K2 and the Tweens

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

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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 http://kepler.nasa.gov/Mission/discoveries/.)

 

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)

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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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