Evolution and magnitudes of candidate Planet Nine

Abstract

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 different 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 efficiency 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 effective 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 L . 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 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 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.

Some physical properties predicted for the putative Planet Nine of the solar system

“…At aphelion, that is, at orbital phase 0.5, the lowest brightnesses are 23.19 and 25.52 mag in R band. Very recently, Linder & Mordasini (2016) explored the magnitude evolution of candidate P9, and our results agree with their results. Despite its faintness, a search with eight-meter class large ground-based telescopes, for example, with the Subaru telescope, may have a chance to find P9 in the near future.…”

Finding Planet Nine: apsidal anti-alignment Monte Carlo results

“…The goal of ⋆ E-mail: carlosdlfmarcos@gmail.com this analytically and numerically supported conjecture is not only to explain the observed clustering in physical space of the perihelia and the positions of the orbital poles of seven ETNOs (see Appendix A for further discussion), but also to account for other, previously puzzling, pieces of observational evidence like the existence of low perihelion objects moving in nearly perpendicular orbits. The Planet Nine hypothesis is compatible with existing data (Cowan, Holder & Kaib 2016;Fienga et al 2016;Fortney et al 2016;Ginzburg, Sari & Loeb 2016;Linder & Mordasini 2016) but, if Planet Nine exists, it cannot be too massive or bright to have escaped detection during the last two decades of surveys and astrometric studies (Luhman 2014;Cowan et al 2016;Fienga et al 2016;Fortney et al 2016;Ginzburg et al 2016;Linder & Mordasini 2016). A super-Earth in the sub-Neptunian mass range is most likely and such planet may have been scattered out of the region of the Jovian planets early in the history of the Solar system or even captured from another planetary system (Li & Adams 2016;Mustill, Raymond & Davies 2016); super-Earths may also form at 125-750 au from the Sun (Kenyon & Bromley 2015, 2016.…”

“…Here, we apply the Monte Carlo approach (Metropolis & Ulam 1949) Ginzburg et al (2016) and Linder & Mordasini (2016) strongly disfavour a present-day Planet Nine located at perihelion and they do not discard the aphelion which is also favoured in .…”

Evolutionary models of cold and low-mass planets: cooling curves, magnitudes, and detectability

“…As described in Mordasini et al (2012b), the calculation of evolutionary sequences in our model is based on the fundamental relation between the change of the total energy of the planet, and its luminosity because of energy conservation, dE tot /dt = −L (for other energy based approaches, see Leconte & Chabrier 2013;Piso & Youdin 2014). In previous versions of our planet evolution model (except for Linder & Mordasini 2016), the thermal energy of the core was, however, neglected. As the second modification of the code, we include it here, considering both the isothermal and adiabatic case.…”