Puffy Planets

Hot air balloons over Malqata, Egypt, site of the jubilee palace of Amenhotep III (ca. 1350 BC)

Recent work by Eric Lopez and Jonathan Fortney brings welcome clarity to the bewildering array of Kepler transit data on small planets. These esteemed planetologists just circulated a preprint entitled “Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition” (hereafter LF13). It addresses questions that have surfaced several times in this blog: How can we distinguish Super Earths from Neptune-like exoplanets? And what is the likely composition of each species? That topic is explored here, here, here, here, and most recently here.

puff threshold

Using the results from a large ensemble of thermal evolution models, LF13 draw a physically motivated boundary between true Super Earths (which are scaled-up versions of Earth, consisting only of heavy elements) and planets like Uranus and Neptune (which maintain at least a small percentage of their mass in a hydrogen/helium (H/He) envelope).

As Lopez and Fortney conclude, “for most of Kepler’s Neptune and sub-Neptune sized planets, radius is quite independent of planet mass and is instead a direct measure of bulk H/He envelope fraction.” They offer a method to estimate the likely composition of low-mass transiting planets simply on the basis of radius. This is an extremely useful contribution, because for the vast majority of Kepler candidates, radius and orbital period are the only reliable information we have.

LF13 find that the maximum size for a typical rocky planet is 1.75 Earth radii (Rea). Although some planets more massive than 5 Earth masses (Mea) may have radii larger than 2 Rea because they consist primarily of ices, with no appreciable contribution from H/He, the vast majority of planets with a substantial rocky component must be smaller than 1.75 Rea. It follows that most planets larger than 2 Rea must have some percentage of H/He in their atmospheres. A well-known example is Kepler-22b, announced in 2011 and sometimes described as a “habitable Super Earth.” According to LF13, however, this object would be a miniature version of Uranus, given its radius of 2.2 Rea.

LF13 describe a hypothetical planet with a radius of 2 Rea and an orbit within its system’s classical habitable zone. Assuming a rocky core and an overall mass of 5 Mea, 0.5% of the planet’s total mass must be H/He. This tiny fraction creates an atmospheric pressure of about 20 kilobars of H/He, which as LF13 say is 20 times higher than the pressure at the bottom of the Marianas Trench, the deepest fissure in Earth’s global ocean. In the habitable zone, such an atmosphere will produce surface temperatures around 3000 K, more than 10 times higher than the mean surface temperature on Earth (288 K). This environment is hostile to liquid water and carbon-based life.

Figure 1. Puffy Planets. Selected transiting planets between 3 and 7 Earth radii, with estimated fractions of hydrogen/helium (H/He). All values except for Neptune are taken from Lopez & Fortney 2013. The approximate H/He fraction for Neptune is inferred from their Table 3. 

The astronomer Robin Wordsworth has presented a sceario in which a rocky planet of 5 Mea with a dissipating hydrogen atmosphere, orbiting a Sun-like star at a distance of 2.5 AU (i.e., well outside the classical habitable zone, near the system ice line), will experience a transient but potentially significant epoch during which it might sustain liquid water. However, this optimistic model seems to suffer from fine-tuning. As even Wordsworth concludes, when it comes to hydrogen, “usually, either far too much or too little of it is present” (Wordsworth 2012). For Kepler planets larger than 2 Rea, it’s “far too much.”

degeneracy on ice

A few years ago, virtually everyone assumed that some subset – maybe the majority – of Super Earths would be “Water Planets” or “Ocean Planets.” The consensus has changed dramatically since the discovery of the Kepler-11 system in 2011. Now investigators routinely model rocky planets with H/He envelopes, while the likelihood of Water Planets is questioned. Nevertheless, LF13 accept the possibility of rock/ice planets, noting that a planet of 10 Mea consisting of 20% rock/metal and 80% water would have a radius of 2.7 Rea. They concede that their model suffers from the same “degeneracy” as previous efforts when it comes to distinguishing icy planets from gassy planets. In other words, the same radius could correspond to very different compositions.

For example, 55 Cancri e has a measured mass and radius of 8.3 Mea and 1.99 Rea, respectively, and is sometimes proposed as a Water Planet (Dragomir et al. 2013). Since its temperature is about 2000 K and its age is around twice that of the Solar System, Diana Dragomir and colleagues argue that a trace hydrogen envelope would have dissipated eons ago, while a substantial fraction of ices might remain.

Without providing a rationale, LF13 model 55 Cancri e as a rocky object instead, proposing a modest H/He envelope amounting to only 0.14% of its bulk composition. However, they leave open the possibility that other planets between 2 and 3 Rea might qualify as Water Planets (and thus Super Earths), as long as they have a large enough fraction of ices in their composition.

If they exist, planets that contain a significant fraction of water or high-pressure ices, but lack a H/He envelope, are of great scientific interest. Nevertheless, they appear to have little relevance for astrobiology. A growing consensus holds that, in order to maintain bodies of liquid water, a rocky planet requires both plate tectonics and a carbon cycle. Neither is possible on the Water Planets proposed by contemporary theorists. An object of 5 Mea whose bulk composition is 25% water will have a differentiated structure, with a rock/metal core surrounded by a layer of high-pressure ice thousands of kilometers thick. This layer would block chemical interactions between atmospheric gases and heavy elements in deeper strata, preventing the development of a carbon cycle (Lammer et al. 2010, Alibert 2013). Yann Alibert finds 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, with the maximum percentage decreasing with increasing mass (Alibert 2013).

In addition, many astrobiologists assume that plate tectonics requires liquid water rather than ice to lubricate continental plates (Korenaga 2010, Lammer et al. 2010). Also widely endorsed is the argument that solid objects above a few times the mass of the Earth, even if they somehow retained thin envelopes of water, cannot support plate tectonics at all (O’Neill & Lenardic 2007, Morard et al. 2011, Stein et al. 2013). Ocean Planets look less and less attractive than they used to.

low-mass cousins

To illustrate their model, LF13 present a table summarizing all confirmed exoplanets smaller than Saturn with reliably measured masses and radii. Although this sample is too small to yield robust statistics, suggestive trends are evident. The six planets with radii between 1 and 2 Rea (where LF13 place the transition from Super Earths to Neptune-like planets) range in mass from 1.9 to 8.45 Mea, with a mean of 5.8 Mea and a median of 6 Mea. The corresponding mass values are remarkably similar for the six planets between 2 and 3 Rea, which LF13 call “sub-Neptunes” and which others have shown to represent the most numerous population of Kepler planets (Petigura et al. 2013). For these planets, the range in mass is 2 to 7.86 Mea, the mean is 5.6 Mea, and the median is 6.7 Mea. According to LF13, objects in this group have mass fractions of H/He ranging from 0.31% to 5%, substantially smaller than the fractions for Uranus and Neptune.

For the 12 planets between 3 and 7 Rea, which by all agreement have H/He envelopes, masses range widely, rising from 7.3 Mea to 68.6 Mea, with a mean of 20.6 Mea and a median of 16.8 Mea. However, confirmed exoplanets are sparse between 25 and 60 Mea; LF13 offer only three examples, none of them between 27 and 40 Mea. Such a gap in the distribution justifies removal of the most obvious outlier, CoRoT-8b. With a mass of almost 70 Mea, CoRoT-8b resembles a gas giant, but its unexpectedly small radius of 6.38 Rea implies a composition dominated by heavy elements. LH13 list its bulk composition as only one-third H/He. If we eliminate CoRoT-8b from the sample of Neptune-like objects, the mass range becomes 7.3 to 26.2 Mea and the mean becomes 14.9 Mea, while the median remains almost the same at 16.3 Mea. A representative sample of this group is illustrated above in Figure 1.

inner system regulars

The latest Kepler data show that puffy planets of 3 to 7 Rea are common within 1 astronomical unit (AU) of Sun-like stars. Objects in this range of radii, as we just saw, have a median mass very similar to Neptune’s. A number of recent studies have calculated the distribution of these planets and their smaller, lower-mass siblings.

Andrew Youdin found that 3 Rea marks a clear divide in the distribution of low-mass planets on short-period orbits (< 50 days) around Sun-like stars (Youdin 2011). Planets of this approximate radius are extremely rare on periods shorter than 7 days, whereas both smaller and larger planets are plentiful in the same orbital space. Youdin interpreted this distribution as a probable result of the thermal evolution of H/He envelopes around low-mass planets that migrate to the immediate vicinity of their host stars. Planets of the lowest mass (less than about 8 Mea) will lose their envelopes completely, leaving bare rocky spheres smaller than 2 Rea. More massive planets with more substantial cores can sustain lightweight atmospheres against stripping, resulting in final radii larger than 3 Rea.

In a more recent analysis using a larger set of Kepler data, Subo Dong and Zhaohuan Zhu characterize the planet population within 0.75 AU of Sun-like stars. This boundary corresponds to an orbit of about 250 days, similar to the orbit of Venus (225 days). They find that planets smaller than 4 Rea have a relatively flat distribution at periods longer than 10 days, whereas planets of 4-8 Rea have a steadily increasing distribution at longer periods (Dong & Zhu 2013). In general, they observe, the relative fraction of “big planets” (those of 3 Rea or more) increases with increasing period, but the increase is most pronounced for planets smaller than 10 Rea (i.e., Saturn-size or less).

Dong and Zhu provide an illuminating overview of the cumulative frequencies of planets of all sizes in the Kepler sample. Within 0.75 AU, planets of 1-2 Rea (which they call “Earth-size”) have a frequency of 28%; those of 2-4 Rea (“super-Earth-size”) have a very similar frequency, at 25%; those of 4-8 Rea (“Neptune-size”) are far less common, at 7%; while those larger than 8 Rea (“Jupiter-size”) are the least common of all, at only 3%.

The relative abundance of dwarfs and rarity of giants has been widely observed. It is rapidly becoming a cornerstone of exoplanetary science, analogous to the abundance of lower-mass stars (M dwarfs) versus their higher-mass (O and B-type) siblings.

REFERENCES

Alibert Y. (2013) On the radius of habitable planets. Astronomy & Astrophysics, in press.

Dragomir D, Matthews JM, Winn JN, Rowe JF, MOST Science Team (2013) New MOST photometry of the 55 Cancri system. In press. Abstract: http://adsabs.harvard.edu/abs/2013arXiv1302.3321D

Dong S & Zhu Z. (2013) Fast rise of “Neptune-size” planets (4-8 Rearth) from P ∼10 to ∼250 days: Statistics of Kepler planet candidates up to ∼0.75 AU. Astrophysical Journal 778, 53.

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.

Lopez ED & Fortney JJ. (2013) Understanding the mass-radius relation for sub-Neptunes: Radius as a proxy for composition. In press. Abstract: http://adsabs.harvard.edu/abs/2013arXiv1311.0329L

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

Morard G, Bouchet F, Valencia D, Mazevet S, Guyot F. (2011) The melting curve of iron at extreme pressures: Implications for planetary cores. High Energy Density Physics 7, 141-144.

Petigura EA, Geoffrey MW, Howard AW. (2013) A plateau in the planet population below twice the size of Earth. Astrophysical Journal 770, 69. Abstract: http://adsabs.harvard.edu/abs/2013ApJ...770...69P

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.

Wordsworth R. (2012) Transient conditions for biogenesis on low-mass exoplanets with escaping hydrogen atmospheres. Icarus 219, 267-273.

Youdin AN. (2013) The exoplanet census: A general method applied to Kepler. Astrophysical Journal 742, 38. Abstract: http://adsabs.harvard.edu/abs/2011ApJ...742...38Y