Evolution and Magnitudes of Candidate Planet Nine
Linder et al
Given the recently renewed interest in a possible additional major body in the outer Solar System, the thermodynamic evolution of such an object was studied, assuming that it is a smaller version of Uranus and Neptune. Aims. We have modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the black body spectrum of distant ice giants. The aim is to provide also estimates of the magnitudes in different bands to assess the object's detectability.
Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 Mearth containing 10, 14, 21, and 37 % H/He in mass that are located at 280, 700, and 1120 AU from the Sun. The core composition was varied from purely rocky to purely icy as well as 50% rock and 50% ice. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity.
We find for the nominal 10 Mearth planet at 700 AU at the current age of the Solar System an effective temperature of 47 K, much more than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth, and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.2, 20.8, 20.1, 19.7, and 11.4, and WISE W1-W4 magnitudes of 20.1, 20.0, 19.5, and 10.4. The Q and W4 band and other observation longward of ~13 microns pick up the intrinsic flux.
If candidate Planet 9 has a significant H/He layer and an efficient energy transport in the interior, then its luminosity is dominated by the intrinsic contribution, making it a self-luminous planet. At a likely position on its orbit near the aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth a V magnitude from the reflected light of 24.2, 23.7, 23.2, and 22.5 and a Q magnitude from the intrinsic radiation of 15.6, 12.4, 9.8, 6.2. The latter would probably have been detected by past surveys.