Habitable Planet Reality Check: Terrestrial Planet Size Limit

Among the lay public, probably one of the most misunderstood astronomical terms that has recently come into common use has to be “super-Earth”. All too often, the assumption is made by too many people that a super-Earth is just a larger size version of the Earth that is otherwise identical to our planet in all ways including its habitability. Nothing could be further from the truth.

Since the Kepler mission is able to determine the size of a planet based on the characteristics of its transit in front of its host star, the Kepler team developed a working nomenclature based only on the size of the planet detected. Planets with radii, RP, less than 1.25 times that of the Earth (or 1.25 RE) were classified as Earth-size. Those with radii in the 1.25 to 2.0 RE range were classified as super-Earths while those in the 2.0 to 4.0 RE range were classified as Neptune-size. The position of Earth-size or super-Earth-size planets in relation to their sun’s habitable zone (and hence their potential habitability) has absolutely no bearing on this size classification. In fact, the majority of Earth-size and super-Earth-size planets detected by the Kepler mission orbit far too close to their suns to be habitable mainly because Kepler is more likely to detect the transits of planets in smaller orbits.

Likewise, the terms Earth-size or super-Earth-size say absolutely nothing about the potential composition of a planet which is another important factor in determining a planet’s potential habitability. Looking at the size of several dozen planets discovered by Kepler with radii of less than 4 RE as well as the masses of those planets measured by precision radial velocity and transit timing variation techniques, it has been possible for astronomers to start to investigate the change in planets’ density (which gives an indication of their bulk composition) as a function of radius. Initial analyses published earlier this year by Marcy et al. as well as by Weiss and Marcy showed that while there was considerable variation from planet to planet in their samples, the density of super-Earths tended to increase with increasing radius as would be expected of rocky planets until a transition is reached somewhere around the 1.5 RE to 2.0 RE range. Larger planets then tended to become increasingly less dense.

Density_vs_Radius

Plot of planet density versus radius for 33 extrasolar planets and the planets in our solar system included in the analysis earlier this year by Marcy et al. (G. Marcy)

The interpretation of this result is that planets with radii greater than about 1.5 RE are increasingly likely to have substantial envelopes of various volatiles such as water (including high pressure forms of ice at high temperatures) and thick atmospheres rich in hydrogen and helium that decrease bulk density. As a result, they can no longer be considered terrestrial or rocky planets like the Earth but would be classified as mini-Neptunes or gas dwarfs depending on the exact ratios of rock, water and gas. The conclusion from this initial work was that there was a important transition in bulk composition that encompassed the upper end of the super-Earth size range from rocky planets to non-rocky planets.

This transition from rocky to non-rocky worlds is important for a number of reasons including assessing the potential habitability of these large worlds. As currently defined by scientists, a habitable world needs to be a rocky or terrestrial planet or moon. Mini-Neptunes or gas dwarfs are unlikely places for life as we know it to start or survive. As a result, the size threshold between rocky and non-rocky worlds is an important parameter in assessing the potential habitability of a planet just like its position relative to its sun’s habitable zone. But the precise value of radius or mass of this transition and its characteristics remained to be determined.

 

New Analysis

A new analysis of this transition from rocky to non-rocky planets was recently submitted for publication by Leslie Rogers who is currently a Hubble Fellow at the California Institute of Technology. In this paper, Rogers confined her analysis to transiting planets with radii less than 4 RE whose masses had been constrained by precision radial velocity measurements. This heterogeneous sample of 47 transiting sub-Neptune size bodies orbiting 27 stars included planets studied by Marcy et al. as part of a Keck HIRES radial velocity measurement campaign as well as five additional planets whose masses had been published earlier based on HIRES measurements. All but four of the planets in the sample had close-in orbits with periods less than 50 days with effective stellar fluxes ranging from 1.1 to 3,700 times that of the Earth. Planets with masses determined by Weiss and Marcy using the innovative transit timing variation technique were excluded from this analysis since this sample of planets may be affected by selection biases that favor low-density planets.

First, Rogers determined the probability that each of the planets in the Kepler-derived sample were rocky planets by comparing the properties of those planets and the associated measurement uncertainties to models of planets with various compositions. Next, she then applied a hierarchical Bayesian statistical approach to assess three different models for mass-radius distribution for the sample of planets. One model assumed an abrupt, step-wise transition from rocky to non-rocky planets while the other two models assumed different types of gradual transitions where some fraction of the population of planets of a given radius were rocky while the balance were non-rocky.

The analysis using all three models had their most likely transition mid-points (i.e. where the abrupt transition takes place in the step-wise model or a 50-50 split in rocky and non-rocky planets exists in the gradual transition models) at about 1.5 RE. Rogers’ analysis mildly favored a step-wise transition over the gradual transition models but she readily admits that a larger sample of planets with radii less than 2 RE with known masses will be required to definitively determine which model more accurately reflects the true mass-radius function of planets. Likewise, Rogers’ found no clear evidence of any dependence on the transition value as a function of stellar flux because of the limited size of her sample. In an effort to assess the sensitivity of her results to the chosen sample, Rogers excluded ten planets with the most uncertain masses and found little change in the results.

Based on a statistical analysis of the sample of planets Rogers chose, the transition from rocky to non-rocky planets takes place at no greater than about 1.6 RE at a 95% confidence level. Assuming a simple linear transition in the proportions of rocky and non-rocky planets, no more than 5% of planets with a radii of about 2.6 RE will have densities compatible with a rocky composition to a 95% confidence level. Adopting the 1.6 RE radius threshold as the limit beyond which planets are increasingly unlikely to have rocky compositions is equivalent to a mass threshold of about 6 ME assuming an Earth-like composition. Rogers notes that many recent models for planet formation indicate that planetary embryos with masses of 6 ME or larger can readily accrete gas directly from the circumstellar disk that surround young stars. Rogers’ result that indicates larger planets are much more likely to be non-rocky seems to provide evidence for this.

An obvious potential counterexample to this maximum rocky-planet size threshold is the case of Kepler 10c which made the news less than two months ago. Dumusque et al. used precision radial velocity measurements from HARPS-N to determine that the mass of this planet is 17 ME or about the same as Neptune’s mass in our Solar System. Combined with the radius of 2.35 RE determined by Kepler measurements, the density of Kepler 10c comes out to be 7.1±1.0 g/cm3 leading Dumusque et al. to claim that it is strong evidence for the existence of massive solid planets. While at first blush this density, which is greater than Earth’s, might lead to the conclusion that Kepler 10c is a rocky planet, Rogers counters that its density is in fact inconsistent with a rocky composition by more than 1σ and that there is only about a 10% probability that Kepler 10c is in fact predominantly rocky in composition. It is much more likely that it possesses a substantial volatile envelope albeit smaller than Neptune’s given its higher density.

 

Impact on Potential Habitable Planets

This new analysis starts to set quantitative limits on the maximum size of not only rocky planets but the maximum size of potentially habitable planets since non-rocky worlds like gas dwarfs and mini-Neptunes are generally considered unlikely sites for life to develop. Rogers specifically mentions the impact of her work on one illustrative case in her paper: Kepler 22b which was the first planet discovered in the habitable zone of another star with an accurately measured radius.

Kepler 22b has a radius of about 2.4 RE but radial velocity measurements to date have been unable to detect it. As a result, only very high upper limits have been set on its mass leaving much ambiguity about its actual properties. But based on Rogers’ analysis of the mass-radius relationship of currently known Earth to super-Earth size planets, the fraction of planets with a radius of 2.4 RE that are rocky is less than 2% to the 95% confidence level. It is much more likely that Kepler 22b has a volatile envelope that contributes significantly to its volume. As a result, it is highly unlikely that Kepler 22b is a terrestrial planet and, assuming that not all terrestrial planets in the habitable zone are necessarily habitable, even less likely that it is habitable. Barring additional scientific evidence to the contrary, it makes little sense to consider Kepler 22b a potentially habitable planet.

HEC_All_ESI

Diagram illustrating the Planetary Habitability Laboratory’s current (as of July 3, 2014) list of potentially habitable exoplanets. According to the latest analysis of Kepler data, all but two of these planets are unlikely to be terrestrial planets never mind potentially habitable planets. Click on image to enlarge (PHL)

To gauge the impact of Rogers’ analysis on other worlds considered by some to be potentially habitable, I have applied her rocky planet size limit criterion to one of the more widely publicized lists of potentially habitable worlds: The Habitable Exoplanet Catalog maintained by the Planetary Habitability Laboratory (PHL) at the University of Puerto Rico at Arecibo. Table 1 below lists the planets from their “main database” for which only the radii are known listed in descending order of their calculated Earth Similarity Index (ESI) value. All data in Table 1 come from the PHL catalog.

 

Table 1: List of PHL Potential Habitable Planets with Known Radii

Name

ESI

RP (Earth = 1)

RP < 1.6 RE

Kepler 62e

0.83

1.61

NO

Kepler 283c

0.79

1.81

NO

Kepler 296f

0.78

1.79

NO

Kepler 61b

0.73

2.15

NO

Kepler 22b

0.71

2.35

NO

Kepler 298d

0.68

2.50

NO

Kepler 62f

0.67

1.41

YES

Kepler 186f

0.64

1.11

YES

Kepler 174d

0.61

2.18

NO

 

As can be seen, seven out of the nine planets on PHL’s list of potentially habitable planets with known radii exceed the 1.6 RE radius limit and are therefore unlikely to be rocky planets. It is more probable that these seven planets are mini-Neptunes or gas dwarfs that are unlikely to support life as we know it. Only two of the planets, Kepler 62f and Kepler 186f are small enough to be likely rocky planets and, at least on the basis of probable composition, should be considered potentially habitable (for a fuller discussion of Kepler 186f, see “Habitable Planet Reality Check: Kepler 186f“).

It should be noted that the case for Kepler 296f is more complicated than earlier assumed and that the data listed in the PHL catalog are incorrect.  It turns out that Kepler 296 is actually a binary star that was unresolved by Kepler which affects the properties of the detected planets that had been derived under the assumption that the star was single.  An analysis of Hubble Space Telescope images of Kepler 296 and other stars recently submitted for publication by Star et al. shows that Kepler 296 actually consists of M0V and M3V red dwarf stars 1,200 light years away with a projected separation of 80 AU.  Since it is not possible to determine which star the detected planets orbit from the Kepler data alone, there are even odds that Kepler 296f orbits one of these components or the other.  If Kepler 296f orbits the brighter A component, Star et al. calculate that it has a radius of 2.4 RE and  orbits closer than the inner edge of this star’s habitable zone.  Given its size and position, it is unlikely to be a rocky planet and even less likely to be habitable.  If Kepler 296f orbits the B component, its orbit would be comfortably inside the habitable zone of this star but it would have a radius of 3.4 RE making it far too large to be a rocky planet.  In either case, Kepler 296f is very unlikely to be a habitable planet.

Kepler_296_HST_Image

Hubble Space Telescope image of the Kepler 296 showing it to be a close binary with the B component on the left and A on the right. It is not currently known which star hosts the five planets detected by Kepler. (Adapted from Star et al./STScI/NASA)

The remaining dozen planets on PHL’s list of potentially habitable planets were discovered by precision radial velocity measurements and do not have measured radii. Still, the potential nature of these planets can be evaluated using the optimistic upper mass limit for rocky planets of 6 ME assuming a planet with a 1.6 RE radius and an Earth-like composition. It must be remembered, however, that precision radial velocity measurements only provide a minimum mass or MPsini of a planet since the inclination of the planet’s orbit to our line of sight, i, is unknown. The inclination of the orbit or the actual planet mass must be determined by other methods.

Table 2 below lists the remaining 12 planets in PHL’s catalog that were discovered using the radial velocity technique. The data in this table were taken directly from the main database for PHL’s Habitable Exoplanet Catalog. These planets are once again listed in descending order of their ESI values which were presumably calculated under the overly optimistic assumption that their actual mass equals their measured minimum mass. Listed in this table is the probability that a randomly oriented orbit for each planet produces an actual planet mass that is less than Rogers’ 6 ME threshold for a rocky planet.

 

Table 2: List of PHL Potential Habitable Planets with Known MPsini

Name

ESI

MPsini/ME

Probability

MP < 6 ME

Terrestrial Planet?

GJ 667Cc

0.84

3.80

37%

Probably not

GJ 832c

0.81

5.40

10%

Highly Improbable

τ Ceti e

0.78

4.29

29%

Probably Not

GJ 180c

0.77

6.40

0%

Highly Improbable

GJ 667Cf

0.77

2.70

54%

Probably Not

GJ 180b

0.75

8.30

0%

Highly Improbable

GJ 163c

0.75

7.26

0%

Highly Improbable

HD 40307g

0.74

7.09

0%

Highly Improbable

GJ 422b

0.71

9.90

0%

Highly Improbable

Kapteyn b

0.67

4.80

20%

Probably Not

GJ 667Ce

0.60

2.70

54%

Probably Not

GJ 682c

0.59

8.70

0%

Highly Improbable

 

Right off, half of the dozen planets on this list have minimum masses that already exceed the 6 ME mass limit and are unlikely to be rocky planets. Folding in the uncertainty of their actual masses, it is much more likely that these planets are gas dwarfs or mini-Neptunes or even larger – in some cases maybe much larger. The remaining six planets on the list are also probably not rocky planets including Kapteyn b and GJ 832c which have been of recent interest (for a fuller discussion about these planets, see “Habitable Planet Reality Check: Kaptyen b” and “GJ 832c: Habitable Super-Earth or Super-Venus?“). With less than even odds that each of these remaining six planets have a mass less than 6 ME, which represents the threshold where less than half of the planets with this mass have a mainly rocky composition, it is much more likely that all of these planets have substantial volatile envelopes and are most likely not terrestrial planets, never mind habitable planets.

What is immediately obvious from the application of Rogers’ analysis of Kepler results is that most planets that have been optimistically considered “potentially habitable” by some are probably not habitable at all. Instead it is much more likely that 19 out of the 21 planets in the main database of PHL’s Habitable Exoplanet Catalog are instead gas dwarfs, mini-Neptunes or larger planets with extensive volatile envelopes. In addition, about three-quarters of the planets on PHL’s list of potentially habitable planets among Kepler’s list of planet candidates are also not likely to be rocky planets because of their large radii. For PHL’s ESI to be of any meaningful scientific value in the future, they need to reevaluate how the ESI is calculated and take into account the probability that a given planet is even a terrestrial planet. In addition, they need to stop assuming that the minimum planet mass derived from precision radial velocity surveys is the equivalent of the actual mass.

 

The Future

While the analysis of this initial sample of planets discovered by Kepler with radii less than 4 RE has set some limits on the maximum size of rocky planets (and hence potentially habitable planets), the sample involved in the work by Rogers, Marcy et al. as well as Weiss and Marcy were rather limited in size. Fortunately, many more planets in this size range remain to be discovered during the ongoing analysis of the database from Kepler’s primary mission and the follow up observations by the Keck HIRES team and others. Yet more planets are expected to be discovered during Kepler’s “K2” extended mission currently underway. NASA’s upcoming TESS (Transiting Exoplanet Survey Satellite) mission should discover still more planets in this size range and will be especially important since this mission will concentrate on brighter stars that can yield more accurate masses of smaller planets via precision radial velocity measurements. With the larger sample the future promises, it should prove possible to not only better define the transition from rocky to non-rocky planets but also discern its dependence on a host of factors allowing scientists to better understand the limits of planetary habitability.

 

Related Reading

“The Transition from Super-Earth to Mini-Neptune”, Drew Ex Machina, March 29, 2014 [Post]

“Habitable Planet Reality Check: Kepler 186f”, Drew Ex Machina, April 20, 2014 [Post]

“Habitable Planet Reality Check: Kapteyn b”, Drew Ex Machina, June 6, 2014 [Post]

“GJ 832c: Habitable Super-Earth or Super Venus?”, Drew Ex Machina, June 27, 2014 [Post]

“Abundance of Earth Analogs”, Drew Ex Machina. June 25, 2014 [Post]

“Habitable Planet Reality Check: 55 Cancri f”, Drew Ex Machina, May 7, 2014 [Post]

“The Extremes of Habitability”, SETIQuest, Volume 4, Number 2, pp. 1-8, Second Quarter 1998 [Article]

 

General References

Xavier Dumusque et al., “The Kepler-10 Planetary System Revisited by HARPS-N: A Hot Rocky World and a Solid Neptune-Mass Planet”, The Astrophysical Journal, Vol. 789, No. 2, Article id. 154, July 2014

Geoffrey W. Marcy et al., “Masses, Radii, and Orbits of Small Kepler Planets: The Transition from Gaseous to Rocky Planets”, The Astrophysical Journal Supplement, Vol. 210, No. 2, Article id. 20, February 2014

Leslie A. Rogers, “Most 1.6 Earth-Radius Planets are not Rocky”, Submitted to The Astrophysical Journal, July 16, 2014 [Preprint]

Kimberly M. Star et al., “Revision of Earth-Sized Kepler Planet Candidate Properties with High Resolution Imaging by Hubble Space Telescope”, Submitted to The Astrophysical Journal, July 3, 2014 [Preprint]

Lauren M. Weiss and Geoffrey W. Marcy, “The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii”, The Astrophysical Journal Letters, Vol. 783, No. 1, Article id. L6, March 2014

Habitable Exoplanet Catalog: Data of Potentially Habitable Worlds, Planetary Habitability Laboratory Web Site [Link]