Predicting the Properties of Planet Nine

The strange clustering observed for the orbits of a class of trans-Neptunian objects in the outer solar system suggests that a massive planet with ~10 times the mass of Earth might exist in the outer solar system, a few hundred times further from the Sun than Earth. This hypothesised planet has been referred to as Planet Nine. Linder & Mordasini (2016) present models on the evolution and properties of Planet Nine.

Figure 1: Artist's impression of a planet that orbits far from its host star.

In the models, Planet Nine is assumed to have the same basic structure as Uranus and Neptune. It is also assumed to have 10 times the mass of Earth and it orbits the Sun at an average distance of 700 AU. The planet's core and envelope masses are 8.6 and 1.4 times the mass of Earth, respectively. The envelope is comprised of hydrogen and helium, while the composition of the planet's core is 50 percent water-ice, 33.3 percent silicates and 16.7 percent iron.

Given these properties, the present temperature of Planet Nine is estimated to be 43 K, far above the equilibrium temperature of about 10 K at 700 AU. This means that the planet's energy budget is dominated by the planet own emission and not by energy from the Sun. The planet's emission is largely driven by cooling and contraction of the planet's core. Also, the planet's present intrinsic luminosity is estimated to be ~0.006 times the intrinsic luminosity of Jupiter, and its present size is 3.66 times the diameter of Earth.

Figure 2: Evolution of the radius of a planet with 10 times the mass of Earth at 700 AU. The planet is comprised of an envelope of hydrogen and helium totalling 1.4 times the mass of Earth, and a core that is made up of 50 percent water-ice, 33.3 percent silicates and 16.7 percent iron. Linder & Mordasini (2016)

Figure 3: Evolution of the effective temperature for the same planet. Linder & Mordasini (2016)

Figure 4: Evolution of the intrinsic luminosity for the same planet. Linder & Mordasini (2016)

Suppose Planet 9 is a super-Earth instead of a planet like Uranus and Neptune. At 10 times the mass of Earth, but without an envelope of hydrogen and helium, Planet Nine is expected to have 1.9 times the diameter of Earth and a lower effective temperature of 38 K. The smaller size and lower temperature would give the planet a much lower intrinsic luminosity and hence make it much more difficult to detect than if it were more like Uranus and Neptune.

Suppose Planet Nine is similar to Uranus and Neptune, but instead of being 10 times the mass of Earth, the planet is 5, 20 or 50 times the mass of Earth. For these masses, the present intrinsic luminosities are ~0.0018, ~0.016 and ~0.078 times the intrinsic luminosity of Jupiter; the present effective temperatures are 40 K, 54 K and 69 K; and the present sizes are 2.92, 4.62 and 6.32 times the diameter of Earth, respectively.

Reference:
Linder & Mordasini (2016), "Evolution and Magnitudes of Candidate Planet Nine", arXiv:1602.07465 [astro-ph.EP]