Monday, December 21, 2015

Quantifying "Earth-like"

Figure 1. Three perspectives on one small planet.

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? 


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. 


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. 


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
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


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. 


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.

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.


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:
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:
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:
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:
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:
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

Saturday, December 19, 2015

Evolutionary Twist

Figure 1. The Sun-like star WASP-47 hosts a transiting Hot Jupiter flanked by two low-mass planets, and all three have periods shorter than 10 days. This was the first and so far the only detection of such a configuration. Above, an artist’s rendering shows a Hot Jupiter in transit across the face of its star. Credit: European Southern Observatory
A few months back I wrote about WASP-47b, the first Hot Jupiter ever found with low-mass planets on nearby orbits. I noted my eagerness to see a theoretical study of the possible formation mechanisms behind this unusual system, while venturing that the orbital architecture of WASP-47 could not have resulted from in situ accretion.

Then last month I took a close look at a study by Konstantin Batygin & Greg Laughlin (2015), who offered a novel explanation for the formation of the inner planets of the Solar System. Their approach folds the evolutionary history of the four terrestrial planets into the Nice Model and the Grand Tack. I observed in passing that, although Laughlin was one of the earliest proponents of in situ theory (which underlies the scenario that he and Batygin proposed), he hadn’t written anything purely theoretical on this topic for quite a while.

Two new preprints respond serendipitously to those conjectures and observations. One is a theoretical study by Batygin, Bodenheimer & Laughlin (2015) on the potential for Hot Jupiters – Hot Jupiters, no less! – to form in situ. The authors develop a new formation scenario for star-hugging gas giants and use numerical simulations to test it. Then they appeal to the WASP-47 system as possible evidence that this mechanism really works.

The second preprint is also highly theoretical. Nathan Kaib and John Chambers (2015) tersely present the results of a large ensemble of numerical simulations designed to test the Nice Model of Solar System evolution. Their findings question the utility of this approach as an explanation for the Late Heavy Bombardment. They can also be interpreted as evidence that our four terrestrial planets formed after, not before, the dynamical instability addressed by the Nice model. Although Kaib & Chambers don’t mention the recent articles by Batygin & Laughlin or Volk & Gladman on the inner Solar System, their conclusions call for rethinking both the Nice model and the Grand Tack.

a burning cradle for baby giants?

The new study by Batygin & colleagues (hereafter B15) is called “In situ formation and dynamical evolution of Hot Jupiter systems.” The title is a misnomer, however, as they don’t actually model the in situ accretion of solids on orbits where Hot Jupiters are observed. Instead, as often happens in simulation studies, they use simplified initial conditions to examine a narrowly defined question: Can a dense planet of sufficient mass, orbiting at or near the inner edge of a protoplanetary nebula, accrete enough ambient hydrogen to balloon into a gas giant?

B15 offer four representative evolutionary sequences in which solid planetary cores at a range of masses follow circular orbits around a Sun-like star at a semimajor axis of 0.05 AU. They “purposely adopted an agnostic viewpoint” regarding formation mechanisms, explaining that their results “are largely independent of how the solid core arises.” The simulations seem equally friendly to x) strict in situ formation involving the accretion of local mass only; y) migration of solids from cooler orbits into the hot inner nebula and subsequent accretion at the new location; or z) migration of fully-formed cores from cooler orbits.

In units of Earth mass (Mea), the core masses they select are 4 Mea, 10 Mea, and 15 Mea. The object of 15 Mea is used in two different set-ups, one with low ambient gas density and the other with higher density. As a reality check, I note that atmosphere-free planets of 10 Mea or more are not attested (Jontof-Hutter et al. 2015), while realistic models of planet formation have great difficulty forming an object of 4 Mea or more at 0.05 AU, where silicate dust sublimates (Dullemond & Monnier 2010).

Regarding gas accretion, B15 concede that insufficient mass in ambient gas would be available in the local feeding zone to build a gas giant at 0.05 AU. Therefore, they assume that the local supply of hydrogen/helium is constantly replenished by the regular flow of gas through the nebula onto the infant star. Their model seems to hinge on the capacity of the short-period planet to capture this inrushing gas.

Across simulations, objects of 15 Mea were the only ones that managed to accrete gas envelopes equal in mass to their solid cores and thereby trigger runaway gas accretion. Thus, they find that the minimum core mass capable of growing into a gas giant in the vicinity of a Sun-like star is 15 Mea.

Figure 2. Light curves of the three inner planets of WASP-47
Phase-folded light curves of the three transiting planets detected by the K2 mission: Becker et al. 2015

B15 conclude that their scenario will regularly produce gas giants, so that in situ formation might “represent the dominant channel for hot Jupiter generation.” They proceed to a discussion of WASP-47b as an example of what this channel might bring.

But I’m not convinced. The likeliest origin for an object of 15 Mea with a semimajor axis around 0.05 AU is migration from a wider orbit where accretion can more readily produce such massive objects. As far as I know, a gas giant can migrate into a hot orbit just as easily as a Neptune-mass object can. So why resort to a two-step process – first migrate the core, then capture the atmosphere – when a well-theorized one-step process (Type II migration) works even better? B15 appear to be offering a solution in search of a problem.

They cite WASP-47 as a rare system in which a compact family of Super Earths somehow managed to promote one of their number to giant status without changing any semimajor axes or otherwise disrupting the rest of the family. But it seems that considerable acrobatics would be needed to achieve this remarkable outcome. For example, how did only one planet get pumped up? What kept the others down?

I suggest that, along with exploring novel in situ explanations for the evolution of WASP-47, the exoplanet community should test whether migration scenarios could explain this architecture with fewer contortions.

Figure 3. The wreck of the Kronan
In 1676, the Swedish warship Kronan capsized while trying to execute a sharp turn under too much sail, causing an explosion in the gunpowder magazine. Few survived. Illustrated is an imaginative (and historically inaccurate) rendering of the disaster by Claus Moinichen in 1686.

does the sailing master have no clothes?

The study by Kaib & Chambers is conducted on a grander scale than B15. They ran almost 300 high-resolution simulations of Solar System evolution to test three different versions of the Nice model and explore the effects of the resulting dynamical instability on the four terrestrial planets. A simulation was considered successful if the final system met three criteria after the instability concluded: A) all four outer planets from Jupiter to Neptune survived, with the orbits of Saturn and Jupiter lying between a 2:1 and 3:1 mean motion resonance; B) all four inner planets also survived on stable orbits; and C) the angular motion deficit of the four inner planets was less than or equal to its present value after their orbits were integrated for an additional billion years.

In all three versions of the initial set-up, the four terrestrial planets were assigned their present masses and orbits. In two versions, the outer system contained Jupiter, Saturn, and three Neptune-like planets. In the third, it contained Jupiter, Saturn, two Neptune-like planets, and two “Super Earths” of 8 Mea each. Among all iterations of these set-ups, the success rate according to Criterion A was 13% to 16%. However, the set-up with six outer planets failed both of the other criteria, while the other two models produced just 1 and 2 systems, respectively, that met Criterion B. Only one iteration of one of these models also met Criterion C. All other iterations lost at least one terrestrial planet (usually Mercury), and many lost two (usually Mercury and Mars).

These results are very likely to inform future discussions of the Nice Model. As Kaib & Chambers conclude:

[W]e find a probability of 1% or less that the orbital architectures of the inner and outer planets are simultaneously reproduced in the same system. These small probabilities raise the prospect that the giant planet instability occurred before the terrestrial planets had formed. This scenario implies that the giant planet instability is not the source of the Late Heavy Bombardment and that terrestrial planet formation finished with the giant planets in their modern configuration.

Notably, the recent study by Volk & Gladman (2015) proposed an approach to the evolution of the four terrestrial planets that dispensed with the Nice Model altogether, suggesting an alternative explanation for the Late Heavy Bombardment. Although I don’t find their alternative persuasive, I hope these efforts inspire further evolutionary studies to address the problem of our denuded inner system.

In the meantime, the findings of Kaib & Chambers might benefit from reframing. As discussed in earlier blog posts, the phenomenon known as the Late Heavy Bombardment or Lunar Cataclysm can be understood in different ways. In one view, it was a self-contained period of heavy cometary impacts that were preceded and followed by long stretches of relative calm; its peak came about 3.8 billion years ago (Gya), at a system age of ~800 million years (Gomes et al. 2005). In another, it was simply one episode in a long, saw-toothed series of bombardments that began with Earth’s accretion and subsided only toward the end of the Archean period, about 2.5 – 3 Gya (Morbidelli et al. 2012, Marchi et al. 2014). Instead of triggering a late and relatively short-lived catastrophe, maybe the dynamic instability happened in the first 100 million years of Solar System history and inaugurated that long and violent epoch of bombardments. The Nice Model would still explain how the massive outer planets nudged and jostled one another into their mature (and usually wider) orbits.

Figure 4. Overview of Earth history

Again, maybe the failure of a single model to explain the final architecture of the inner as well as the outer Solar System is another clue that we need a new picture of inner system evolution. What if the Grand Tack triggered an inner system catastrophe, as modeled by Batygin & Laughlin (2015), but the resulting mess did not immediately resolve into a four-planet system? Maybe the battle of oligarchs that followed Jupiter’s retreat from the Sun’s inner territories was still raging while Neptune was decimating the outer realms. Maybe lasting peace in the inner system was contingent on resolving tensions among the outer worlds, a resolution that evidently hinged on the exile of a Uranus-type planet. Maybe the final detente between Jupiter and Saturn was what enabled Earth to dominate its three smaller siblings.


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
Batygin K, Bodenheimer P, Laughlin G. (2015) In situ formation and dynamical evolution of Hot Jupiter systems. In press. Abstract: 2015arXiv151109157B
Becker J, Vanderburg A, Adams F, Rappaport S, Schwengler H. (2015) WASP-47: A Hot Jupiter system with two additional planets discovered by K2. Astrophysical Journal Letters 812, L18. Abstract: 2015ApJ...812L..18B
Dullemond CP, Monnier JD. (2010). The inner regions of protoplanetary disks. Annual Review of Astronomy & Astrophysics 48, 205-239.
Gomes R, Levison HF, Tsiganis K, Morbidelli A. (2005) Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets. Nature, 435: 466-469. Abstract: 2005Natur.435..466G
Jontof-Hutter D, Ford EB, Rowe JF, Lissauer JJ, Fabrycky DC, Christa Van Laerhoven5, Agol E, Deck KM, Holczer T, Mazeh T. (2015) Robust TTV mass measurements: Ten Kepler exoplanets between 3 and 8 Mearth with diverse densities and incident fluxes. In press.
Kaib NA, Chambers JE. (2015) The fragility of the terrestrial planets during a giant planet instability. Monthly Notices of the Royal Astronomical Society. In press. Abstract:
Marchi S, Bottke WF, Elkins-Tanton LT, Bierhaus M, Wuennemann K, Morbidelli A, Kring DA. (2014) Widespread mixing and burial of Earth’s Hadean crust by asteroid impacts. Nature 511, 578-582. 2014Natur.511..578M
Morbidelli A, Marchi S, Bottke WF, Kring DA. (2012) A sawtooth-like timeline for the first billion years of lunar bombardment. Earth and Planetary Science Letters 355, 144-151. Abstract:
Volk K, Gladman B. (2015) Consolidating and crushing exoplanets: Did it happen here? Astrophysical Journal Letters, 806: L26. Abstract: 2015ApJ...806L..26V