## Super-Earths and Mini-Neptunes

Low-Mass Habitable Zone Planets (artist images)

Our Solar System did not prepare us for what we would discover orbiting other stars. Instead, it told us that planets fall into neat categories: Gas giants made mostly of hydrogen and helium (of which Jupiter and Saturn are the archetypes), ice giants made mostly of water (for which Uranus and Neptune are representatives), and solid terrestrial planets with comparatively thin atmospheres — that would be the planets of the inner solar system and the one right under your feet). Since the discovery of thousands of planets orbiting other stars, and the measurement of their masses and densities, it has become clear that not all planets fit into this paradigm. Significantly, unless rocky worlds have an optimistically high abundance, what may be the most abundant type of planet in the Galaxy is a sort of mix between low-density, volatile-rich Neptune-like planets and rocky terrestrial planets. The Solar System features no such planet — after Earth, the next most massive planet is Uranus at ~14.5 times as massive. A casual look at the entirety of discovered transiting planet candidates discovered by Kepler reveals the magnitude of this problem.

While Kepler is no longer observing its original field, the massive amount of data can still be combed through to reveal new planet candidates. Here, previously discovered planet candidates are blue dots, and newly announced planet candidates are yellow. A few things are noteworthy. Firstly, the overwhelming majority of the newly discovered planet candidates have reasonably long orbital periods. This can be expected as shorter period planets have been detectable in the existing data for longer, and have had time to be spotted already. Secondly, and not really the point of this post… they’re still finding warm Jupiters in the data? Wow! What’s up with that? I would have thought those would have been found long ago.

With the obvious caveat that lower regions of that diagram feature harder to detect planets leading to that part being less populated than would be the case if all planets were detected, it would appear that there is a continuous abundance of planets from Earth-sized to Neptune-sized. While radius and mass may only be loosely related, it may also be that there is a continuous abundance of planets from Earth-mass to Neptune-mass, as well. Not having an example of such an intermediate planet in the Solar System, we really don’t know what to expect for what these planets are composed of. As such we began to call them (sometimes interchangeably) super-Earths or Mini-Neptunes. Are they enormous balls of rock with Earth-like composition extending up toward maybe 10 Me? Are they dominated by mass by a rocky core with a thick but comparatively low-mass hydrogen envelope? Do they have some fraction of rock, water and gas? Are they mostly entirely water with a minimal gas envelope? Answering this question would require some constraints on the masses of these planets, as it would allow one to know their density.

The first data point was CoRoT-7 b, the first transiting super-Earth — discovered before Kepler. The host star is very active, leading to a lot of disagreement in the literature about its mass, but further work seems to have settled on a rocky composition for the planet with ~5 Me. Great! Next data point was the transiting super-Earth orbiting GJ 1214, a ~6.5 Me planet with a much lower density, which is too low to be explained by even a pure water composition. This is decidedly not Earth-like. Additional measurements by highly precise spectrometers (namely HARPS and SOPHIE) of Kepler discovered planets have allowed for more data to be filled in, and an interesting trend can be seen.

Mass-Radius Diagram of Extrasolar Planets with RV-Measured Masses

Interestingly, planets less than ~1.6 Earth-radii seem to have not only solid, but Earth-like compositions. It’s worth noting that only planets where the mass measurement is acquired through Doppler spectroscopy are shown here. Planets like the Kepler-11 family where the masses have been derived by transit timing variations are not shown. If these planets are added, the adherence to the Earth-like composition is much less strict. This may imply that planets which have masses measurable by detectable transit timing variations have had a different formation history and therefore a much lower density. Further data will be very useful in addressing this issue.

On a somewhat unrelated topic, several new habitable planet candidates have been validated by ruling out astrophysical false positives. Among them is Kepler-442 b, which appears to me to be a more promising habitable planet candidate than even Kepler-186 f. Some newly discovered but not yet validated habitable planet candidates have been found as well, including one that appears to be a near Earth-twin.

New Kepler habitable planet candidates

## Habitable Value

Planets at Kapteyn’s Star (source)

Since the last post on this blog, there have been two additional habitable planet candidates announced. First, a two-planet system orbiting the very nearby, very old red dwarf Kapteyn’s Star was reported by Anglada-Escudé et al. The inner planet, the habitable zone world, at 4.8+0.9-1.0 ME is probably a mini-Neptune or micro-Jovian planet, based on its mass — the overwhelming majority of planets of this mass whose radii are known are clearly low-density worlds. The outer world is a cold super-Earth, and probably the same type of planet. Kapteyn’s Star is a member of the Galactic halo, and is quite ancient at ~11 Gyr old. The apparent fact that the Universe was assembling habitable planets when it was less than 3 Gyr old may have interesting implications for the Fermi Paradox, but I won’t go into that here.

Next is Gliese 832 c. In 2008, Bailey et al. reported the presence of a Jupiter-analogue orbiting the nearby red dwarf system GJ 832, and then last week, we learned of second planet, a super-Earth type planet straddling the inner edge of the habitable zone, reported by Wittenmyer, et al. It is almost certain that this planet is not habitable, certainly not to life “as we know it.” The planet’s mass comes in at 5.4±1.0 ME, and therefore likely a mini-Netune / micro-Jovian, much like Kapteyn’s Star b.

Then wandering through the news as I do on a daily basis, I found this

Note the description of the planet as “among the most habitable,” with artist images depicting oceans, lush green land, and so on, despite the description of the planet in the discovery paper as

However, given the large mass of the planet, it seems likely that it would possess a massive atmosphere, which may well render the planet inhospitable. Indeed, it is perhaps more likely that GJ 832c is a “super-Venus,” featuring significant greenhouse forcing.

And this was being generous! I personally thought the discovery of planets at Kapteyn’s Star was much more interesting than the discovery of GJ 832 c, but apparently news cycles have a different standard than I do as to what amounts to an interesting world. That standard, with respect to exoplanet discoveries, is the Earth Similarity Index (ESI) that the Planetary Habitability Laboratory uses to evaluate a planet’s habitability. A quick look at their site shows that, sure enough, GJ 832 c is the third most highly ranked exoplanet.

This is not the first time I have complained about the PHL. But this time I will instead work on providing an alternative method of evaluating a planet’s habitability. A child could look at the above diagram and tell you Kepler-186f was the most “Earth-like” of those planets based on their appearance, but to be rigorous and useful, we need a system to quantify a planet’s habitability. Let’s first look at how the ESI is determined.

$\displaystyle ESI=\prod_{i=1}^n\left(1-\left|\frac{x_i-x_{i_0}}{x_i+x_{i_0}}\right|\right)^\frac{w_i}{n}$

Where $x_i$ is the n-th property of the planet — in this case, either radius, density, escape velocity or surface temperature — $x_{i_0}$ is the value of this property for Earth, and $w_i$ is the weight exponent of a property. For the parameters usually used by the ESI, these values are

 Property Reference Weight Exponent Radius 1 $R_\oplus$ 0.57 Density 1 $\rho_\oplus$ 1.07 Escape Velocity 1 $V_{e_\oplus}$ 0.70 Surface Temperature 288 K 5.58

The formula I will use to evaluate the habitability of an exoplanet will be rather anthropocentric – for all I know, solid, hot super-Earth-type planets like Kepler-10 b may be the most frequently inhabited planets in the Galaxy, but all I know of is Earth-life, and so this formula will be centered around finding Earth-like life. It will effectively be based on Guassian distributions, and will take the form

$\displaystyle H = \prod_{i=1}^4 \frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{(x_i-\mu)^2}{2\sigma^2}\right)$

Here, μ acts as a reference value much as in the ESI formula, σ describes the broadening of the distribution and will effectively be used to determine the tolerance of variation on a particular parameter, and $x_i$ is the parameter we look at. As the product sign suggests, we calculate this for each of four parameters and multiply the results. Here, the four parameters are the stellar temperature, planet mass, planet radius, and planetary insolation.

For the stellar temperature, I chose σ=0.001 and μ=5500, which is some 277 K cooler than our sun. It seems that early K dwarfs are probably a sort of “sweet spot” for planet habitability. As such, if you found an Earth-analogue around an early K dwarf, it would rank higher on this scale than Earth itself. For the planetary mass and radii, I chose μ=1.0 for obvious reasons, and chose σ=5 and σ=0.75, respectively — punishing radius pretty heavily. Lastly, I chose insolation values of μ=1 and σ=1. All values of σ are in terms of that of Earth. Lastly, the values were normalised to make 1 the highest achievable value.

Unsurprisingly, the Solar System is the clear winner, followed by Kepler-186 f, which I made a big deal about earlier this year. The GJ 581 system, which was celebrated as hosting the first habitable planet candidates in the latter years of the last decade, doesn’t even make it up to 10-5, nor does GJ 832 c.

 Planet H Earth 0.96635 Venus 0.61220 Kepler-186 f 0.18525 Kepler-62 f 0.09104 Mars 0.04304 Kepler-62 e 0.00530 Kepler-283 c 0.00005 Kepler-296 Af 0.00003

I would say this set-up makes a lot more sense than the one the PHL is using. Anything below 0.1 is probably not worth a raised eyebrow these days.