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
Barnes R, Deitrick R, Luger R, Driscoll PE, Quinn TR, Fleming DP, Guyer B, McDonald DV, Meadows VS, Arney G, Crisp D, Domagal-Goldman SD, Lincowski A, Lustig-Yaeger J, Schwieterman E. (2016) The habitability of Proxima Centauri b I: Evolutionary scenarios. In press. Abstract: 2016arXiv160806919B

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
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
Hamill J. “Life, But Not As We Know It.” The Sun, 24 February 2017.
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.
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.

Quantifying "Earth-like"

Figure 1. Three perspectives on one small planet.

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Writers throughout the twentieth century engaged in speculation on extraterrestrial life: not only life as we know it, but life as we never knew it. Lately, however, interest has shifted away from such intriguing prospects as crystalline colonial organisms, sentient plasma clouds, and the ecologies of gas giant atmospheres, toward the more prosaic question of carbon-based life on Earth-like worlds. Current investigations invoke habitable zones and habitable planets, which are defined by the conditions that enabled our own mundane biosphere to emerge and endure (Figure 1).

The hydrocarbon lakes of Titan and the subsurface oceans of Enceladus and Europa remain topics of keen interest. For all we know, these icy worlds might support exotic biochemistries based on carbon compounds. But we have no secure way of detecting similar environments in exoplanetary systems, whether by present methods or those expected for some time to come (Kasting & Catling 2003, Kasting et al. 2014). This restriction indefinitely tethers our extrasolar speculations to Earth. The best response to such restraint might be simply to look in the mirror. What are the limits of “Earth-like?” Which parameters of our own world can tell us when we’ve found an extrasolar cousin or sibling? 

orbit 

The most widely discussed feature of exoplanetary systems is the habitable zone – the range of orbits where the host star’s flux would permit surface bodies of water on a rocky planet with the appropriate mass and atmosphere. Obviously, Earth is such a planet, so we know where to look for the Solar System’s habitable zone. Recent research continues to explore this concept (Kopparapu et al. 2013, Zsom et al. 2013, Kasting et al. 2014). Kopparapu & colleagues express the more or less standard view: The habitable zone of a G-type star with the same mass as our Sun extends from about 0.9 to 1.5 astronomical units (AU). For a K-type star of 0.75 Solar masses (Msol) the approximate boundaries are 0.5 – 0.9 AU. For an M dwarf of 0.4 Msol, they shrink to 0.15 – 0.30 AU. 

mass 

It is also universally accepted that a planet needs some minimum mass in order to sustain an active rheology, robust atmosphere, and surface water over billions of years. Mars, at 0.11 Earth masses (Mea), is evidently too lightweight to fulfill this condition, whereas Venus, at 0.81 Mea, would be just right if only its orbit were wider. The lower boundary for mass must be somewhere in between. In a classic study, James Kasting and colleagues (1993) defined a habitable planet as “several times more massive than Mars.” They also reasoned that larger planets “have higher internal heat flows and should therefore be able to maintain tectonic activity” for substantial periods. As far as I know, the only researchers who have offered a precise value for the minimum habitable mass are Sean Raymond and colleagues (2006, 2007), who propose 0.3 Mea.

Finding the maximum mass, however, has been contentious. At least two factors are in play: plate tectonics and atmospheric accretion. 

tectonics 

Back in 1993, Kasting & colleagues noted that the carbon-silicate cycle is a necessary enabler of life on Earth. Although they didn’t mention it, this cycle is supported by plate tectonics (Figure 2), a process foregrounded by most subsequent discussions of extrasolar life.

More than a decade later, when theoretical discussions of Super Earths commenced, several studies examined the habitability of planets in the range of 1 to 10 Mea. These objects were typically assigned Earth-like compositions and heavy element atmospheres – rather than, for example, extended hydrogen/helium (H/He) envelopes. At least one study argued that plate tectonics would be “inevitable” on such Super Earths (Valencia et al. 2007). Similar conclusions were implicit in other literature of the time.

Figure 2. Volcanic eruptions are among the most visible indicators of the active geology that sustains habitable conditions on Earth. This photo shows the 1990 eruption of Redoubt Volcano along the coast of Cook Inlet in Alaska. Credit: Wikimedia

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Then came the skeptics. Some have argued that solid objects above a few Earth masses are unlikely to support plate tectonics (O’Neill & Lenardic 2007, Korenaga 2010), or at least that the likelihood shrinks as mass increases (Stein et al. 2013, Stamenkovic & Breuer 2014). Others are more optimistic, and the debate is far from over.

In the meantime, it would be helpful to know exactly what “a few Earth masses” means. If there’s an upper mass limit on tectonics, what is it?

A clue just came in a preprint by Cayman Unterborn & colleagues (hereafter U15). Seeking to define “Earth-like,” they make plate tectonics the primary criterion. To generalize across star systems, they propose a three-layer model for terrestrial planets: a mostly iron core surrounded by magnesium silicate minerals, in proportions that will vary from world to world, distributed in a dense lower mantle that transitions to a lighter upper mantle. In Earth, the bulk mass percentage for each layer is respectively 32%, 51%, and 17%. U15 argue that planets with mantle fractions and convective regimes similar to Earth will experience plate tectonics.

To illustrate (their Figure 8), they offer a schema of masses, radii, and chemical compositions that meet this condition, extending as high as an object of 5 Mea and 1.5 Rea. Although they don’t explicitly discuss a mass limit for mantle convection, they do argue that plate tectonics is possible on all the rocky planets encompassed by their schema. As a real-life example they offer Kepler-36b, a classic Hot Super Earth on a 14-day orbit with an approximate mass and radius of 4.45 Mea and 1.49 Rea, respectively.

The findings of U15 invite comparison with the recent work of Courtney Dressing & colleagues (hereafter D15) on the structure of terrestrial planets. D15 tried to find a single composition that could explain the masses and radii of Earth, Venus, and five well-characterized extrasolar terrestrials (CoRoT-7b; Kepler-10b, -36b, -78b, and -93b). By contrast, U15 tried to generalize from Earth’s parameters to construct a flexible model that would encompass all potentially Earth-like planets. This difference in goals might explain why D15 used a simpler model of planet structure, with only two layers: a pure iron core accounting for 17% of the total mass and a magnesium silicate mantle accounting for 87%.

Notably, their solution involves a much less massive core than the one proposed by U15. Hence they find a smaller planetary mass at each radius than do U15. As their real-life example of a terrestrial planet, D15 offer Kepler-93b, for which they prefer a mass of about 4 Mea and a radius of 1.48 Rea. For the same radius, U15 provide a mass 10% higher. However, the mismatch between the two studies falls within the range of uncertainties for the parameters of the five exoplanets modeled by D15. For Kepler-93b, they defined the mass range as 3.34-4.70 Mea, while for the same mass range U15 provided a range in radius of about 1.35-1.50 Rea, which encompasses D15’s preferred value.

Happily, then, the results of U15 appear consistent with the those of D15, whose model has been widely endorsed. Their conclusions have the further appeal of supporting plate tectonics on selected planets massing up to 5 Mea. This is a more generous upper bound than I’ve imagined in recent years.

Nonetheless, it’s clear that an appropriate mantle structure is insufficient by itself to guarantee either plate tectonics or life. Water and atmosphere make critical contributions.

Figure 3. The total water content of Earth and Europa compared. Even though Europa is only about 1% of Earth’s mass, it contains more water by mass than Earth. Credit: K. P. Hand

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water 

The factors governing Earth-like physical conditions and carbon-based life have complex interdependencies. Life needs water, and oceans need plate tectonics, but tectonics also needs oceans (Korenaga 2010, Lammer et al. 2009, 2010). Lubrication is required to facilitate plate movement, and apparently ice won’t do: the eternal wandering of continents is borne by water.

For truly Earth-like conditions, however, the amount of water requires titration. Too much is just as bad as not enough, and an excess of water seems quite easy for young planets to accrete, at least according to simulations of Solar System history (Raymond et al 2007). Helmut Lammer & colleagues (2009) pointed out that a rocky planet covered by a water layer 100 km deep, as modeled by studies of “Ocean Planets” (e.g., Leger et al. 2004), would be unsuitable for the development of life. Regardless of temperature, high-pressure ices would form at the bottom of such an ocean and prevent interaction between the water layer and chemicals in the crust. Without this interaction, life could not arise, and the carbon-silicate cycle would not emerge.

Even though we were told as children that three-quarters of our planet is covered by oceans, that water layer is remarkably thin (Figure 3). The total water inventory of Earth, including water in the mantle, is quite small: just 0.05% Mea (Raymond et al. 2014). Yann Alibert (2014) found that a planet of Earth mass and composition can maintain both a global ocean and a carbon cycle only if its water content is 2% or less by mass, with the maximum percentage falling rapidly with rising planet mass. So far, that seems to be the best available constraint on water inventory.

It’s worth noting that although Alibert’s upper limit is 40 times greater than Earth’s current reservoir, it’s still 5 to 25 times smaller than the water fractions proposed for Sauna Planets and Water Worlds. 

atmosphere 

An atmosphere is generally assumed as a prerequisite for life. One notable exception involves airless bodies like Europa, where biochemistries could evolve in shallow subsurface oceans. However, our focus is Earth-like planets with masses that exceed Europa’s by more than an order of magnitude. These objects are believed to accrete or outgas significant atmospheres during their formation and early evolution.

Any planet above the minimum Earth-like mass (defined here as 0.3 Mea) will likely retain its gas envelope as long as it can withstand the high levels of extreme ultraviolet (XUV) flux emitted by young stars. Planets orbiting near the star are the most vulnerable to atmospheric erosion, while those with masses of several Mea have the best protection.

Pre-Kepler discussions took it for granted that any object under 10 Mea would be incapable of supporting an H/He envelope. Then in 2011 came the discovery of the Kepler-11 system, where at least four planets with masses between 2 and 8 Mea revealed puffy silhouettes consistent with deep H/He atmospheres. Many comparable Kepler planets have been characterized since then. It is now understood that rocky cores similar in mass to Earth can have radically more extensive envelopes. Since H2 is a greenhouse gas, and H/He atmospheres produce surface pressures far in excess of Earth’s, even relatively low-mass planets with deep gas envelopes will not sustain surface bodies of water. By definition, they are not Earth-like.

Two recent studies, led respectively by Rebekah Dawson and Helmut Lammer, explored the conditions needed for terrestrial planets up to 5 Mea to accrete and sustain puffy envelopes. While taking different approaches, these two groups found a similar lower boundary for envelope survival: 2 Mea. Above that mass, unless they orbit very close to their host stars, most planets will accrete and retain H/He atmospheres. Below that mass, even on cooler orbits, primordial H/He will dissipate.

Dawson & colleagues (hereafter D15) conducted N-body simulations to study the in situ accretion of rocky objects in protoplanetary disks of varying metallicity, along with their atmospheric evolution up to the dispersion of the nebular gas. They did not address the photoevaporation of primitive atmospheres, a factor that becomes significant only after the nebula disperses. Nonetheless, they cited Lopez & Fortney (2014) for a discussion of atmospheric loss at later stages of system evolution.

The central aim of D15 was to investigate the relationship between the surface density of solid materials suspended in the primordial nebula and the mass and atmospheric composition of the resulting planets. Their simulations followed the evolution of rocky embryos orbiting a Sun-like star between 0.04 and 1 AU in the presence of a dusty H/He nebula that dissipated after 1 million years. The embryos grew by mergers and accreted gas according to their mass. D15 found that 1) planetary cores smaller than 2 Mea did not accrete substantial envelopes from the nebula, and 2) cores of 2 Mea or more could form within 1 million years only in protoplanetary disks with a high surface density of solids. Such environments are typical of highly metallic stars even without significant gas-driven migration of planetesimals or embryos.

D15 also concluded that the inner nebulae of stars with ordinary or depleted metallicity can still achieve a sufficient surface density to build gas dwarfs if they experience migration of solids from outer orbits. In other words, D15’s approach does not require “strict” in situ accretion (Chiang & Laughlin 2013). They even permit the migration of full-formed gas dwarfs from outside 1 AU, as in Lee & colleagues (2014, 2015).

This study raises interesting questions on many points, including realistic timeframes for nebula dispersion and the effect of mixed migration pathways on the composition of planets that achieve habitable orbits. Nevertheless, the answers probably wouldn’t change D15’s most salient findings on envelope accretion by young planets. They conclude that planets under 2 Mea are unlikely to capture or sustain H/He atmospheres, while planets above that mass will do so under typical conditions. This result provides a clear constraint on definitions of “Earth-like.”

Figure 4. Since massive rocky objects are likely to accrete deep hydrogen atmospheres, the range of Earth-like planets is narrow, extending from about one-third to twice the mass of Earth. Shown above are four NASA photographs of our planet scaled according to the mass-radius relationships of Unterborn et al. (2015). For perspective, one photogenic but out-of-range object – Mars – is included at far left.

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An earlier study by Lammer & colleagues (hereafter L14) had already looked at the evolution of gas-enveloped planets after nebula dispersion. They studied a single phase of the process under idealized conditions, modeling rocky planets with masses between 0.1 and 5 Mea orbiting a Solar twin at 1 AU. All planets were assumed to reach their final core masses in the presence of the primordial nebula, and to accrete H/He envelopes in proportion to their mass.

L14 differed sharply from D15 in their handling of gas accretion, since even sub-Earth objects in their model captured H/He. Nor did they advance any argument regarding surface densities of solids or the formation pathways of their theoretical planets. Their approach appears agnostic to these factors.

In the most favorable variations on their model, some Super Earths of 5 Mea reached the threshold of runaway gas accretion. In real systems these would become gas giants. The rest, along with all other planets of lower mass, captured smaller but still substantial H/He envelopes before the nebula dispersed. With the loss of this protective cloud, however, the effects of XUV flux became significant.

L14 found that rocky planets down to 2 Mea –in some cases even as low as 1 Mea – suffered minimal atmospheric loss during the phase of “saturated” flux in the first 100 million years of stellar evolution. These planets were able to retain their H/He envelopes indefinitely, resembling typical Kepler planets with masses of 2-5 Mea and radii of 2-4 Rea. Less massive planets, however, lost their envelopes.

Considering L14’s findings alongside the other constraints discussed so far, we see some major shrinkage in the likely mass range of Earth-like planets around Sun-like stars. Evidently it’s about 0.3 to 2 Mea (Figure 4), with potential outliers at slightly higher masses. Given the level of XUV flux typical of the habitable zones of late F, G, and early K-type stars, all planets under 1 Mea lose their primordial H/He, whereas most planets over 2 Mea retain it.

L14 proposed that the relative dustiness of the nebula would be a critical factor determining the survival of H/He envelopes around planets over 1 Mea. Some fraction of rocky planets between 2 and ~2.5 Mea might end up with friendly atmospheres of nitrogen and carbon dioxide, but that outcome becomes vanishingly less likely with increasing mass.

The only exception might be planets that reached their final bulk during a phase of giant impacts after the nebula dissipated. This is actually how the Solar System’s small planets formed, but recent work suggests that our system’s evolutionary history is unique. In other potential evolutionary scenarios, we could imagine a collision between two Super Earths of 1.8 Mea each, which (after the dust settles) would create a single gas-free planet of about 3.5 Mea. Since the collision happens after nebula dispersion, the new planet cannot accrete any additional atmosphere. Thus it evolves into a truly super-sized Earth with volcanoes, oceans, and all the rest. Scenarios like that might be rare, though.

On firmer ground, the complementary results of D15 and L14 indicate that rocky planets of 0.3–2.0 Mea and 0.7–1.2 Rea will be free of troublesome H/He envelopes. Depending on the specifics of formation pathways and XUV flux, these planets would make plausible candidates for Earth 2. 

spectral type 

But don’t forget about that X-ray and XUV flux. Indeed, it’s been getting a lot of attention over the past year or so. Most of the studies discussed in this posting used stars of the same mass and effective temperature as our Sun for their standard. The underlying assumption is that factors relevant to thermal environment, such as the location of the system habitable zone, can be scaled to fit stars of different effective temperatures, luminosities, and colors.

But stellar evolution places a limit on such scaling. The earliest discussions of extrasolar life noted that stars above a certain mass – around 1.5 times Solar (1.5 Msol) – have a main sequence lifetime too brief to permit the evolution of life. Even if a planet of the right mass and composition were to orbit comfortably in the habitable zone of an A-type star of 1.8 Msol, it would barely have time to cool down and recover from asteroid bombardment before its parent star began expanding and reddening into the subgiant stage. Rising temperatures would then boil off the planetary ocean and sterilize any emergent biosphere.

Fortunately, high-mass stars of spectral types A, B, and O represent less than 1% of the stellar population in our region of the Milky Way. What about M dwarfs, which account for three-quarters of all main sequence stars? Questions regarding the habitability of their planets are getting complicated.

Earlier studies noted that the close-in habitable zones of M dwarfs would constrain planets with the appropriate insolation to be tidally locked, without benefit of a day/night cycle. M dwarfs are also more likely than higher-mass stars to erupt in intense flares that could destroy volatiles and erode the atmospheres of close-in planets. Nevertheless, neither factor seems an insurmountable barrier to the emergence of life. Presumably organisms could evolve in non-stop daylight and eventually colonize darker longitudes, while robust atmospheres would shield surface ecologies against occasional flares.

Recent literature, however, finds new causes for doubt. A study by Luger & Barnes (2015) provides several reasons for pessimism about the habitability of M dwarf planets. In addition to the propensity of red stars to undergo extreme flaring events, Luger & Barnes note the antagonistic qualities of their evolutionary history. Newborn stars under about 0.65 Msol spend several hundred million years at luminosities one to two orders of magnitude higher than their main sequence brightness. Yet planet formation around any star happens on a much shorter timescale, within a few tens of millions of years after stellar ignition. Luger & Barnes demonstrate what that mismatch in developmental histories means for water and life. Planets that form in a young M dwarf’s habitable zone will freeze out once the star matures, whereas planets that end up in the mature star’s habitable zone will have been roasted for a billion years by intense X-ray and XUV flux, including violent flares. The cool planets will be too cold, while the warm planets will be stripped of volatiles.

These results make M dwarf stars less attractive as potential hosts of Earth-like planets than they looked just a few years ago. It seems that sensibly Sun-like stars in the approximate range of 0.7–1.3 Msol are once again the best choice of parents, at least if you want to grow up to be green. 

perspectives on known space 

In the context of the other constraints outlined here, the findings of Luger & Barnes also call for a harder look at the clutch of small Kepler planets proposed over the past few years as potential Earth analogs. Among the six candidates confirmed to date, four orbit stars less massive than 0.65 Msol – M dwarfs by any other name. Ironically, these are the four smallest planets of the lot (Kepler-438b, -186f, -395c, -442b), with radii ranging from 1.12 to 1.34 Rea. Since all have periods shorter than 130 days, and two have periods shorter than 40 days, they all might have suffered complete desiccation. In fact, a new study just reported that Kepler-438b, with a semimajor axis of only 0.17 AU, experiences powerful flares from its host star that make it vulnerable to complete loss of atmosphere (Armstrong et al. 2015). None of these candidates seem truly Earth-like.

The other two planets (Kepler-62f, -452b) orbit hotter stars on longer orbital periods, so they appear to occupy their systems’ long-term habitable zones. By some definitions their radii place both of them at or near the upper edge of the Earth-like range, but according to the criteria established in this discussion, 452b is definitely, and 62f is probably, just too big.

Assuming the proposed radius of 1.41 Rea, an Earth-like composition would confer a mass of 3.5–4 Mea on Kepler-62f, following the models of Dressing et al. (2015) and Unterborn et al. (2015), respectively. Either value would be consistent with plate tectonics (at least according U15). But we have no constraints on this object’s true mass. It seems just as likely to be a less dense and thus less massive planet with a large volatile content: either a deep global ocean, failing the criterion for water, or a remnant H/He envelope, failing the criterion for atmosphere. According to the results of Lammer et al. (2014) and Dawson et al. (2015), it could be a relatively hospitable rocky planet of 3.5–4 Mea only if it formed by giant impacts after the system’s protoplanetary nebula dissipated. Because 62f is part of compact multiplanet system with four inner companions, however, a history of dynamical upset seems unlikely.

Assuming a radius 1.63 Rea, Kepler-452b has a similar range of potential compositions, although the all-rocky option is even more unlikely. At 5–6 Mea, an ice- and hydrogen-free planet would also need to be iron-free to achieve a radius so large. Such a composition isn’t plausible, and even if it were, it’s hard to see how plate tectonics might develop. A water world or an unlucky Earth-mass object with a residual H/He shroud seems more likely.

Given all these disappointing candidates, imaginary Earth-like planets (Figure 5) will have to do for a while longer.

Figure 5. Concocted Earth-like planets across an order of magnitude in mass, following the mass-radius curves of Unterborn et al. 2015. For rocky worlds, radius increases more slowly than mass, so the most massive object pictured here is not quite double the radius of the least massive. Note that the fanciful world of 3 Mea is very likely an outlier; most hydrogen-free planets are expected to be under 2 Mea and 1.2 Rea, like the other five examples. (In the diagram, RE = Earth radius, ME = Earth mass.) My gratitude to everyone who lives in these worlds.

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REFERENCES

Alibert Y. (2014) On the radius of habitable planets. Astronomy & Astrophysics 561, A41.

Armstrong DJ, Pugh CE, Broomhall AM, Brown DJA, Lund MN, Osborn HP, Pollacco DL. (2015) The host stars of Kepler’s habitable exoplanets: Superflares, rotation and activity. Monthly Notices of the Royal Astronomical Society. Abstract: http://mnras.oxfordjournals.org/content/455/3/3110.abstract

Chiang E, Laughlin G. (2013) The minimum-mass extrasolar nebula: in situ formation of close-in Super-Earths. Monthly Notices of the Royal Astronomical Society 431, 3444-3455. Abstract: 2013MNRAS.431.3444C

Dawson RI, Chiang E, Lee EJ. (2015) A metallicity recipe for rocky planets. Monthly Notices of the Royal Astronomical Society 453, 1471-1483. Abstract: 2015MNRAS.453.1471D

Dressing CD, Charbonneau D, Dumusque X, Gettel S, Pepe F, Cameron AC, et al. (2015) The mass of Kepler-93b and the composition of terrestrial planets. Astrophysical Journal 800, 135. Abstract: http://adsabs.harvard.edu/abs/2015ApJ...800..135D

Kasting JF, Whitmire DP, Reynolds RT. (1993) Habitable zones around main sequence stars. Icarus 101, 108-128.

Kasting JF, Catling D. (2003) Evolution of a Habitable Planet. Annual Review of Astronomy and Astrophysics 41, 429-463.

Kasting JF, Kopparapu R, Ramirez RM, Harman CE. (2014) Remote life-detection criteria, habitable zone boundaries, and the frequency of Earth-like planets around M and late K stars. Proceedings of the National Academy of Sciences 111, 12641-12646. Abstract: http://adsabs.harvard.edu/abs/2014PNAS..11112641K

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. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...765..131K

Korenaga J. (2010) On the likelihood of plate tectonics on Super-Earths: Does size matter? Astrophysical Journal Letters 725, L43-L46.

Lammer H, Selsis F, Chassefiere E, Breuer D, Griessmeier J-M, Kulikov YN, et al. (2010) Geophysical and atmospheric evolution of habitable planets. Astrobiology 10, 45-68.

Lammer H, Stökl A, Erkaev NV, Dorfi EA, Odert P, Güdel M, Kulikov YN, Kislyakova KG, Leitzinger M. (2014) Origin and loss of nebula-captured hydrogen envelopes from ‘sub’- to ‘super-Earths’ in the habitable zone of Sun-like stars. Monthly Notices of the Royal Astronomical Society 439, 3225-3238. Abstract: 2014MNRAS.439.3225L

Lee EJ, Chiang E, Ormel CW. (2014 ) Make Super-Earths, not Jupiters: Accreting nebular gas onto solid cores at 0.1 AU and beyond. Astrophysical Journal 797, 95. Abstract: 2014ApJ...797...95L

Lee EJ, Chiang E. (2015) Breeding Super-Earths and birthing Super-Puffs in transitional disks. In process. Abstract: 2015arXiv151008855L

Leger A, Selsis F, Sotin C, et al. (2004) A new family of planets? “Ocean Planets.” Icarus 169, 499-504. Abstract: http://adsabs.harvard.edu/abs/2003ESASP.539..253L

Lopez ED, Fortney JJ. (2014) Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition. Astrophysical Journal 792, 1. Abstract: 2014ApJ...792....1L

Luger R, Barnes R. (2015) Extreme water loss and abiotic O₂ buildup on planets throughout the habitable zones of M dwarfs. Astrobiology 15, 119-143. Abstract: 2015AsBio..15..119L

Merritt A. (1920) The Metal Monster. Serialized in Argosy All-Story Magazine; reprinted by Avon Books, 1941 & subsequent editions.

O’Neill C & Lenardic A. (2007) Geological consequences of super-sized Earths. Geophysical Research Letters 34.

Raymond SN, Quinn T, Lunine JI. (2007) High-resolution simulations of the final assembly of Earth-like planets 2: Water delivery and planetary habitability. Astrobiology 7, 66-84. Abstract: 2007AsBio...7...66R

Raymond SN, Mandell AM, Sigurdsson S. (2006) Exotic Earths: forming habitable planets with giant planet migration. Science 313, 1413-1416.

Raymond SN, Scalo J, Meadows VS. (2007) A decreased probability of habitable planet formation around low-mass stars. Astrophysical Journal 669, 606-614. Abstract.

Raymond SN, Kokubo E, Morbidelli A, Morishima R, Walsh KJ. (2014) Terrestrial planet formation at home and abroad. In Protostars and Planets VI, eds. Beuther H, Klessen RS, Dullemond CP, Henning T. Tucson: University of Arizona Press, pp 595-618.

Sagan C, Salpeter EE. (1976) Particles, environments, and possible ecologies in the Jovian atmosphere. Astrophysical Journal Supplement Series 32, 737-755.

Stamenkovic V, Breuer D. (2014) The tectonic mode of rocky planets: Part 1 Driving factors, models & parameters. Icarus 234, 174-193. Abstract: 2014Icar..234..174S

Stein C, Lowman JP, Hansen U. (2013). The influence of mantle internal heating on lithospheric mobility: Implications for super-Earths. Earth and Planetary Science Letters 361, 448-459.

Unterborn CT, Dismukes EE, Panero WR. (2015) Scaling the Earth: A sensitivity analysis of terrestrial exoplanetary interior models. In press. Abstract: 2015arXiv151007582U

Valencia D, O’Connell RJ, Sasselov DD. (2007) The inevitability of plate tectonics on Super-Earths. Astrophysical Journal 670, L45-L48. Abstract: 2007ApJ...670L..45V

Zsom A, Seager S, de Wit J, Stamenkovic V. (2013) Toward the minimum inner edge distance of the habitable zone. Astrophysical Journal 778, 109. Abstract: 2013ApJ...778..109Z