Evolution and magnitudes of candidate Planet Nine

Linder, Esther; Mordasini, Christoph (2016). Evolution and magnitudes of candidate Planet Nine. Astronomy and astrophysics, 589(A134), A134. EDP Sciences 10.1051/0004-6361/201628350

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Context. The recently renewed interest in a possible additional major body in the outer solar system prompted us to study the thermodynamic evolution of such an object. We assumed that it is a smaller version of Uranus and Neptune.
Aims. We modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the blackbody spectrum of distant ice giant planets. The aim is also to provide estimates of the magnitudes in di↵erent bands to assess whether the object might be detectable.
Methods. Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 M that are located at 280, 700, and 1120 AU from the Sun. The core composition, the fraction of H/He, the e ciency of energy transport, and the initial luminosity were varied. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity.
Results. We find for a nominal 10 M planet at 700 AU at the current age of the solar system an e↵ective temperature of 47 K, much higher than the equilibrium temperature of about 10 K, a radius of 3.7 R , and an intrinsic luminosity of 0.006 LX. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.4, 21.0, 20.1, 19.9, and 10.7, and WISE W1-W4 magnitudes of 20.1, 20.1, 18.6, and 10.2. The Q and W4 band and other observations longward of about 13 μm pick up the intrinsic flux.
Conclusions. If candidate Planet 9 has a significant H/He layer and an e cient 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 aphelion, we estimate for a mass of 5, 10, 20, and 50 M a V magnitude from the reflected light of 24.3, 23.7, 23.3, and 22.6 and a Q magnitude from the intrinsic radiation of 14.6, 11.7, 9.2, and 5.8. The latter would probably have been detected by past surveys.

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