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Kepler-138 Exoplanet System

Water worlds and a small Mars-mass planet around a red dwarf //

Kepler-138, also known as KOI-314, is a real system of four known exoplanets located 218.1 light-years away in the constellation Lyra. The host star Kepler-138 is a fairly young red dwarf between 1.0 to 2.7 billion years old. It possesses an M1V spectral type with ~0.5 solar masses and radii, corresponding to a surface temperature of 3835 K (3562 °C) and luminosity ~6% that of the Sun. Three exoplanets were confirmed around this star in 2014, followed by a fourth in 2022. In order of orbital distance, they are Kepler-138 b, c, d and e. The planets form a curious configuration that resembles a more compact version of the inner Solar System (Mercury, Venus, Earth, Mars) with the smallest, b, being followed by two larger twins c and d and then another small outer planet e.

Exploring this system sequentially, we first arrive at Kepler-138 b. It is an analogue of Mars and among the smallest exoplanets discovered so far with only 7% the mass of Earth and 64% our planet’s radius. The object hugs its star in a tight orbit, with a "year" lasting only 10.3 days. In contrast to the cold and barren Mars, Kepler-138 b is suggested to have a hot and thick envelope on top of a rocky interior. Whether this layer is in the form of water or other gases is yet to be determined, but it is unlikely to be made of hydrogen as such lightweight elements would have been swiftly lost to the stellar wind.

The next two bodies Kepler-138 c and d are twin super-Earths. They are around 50% larger than our home planet at 2.3 and 2.1 times the mass. The duo were initially considered strikingly different with c being thought of as rocky and d having high volatile content like a miniature gas giant. A recent study instead suggests that they are both ocean worlds with 2000-km-deep water mantles. Water is believed to comprise 9% and 11% of their respective total mass—equal to an astonishing volume of ~1000 Earth oceans. However, the planets' orbital periods of 13.8 and 23.1 days are too short to be in the habitable zone. These oceans might more so resemble steam cookers than anything that could harbour life.

The last planet Kepler-138 e follows a slightly eccentric 38.2-day orbit at the inner edge of the habitable zone. With a mass of 0.43 Earths, it stands as an intermediate between Mars and Venus. Not much else is known about this object given the recency of its discovery, but it is probably larger than b and smaller than c/d.

This simulation replicates the Kepler-138 system from real data wherever possible, but select design choices or fictional elements may be incorporated due to knowledge gaps:

• Precise properties of the host star Kepler-138 are debated, with estimates of 0.52–0.59 solar masses and 0.442–0.582 solar radii. This simulation uses the values provided by the discoverers of Kepler-138 e on account of this being the most recent study on the system.
  
• The article that suggests a thick envelope around Kepler-138 b lists its mass as 0.187 Earths. This is more than double the current estimate of 0.07 Earths. If the latter is correct and planet b is indeed a lower-mass object, it may be less likely to retain this envelope. Nevertheless, this simulation imagines a Venus-like world with a runaway greenhouse effect.
  
• While Kepler-138 c and d are most likely water worlds, they are probably not "hycean" planets[en.wikipedia.org]—oceanic super-Earths with significant amounts of hydrogen. For instance, planet d cannot have more than 0.01% hydrogen by mass if it were to match its observed radius. Any hydrogen will also be vulnerable to mass loss over a 10-million-year timescale, which is much shorter than the system’s estimated age of >1 billion years. Thus, I have elected to use only limited amounts of hydrogen in their composition.
  
• The true size of Kepler-138 e is unknown. Assuming an Earth-like composition, Universe Sandbox models its radius at 0.782 times Earth's. Given the apparent abundance of water in this system, I’ve imagined the planet as an ashy and volcanically-active marine world, with clusters of archipelagos and calderas jutting out above the waves.
  
• Per the above design choices, planet classifications in this simulation are as follows: Kepler-138 b, hot arid sub-Terra; Kepler-138 c/d, warm superoceanic super-Terra(s); Kepler-138 e, temperate marine Terra.

A special mention to @Gluestick_55 for requesting this system.



2MASS J19213157+4317347, Kepler-138, KOI-314, Gaia DR3 2102053446751282944, AP J19213157+4317347, KIC 7603200, TIC 159376971, Gaia DR2 2102053446751282944

• Almenara, J.M., Diaz, R.F., Dorn, C., Bonfils, X. and Udry, S., 2018. Absolute densities in exoplanetary systems: photodynamical modelling of Kepler-138. Monthly Notices of the Royal Astronomical Society, 478(1), pp.460-486.
  
• Jontof-Hutter, D., Rowe, J.F., Lissauer, J.J., Fabrycky, D.C. and Ford, E.B., 2015. The mass of the Mars-sized exoplanet Kepler-138 b from transit timing. Nature, 522(7556), pp.321-323.
  
• McQuillan, A., Mazeh, T. and Aigrain, S., 2013. Stellar rotation periods of the Kepler objects of interest: A dearth of close-in planets around fast rotators. The Astrophysical Journal Letters, 775(1), p.L11.
  
• Piaulet, C., Benneke, B., Almenara, J.M., Dragomir, D., Knutson, H.A., Thorngren, D., Peterson, M.S., Crossfield, I.J., M.-R. Kempton, E., Kubyshkina, D. and Howard, A.W., 2023. Evidence for the volatile-rich composition of a 1.5-Earth-radius planet. Nature Astronomy, 7(2), pp.206-222.
  
• Souto, D., Cunha, K., García-Hernández, D.A., Zamora, O., Prieto, C.A., Smith, V.V., Mahadevan, S., Blake, C., Johnson, J.A., Jönsson, H. and Pinsonneault, M., 2017. Chemical Abundances of M-Dwarfs from the Apogee Survey. I. The Exoplanet Hosting Stars Kepler-138 and Kepler-186. The Astrophysical Journal, 835(2), p.239.