Figure 1: Artist’s impression of a rocky planet.
Located roughly 200 light years from Earth, Kepler-138 is a red dwarf star that is much fainter and cooler than the Sun. Observations by NASA’s Kepler space telescope have led to the detection of three planets circling Kepler-138. The three planets were detected using the transit technique and are identified as Kepler-138 b, Kepler-138 c and Kepler-138 d. When a planet passes in front of (i.e. transits) its parent star, it causes a slight drop in the observed brightness of the star, allowing the size of the planet to be measured. Additionally, the interval between consecutive transits is the planet’s orbital period. The transit technique allows the sizes and orbital periods of the planets around Kepler-138 to be determined.
In a multi-planet system, gravitational perturbations between neighbouring planets can cause the transit timing for each planet to vary. This effect is particularly sensitive to planets that are closely spaced or near orbital resonances. The three planets around Kepler-138 are in orbital resonances and exhibit observable transit timing variations (TTV). Kepler-138b and Kepler-138c orbit near the 4:3 resonance (i.e. Kepler-138 b completes 4 orbits for every 3 orbits of Kepler-138 c); while Kepler-138 c and Kepler-138 d orbit near the 5:3 resonance (i.e. Kepler-138 c completes 5 orbits for every 3 orbits of Kepler-138 d).
Figure 2: TTV signals of the three planets orbiting Kepler-138. (a) TTV of Kepler-138 b; (b) TTV of Kepler-138 c; (c) TTV of Kepler-138 d. Jontof-Hutter et al. (2015).
Figure 3: Mass-radius diagram of well characterized planets smaller than 2.1 Earth radii. Prior exoplanet characterizations and 1σ uncertainties are shown as grey points. Black points from left to right are Mercury, Mars, Venus and Earth. Red data points are the results for the planets of Kepler-138. Open circles mark previously measured masses for Kepler-138 c and Kepler-138 d. Error bars mark published 1σ uncertainties for the planets of Kepler-138, and masses and radii of all other characterized exoplanets within this size range. The curves mark bulk densities of 1 g/cm³, 3 g/cm³ and 10 g/cm³. Jontof-Hutter et al. (2015).
Measuring the TTV signals allows the masses of the three planets around Kepler-138 to be estimated. By knowing the mass and size of a planet, it allows the planet’s density and its bulk composition to be determined to see whether the planet is predominantly made up of rock, water or gas. Here are the properties of the three planets around Kepler-138:
- Kepler-138 b has an orbital period of 10.3 days, 0.522 times the Earth’s radius, 0.066 times the Earth’s mass, a density of 2.6 g/cm³ and it receives an incident stellar flux that is 6.81 times what Earth gets from the Sun.
- Kepler-138 c has an orbital period of 13.8 days, 1.197 times the Earth’s radius, 1.970 times the Earth’s mass, a density of 6.2 g/cm³ and it receives an incident stellar flux that is 4.63 times what Earth gets from the Sun.
- Kepler-138 d has an orbital period of 23.1 days, 1.212 times the Earth’s radius, 0.640 times the Earth’s mass, a density of 2.1 g/cm³ and it receives an incident stellar flux that is 2.32 times what Earth gets from the Sun.
Kepler-138 b, the innermost of the three planets around Kepler-138, is roughly the same size as Mars and its density is also consistent with a rocky composition like Mars. With less than one-tenth the Earth’s mass, Kepler-138 b is currently the lightest known exoplanet with a measured mass. The two outer planets, Kepler-138 c and Kepler-138 d are both similar in size to Earth. However, Kepler-138 c and Kepler-138 d have very different densities. Kepler-138 c has a high density which indicates a rocky composition, while the density of Kepler-138 d is less than half of Earth’s and suggests that a large portion of its composition is in the form of low density materials such as water or hydrogen. All three planets around Kepler-138 receive much more incident stellar flux than Earth gets from the Sun and are too hot to be habitable.
Jontof-Hutter et al., “The mass of the Mars-sized exoplanet Kepler-138 b from transit timing”, Nature 522, 321-323 (18 June 2015)