

pebble pile-up with outward migration
Raymond & colleagues (hereafter R16) take a completely different approach to the problem, one that does not involve either a primordial clutch of small planets or an inner system catastrophe. Although R16 note that their model is consistent with the Grand Tack, they emphasize its theoretical independence. Their starting point is actually the scenario of “Inside-Out Planet Formation,” as presented in an article of the same name by Sourav Chatterjee and Jonathan Tan (2014). Figure 2 provides a high-level summary.
R16 begin with the very earliest stages of accretion in the Solar nebula. They hypothesize that a large rocky planet assembled out of pebbles orbiting near the inner edge of the nebula, at an approximate semimajor axis of 0.1 AU. This object was proto-Jupiter (Figure 2.iii). Once it attained a few Earth masses, it was subject to torques exerted by the ambient gases, which caused it to migrate outward to a semimajor axis of about 5 AU. Along the way, the migrating core cleared all solid material from the nebula interior to 1 AU, shepherding some of it onto exterior orbits. This shepherding process likely resulted in the formation of a second core – proto-Saturn – which young Jupiter continued to herd during its journey into cooler regions of the nebula. Both objects accreted mass during this process, eventually initiating the runaway accretion of extensive envelopes of hydrogen and helium (H/He).
As R16 argue, this scenario explains why the area inside Mercury’s orbit is completely empty of mass. The rocky material that originally accumulated in this space was accreted by young Jupiter, which continued accreting and scattering planetesimals as it ascended beyond the radii that would later mark the orbits of Earth and Mars. Once Jupiter attracted sufficient H/He to become a gas giant planet, it opened a gap in the surrounding nebula, initiating the process of Type II migration. Then, having arrived in the cool zone, Jupiter immediately turned around and retraced its path.
By this stage in the narrative we’ve reached the threshold of the Grand Tack. Saturn was now following Jupiter instead of being herded ahead of it, and the gap between the two planets kept narrowing until their orbits entered a mean motion resonance. At that point, when Jupiter had reached a radial distance of about 2 AU (Brasser & al. 2016), the direction of their migration switched again and they sailed into the outer nebula for the last time.
Figure 3. Jupiter Ascending with Ganymede

A boy and his eagle: Ganymede & Jupiter. In Greek mythology, Ganymede was a Trojan prince of uncommon beauty. Spying him from on high, Zeus (Latin Jupiter) assumed the form of an eagle, swooped down to Earth, and carried the boy back up to Mount Olympus, where Ganymede became the cupbearer of the gods. The beverage he served in heaven was nectar, a delicious liquid that confers immortality. In 1906, the Anheuser-Busch Brewing Ass’n appropriated the myth of Ganymede to promote their own version of heavenly nectar: Budweiser beer, now one of the most popular alcoholic beverages on Earth. Credit: Wikimedia.

The full scenario involves a double zigzag that calls to mind the mark of Zorro (Figure 1). Jupiter’s outward-inward-outward path also recalls a Greek myth in which Zeus (the Greek equivalent of Roman Jupiter) swooped down into the terrestrial zone, abducted a youth named Ganymede, and carried him aloft into the upper spheres of heaven (Figure 3). Indeed, it seems likely that Jupiter’s satellite system – of which Ganymede is the most prominent member – formed just as the Solar nebula was dissipating (Alibert & al. 2005). In the Grand Zigzag scenario proposed by R16, this process is constrained to occur when Jupiter arrived in the vicinity of its present orbit, potentially bearing a circumplanetary disk of solids (proto-Ganymede) enriched by the planet’s wanderings through the nebula.
Wisely, R16 ask whether this intricate sequence of events is “a generic process” or a relatively rare occurrence “confined to only a limited range of conditions.” While they lean toward the first option, they concede that planetary systems containing both an inner system of Super Earths and an outer system of gas giants would be challenging to explain in the context of the Grand Zigzag. In this regard I hasten to note that Chatterjee & Tan (2014) originally developed their model of inside-out planet formation to explain the architecture of tightly packed systems of low-mass planets such as Kepler-11 and Kepler-20, not mixed-mass systems resembling HD 219134, Kepler-167, or our Solar System. The adoption of this approach by R16 appears quite novel in the context of the prehistory of the Solar System, where its application - in my view – seems tortuous.
critique of competing models
My favorite section of R16 is their discussion of alternative explanations for the missing mass in the inner Solar System. The authors make quick work of two studies to which they themselves contributed: Morbidelli & al. 2016, which explains the void as a lingering effect of the condensation front for silicate dust in the primordial Solar nebula, and Izidoro & al. 2015, which argues that the formation of Jupiter blocked the migration of solids from the outer system, starving the inner system of the mass it needed to form short-period Super Earths. Neither approach holds up under their analysis. I find this skeptical attitude particularly impressive, since healthy self-criticism is essential in scholarly work.
R16 dispose of VG15 with similar ease, arguing that the furious impacts invoked to explain the disappearance of several primeval planets “would not have fallen in the ‘super-catastrophic’ regime” needed to achieve total annihilation. Instead, the debris from any erosive impacts would simply be swept up by the remaining planets in the inner Solar System. R16 thereby confirm my own doubts that a whole subsystem of planets could vanish without a trace, but they do so with a better-informed argument than I could hope to make. As they conclude, “we do not expect that a system of close-in terrestrial planets could self-destruct.”
R16 devote considerably more space to their takedown of BL15. First, they find that the “massive pulse of collisional debris” generated by Jupiter’s inward migration in that scenario would merely accelerate mass accretion by any planets forming in the inner system. Second, they argue that this swarm of debris would not be physically capable of shepherding a clutch of Super Earths into ever-shrinking orbits. Instead, they suggest that this catastrophic outcome was just an artifact of the simulation code used by BL15. In reality, they contend, a mass of planetesimals would “self-interact and grow” rather than push a planet to the brink of its host star’s gravity well. Finally, R16 challenge the notion that planets can simply be pushed into their stars, because all evolving protoplanetary disks develop a cavity interior to about 0.1 AU where gas dynamics cease. An object forced into this void, they say, would be more likely to stabilize on a new orbit than to set the controls for the heart of the Sun.
In parting, R16 note a striking irony in the model presented by BL15. Whereas Batygin & Laughlin “invoke the rapid inward drift of solids to destroy super-Earths,” many other models have proposed the same process to create them.

Twenty-first century superstars Channing Tatum and Eddie Redmayne appeared in this star-crossed science fiction epic. “Jupiter” herself was played by Mila Kunis. All three actors have seen much more success in other movies.

Sometimes I wonder if I’m getting mental whiplash from the barrage of new theories about the evolution of our own planetary system and others. Nevertheless, when it comes to activities of the mind, I’d prefer an embarrassment of riches to an empty cupboard!



Alibert Y, Mousis O, Benz W. (2005) Modeling the Jovian subnebula. I. Thermodynamic conditions and migration of proto-satellites. Astronomy & Astrophysics 439, 1205-1213.
Batygin K, Laughlin G. (2015) Jupiter’s decisive role in the inner Solar System’s early evolution. Proceedings of the National Academy of Sciences 112, 4214-4217. Abstract: 2015PNAS..112.4214B
Brasser R, Matsumura S, Ida S, Mojzsis SJ, Werner SC. (2016) Analysis of terrestrial planet formation by the Grand Tack model: System architecture and tack location. Astrophysical Journal 821, 75.
Chatterjee S, Tan JC. (2014) Inside-out planet formation Astrophysical Journal 780, 53.
Izidoro A, Raymond S, Morbidelli A, Hersant F, Pierens A. (2015) Gas giant planets as dynamical barriers to inward-migrating Super-Earths. Astrophysical Journal Letters 800, L22.
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.
Pierens A, Raymond SN. (2011) Two phase, inward-then-outward migration of Jupiter and Saturn in the gaseous solar nebula. Astronomy & Astrophysics 533, A131. Abstract: 2011A&A...533A.131P
Raymond SN, Izidoro A, Bitsch B, Jacobson SA. (2016) Did Jupiter’s core form in the innermost parts of the Sun’s protoplanetary disk? Monthly Notices of the Royal Astronomical Society 458, 2962-2972. Abstract: 2016MNRAS.458.2962R
Volk K, Gladman B. (2015) Consolidating and crushing exoplanets: Did it happen here? Astrophysical Journal Letters, 806: L26. Abstract: 2015ApJ...806L..26V


Sunday, July 10, 2016

HIP 41378: A Compact Planet Sampler

Figure 1. Candidate planets of HIP 41378 represented at their relative sizes (radii from Vanderburg et al. 2016). Planets b and c are the only objects with formal validation. The orbital periods of the three outer candidates remain uncertain, and the discovery team provided no data on semimajor axes. Nor could they establish whether the period of candidate e is longer or shorter than that of candidate d.

The ongoing K2 Mission can’t compare with the original Kepler Mission in terms of the sheer number of planet candidates identified. Nevertheless, some K2 discoveries rival the astrophysical interest of Kepler’s crown jewels. Last year’s game-changing results from WASP-47 have been discussed a few times in this blog. A few weeks ago the world received advance notice of another amazing K2 find: a rich, high-multiplicity, mixed-mass system of five planets transiting HIP 41378, described in a recent preprint by Andrew Vanderburg & colleagues (Figure 1).

As the discovery team notes at the outset, “K2 is not as sensitive to planetary systems with complex architectures as the original Kepler mission” (Vanderburg et al. 2016). That’s because K2 can observe a given star for a maximum of approximately 80 days, instead of the three-plus years of continuous staring enabled by Kepler. But in the case of HIP 41378, a happy coincidence enabled the detection of five different companions within the available period of data collection (Figure 2). Two of them have repeating transits and the other three have a single transit each.

Figure 2. Light curves for five transiting planet candidates around HIP 41378

Phase-folded light curves for each of the candidate planets in the HIP 41378 system. Adapted from Figure 2 in Vanderburg & al. 2016.

A few definitions are in order. “High-multiplicity” is now in general use as a descriptor for systems with three or more planets. “Mixed-mass” is (I believe) my own coinage, referring to systems with at least one low-mass planet (an object less massive than about 50 Earth masses [50 Mea] with a bulk composition dominated by heavy elements) and one gas giant planet (an object of 50 Mea or more with a bulk composition dominated by hydrogen/helium). “Rich mixed-mass” is my own concept, referring to mixed-mass systems containing a minimum of two low-mass planets. (According to my terminology, then, all “rich mixed-mass” systems are automatically “high-multiplicity.”)
Note that all three of these descriptors apply to our Solar System. To date, however, fewer than 20 exoplanetary systems – among the many thousands now known – can be described as “rich mixed-mass.” HIP 41378 adds to their number.
Among systems published to date, the one that most closely resembles HIP 41378 is our friend Kepler-90, which supports an astonishing ensemble of seven planets ranging in radius from 1.2 Rea (Earth-like) to 11.3 Rea (Jupiter-like) on orbits shorter than a single Earth year.
Before cueing the Hallelujah Chorus, however, we should be aware of the limits of the K2 data. As the investigators concede, only two of the candidate planets around HIP 41378 have been formally validated by analysis of at least two transits. These two are HIP 41378 b and c, with respective orbital periods of 15.6 days and 31.7 days. For the other three candidates, Vanderburg & colleagues used the duration of each recorded transit to distinguish among them. They applied the letters d through f to designate objects with increasingly longer transit times and (potentially) longer orbital periods.
The investigators then calculated the probability that one or more of the candidates with a single transit were false positive detections. Using the K2 dataset, they found that a system with five transiting planets was 100 million times more likely than a system with two planets and three false positives. But they also found that the five-planet model was only 200 times more likely than a model with four planets and one false positive. Thus, the five-planet interpretation is probable but hardly certain.
The SIMBAD database assigns a spectral type of G1 IV to the host star, HIP 41378. The investigators prefer to describe it as a “slightly evolved late F-type star.” Its mass is 1.15 times Solar (1.15 Msol),  similar to Kepler-90 at 1.13 Msol. Its metallicity (endowment of elements heavier than hydrogen) is -0.11, meaning that the star is less enriched in metals than our Sun. Its distance is estimated at 116 parsecs, much nearer than most systems in the Kepler sample. Nevertheless, HIP 41378 still lies outside the region where radial velocity searches have typically been able to identify low-mass planets in the Super Earth range.
Vanderburg & colleagues argue that candidates HIP 41378 d through f have likely orbital periods exceeding 100 days. Their best guess for each period appears in Table 1. For simplicity, both the table and Figure 1 depict the five planets in alphabetical order, since the confidence intervals for the period of planet d overlap with those for planet e. Luckily, the estimates for planetary radii are more firmly grounded in transit data.
Table 1. HIP 41378 system parameters
Tags: Radius = planet radius in Earth units (Rea); Preferred Period = likely orbital period in days; Period Range = likely range in days of orbital period.
According to comparisons with transiting planets that have well-constrained mass estimates, planets b and c have likely masses in the range of 2 to 10 Mea; planet d is in the range of 5 to 26 Mea; planet e is a tween in the range of 15 to 40 Mea; and planet f is a gas giant in the range of 63 Mea (the mass of HAT-P-18b) to 318 Mea (the mass of Jupiter). Given their ample radii, even the smallest of these planets must have hydrogen/helium envelopes.
Despite the absence of purely rocky planets, HIP 41378 counts as a rich mixed-mass system. Its assortment of radii likely corresponds to an assortment of planetary species and bulk compositions. Like Kepler-90, it resembles a compact planet sampler (Figure 3), offering a planet population almost as diverse as our own Solar System within a space comparable to the orbital radius of the Earth.
Vanderburg & colleagues note that the system’s host star is bright enough for high-precision radial velocity measurements. Such data could confirm the reality of the transiting candidates and constrain the mass and orbital period of HIP 41378 f, and potentially of the smaller planets as well. The information could also help us understand the formation process of systems like HIP 41378 and our own Solar System.

Figure 3. A chocolate candy sampler


Andrew Vanderburg, Juliette C. Becker, Martti H. Kristiansen, Allyson Bieryla, Dmitry A. Duev, Rebecca Jensen-Clem, Timothy D. Morton, David W. Latham, Fred C. Adams, Christoph Baranec, Perry Berlind, Michael L. Calkins, Gilbert A. Esquerdo, Shrinivas Kulkarni, Nicholas M. Law, Reed Riddle, Maissa Salama, Allan R. Schmitt. Five Planets Transiting a Ninth Magnitude Star. Astrophysical Journal Letters, in press. Abstract: 2016arXiv160608441V


Monday, July 4, 2016

K2 and the Tweens

Figure 1. Selected low-mass planets with measured masses that have radii between those of Uranus and Saturn.

The Kepler space telescope was launched in 2009 on an ambitious mission to find Earth-like planets transiting stars in deep space. Initial results started arriving in 2010, and by 2011 it was clear that Kepler had revolutionized our understanding of exoplanets. In 2013, Kepler scientists began publicizing their best candidates for potentially Earth-like planets. Then, just one month after the first such announcement, the spacecraft’s pointing system malfunctioned, ending the original mission.
Unlike the Hubble Space Telescope, which is an artificial satellite orbiting the Earth at a low altitude, the Kepler spacecraft follows an independent orbit around the Sun. Thus no rescue operation was possible. Nonetheless, the astronomical community responded to Kepler’s mishap by applying the same ingenuity that they devoted to the initial problem of identifying Earth-like planets around distant stars.
Kepler originally relied on four reaction wheels to aim its grid of light sensors with the exquisite precision needed for continuous observation of the many thousands of stars selected for study. Although one reaction wheel broke down early in the mission, the spacecraft was designed to function with three, so the search for transiting planets continued. It was the breakdown of the second reaction wheel that terminated the telescope’s capacity for precision pointing.
Astronomers determined that Kepler could still observe stars whose sky-projected locations coincided with the ecliptic – that is, the plane of the Earth’s orbit around the Sun. Gravity combined with the pressure of Solar radiation could keep the sensors pointed for observing runs lasting a maximum of about 80 days. At the end of each run, the spacecraft’s thrusters could be fired to reposition the field of view (Howell & al. 2014).
This plan was nicknamed “K2” or “Second Light” (Figure 2). It went into effect early in 2014, and the Kepler telescope has continued to find new planets ever since. Given finite fuel supplies and the need to fire thrusters periodically, K2 has a limited lifetime.
Figure 2. Overview of the K2 Mission
As of early July, K2 has unveiled 44 new planets, including four new Hot Jupiters and a few dozen low-mass planets. Some are members of multiplanet systems. K2 has also contributed new data on a handful of previously discovered Hot Jupiters. Many results have been spectacular, such as the discovery of WASP-47d and e, two low-mass planets in a previously known Hot Jupiter system; K2-25b, the first small planet ever identified in a star cluster (the Hyades, our next-door neighbor in the Orion Spur); K2-33b, a puffy newborn planet orbiting an M dwarf in the nearby Upper Scorpius star-forming region; and HIP 41378, a compact mixed-mass system orbiting a bright F star.
One bonus associated with K2 is that the stars it observes are generally closer than those targeted by Kepler. Their proximity makes it easier to collect follow-up data with other instruments. In the most recent release of Kepler findings, 76% of Kepler host stars have distance estimates, with a median of 772 parsecs. A similar percentage of K2 host stars (71%) also have distance estimates, with a much smaller median of 183 parsecs. (All population-level data on K2 planets were retrieved from the Table of Confirmed K2 planets at
Unfortunately, K2 doesn’t seem very sensitive to rocky planets like Earth, defined as those with radii of 1.5 Earth units (1.5 Rea) or less. Whereas 25% of planets in the full Kepler sample have radii in this range, only one K2 planet does (K2-19d). Similarly, the median radius among Kepler planets is 2.15 Rea, notably smaller than the median of 2.59 Rea for the K2 sample. (Check out the postscript at the end for a more recent perspective.)
The silver lining in this cloud is the trove of K2 tweens, which I define as planets with radii between those of Uranus (4 Rea) and Saturn (9.4 Rea). Objects of this size are unknown in our Solar System and relatively rare in the Kepler sample (7% of the total). To date, however, K2 has returned 10 such exoplanets, representing almost 25% of the total. Seven out of 10 have mass measurements, obtained by analysis of transit timing variations (TTVs) or radial velocity (RV) observations or both. These discoveries make a valuable contribution to the field of planetology, since the blurry boundary between the two major planetary species – low-mass planets and gas giants – falls somewhere between Uranus and Saturn.
Although everyone agrees that Jupiter and Saturn are gas giant planets, the exact definition varies somewhat from source to source. Here’s the one I find most appropriate: A gas giant planet is an object whose bulk composition is more than 50% hydrogen and helium. The range of masses among extrasolar giants is approximately 60 to 4000 Mea, corresponding to about 0.20 to 13 Jupiter masses (Mjup). The median mass is about 1.8 Mjup. However, the precise upper and lower mass boundaries of the mass distribution are uncertain. Some authors have placed the lower boundary as low as 30 Mea (0.10 Mjup), while others have placed the upper boundary as high as 25 Mjup.
Figure 1 shows three well-characterized K2 tweens alongside four better-characterized planets in our Solar System and its immediate neighborhood. All the objects pictured have hydrogen/helium atmospheres, but the proportion of heavy elements (rock, metal, and ice) varies substantially.
Table 1. Twenty Transiting Tweens with Measured Masses

*Several conflicting masses have been reported for K2-19b and c. Mass estimates for the K2 planets are generally less secure than those available for the other exoplanets of this selection.
Tags: Rea = planet radius in Earth units; Mea = planet mass in Earth units; H/He = planet mass fraction attributed to hydrogen/helium; Period = planet orbital period in days; a = planet semimajor axis in Earth units; Msol = star mass in Solar units; Dist. = system distance in parsecs (1 parsec = 3.26 light years)

Table 1 offers a larger and more representative sample of tweens selected from various populations: the Kepler catalog, which encompasses a prominent subset of circumbinary tweens; ground-based transit searches, sometimes supplemented by space-based observations; the CoRoT catalog; and the current K2 sample. As available, the table includes an estimate of the mass fraction attributable to the hydrogen/helium (H/He) envelope around each planet (Dodson-Robinson & Bodenheimer 2009, Doyle & al. 2011, Cochran & al. 2011, Welsh & al. 2012, Lopez & Fortney 2014, Bakos & al. 2015, Petigura & al. 2016).

The criterion for inclusion in this table is the availability of a mass estimate. Nevertheless, some estimates are more robust than others. For example, the five nearest tweens have more precise RV data than any of the K2 tweens.

The K2-19 system in particular presents a unique conundrum. Two of its three planets (b and c) orbit near a 3:2 mean motion resonance, which produces significant TTVs, while the host star is bright enough to permit ground-based RV studies. This happy coincidence might be expected to yield highly precise results for the masses of both planets. However, that’s not how things have turned out. Through an analysis of TTVs, Barros & al. (2015) estimated masses of 44 Mea for K2-19b and 15.9 Mea for K2-19c. In another TTV study, Narita & al. (2015) could not determine a mass for K2-19b, but they found a value of about 20 Mea for K2-19c, formally consistent with the results of Barros & al. A subsequent RV study by Dai & al. (2016) found 28.5 Mea for K2-19b and 25.6 Mea for K2-19c. Finally, a study by Nespral & al. (2016) obtained new RV data indicating a mass of 71.7 Mea for K2-19b, but K2-19c was undetectable in their dataset. The authors followed up with a TTV analysis that found a mass of 57.7 Mea for K2-19b and 9.4 Mea for K2-19c.

The conflicting results of these four studies give me pause: it looks like less data is better than more! We can keep pursuing our dreams of illumination by distant stars only if we’re ready to shrug off a lot of troublesome details.

Having done so, let’s look again at the tweens in Table 1. First, the bulk mass fraction of H/He appears to increase along with increasing radius, consistent with the hypotheses of Lopez & Fortney (2014). Second, overall mass also tends to increase with radius, although the trend is less consistent. Third, the two tweens with the largest radii – Kepler-16b and Kepler-34b – come close to fulfilling my definition of a gas giant, since they have H/He fractions in the vicinity of 50%, and they fall in the expected mass range for giant planets (both in excess of 60 Mea).

However, this neat picture is complicated by predictions for the internal structure of the four most massive tweens in the table. Although CoRoT-8b, HD 149026 b, Kepler-16b, and Kepler-34b have larger endowments of H/He than most of the other tweens, their envelope fractions are still much smaller than the norm for well-constrained gas giant planets, which range from 75% to 95%. Given estimated heavy element masses of 30 to 60 Mea, each of these big tweens could have contributed solid cores to as many as six planets like Jupiter and Saturn.

super-puff tweens
Note that my selection in Table 1 is biased in favor of RV data. Many studies have found that mass estimates derived from RV measurements are systematically larger than those based on TTV analyses. Furthermore, for systems where both TTVs and RV observations are available, the two methods frequently produce widely divergent results. The exceptions are those rare cases with data of extremely high precision.
When we turn to the sample of tweens for which TTVs provide the only evidence of mass, we find unexpectedly lightweight objects. Such tweens have been nicknamed “super-puffs.” The classic example is Kepler-11, whose radius (4.18 Rea) is about 5% larger than Neptune’s, while its TTV mass (8.4 Mea) is less than 50% of Neptune’s. Lopez & Fortney (2014) calculate its mass fraction of H/He as 15%. The four well-constrained tweens in Table 1 with similar mass fractions (GJ 3470 b, GJ 436 b, HAT-P-11b, HATS-7b) are notably more massive, with values in the range of 13 to 38 Mea.
Another multiplanet system, Kepler-223, rivals the compact structure and extensive TTVs revealed in Kepler-11. The four planets of Kepler-223 have orbital periods ranging from 7 to 20 days, arranged in an interlocking pattern of resonances: planets b and d orbit very close to a 2:1 mean motion resonance, as do planets c and e (Mills & al. 2016). TTV analyses yield a narrow selection of masses for these four, ranging from 4.8 Mea for planet e to 8 Mea for planet d. The two bookends of this range also happen to fit my definition of tweens: Kepler-223d has a radius of 5.24 Rea and Kepler-223e of 4.6 Rea. Although Mills & al. do not calculate the H/He mass fraction for these objects, they must surpass our estimates for Uranus and Neptune.
Despite their status as outliers, the four super-puffs orbiting Kepler-223 are easier to explain than the four massive tweens discussed in the previous section. Considerable theoretical work has established that planets as lightweight as 2 Mea can accrete H/He envelopes from their native nebulae and retain them against stripping by stellar flux, as long as their obits are cool enough. Still larger core masses can withstand still higher levels of irradiation, maintaining extended atmospheres over the main sequence lifetimes of their host stars. The real problem is to account for musclebound tweens like CoRoT-8b and HD 149026 b.
why tweens but not giants?
As Erik Petigura & colleagues recently noted (2016), the K2 tweens and their cousins in other extrasolar catalogs raise critical questions about planet formation. How can these objects assemble such massive heavy element cores and deep H/He envelopes without undergoing runaway accretion – the pathway that leads to the birth of a bona fide gas giant?
Before Kepler, we already knew that the mass range for planets dominated by H/He extended as low as 60 Mea. HAT-P-18b, with a mass of only 63 Mea, is a twin of Jupiter in radius, requiring a highly inflated H/He envelope. Similarly, HAT-P-12b has a radius of 10.8 Rea (about 4% smaller than Jupiter’s) and a slightly larger mass of 67 Mea, requiring an envelope almost as deep.
Petigura & colleagues suggest that puffy tweens (and presumably puffy gas giants like these two HATs) formed far beyond their systems’ ice line, where extensive envelopes can be accreted quickly and easily, and then migrated inward to their present orbits. Ironically, this is similar to the scenario that Dodson-Robinson & Bodenheimer (2009) proposed some years earlier to account for the opposite problem – the anomalously massive core of another tween, HD 149026 b.
In both cases, long-range migration has been invoked: through a gas-rich nebula to form tweens with unusually deep H/He envelopes, and through a metal-rich nebula to form tweens with unusually large heavy-element cores.
I suspect that the true explanation for these dissimilar outliers will be more complicated, likely involving the chemical composition of the nebula but also requiring  evolving structures that alternately concentrate mass at particular radial locations and then encourage migration, either inward or outward. Recent advances in the imaging and analysis of planet-forming nebulae have inspired a growing number of theoretical studies that are bound to shed light on these questions.

postscript on July 23, 2016

This past week, Ian Crossfield & colleagues issued a preprint entitled “197 Candidates and 104 Validated Planets in K2’s First Five Fields” (hereafter C16). It upends some of the descriptive statistics on the K2 sample in this blog post, even though I used data retrieved only three weeks ago. C16 offer a table listing key parameters of the planet candidates they identified (their Table 8). It includes 93 confirmed planets, versus NASA’s list of 44 confirmed planets on July 4. Where the two samples overlap, the stellar and planetary parameters listed in C16 are often at odds with the ones offered by NASA, and it’s not clear to me which numbers are preferable.

C16 find 16 planets smaller than 1.5 Rea (meaning that they’re likely to be terrestrial rather than gassy), whereas I identified only one in the recent NASA data. Among those 16 small planets from C16, all but 3 have orbital periods shorter than 10 days, and all but 2 orbit M dwarfs. The 2 proposed terrestrials orbiting Sun-like stars – K2-36b and K2-80c – have periods of 1.42 and 5.61 days, respectively, implying surface conditions that are literally hellish.

I also observed a median orbital period of 8.5 days and a median radius of about 2.6 Rea. C16 find a similar median period (8.6 days), but for radii they present a smaller median of 2.3 Rea. Oddly, my own inspection of their Table 8, using the same approach that I applied to the older NASA data, suggests a median of 2.4 Rea. Regardless of which number is more accurate, the new value is closer to the median in the Kepler sample, which is just 2.15 Rea.

Finally, C16 report 12 planets with radii between Uranus and Saturn, similar to the 10 I found in the NASA selection. Given their larger overall sample, the fraction of tweens amounts to 13% of the total, versus 23% for the NASA sample.

C16 conclude with a cautionary statement: “Lists of K2 candidates and/or validated planets are not currently suitable for the studies of planetary demographics that Kepler so successfully enabled.” I am duly chastened.  

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