The Small Mars Problem

Figure 1. All planets and dwarf planets orbiting within 6 astronomical units (AU) of our Sun, shown at their relative diameters.

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From afar, our Solar System looks regular and well-organized. At its center is a large, massive sphere of incandescent gases (the Sun) surrounded by eight smaller and less massive spheres of heavier elements (the planets) distributed in concentric orbits out to a distance of about 4.5 billion km/2.8 billion miles.

The orbital distribution of the eight planets also seems regular, at least at first glance. Smaller, rocky worlds are confined to the inner system, while larger, gaseous worlds dominate the outer system. Planet sizes follow a curve, rising from the inner to the middle planets and then declining again from the middle to the outer planets.

In more specific terms, mass and radius increase along with distance among the three planets closest to the Sun (Mercury through Earth). Both parameters peak at the orbit of the fifth planet, Jupiter, which is almost a dozen times the radius and more than 300 times the mass of Earth. Then, from Jupiter through Uranus, the seventh planet, both mass and radius decline substantially along with distance from the Sun.

But this orderly progression of planet sizes has two notable interruptions: Mars and Neptune. If the distribution of planets were truly regular, Mars would be larger and more massive than Earth, and Neptune would be smaller and less massive than Uranus. Instead, the Red Planet has only 53% of Earth’s radius (0.53 Rea) and 11% of its mass (0.11 Mea), while the Azure Planet, at 17.2 Mea and 3.9 Rea, has about 98% of the radius of Uranus but 119% of its mass.

How did that happen?

In the present post I’m going to ignore the oddity of Neptune and concentrate on the Martian half of the question. My rationale is that Mars occupies our system’s classical habitable zone, and therefore – along with Earth and Venus – plays a critical role in theories of the habitability of extrasolar planets. If mass had been more uniformly distributed in the inner Solar System, Mars would be more massive than it is. If its mass were in the range of 1 to 2 Mea, Mars would likely be able to sustain a magnetic field, plate tectonics, surface water, and long-term habitability. Therefore, if we want to understand the potential system architectures that might support life-bearing planets, we need to understand why Mars is so small.

Figures 1 and 2 highlight the Small Mars Problem and the Great Martian Gap, which is the name I just invented for the general depletion of mass between Earth and Jupiter. The planet Mars and the dwarf planet Ceres orbit within this gap at 1.52 AU and 2.77 AU, respectively. With a little more than 1% of the mass of our Moon, Ceres accounts for fully one-third of all mass in the Asteroid Belt, which is concentrated between 2.2 and 3.3 AU (the latter boundary provided by the 2:1 resonance with Jupiter's orbit; Jewitt et al. 2009). The entire region between the orbits of Earth and Jupiter contains less than 0.12 Mea, with little Mars accounting for 99% of the total. By contrast, the region extending inward from Earth’s orbit to the Sun contains 1.87 Mea, yet Earth, the most massive object, accounts for only 53% of the total.

Figure 2. The Great Martian Gap

Blue numbers along the bottom refer to astronomical units (AU), where the Earth/Sun separation = 1. Planets are shown at their relative sizes and relative distances from the Sun, with separate scales for radius and distance. As astronomers have long noted, mass is severely depleted between the orbit of Jupiter at 5.2 AU and the orbit of Earth at 1 AU (see Weidenschilling 1977).

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zigzag migration

Recent studies by Konstantin Batygin & Greg Laughlin (2015) and by Sean Raymond & colleagues (2016) have presented conflicting scenarios to explain the Small Mars Problem and the Great Martian Gap. Both involve zigzag migratory paths for Jupiter during the primordial phase of system evolution.

Batygin & Laughlin based their approach on earlier models by Kevin Walsh & colleagues (2011) and Pierens & Raymond (2011), in which Jupiter formed in the outer Solar System (somewhere beyond 3 AU) and then migrated first inward and then outward again. The popular name for this scenario (blogged here and here) is the Grand Tack. According to Batygin & Laughlin, these maneuvers not only swept most solid mass out of the region exterior to Earth’s present orbit, but also created an instability that emptied the region interior to 0.7 AU.

Raymond & colleagues took a very different approach based on the “inside out” model of planet formation presented by Chatterjee & Tan (2014). Contrary to his own earlier work, Raymond’s group proposed that Jupiter formed in the inner Solar System near the Sun, and then migrated first outward, then inward, and finally outward again, depleting the region inward of Venus and wreaking havoc beyond Earth.

sweeping secular resonances

While the Grand Tack has been more widely discussed and endorsed than the inside-out scenario, both explanations have been faulted. Now Benjamin Bromley & Scott Kenyon (2017) present an alternative approach in which “sweeping secular resonances” with Jupiter’s orbital motion, rather than any migratory scenario, become the mechanism for clearing the Great Martian Gap. Their model implies a less dramatic but equally consequential role for Jupiter, and I suspect that it can be extended to explain similar gaps observed in the architecture of multiplanet systems around other stars.

To develop their model, Bromley & Kenyon (hereafter BK17) conducted extensive numerical simulations based on earlier work by and with their collaborators Makiko Nagasawa and Edward Thommes (Nagasawa et al. 2007, Thommes et al. 2008). They also note recent work on the same problem by Xiaochen Zheng & colleagues (2017).

BK17 begin with the familiar theoretical construct of the Minimum Mass Solar Nebula (blogged here). They assume that a dusty gas nebula (generally known as a protoplanetary disk) is present at the outset of their simulations. Jupiter is fully formed at its current semimajor axis of 5.2 AU (Figure 2), having cleared a gap in the disk for 1 AU on either side of its orbital path. A swarm of planetesimals orbits inward of this gap, while Saturn orbits well beyond it. Both gas giants exert gravitational effects on their surroundings, and the disk itself has gravity. In addition, the orbit of Jupiter is slightly eccentric, but probably less so than its present value of 0.05. BK17 assume an eccentricity of 0.03 in their simulations.

The key factor in their approach is the n5 resonance (“nu-5,” Greek letter nu with superscript 5), a “secular” or “very long-term” resonance between the motion of the protoplanetary disk and Jupiter’s orbital period. BK17 define the nu-5 resonance as the location “where the local apsidal precession rate matches Jupiter’s rate of precession,” and note that a planetesimal or protoplanet at this location will be perturbed by Jupiter’s gravitational influence onto a highly eccentric orbit. The likely result will then be either collision with another planet or protoplanet, engulfment by the Sun, or ejection from the Solar System.

In the early Solar System, when the gas disk was still present, the nu-5 resonance was located in the vicinity of the present Asteroid Belt (Zheng et al. 2012). As the gas dissipated, the resonance moved inward, destabilizing (“shaking up”) the orbits of protoplanets and planetesimals and effectively clearing out a substantial mass in solids. After the gas was completely depleted, the nu-5 resonance reached its present position inside the orbit of Venus. This sweeping shake-up created the Great Martian Gap while leaving behind enough mass to build Earth and Venus, as well as their two by-blows, Mercury and Mars.

BK17 discovered that several different factors were critical to reproducing the mass of Mars and the present-day Asteroid Belt within the time constraints provided by the known age of Mars. These include the mass of the perturbing planet, its distance from the system habitable zone, and the timing and speed of the sweeping secular resonance generated by its orbital motion.

Regarding mass, BK17 find that only a “Jupiter-mass planet” can produce the magnitude of perturbation required to induce a shake-up in the protoplanetary disk of a Sun-like star. Unfortunately, they don’t provide a precise value for the necessary mass – for example, would an object of Saturn’s mass (95 Mea) be sufficient? They also note that a “super-Earth” would be massive enough to produce sweeping secular resonances in an M dwarf system, likely referring to an object in the range of 1-10 Mea (see, e.g., Kenyon & Bromley 2009).

Regarding orbital location, they find that the masses of Earth and Mars depend sensitively on the semimajor axis of Jupiter at the time of the sweeping resonance. If Jupiter had been substantially farther from the Sun, the resonance would never have reached the orbit of Mars, and Mars would have grown much bigger than it actually did – presumably massive enough to support a habitable environment. But if Jupiter had been substantially closer to the Sun, and thus closer to the system habitable zone, the resonance would have inhibited the formation of Earth in the same way that it stunted the growth of Mars when Jupiter was at 5.2 AU. Instead of one living planet, our system would have none at all.

Regarding the timing of the sweeping secular resonance, BK17 note that its schedule is determined by the lifetime of the protoplanetary disk. As we saw in an earlier post, the system age when gas dissipation commences can fall anywhere between 1 and 10 million years. At the early end of that range, according to BK17, dissipation accompanied by shake-up would have extremely negative consequences for rocky planet formation, as it would destroy planetesimals before they had time to accrete into protoplanets. At the latter end, however, the effects would be modest, since accretion would already be well advanced, potentially permitting the growth of Earth-size planets out to a distance of 3 AU. In the case of our Solar System, we can assume that the shake-up happened before a system age of about 4 million years, given radiometric evidence that Mars was fully formed by then.

The rate of disk dispersal also matters. Although many studies have found that gas dissipation happens rapidly, requiring less than half a million years from start to finish (Williams & Cieza 2011), variation is inevitable: some disks take longer than others to disperse. BK17 find that the relative speed of dissipation strongly affects the outcomes of secular resonance sweeping. If the gas dissipates quickly, the resonance sweeps inward at the same rate, resulting in minimal disruption of the planetesimal population. If the gas dissipates more slowly, the resonance becomes increasingly more destructive, clearing larger and larger quantities of solid mass from the system.

Figure 3. Calaveras street sweepers on the Day of the Dead

From a print by José Guadalupe Posada (1852-1913)

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extrasolar asteroids and orbital gaps

Although BK17 are interested primarily in the evolution of our Solar System, they attempt to generalize some of their results to extrasolar locales. Their chief concern is the occurrence of extrasolar analogs of the Asteroid Belt. They argue that most systems with a gas giant in Jupiter’s approximate location (i.e., just outside the system ice line, where accretion is maximized) will experience a sweeping secular resonance whose outcome will be a ring of rocky debris in the inner system. While they concede that few such structures have been discovered to date (HD 69830 is most familiar), they attribute these limited findings to the difficulty of discerning modest aggregations of warm debris even around nearby stars. In the future, they predict, more sensitive searches will be more successful.

I suggest that the implications of their model are much broader than their relevance to extrasolar asteroid belts, and far more dispiriting. If sweeping secular resonances are common in systems with cool gas giants, then the outlook for habitable planets is even less promising than I thought. Here’s why.

An important focus of this blog is the possibility of Solar System analogs – that is, exoplanetary systems containing cool giants whose orbital parameters would permit the survival of Earth-mass planets (0.5-2 Mea) in the local habitable zone. (For recent posts on this topic, see here and here.) My January search of the Extrasolar Planets Encyclopaedia identified 17 such systems located within 60 parsecs/196 light years. All center on Sun-like stars in the range of 0.85-1.15 Solar masses, so their habitable zones have boundaries similar to those proposed for our own system (0.99-1.70 AU; Kopparapu et al. 2013).

Among the Jupiter analogs in these systems, semimajor axes range from 3 AU to 5.2 AU, and more than half orbit inside 4 AU. According to the findings of BK17, virtually all these systems will have experienced a sweeping secular resonance very similar to the one they propose for the Solar System. Because all but one of the 17 confirmed Jupiter analogs orbits closer to the local habitable zone than does our own Jupiter, the depletion of mass in this favored region is likely to be even more extreme than it was at home. Therefore, habitable planets appear to be less likely in the existing sample of Solar System analogs than they are in the Solar System.

To put it another way: BK17 have just shown that gas giant planets are even more unfriendly to the formation and survival of habitable planets than we already suspected. It’s not enough for the giant to reside outside the system ice line in a configuration that permits an Earth-like planet to maintain an Earth-like orbit. The giant must also be distant enough from the central star that the sweeping secular resonance generated by its orbit was insufficient to clear solid mass from the local habitable zone. Even Jupiter managed to evacuate mass from more than half of the radial extent of our own habitable zone, drastically reducing our system’s potential to produce life-bearing planets. Now it looks like extrasolar Jupiters might be still more likely to foreclose the possibility of life around other stars.

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REFERENCES

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

Bromley BC, Kenyon SJ. (2017) Terrestrial planet formation: Dynamical shake-up and the low mass of Mars. Astronomical Journal 153, 216. Abstract: 2017AJ....153..216B

Chatterjee S, Tan JC. (2014) Inside-out planet formation. Astrophysical Journal 780, 53.

Jewitt D, Moro-Martín A, Lacerda P. (2009) The Kuiper Belt and Other Debris Disks. In Astrophysics in the Next Decade, edited by Harley A. Thronson, Massimo Stiavelli, Alexander Tielens. Springer. Abstract: 2009ASSP...10...53J

Kopparapu R, Ramirez RM, Kasting JF, Eymet V, Robinson TD, Mahadevan S, Terrien RC, Domagal-Goldman S, Meadows V, Deshpande R. (2013) Habitable zones around main-sequence stars: New estimates. Astrophysical Journal 65, 131.

Kenyon SJ, Bromley BC. (2009) Rapid formation of icy super-Earths and the cores of gas giant planets. Astrophysical Journal 690, L140-L143.

Nagasawa M, Thommes EW, Kenyon SJ, Bromley BC, Lin DNC. (2007) The diverse origins of terrestrial-planet systems. In Protostars and Planets V, edited by B. Reipurth, D. Jewitt, K. Keil. University of Arizona Press, pages 639-654. Abstract: 2007prpl.conf..639N

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

Thommes E, Nagasawa M, Lin DNC. (2008) Dynamical shake-up of planetary systems. II. N-body simulations of Solar System terrestrial planet formation induced by secular resonance sweeping. Astrophysical Journal 676, 728-739. Abstract: 2008ApJ...676..728T

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

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

Zheng X, Lin DNC, Kouwenhoven MBN. (2017) Planetesimal clearing and size-dependent asteroid retention by secular resonance sweeping during the depletion of the Solar Nebula. Astrophysical Journal 836, 207.

TRAPPIST-1 and Kepler-11: Revised Masses

Figure 1. Revised masses and radii for the seven planets of TRAPPIST-1, as estimated by Wang & colleagues (2017). Results from Gillon & colleagues (2017) are shown for comparison. Image source: Figure 5 of Wang et al. 2017, with new labels.

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A few months ago, Michaël Gillon & colleagues reported a remarkable seven-planet architecture for a nearby ultra-cool red dwarf, TRAPPIST-1. In their analysis, six out of the seven transiting planets in this tightly packed system have densities in the range of Earth, Venus, and Mars – and no fewer than three occupy the system habitable zone. Those findings were based in part on a 20-day campaign of nearly continuous observation by the Spitzer Space Telescope.

Now Songhu Wang & colleagues have presented a rather different picture of the TRAPPIST-1 family, based on more than 70 days of monitoring by the Kepler Space Telescope during the K2 Mission. Even though Kepler’s current precision is inferior to that of Spitzer, the availability of data covering a much longer period of time still permits a more robust characterization of these planets than was possible for Gillon’s group. Like their predecessors, Wang & colleagues analyzed variations in transit times to estimate the masses and densities of the planets. Thanks to their augmented dataset, they were able to include all seven in their calculations, and not just the inner six.

The periods, semimajor axes, and equilibrium temperatures of the TRAPPIST planets are unchanged, and only two of them have smaller radii. Nevertheless, many planetary masses, and all densities, are dramatically different. Figure 1 and Table 1 contrast the results of Wang & colleagues with those of Gillon & colleagues. Figure 2 depicts the planets at their relative sizes and densities according to Wang’s group (revised from the first figure in my previous post on TRAPPIST-1).

Table 1. Comparison of TRAPPIST-1 parameters from Wang et al. and Gillon et al.

Period is expressed in Earth days; radius, mass, and density are expressed in Earth units.

(W) = Wang et al. 2017; (G) = Gillon et al. 2017.

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a super mercury among super ganymedes?

As we compare the findings of these two teams, we need to remember that both of them reported their results with large uncertainties (as shown in Table 1). For five out of seven planets, the results on mass from both groups are formally equivalent. The exceptions are planet e, for which the difference between Wang’s highest estimate and Gillon’s lowest is only 2% of an Earth mass (0.02 Mea), and planet h, for which Gillon’s group reported no mass at all. Moreover, for the three innermost planets (b, c, d), the densities estimated by Wang’s group are formally consistent with a rocky composition like Earth’s, again within uncertainties.

But if we focus on the interpretations that each group actually prefers, the differences become too wide to bridge. According to Wang’s group, only the three innermost planets might be rocky in composition, with planet c requiring major enrichment in iron to explain its large mass. Planets b and d, on the other hand, must be either depleted in metals or enriched in volatiles, or both, to achieve their proposed densities. At 62% and 72% of Earth, respectively, their closest analogs in our Solar System are the Moon and Mars.

Figure 2. Revised densities for the planets of TRAPPIST-1

The seven planets of TRAPPIST-1 are shown at their relative sizes, with colors corresponding to the densities estimated by Wang et al. 2017. Yellow shading marks the system habitable zone. Except for planet c, all densities are lower than those preferred by Gillon et al. 2017. This result suggests an internal composition with a rocky core enveloped in a layer of ice. (Update of Figure 1 in a previous post on the same system.)

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The next three planets (e, f, g), which occupy the habitable zone, have densities similar to those of Ganymede, Titan, and Callisto, the largest moons of Jupiter and Saturn. The bulk composition of those moons is approximately one-third water ice and two-thirds rock (Hussmann et al. 2015). A similar abundance of ice, possibly accompanied by depletion in metals, is needed to explain the relatively large radii and low masses of this temperate TRAPPIST trio.

For planet h, the smallest and coolest member of the family, the estimated density has such large uncertainties that we can say only that the numbers are equally consistent with a substantial hydrogen envelope (like Uranus), a composition completely dominated by hydrogen (like Saturn), or a rock/metal object with a modest percentage of water ice but no gaseous hydrogen at all (like Europa). Nevertheless, the transit timing data also provide an upper limit on this object’s mass, so we know that planet h is too lightweight to retain a hydrogen atmosphere unless it is constantly replenished by volcanic outgassing. Therefore, this little world’s bulk composition is probably similar to that of the three planets in the habitable zone.

From the new perspective offered by Wang & colleagues, the seven planets of TRAPPIST-1 present far more variety in bulk composition and surface environments than earlier data suggested. Indeed, if we accept the accuracy of these new findings – and I don’t see why we shouldn’t – we can no longer describe TRAPPIST-1 as a system with several Earth-like planets. Instead, we see a single terrestrial planet (c) enriched in iron, with an equilibrium temperature too high to permit surface bodies of water, accompanied by six lightweight planets that variously resemble scaled-up versions of Mars (density 0.71 Earth) and the three largest moons in our Solar System (Callisto, Titan, and Ganymede; respective densities 0.33, 0.34, and 0.35 Earth). Because three of the least dense planets (e, f, g) occupy the system habitable zone, our most optimistic conjecture is that they are ocean worlds with liquid seas sloshing atop layers of high-pressure ice (Kuchner 2003, Leger et al. 2004).

This isn’t an especially promising outlook for anyone who seeks exotic alien organisms, but if your models allow low-density ocean planets to support life (Noack et al. 2016), you can still imagine undulant sea creatures populating the hydrospheres of one or more of these little worlds.

Figure 3. Exotic aquatic life on Earth

Nembrotha cristata (left), a tropical sea slug, by Chriswan Sungkono; Hapalochlaena lunulata (right), a highly venomous octopus native to the Philippines, photographer unknown.

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younger star, fatter planets

In related news, a team led by Megan Bedell has offered revised masses and densities for the six transiting planets of Kepler-11. This is the benchmark system for all studies of extrasolar planetology, as it was the first place where astronomers could obtain sufficiently precise data on the transit times of multiple interacting planets to permit estimation of their masses. Back in 2011, when the system was announced, everyone was shocked to learn that planets not much heavier than Earth could support greenhouse atmospheres inflated with hydrogen and helium.

By now, of course, that weirdness is pretty well digested, but Kepler-11 still retains the power to amaze. With transit data extending over the full Kepler mission, this system has already benefited from repeated analyses that led to revisions (mostly downward) in the masses of its six planets. Improved results became available for the first time in 2013, when Jack Lissauer and colleagues published new physical and orbital parameters for the whole system (blogged here).

Now, four years later, we have another update. It’s important to note that the new findings are not based on any new transit data. (As far as I know, no transits of Kepler-11 have been observed since the termination of data collection by the Kepler Mission in 2013.) Instead, the revised parameters are based on precise observations of the host star. Although previous studies have always noted a close resemblance between Kepler-11 and our Sun, Bedell & colleagues go further: they characterize the star as a “Solar twin.”

Contrary to Lissauer’s group, who estimated a stellar age in the range of 7 to 10 billion years, a stellar mass 96% Solar (0.96 Msol), and a stellar radius 105% Solar (1.05 Rsol), Bedell’s group finds that the star is a bit younger than our Sun (3.2 ±0.9 billion years versus 4.55 billion years), with a larger mass (1.04 Msol) and a slightly revised radius (1.02 Rsol). Because most planetary data depend sensitively on the properties of the host star, these new values lead to further revisions in our understanding of the planets.

Table 2. Comparison of Kepler-11 parameters from Bedell et al. and Lissauer et al.

Notes: a = semimajor axis in astronomical units; period = orbital period in days.

B 17 = Bedell et al. 2017; L 13, L 11 = Lissauer et al. 2013, 2011.

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Table 2 compares three generations of data on Kepler-11. It’s readily apparent that most of the new parameters offered by Bedell’s group represent a reversion in the direction of the initial findings from 2011. Specifically, all the masses proposed by Bedell’s group are larger than the ones published by Lissauer & colleagues in 2013, as are all radii except for planet g, where we see no change. Yet in comparison with the 2013 update, the latest estimates have less extreme consequences for planetary composition.

As the authors note, the upward revisions in masses and radii result in an average increase of almost 50% in the planets’ bulk density. But the big picture stays mostly the same. As before, all Kepler-11 planets with well-constrained masses are more lightweight than Uranus (14.5 Mea). As before, planets c through f are unambiguously puffy, requiring hydrogen envelopes to bring their ample radii in line with their relatively puny masses (all <10 Mea).

The most consequential change involves planet b, to which the parameters announced in 2013 allowed Lopez & Fortney (2014) to attribute a bulk mass fraction in hydrogen of about 0.5%. Their interpretation seems counterintuitive – I mean, how could an object under 2 Mea retain any hydrogen at all after aeons of extreme irradiation? Nevertheless, to my knowledge, it has been broadly accepted.

The newly estimated density of 0.445 Earth strengthens the argument that planet b is an amalgam of rock and ice, rather like Europa, which has a bulk density of 0.55 Earth. No lightweight envelope is needed to explain its radius. Although I doubt that the findings of Bedell’s group are the last word on Kepler-11b, they offer a physically plausible model of the bulk composition of this benchmark extrasolar planet.

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REFERENCES

Bedell M, Bean JL, Meléndez J, Mills SM, Fabrycky DC, Freitas FC, Ramírez I, Asplund M, Liu F, Yong D. (2017) Kepler-11 is a Solar Twin: Revising the masses and radii of benchmark planets via precise stellar characterization. Astrophysical Journal 839, 94.

Gillon M, Jehin E, Lederer SM, Delrez L, de Wit J, Burdanov A, Van Grootel V, Burgasser A, Triaud A, Opitom C, Demory B-O, Sahu DK, Bardalez-Gagliuffi D, Magain P, Queloz D. (2016) Temperate Earth-sized planets transiting a nearby ultracool dwarf star. Nature 533, 221-224. Abstract: 2016Natur.533..221G

Gillon M, Triaud A, Demory B-O, Jehin E, Agol E, Deck KM, Lederer SM, de Wit J, Burdanov A, Ingalls JG, Bolmont E, Leconte J, Raymond SN, Selsis F, Turbet M, Barkaoui K, Burgasser A, Burleigh MR, Carey SJ, Chaushev A, Copperwheat CM, Delrez L, Fernandes CS, Holdsworth DL, Kotze EJ, Van Grootel V, Almleaky Y, Benkhaldoun Z, Magain P, Queloz D. (2017) Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1. Nature 542, 456-460. Abstract: 2017Natur.542..456G

Hussmann H, Sotin C, Lunine J. (2015) Interiors and evolution of icy satellites. In Treatise on Geophysics, Volume 10: Physics of Terrestrial Planets and Moons, ed. G. Schubert. Elsevier B.V.

Kuchner MJ. (2003) Volatile-rich Earth-mass planets in the habitable zone. Astrophysical Journal 596, L105-L108.

Leger A, Selsis F, Sotin C, et al. (2004) A new family of planets? “Ocean Planets.” Icarus 169, 499-504.

Lissauer JJ, Jontof-Hutter D, Rowe JF, Fabrycky DC, Lopez ED, Agol E, et al. (2013) All six planets known to orbit Kepler-11 have low densities. Astrophysical Journal 770, 131. Abstract: 2013ApJ...770..131L

Luger R, Sestovic M, Kruse E, Grimm SL, Demory B-O, Agol E, Bolmont E, Fabrycky D, Fernandes CS, Van Grootel V, Burgasser A, Gillon M, et al. (2017) A terrestrial-sized exoplanet at the snow line of TRAPPIST-1. In press.

Noack L, Höning D, Rivoldini A, Heistracher C, Zimov N, Journaux B, Lammer H, Van Hoolst T, Bredehöft JH. (2016) Water-rich planets: How habitable is a water layer deeper than on Earth? Icarus 277, 215-236.

Wang S, Wu DH, Barclay T, Laughlin GP. (2017) Updated masses for the TRAPPIST-1 planets. In press. Abstract: 2017arXiv170404290W

TRAPPIST-1 and the Seven Dwarfs

Figure 1. The seven planets of TRAPPIST-1 are shown at their relative sizes, with colors corresponding to the densities estimated by Gillon et al. 2017. The area shaded in yellow represents the system’s habitable zone. Planet f is the most similar to Earth in radius, but not in mass or density (see Table 1). The density of planet h has not been estimated yet.

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The TRAPPIST-1 system has been collecting superlatives since it was first announced just 10 months ago. With a mass only 8% of our Sun, the system’s ultra-cool M dwarf host is the smallest and least massive star ever detected at the head of a family of bona fide planets. Michaël Gillon & colleagues initially reported three Earth-sized objects (b, c, d) transiting this rosy little orb in May of 2016. All have periods shorter than 10 days. With their discovery, TRAPPIST-1 became the nearest star known to host multiple transiting planets (hereafter tranets), as the system is located only 39 light years (12 parsecs) away in the Sun’s back yard. In addition, these objects constitute the first multi-tranet system ever detected by a ground-based telescope – the TRAPPIST instrument in La Silla, Chile. All the other multi-tranet systems known at the time of the discovery were originally detected by the Kepler Telescope, a space-based observatory on an independent orbit around our Sun.

Gillon & colleagues determined that these three tranets did not have hydrogen atmospheres, given their small radii. On theoretical grounds, the astronomers also argued that they were more likely to include a significant icy component than to be purely rocky objects, given our current understanding of the protoplanetary disks surrounding very low-mass stars. The discovery team concluded by expressing their hopes for more precise characterization of the system parameters with more powerful telescopes.

Those hopes have now been partially fulfilled, and the view is astounding. Three weeks ago, Gillon’s team made global headlines that momentarily eclipsed the nonstop buffoonery of the American president. In brief: four additional tranets have been confirmed around TRAPPIST-1, bringing the total to seven. The new discoveries were made on the basis of an extensive observational campaign using the Spitzer Space Telescope (Gillon et al. 2017). Then, just this week, members of the same scientific team reported follow-up data obtained by the K2 program, which uses the Kepler Telescope (Luger et al. 2017). The new findings further constrain the system parameters.

Analyses of the data provided by all telescopes established that at least six of the seven planets experience transit timing variations. These data enabled an estimate of the masses and densities of all but planet h, the outermost. Not only do the six inner tranets resemble Earth and Venus in size and mass – three of them (e, f, g) occupy the system habitable zone (see Figure 1).

As a colorful header in The Sun proclaimed, “Nasa says TRAPPIST-1 solar system could be teeming with ‘exotic’ alien life forms!”

Figure 2. Comparing TRAPPIST-1 to our Solar System

Image Credit: European Southern Observatory

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three terrestrial planets in the liquid water zone

If TRAPPIST-1 were a G-type star like our Sun, or a K-type star like Epsilon Eridani or HD 219134, this news would rank among the greatest discoveries in the history of science. As it is, however, the primary of this fascinating system is barely a star at all. It’s a red dwarf of spectral type M8, even smaller and dimmer than Proxima Centauri. It’s so lightweight that it barely crosses the threshold between stars, which are the sites of nuclear fusion, from brown dwarfs, which are not.

But the problem isn’t the diminutive size or puny luminosity of TRAPPIST-1 (see Figure 2 for perspective). It’s the evolutionary history of M dwarfs, as detailed in an earlier blog post. During the first billion years of their development, these stars are hotter and more prone to destructive outbursts, and they emit a much higher flux of X-rays, than during the far longer period of their maturity. Any planet that currently orbits in the habitable zone of an M dwarf – including Proxima Centauri b and TRAPPIST-1e, 1f, and 1g – was subject to high temperatures, high levels of extreme ultraviolet radiation, and frequent stellar flares for hundreds of millions of years, potentially stripping away its reservoir of water and much of its atmosphere.

Even the writers for The Sun know a thing or two about M dwarfs and the problem of extrasolar habitability. The article I cited above also engaged in a little analysis:

Now [Nasa’s] top scientists are trying to work out whether these worlds are abundant with extraterrestrial beings – or as dead as a terrestrial doorknob. Nasa boffins suggested the planets “could harbour exotic lifeforms, thriving under skies of ruddy twilight.”

However, they could also be barren wastelands because their parent star is a red dwarf, a relatively cool type of sun that could wipe out early lifeforms before they have a chance to evolve into sentient beings.

“A bumper crop of Earth-size planets huddled around an ultra-cool, red dwarf star could be little more than chunks of rock blasted by radiation, or cloud-covered worlds as broiling hot as Venus,” Nasa warned. (Hamill 2017)

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Table 1. TRAPPIST-1 system parameters

Tags: Period = orbital period in days; a = semimajor axis in astronomical units (AU); Mass = mass in Earth units; Radius = radius in Earth units; Density = density in Earth units; Teq = equilibrium temperature in Kelvin. All data derive from Gillon et al. (2017) and Luger et al. (2017).

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system architecture

Now let’s get behind the headlines and put this discovery in context (see Table 1). A key detail that was omitted by the mainstream media is the system’s unique orbital architecture. Among the 3,593 exoplanetary systems in the current census, just three are reported to host as many as seven planets. Those are Kepler-90, HD 10180, and now TRAPPIST-1, which immediately becomes the odd man out. Unlike TRAPPIST-1, the first two systems center on Sun-like stars: Kepler-90 has a mass of 1.13 Solar masses (Msol), HD 10180 of 1.06 Msol. These two stars also host a greater diversity of planets than TRAPPIST-1. Each supports at least one gas giant and six smaller planets with likely masses in the range of Super Earths, gas dwarfs, and tweens. By contrast, all seven planets orbiting TRAPPIST-1 have estimated masses within 50% of Earth and Venus, suggesting that all are probably rocky, with at most a small contribution from volatile constituents. This is the most uniform family of planets among known systems with at least six of them.

TRAPPIST-1 is also the most tightly packed collection of planets discovered to date. The outermost planet of HD 10180 has a cool semimajor axis of 3.4 AU, while the outermost planet of Kepler-90 orbits at about 1 AU (the same as the distance of Earth from the Sun). Among the known six-planet systems, the outermost planets of Kepler-11 and Kepler-20 have semimajor axes of 0.46 AU and 0.35 AU, respectively. By contrast, the semimajor axis of the seventh planet (h) of TRAPPIST-1 is only 0.06 AU, similar to the orbit of a Hot Jupiter. In this regard, the system’s nearest rivals are Kepler-444, with five subterrestrial planets orbiting within 0.08 AU, and Kepler-80, with five terrestrial and gas dwarf planets within a similar radius. Both of the latter systems center on K-type stars, demonstrating that ultra-compact architectures are not unique to ultra-cool M dwarfs.

Because we can observe all seven planets in transit, we know that the TRAPPIST-1 system is completely “flat” or co-planar: all seven orbit in the same spatial plane. All also appear to be engaged in orbital resonances, since the periods of each pair of adjacent planets can be expressed as the ratio of two small integers. From planet b to planet h, the ratios are 8:5 (b/c), 5:3 (c/d), 3:2 (d/e), 3:2 (e/f), 4:3 (f/g), and 3:2 (g/h) (Gillon et al. 2017, Luger et al. 2017). These commensurabilities translate into relationships extending to sequences of three and four TRAPPIST-1 planets, both adjacent and non-adjacent.

The best-known example of an orbital architecture with at least three objects in a resonant chain appears in Jupiter’s satellite system, where the periods of Io, Europa, and Ganymede conform to a ratio of 4:2:1. This relationship is known as a Laplace resonance, in honor of the first astronomer to describe it (Pierre-Simon de Laplace) This and similar instances of interlocking resonances are likely to enhance the long-term stability of any system architecture (Gillon et al. 2017).

Nonetheless, the unparalleled intricacy of the architecture of TRAPPIST-1 takes this configuration to a whole new level (Figure 3), with several critical implications for our understanding of the system. First, in situ formation could not have produced such a clockwork mechanism. These seven planets must have formed at a greater distance from the star – probably outside the current system ice line, which lies at a radial distance of about 0.06 AU (equivalent to the present orbit of planet h). Subsequent interactions with the primordial nebula caused them to migrate inward to their present locations very early in system history.

Figure 3. A triple transit of TRAPPIST-1

This figure illustrates the light curve of TRAPPIST-1 on a day when three of its planets – c, e, and f – transited almost simultaneously. Given the system’s multi-resonant orbital architecture, simultaneous transits must be frequent. Image credit: Gillon et al. 2017.

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Second, these tightly packed orbits give rise to powerful gravitational interactions that cause transit timing variations (TTVs), as in the classic case of Kepler-11. The TTVs observed in TRAPPIST-1 enable estimates of the masses of the six inner planets, and thus of their physical compositions. Outside the Solar System, comparable data are in extremely short supply.

Third, the dynamical history of TRAPPIST-1 must have been extremely peaceful, with none of the perturbations or scattering events that are theorized for the Solar System and many extrasolar systems. Such instances of interplanetary violence would have disrupted the interlocking orbital structure we observe today.

planetology

Our Sun is known to host 29 naturally spheroidal objects, comprising 8 planets, 2 dwarf planets (Ceres and Pluto), and 19 regular moons. Only 6 of these 29 spheres consist primarily of rock, with a minimum of volatile content: Earth’s only Moon, Jupiter’s moon Io, and the 4 inner planets from Mercury to Mars. Earth is the densest object among these six (1.0 in the scale used by Gillon & colleagues, or about 5.5 g/cm-3), while our Moon is the most rarefied (just 61% of Earth’s density).

As shown in Table 1 and Figure 2, the six well-characterized planets of TRAPPIST-1 are remarkably similar in size and mass to Earth and Venus, and remarkably similar in density to the six rocky spheres of our Solar System. Both TRAPPIST-1c and -1g are more massive than Earth by a factor of about one-third; the others are intermediate in mass between Venus and Mars. TRAPPIST-1c is also a bit denser than Earth (117%), possibly because of enrichment in iron. The densities of the other five planets range from TRAPPIST-1g at 94% of Earth (virtually identical to Venus) to TRAPPIST-1f at 61% of Earth (virtually identical to the Moon). Therefore, it is quite possible that all six inner planets are rocky.

On theoretical grounds, however, Gillon & colleagues prefer a mixed composition of rock and ice for planets b through g. They argue that these objects most likely formed in the outer system, where ices would be more abundant than refractory elements. We can get a helpful perspective on their potential compositions by examining the spherical icy moons in our own Solar System (three around Jupiter, seven around Saturn, five around Uranus, and one each around Neptune and Pluto). Their interior structure includes rock and ice in varying proportions. The three largest – Ganymede, Titan, and Callisto – are each about one-third ice and two-thirds rock (Hussmann et al. 2015). With the notable exception of Europa, which is only about 7% ice, the mid-size moons in this sample tend to be at least 40% ice (Hussmann et al. 2015). Thus, we might expect planets as large as the TRAPPIST seven to accrete about 30%-50% of their original mass in ice. Later, after migrating into their present orbits, they would have endured intense irradiation over geological timescales, reducing their overall volatile content.

More massive planets on cooler orbits would be expected to retain more volatiles than warmer, less massive objects. Nonetheless, even though we see some association between mass and density in the TRAPPIST family – for example, the two most massive planets (c and g) are also the densest – we also see anomalies. Planet b is hotter and less massive than planet c, but it is also much less dense. One possible explanation is that it is a purely rocky planet with enrichment in silicates relative to iron, like Io and our Moon.

Luger & colleagues remind us that tidal heating is yet another consequence of the interlocking resonances that structure the TRAPPIST-1 system. It is also likely to be a factor in the thermal evolution of these seven planets. Luger’s group argues that planet b could have a tidal flux similar to that of Io (which also participates in a multi-resonant chain), potentially generating intense volcanism. Thus, it might be no coincidence that the density of planet b (66% Earth) is also very similar to the density of Io (64% Earth). Planets c through e experience lesser tidal effects, but still much stronger than the heat flux caused on Earth by our homeworld’s radioactive core. These planets might also experience volcanism comparable to Io’s. The more distant planets f through h appear to have avoided such a sizzling history.

All seven planets might still support atmospheres, even if their original envelopes were stripped by stellar irradiation at primordial times. Various sources of outgassing, including volcanism, would readily regenerate a lost atmosphere around a rocky planet (see discussion in Barnes et al. 2016).

exotic alien life-forms?

So here we have a system with not one, not two, but three Earth-size, Earth-mass planets whose blackbody equilibrium temperatures are consistent with surface bodies of water. Unfortunately, we have no information on the actual surface temperatures of these worlds, nor do we know whether water in any form is present on any of them. Our knowledge of the evolutionary history of M dwarfs predisposes us in the direction of pessimism, as illustrated by the excerpt from The Sun quoted above. Nevertheless, members of the original discovery team for TRAPPIST-1 conducted an analysis of the thermal evolution of this system, returning a more optimistic conclusion: “Depending on their initial water contents, [the planets of TRAPPIST-1] could have enough water to remain habitable” (Bolmont et al. 2017).

However, their conclusion did not take into account the tidal heating that is likely generated by the interlocking resonances in which the system’s seven planets participate. This omission is perfectly understandable, since the analysis offered by Bolmont & colleagues was based on the three-planet model presented in the original discovery paper (Gillon et al. 2016). That paper simply noted, “In some cases tidal heating could trigger a runaway greenhouse state.” The more recent analysis by Luger & colleagues (2017) presents exactly the case in which tidal heating would produce this unhappy outcome.

As a result, I remain agnostic about the possibility of life-bearing environments in the TRAPPIST-1 system. I don’t reject it out of hand, especially given the prospect of three terrestrial planets in the system habitable zone (not to mention the potential for various factors to lift the temperatures of planets g and h into habitable levels). But so many other hostile factors are in play that it seems inappropriate to sing a cheery song about the inevitability and ubiquity of life.

Dead or alive, these planets remain fascinating objects of study. Because they transit so frequently and are situated so close to home, we can look forward to more and more conclusive data on their surface conditions over the next few years.

celebrity septets

Given the remarkable nature of this discovery, especially its potential to create buzz in various desirable audiences, NASA invited the general public (or at least people with Twitter accounts) to suggest names for the seven planets of TRAPPIST-1. This was an unusual move, since the standard practice is to use robotic catalog numbers with alphabetic suffixes, such as Kepler-62f and HD 95872 b. In this case, the fact that seven names are involved should inspire creativity, since so many cultural phenomena involve groups of seven: the seven seas, the seven deadly sins, the seven classical planets, the seven days of the week, the seven hills of Rome, the seven swans a-swimming, the seven stars of the Pleiades, the Seven Samurai, the Seven Against Thebes, the Seven Sisters of Academia, the seven wonders of the world, and of course the very first septet that popped into my head:

So how about a system with planets named after Tydeus, Hippomedon, Amphiaraos, Polyneikes, and the other ill-fated warriors in Aeschylus’ Theban septet? Alas, those choices are probably too recherché and hard to pronounce for typical consumers of modern infotainment. Sloth, Greed, and Lust would present no such problems, but might they be too racy? Could Aventine, Viminal, Caelian, Capitoline, and so forth strike an appropriately classical note without seeming too recondite?

In light of the predictable objections, I’m favoring homier alternatives – maybe Happy, Dopey, Sleepy, and the rest of the dwarf mining crew, or maybe an even simpler schema based on the days of the week – Monday for tranet b through Sunday for tranet h, with Thursday, Friday, and Saturday assigned to the lucky trio in the habitable zone. (As in, “We’re spending a month on Saturday to ski the tropical glaciers, then rocketing off to Thursday for windsailing in the twilight zone.”)

With so many rich possibilities, the response to NASA’s invitation has been even more childish and absurd than I anticipated. I clearly overestimated the intelligence of the Twitterverse. Respondents tweeted names like Planet McPlanetface and Moony McMoonface, plus a set of seven taken from the principal characters in an American sitcom, Friends (which I confess I’ve never seen), plus another septet based on the titles of the first seven movies in the Fast & Furious franchise (ditto).

Alongside many whimsical suggestions to use the names of the Seven Dwarfs, which I heartily endorse, a few serious options emerged. One involves the names of seven of the eleven official Trappist breweries, from Achel to Westvleteren. That suggestion makes sense because TRAPPIST (Transiting Planets and Planetesimals Small Telescope), the acronym that names the telescope as well as the planetary system, was intentionally crafted to reflect the research group’s fondness for Trappist beer. Another suggestion was to name the planets after the seven astronauts who died in the crash of the Challenger. You might still be able to check out the March 2 issue of The Telegraph and the March 3 issue of The Daily Mail to see a selection of these candidates.

As it turns out, however, NASA was just kidding. It looks like we’ll have to use those old catalog numbers after all. Far better that outcome than Planet McPlanetface or Furious 7!

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REFERENCES
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Bolmont E, Selsis F, Owen JE, Ribas I, Raymond SN, Leconte J, Gillon M. (2017) Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs: Implications for the planets of TRAPPIST-1. Monthly Notices of the Royal Astronomical Society 464, 3728-3741. Abstract: 2017MNRAS.464.3728B
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