Mega-Earths and Chthonian Planets

Over the years, the search for exoplanets has shown that exoplanets vary enormously in size, mass, composition, and nearly every conceivable parameter. Many of the discoveries were surprising and unexpected. Even so, rocky planets are not known to exceed ~10 times the mass of Earth. It is believed that a more massive rocky planet would have such an enormous gravitational pull that it would accrete a gas envelope during formation and end up either as an ice giant like Neptune or a gas giant like Jupiter. All that changed when Dumusque et al. (2014) reported the discovery of the first bona fide rocky planet with a mass exceeding 10 times the mass of Earth. “We were very surprised when we realized what we had found,” says astronomer Xavier Dumusque of the Harvard-Smithsonian Center for Astrophysics, who led the data analysis and made the discovery.

 Figure 1: Artist’s impression of a large rocky planet.

Kepler-10 is a Sun-like star located 560 light years away in the constellation of Draco. It hosts two transiting planets - Kepler-10b and Kepler-10c. Both planets were detected by NASA’s Kepler space telescope and their discoveries were announced in 2011. Based on how much light from its parent star each transiting planet blocks, Kepler-10b is estimated to be 1.47 times the Earth’s diameter, while Kepler-10c is 2.35 times the Earth’s diameter. The orbital periods of Kepler-10b and Kepler-10c are 20.1 hours and 45.3 days, respectively. It is clear from the orbital periods that both planets are rather close-in to their parent star, especially Kepler-10b. The equilibrium temperature on Kepler-10b is a searing 2169 K, while the equilibrium temperature on Kepler-10c is a far cooler 584 K, albeit still a few times the boiling temperature of water.

Kepler-10b is actually the first confirmed rocky planet to be discovered outside the Solar System. With its aforementioned size and a measured mass of 3.33 ± 0.49 Earth-masses, Kepler-10b has a density of 5.8 ± 0.8 g/cm³. For comparison, the density of Earth is 5.515 g/cm³. However, the mass of the second planet, Kepler-10c, remains unknown until Dumusque et al. (2014) used the HARPS-North instrument on the Telescopio Nazionale Galileo in the Canary Islands to measure the gravitational “tugging” Kepler-10c exerts on its parent star. The mass of Kepler-10c turns out to be 17.2 ± 1.9 Earth-masses. With its size and mass known, the density of Kepler-10c is 7.1 ± 1.0 g/cm³, making it the first confirmed rocky planet with more than 10 times Earth’s mass.

Kepler-10c is clearly an outlier in the mass-radius diagram (Figure 4). Its bulk composition is dominated by rocky material (i.e. silicates) and a significant amount of water amounting to between 5 to 20 percent of the planet’s mass. Most of the water is expected to be in the form of exotic high-pressure ices. Moreover, the host star of Kepler-10c is an old star that formed 10.6 billion years ago, when the universe was only 3 billion years old. Back then, heavy elements such as the iron and silicon required to form rocky planets were less common. The discovery of Kepler-10c shows that rocky planets can readily form early in the universe’s history. This is favourable for life since Earth itself is a rocky planet.

The news release by the Harvard-Smithsonian Center for Astrophysics calls Kepler-10c a “mega-Earth”. This is because Kepler-10c is well above the upper limit of 10 Earth-masses that is commonly used for the term “super-Earth”. Besides, the term “mega-Earth” seems to have caught on pretty well. It is likely that Kepler-10c is the first bona fide example of a population of rocky planets with masses exceeding 10 times the mass of Earth. Another planet, Kepler-131b, lies around the same location on the mass-radius diagram as Kepler-10c (Figure 4). However, the mass of Kepler-131b is not known accurately enough to confirm whether it is indeed a rocky planet. Kepler-131b has a mass of 16.1 ± 3.5 Earth-masses and 2.4 ± 0.2 times the Earth’s diameter.

Figure 2: Transit light curves of Kepler-10b (left) and Kepler-10c (right) along with the best-fit models. Dumusque et al. (2014).

 Figure 3: Radial velocity curves of Kepler-10b (left) and Kepler-10c (right). The radial velocity data shows how much gravitational tugging each planet exerts on its host star and so allows the mass of each planet to be estimated. Dumusque et al. (2014).

Figure 4: Mass-radius diagram for planets smaller than 4 Earth-radii and that present a mass determination better than 30 percent. The only exception are the planets from the Kepler-11 planetary system that are shown here because they have raised the issue that there may be planets with extended envelopes of hydrogen and helium even at masses less than 5 times the Earth’s mass. Filled symbols are used when the precision on the mass is better than 20 percent, highlighting measurements where an in-depth analysis of the planet composition can be done. On the mass-radius diagram, Kepler-10c is the only high-density planet more massive than 10 Earth-masses for which the precision in mass is better than 20 percent. Dumusque et al. (2014).

Enormously massive rocky planets can also form from the remnant cores of evaporated gas giant planets. This class of planets was proposed by Hebrard et al. (2003) and are called “Chthonian” planets. A gas giant planet that is in a close-in orbit around its parent star (i.e. a hot-Jupiter) can experience sufficient heating and tidal forces that can cause its layers of hydrogen and helium to be stripped away, leaving behind a remnant rocky core. Although a gas giant planet’s rocky core generally makes up only a small fraction of the planet’s total mass, it can still be up to tens of Earth-masses, and possibly more. At such close proximity to its parent star, a Chthonian planet is most probably tidally-locked, with a permanent dayside and nightside. The planet’s dayside would be a blistering inferno and the glare from its illuminated surface would be blinding, hundreds of times brighter than desert sands at noontime on Earth. A lava ocean and possibly even pools of molten metal may be present on the hellish dayside.

Observations from NASA’s Kepler space telescope have turned up three planets that could be Chthonian planets. The three planets, Kepler-52b, Kepler-52c and Kepler-57b, have maximum masses between 30 and 100 times the mass of Earth, as determined via transit timing variations (TTVs) by Steffen et al. (2012). Nevertheless, the planets are each only around twice Earth’s diameter. If their true masses are indeed close to their estimated maximum masses, then their densities would be larger than an iron planet of the same size. These high-density planets could represent the naked cores of gas giant planets that have lost their hydrogen-helium layers. After the formation of a gas giant planet, its stupendous layers of hydrogen and helium “crushes” the central solid core under extraordinarily high pressures, compressing the solid core to higher densities. The results from a study by Mocquet at al. (2014) show that the solid core left behind following the evaporation of a gas giant planet can remain in its compressed state for billions of years.

Figure 5: Artist’s impression of a gas giant planet.

 Figure 6: Artist’s impression of a high-density solid planet.

A study by Seager et al. (2007) suggests that massive O and B stars with 5 to 120 times the mass of the Sun can have very hefty protoplanetary disks containing large amounts of heavy elements. The strong UV radiation and stellar winds from these stars can photo-evaporate the volatiles from their protoplanetary disks, leaving only the solid material behind. As a result, massive solid planets with hundreds to thousands of times Earth’s mass may be able to form around these massive stars. The gravity on the surface of such a rocky behemoth can be crushingly huge. For example, a rocky planet with an Earth-like composition but with 1000 times the Earth’s mass would be ~3 times the Earth’s diameter and would have a surface gravity ~100 times stronger than on Earth (Figure 8).

Figure 7: Artist’s impression of a rocky planet.

 Figure 8: Mass-radius relationships for solid planets. The solid lines are homogeneous planets. From top to bottom the homogeneous planets are: hydrogen (cyan solid line); a hydrogen-helium mixture with 25% helium by mass (cyan dotted line); water-ice (blue solid line); silicate (MgSiO3 perovskite; red solid line); and iron (Fe; green solid line). The non-solid lines are differentiated planets. The red dashed line is for silicate planets with 32.5% by mass iron cores and 67.5% silicate mantles (similar to Earth) and the red dotted line is for silicate planets with 70% by mass iron core and 30% silicate mantles (similar to Mercury). The blue dashed line is for water planets with 75% water-ice, a 22% silicate shell and a 3% iron core; the blue dot-dashed line is for water planets with 45% water-ice, a 48.5% silicate shell and a 6.5% iron core (similar to Ganymede); the blue dotted line is for water planets with 25% water-ice, a 52.5% silicate shell and a 22.5% iron core. The blue triangles are Solar System planets: from left to right Mars, Venus, Earth, Uranus, Neptune, Saturn, and Jupiter. The magenta squares denote the transiting exoplanets. Note that electron degeneracy pressure becomes important at high mass, causing the planet radius to become constant and even decrease for increasing mass. Seager et al. (2007).

References:

- Dumusque et al. (2014), “The Kepler-10 planetary system revisited by HARPS-N: A hot rocky world and a solid Neptune-mass planet”, arXiv:1405.7881 [astro-ph.EP]

- Hebrard et al. (2003), “Evaporation rate of hot Jupiters and formation of Chthonian planets”, arXiv:astro-ph/0312384

- Steffen et al. (2012), “Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations”, arXiv:1201.5412 [astro-ph.EP]

- Mocquet at al. (2014), “Very high-density planets: a possible remnant of gas giants”, Philosophical Transactions of the Royal Society A, Volume 372, No. 2014

- Seager et al. (2007), “Mass-Radius Relationships for Solid Exoplanets”, arXiv:0707.2895 [astro-ph]