Where is the dividing line between a large, rocky planet and a ‘mini-Neptune?’ It’s a critical issue, because life is at least possible on one, unlikely on the other. But while we’re getting better at figuring out planetary habitable zones, the question of how large a planet can be and remain ‘terrestrial’ is still unresolved. As Andrew LePage explains below, our view of potentially habitable planets like Kepler-452b depends upon how we analyze this matter — clearly, just being in or near the habitable zone isn’t enough. A prolific essayist with over 100 articles in venues like Scientific American and Sky & Telescope, LePage writes the excellent Drew ex Machina site, where his scrutiny of recent exoplanet finds is intense. The work seems a natural fit given his day job at Visidyne, Inc. near Boston, where he specializes in the processing and analysis of remote sensing data.

by Andrew LePage


A couple of weeks ago, the media was filled with reports about the discovery of Kepler 452b. While NASA’s Kepler mission had found a number of potentially habitable planets earlier, all of these previous discoveries orbited dim K and M-dwarf stars which are very different than our Sun and present a number of still unresolved issues affecting habitability (see A Review of the Best Habitable Planet Candidates in Centauri Dreams for a full review of earlier finds). What made this new Kepler find unique was that Kepler 452b was a nearly-Earth-sized planet orbiting inside the HZ of a Sun-like star – the first of potentially many more such exoplanets to come from the continuing analysis of Kepler’s data set. But being a bit of a skeptic when it comes to often overhyped media reports about the potential habitability of any newly discovered exoplanet, I wanted to dig deeper into this claim.

Is It in the Habitable Zone?

According to the discovery paper submitted for publication in The Astronomical Journal with Jon Jenkins (NASA Ames Research Center) as the lead author, Kepler 452 is a G2 type star like the Sun with a surface temperature of 5757±85 K, a mass of 1.04±0.05 times that of the Sun and a radius of 1.11 +0.15/-0.09 times the Sun’s. Based on these data, it can be calculated that Kepler 452 has a luminosity about 20% greater than that of the Sun making this it a slightly heavier and brighter version of the Sun. Comparison of the known properties of this star with standard models of stellar evolution yields an age of 6±2 billion years or about 1½ billion years older than the Sun and its system of planets. Compared to the stars earlier announced with potentially habitable exoplanets, Kepler 452 was certainly quite Sun-like.

While a full assessment of the habitability of any exoplanet would require very detailed information about all of its properties, obtaining such information is simply beyond the reach of our current technology. At this early stage in our search for other Earth-like worlds, the best we can do is compare what properties we can derive to our current expectations of the range of properties for habitable worlds to determine if a new find is potentially habitable. One of those important set of properties is the orbit of an exoplanet. According to Jenkins et al., Kepler 452b is in a 384.84-day orbit with an average orbital radius of Kepler 452b is 1.046 +0.019/-0.015 AU. This orbital radius is far outside that where a planet would become tidally locked and be affected by severe stellar flare activity – two unresolved issues that call into question the potential habitability of worlds tightly orbiting much dimmer stars like those found to date.

This orbital radius combined with the stellar properties yields an effective stellar flux for Kepler 452b that is 1.10 +0.29/-0.22 times that the Earth receives from the Sun. This effective stellar flux places Kepler 452b just inside the conservative HZ of a Sun-like star as defined by the runaway greenhouse limit. Given the current uncertainties in the properties of Kepler 452b and the star it orbits, Jenkins et al. calculate that there is only a 28.0% probability that Kepler 452b actually orbits inside of the conservatively defined HZ but there is a 96.8% chance that it orbits inside a more optimistic definition of the HZ corresponding to early conditions on Venus. However, it appears that Jenkins et al. used a definition of the HZ limits for an Earth mass planet. If Kepler 452b has a mass closer to five times that of the Earth (or 5 ME), which is likely to be the case, the effective stellar flux for the inner edge of the HZ increases from 1.10 to 1.18 times that of the Earth raising the chances that Kepler 452b orbits inside of the HZ to probably better than even odds. And since Kepler 452, like all stars, would have been dimmer in its youth, Kepler 452b would have been even more comfortably inside the HZ for billions of years. Considering all these facts combined with the limitations of current models in defining the true inner boundary of the HZ, this is close enough even for this skeptic to consider Kepler 452b as potentially habitable at least in terms of its orbit and effective stellar flux.

Is It a Rocky Planet?

The other important planetary property we can measure using current detection techniques is the size of a planet. Unfortunately, it is here where many past discoveries have run into trouble. It has been suspected for some time now that somewhere between the size of the Earth (or 1 RE) and Neptune with a radius of 4 RE, planets transition from being predominantly rocky with some chance of being habitable like the Earth to being rich in volatiles such as water, hydrogen and helium becoming mini-Neptunes with little chance of being habitable in the conventional sense. Based on recent analyses of Kepler data on the radius of exoplanets smaller than Neptune combined with independently derived masses from radial velocity measurements and other techniques, we now know that this transition from predominantly rocky worlds to predominantly volatile-rich worlds occurs somewhere around 1½ to 2 RE although the precise value and nature of this transition is uncertain due to the small number of planets with measured radii and precisely determined masses in this size range as well as the measurement uncertainties of those values (see The Transition from Rocky to Non-Rocky Planets in Centauri Dreams).


Image: This artist’s concept compares Earth (left) to Kepler-452b, which is about 60 percent larger in diameter. Credit: NASA/JPL-Caltech/T. Pyle

While many earlier claims of finding potentially habitable planets have run afoul of this transition and turned out to be much more likely to be mini-Neptunes than rocky terrestrial planets, in recent months astronomers have started making some effort to address this issue in discovery papers of potentially habitable planets including Jenkins et al.. Based on the analysis of the Kepler photometric data and the properties of the star, Jenkins et al. report that Kepler 452b has a radius of 1.63 +0.23/-0.20 RE which is close to the transition value. Based on their calculations, Jenkins et al. claimed that there was a better than 50% chance that Kepler 452b is a rocky planet. But how did they arrive at this figure?

Jenkins et al. used two different distributions of probable radius values for Kepler 452b and compared them to two different published mass-radius relationships for sub-Neptune sized planets to calculate the odds that their find has a density consistent with a predominantly rocky composition. The radius value distributions were derived from the measured 1.63 +0.23/-0.20 RE radius of Kepler 452 combined with two different models used to determine the host star’s properties. The first model, SPC (Spectral Parameter Classification), determines the star’s parameters by comparing its spectrum to a collection of synthetically generated stellar spectra to find the best fit. The second model, called SpecMath, is considered more conservative and compares the star’s spectrum to a collection of 800 well-studied stellar spectra to derive the star’s properties.

To calculate the probability that Kepler 452b is a rocky planet based on those radius distributions, Jenkins et al. used two different mass-radius relationships. The first was formulated by graduate student Lauren Weiss and famed exoplanet hunter Geoff Marcy (University of California – Berkeley) which was published in March 2014. Weiss and Marcy fitted radius and mass data for 65 exoplanets to come up with a deterministic mass-radius function where a particular radius value corresponds to a single mass value. While simple, this model admittedly does not reflect the fact that exoplanets with a particular radius value can actually have a range of possible mass values reflecting a variety of bulk compositions.

The second mass-radius relationship used by Jenkins et al. was derived by Angie Wolfgang (University of California – Santa Cruz), Leslie A. Rogers (California Institute of Technology), and Eric B. Ford (Pennsylvania State University) and was submitted for publication in April of 2015. They evaluated data for 90 exoplanets using a hierarchal Bayesian technique which allowed them not only to derive the parameters for a best fit of the available data, but also to quantify the uncertainty in those parameters as well as the distribution of actual planetary mass values. Using their approach, they derived a probabilistic mass-radius relationship where the most likely mass and the distribution of likely values are determined that better reflects the uncertainties in the data and the fact that exoplanets with a particular radius value can have a range of actual masses (for a detailed discussion of this work, see A Mass-Radius Relationship for ‘Sub-Neptunes’ in Centauri Dreams).

Using the radius distributions for Kepler 452b derived from SPC and SpecMath, Jenkins et al. found that the mass-radius relationship created by Weiss and Marcy yielded 64% and 40% probabilities, respectively, that their new find has a bulk density consistent with models of rocky planets. When employing the mass-radius relationship of Wolfgang et al., they found a 49% and 62% probability, respectively, that Kepler 452b is a rocky planet. The average of these results is the origin of the quoted greater than 50% odds that the new find is a rocky planet.

Is It Really a Rocky Planet?

While this is a clever solution to a difficult problem, there are problems with this approach. First of all, while the work of Weiss and Marcy was an excellent first attempt to derive the mass-radius relationship using the newly available Kepler data set, the relationship derived by Wolfgang et al. is superior since it uses more data of higher quality that is analyzed in a mathematically more rigorous way. While Jenkins et al. recognize this and prefer the higher probabilities calculated using Wolfgang et al., they used the parameters of the mass-radius relationship derived using all 90 planets with radii up to 4 RE in the original analysis. Based on earlier work by Leslie Rogers, it was recognized that the transition from being predominantly rocky to predominantly volatile-rich takes place at radius values no greater than 1.6 RE (for a full discussion of this work, see Habitable Planet Reality Check: Terrestrial Planet Size Limit on my web site, Drew Ex Machina).

When Wolfgang et al. analyzed just the subset of exoplanets with radii less than 1.6 RE, they derived different parameters for the mass-radius relationship for these smaller planets. For a planet with a radius of 1.6 RE, for example, the most probable mass when using parameters derived from fitting all planets with radii less than 4 RE, as used by Jenkins et al., comes out to about 5 ME. If the parameters derived from just smaller planets with radii less than or equal to 1.6 RE are used, a smaller probable mass value of 4 ME is found. As a result, the probabilities derived by Jenkins et al. are biased towards higher mass outcomes with corresponding higher probabilities of finding Kepler 452b to be a rocky planet.

A better approach for determining the probability that Kepler 452b is a rocky planet would be to compare its properties directly to the population of exoplanets with known radii and accurately determined masses. Unfortunately, Rogers’ paper does not include a simple function that others can use to calculate such a probability since this was outside the scope of her work. Despite this shortcoming, the title of her paper published in March 2015 in The Astrophysical Journal really says it all: “Most 1.6 Earth-Radius Planets are not Rocky”. In other words, Kepler 452b with a radius of 1.63 RE is most likely not a rocky planet but is a mini-Neptune instead, contrary to the claims by Jenkins et al..

Other astronomers trying to calculate the odds that their finds are rocky planets or not have derived probabilities in different ways. Guillermo Torres (Harvard-Smithsonian Center for Astrophysics) on January 6, 2015 announced the discovery of eight habitable zone planets using Kepler data where they quantified the probabilities that their finds were rocky (see Habitable Planet Reality Check: 8 New Habitable Zone Planets on my web site, Drew Ex Machina). Although somewhat different from the method used by Rogers, the approach used by Torres et al. to calculate the probability that a planet with a particular radius is rocky gives qualitatively similar results. Using their model, the chances that Kepler 452b is rocky is about 45%. This is closer to the low-end 40% figure derived by Jenkins et al. than the often quoted “greater than 50%” figure.

Unfortunately, the chance that Kepler 452b is a terrestrial planet might not be as good as even 40%. Recent work by Rebekah I. Dawson, Eugene Chiang and Eve J. Lee (University of California – Berkeley) recently submitted for publication in Monthly Notices of the Royal Astronomical Society strongly suggests that planets with masses greater than about 2 ME (which would have a radius of about 1.2 RE, assuming an Earth-like bulk composition) which orbit stars with a high metallicity are more likely to be mini-Neptunes. This is because stars with higher metallicities tend to have more solid material available to form planetary embryos more quickly making it more likely for them to acquire some gas directly from the protoplanetary disk before it dissipates. Only 1% or 2% of a planet’s total mass in hydrogen and helium is sufficient to puff up its observed radius and make it a mini-Neptune. Stars with lower metallicity values tend to form planetary embryos more slowly and they might not reach the required 2 ME mass threshold fast enough to begin to acquire any more than trace amounts of gas before it has already dissipated from the protoplanetary disk. With a iron-to-hydrogen ratio about 60% higher than the Sun, Kepler 452 has a slightly higher metallicity than the Sun increasing the odds somewhat that Kepler 452b is a mini-Neptune. Taken together with Rogers work, this strongly suggests that the odds that Kepler 452b is a rocky planet are less than 50% not greater as is being claimed.


To be perfectly honest, quibbling over a couple of tens of percent probability one way or the other about the nature of Kepler 452b is most likely not all that important considering the uncertainties in its properties as well as the still substantial uncertainties in the mass-radius relationships available at this time. In the end, we will have to wait for a more definitive derivation of the mass-radius relationship and a more quantitative description of the nature of the transition from rocky planet to mini-Neptune to settle this question more accurately. Despite the outstanding issue of the nature of Kepler 452b, it still has very real prospects of being potentially habitable. But even if it proves not to be, future studies of its properties will provide scientists with vital information on the limits of planetary habitability.

While some might be disappointed by this less rosy assessment, it should be remembered that scientists are still actively analyzing the Kepler data set and performing follow up observations. There are already several potentially habitable Earth-size planet candidates found orbiting Sun-like stars that are being actively studied by members of the Kepler science team and their colleagues. It is only a matter of time before the discovery of true “Earth twins” is announced.

The preprint of the Kepler 452b discovery paper by Jenkins et al., “Discovery and Validation of Kepler-452b: A 1.6-RE Super Earth Exoplanet in the Habitable Zone of a G2 Star”, can be found here.