## 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

As anyone with any contact to the outside world knows, the planet Venus transited its own star as seen from our perspective this week. The only thing separating this from being nearly identical to an exoplanet (aside from the obvious difference in distance) is that as Earth orbits the same star, our perspective keeps changing, denying us the ability to observe a transit every Venusian revolution (there are also some issues with the differences in the inclinations between the two orbits that play a vital role in making this an uncommon phenomenon for us).

The above image, taken by the JAXA/NASA Hinode spacecraft shows for Venus what happens essentially each time an exoplanet transits its star. The Kepler spacecraft watches thousands of planets do this, but not quite as dramatically, for Kepler cannot resolve the discs of its 150,000 target stars, and instead has to rely on the characteristic dimming of the star as the planet blocks some of the star’s light.

Notice the entire limb of the planet is visible, even the part that is not yet over the solar disc. Sunlight is passing through the Venusian atmosphere and is scattered every which way, some of it reaching us for us to observe. The colour of the sunlight will be changed as it filters through the atmosphere, just like on Earth where our atmosphere turns sunsets and sunrises red. This is exactly what is observed from Earth when we determine the compositions of extrasolar planet atmospheres through transmission spectroscopy.

## Dancing in the Dark

Epislon Eridani, the nearest known planet-hosting star other than the sun.

The motion of a star around the barycentre of a planetary system is not necessarily confined to detectability through indirect methods only. The barycentric motion of a star in a planetary system can, with sufficient precision, be directly observed. Logically, the larger the star’s barycentric semi-major axis, the more easy it would be to observe such a motion. However very long, multi-decade period orbits are harder to observe simply because they progress at timescales comparable to the human lifespan. As such, astrometry is biased toward intermediate-period, massive planets.

Often, the barycentric motion of a star will be tiny. Our sun being an example rarely diverges from two solar-radii from the Solar System barycenter. Across the extreme distances, these changes are difficult to resolve, leading to large error bars that can swamp out the real orbital motion. For this reason, it is often the case that a large number of measurements are required to build up confidence in the detection of an astrometric signal, much as with the Doppler spectroscopy method.

While the above plot is messy, it makes clear that the stellar orbit is far from face-on. It gives us a rough measurement of the stellar orbit’s inclination.

The advantages of astrometry justify the difficulty in performing it for planetary systems. By directly observing the barycentric motion of a star, it is possible to reconstruct the orbit of the orbiting planet fully in 3D (while distinguishing which node is the ascending node, $\it{\Omega}$, will require a combination of astrometric and radial velocity data). Because astrometry provides the full 3D orbit, the inclination may be measured and thus the true mass of the planet is found, resolving the inclination degeneracy that plagues Doppler spectroscopy.

Because the star is not the only thing in motion, some work is needed before jumping into searching for exoplanet-induced astrometric signals. Firstly, the proper motion (the natural drift of the position of the star in the sky as the result of each star’s independent galactocentric orbit) of the star must be modelled out. Additionally, the orbital motion of Earth around the Sun will cause another signal in the astrometric data that must be modelled out. After this is done, whatever remains must be the intrinsic motion of the star under the influence of other bodies.

To give some idea of comparison, from “above” the solar system, the sun’s astrometric signal would look like this.

The large yellow circle represents the diameter of the sun, and the black line is the path it takes, due to the influence of the planets in our solar system. Jupiter and Saturn dominate the astrometric signal. The other planets aren’t detectable in this timespan. Notice that the amplitude of the astrometric variation is comparable to the diameter of the star itself. More specifically, for a star with a distance$D$and a single orbiting companion, the astrometric amplitude can be estimated as

$\displaystyle \alpha = \arctan{\left( \frac{a * q}{D(q+1)} \right)}$

where q is the mass ratio between the planet and the star$M_p / M_*$, and a is given as

$\displaystyle a = (G(M_* + M_p))^{1/3} (P/2 \pi)^{2/3}$

The need for precision thus makes itself apparent. So far, very few extrasolar planets have been detected this way. On the positive side, radial velocity candidates whose true masses are significantly higher than their RV-derived minimum mass have larger than expected amplitudes. This makes astrometry quite effective at determining if exoplanet candidates are actually low mass or even main sequence stars. In most cases, astrometry can set an upper limit to the astrometric amplitude, which translates directly into an upper limit for the planet’s mass. This can permit even a non-detection to secure the planetary nature of a candidate extrasolar planet.

## Bulk Properties of the Planets

Even without going outside our solar system, we can take a look at the eight that are well known to even our children and get a preliminary grasp on the types of the planets that we can expect to find throughout the Universe. Looking at the graphic above, which has the size of our planetary system’s members to scale (but not their separations from each other), we readily note that the planets available to use for close study assume a wide variety of appearances and sizes. Furthermore, they visually seem to fall into two or three different classifications. Let’s take a more quantitative approach to comparing these planets.

The planets that we are most intuitively familiar with are the smallest members of the planetary zoo. They are the terrestrial planets, and are composed of rock and metal, silicates and iron. They have high densities and sudden phase transition boundaries between states of matter separating their solid and gaseous components (which we might call a “surface”). For our solar system, this corresponds to the planets Mercury, Venus, Earth and Mars.

Because Earth is the most massive representative of this type of planet that we have available to us for study, terrestrial planets of ~Earth-mass are generally called “Earth-like,” but this similarity is in bulk composition alone, and is not to imply habitability. The term is loose enough that even the infernally hellish Venus would fit the description. It’s important to remember that the differences between Earth and Venus are “skin-deep” so to speak. That which makes the two planets so different is confined to a thin layer of gases clinging onto their surfaces, and is a negligible fraction of the planet’s total mass. Planets that are more massive than Earth, typically about twice the mass of Earth and above, are called “super-Earths,” but the term is a loose one.

Being the prototypical terrestrial planet, the mass of Earth defines one of the more commonly used mass measurements. One “earth-mass,” $M_\oplus$, is a mass unit of mass equivalent to the mass of Earth.

Moving further out in the Solar System, we find the gas giant planets Jupiter and Saturn.

The Bulk Composition of the Gas Giants by Mass

These planets are those who have the majority of their mass in the form of “gases,” or at least those elements labelled so on the Periodic Table. As the depth into the planet increases, the atmospheric pressure increases considerably. Deep within the planet, the pressure is great enough that the gas slowly transitions into a liquid, with exotic properties that generate enormously powerful magnetospheres. At their centre may exist a core of solid material of several Earth-masses.

As a planet-forming disk evolves, it’s composition will change such that the gas-to-dust ratio drops until all of the gas has either fallen into the star, been accreted by planets, or pushed out of the planetary system through the radiation pressure of sunlight from the star. Therefore, planets that form first will more closely resemble the composition of the disk where they were formed. We can tell therefore that Jupiter formed first as its composition most closely resembles not only the sun, but that of the protoplanetary disk out of which it formed as well. In the case of gas giants, large solid cores of several Earth-mass grow in size until they begin runaway accretion of hydrogen from the disk (this typically occurs at a mass of ~10$M_\oplus$). Furthermore, Saturn formed later, as is evidenced by the lower gas-to-rock fraction.

Jupiter is the most massive example of this class of planets in our Solar system and therefore sets another unit of mass, the “Jupiter-mass,”$M_J$, roughly equal to 318$M_\oplus$,

Further out in the Solar system lie the planets that formed later, and had access to only the scraps of what was left of the hydrogen and helium in the disk. Their compositions are dominated by the ices that condensed out of the volatiles in the disk. These planets are called the “ice giants,” and are represented by Uranus and Neptune.

Bulk Composition of the Ice Giants by Mass

Like the gas giants, their atmospheres get thicker with depth but they reach a boundary that is more compositional than arising from a state of matter, where the composition goes from an H-He envelope to an icy mantle, likely dominated by water ice with other volatiles (ammonia, methane, etc). There is likely not a quick phase transition between corresponding to a surface on such planets.

Neptune is the most massive of these planets in our Solar System, and is thus the prototypical “Neptune-like planet.” A unit of mass based off Neptune can obviously be conceived, but it is not used much in practice. With Neptune having a mass of ~17$M_\oplus$, the masses for these planets are usually expressed in terms of$M_\oplus$or$M_J$.

When the masses and radii of the Solar System planets are plotted, they group fairly nicely sorted by their type.

Mass-Radius Diagram for the Solar System

In an upcoming post, we’ll look at doing this for extrasolar planets to see how our solar system fits into the range of extrasolar planet masses and radii and how well these neat cookie-cutter categories hold up in the wealth of examples of extrasolar planets with measured masses and radii to date.