2016A&A...592A..86T

Context. Nothing is known as yet about the physical properties of the putative Planet Nine (P9), which is hypothesized to orbit at the fringes of the solar system. Two groups of observers are using the eight-meter Subaru telescope to search for P9. Early estimates and predictions are important to characterize this hypothetic planet. We here predict some properties to compare them with the observed physical properties when Planet Nine has been unambiguously detected comparisons between the predicted and observed physical properties.
Aims. We estimate the size, apparent observable brightness, shortest rotation period, and extension of the stable orbital region of possible satellites of P9.
Methods. Using the predicted mass and adopting a possible mean bulk density range of P9, we computed its radius and assumed a domain for its geometric albedo. We then determined the apparent magnitude along its elliptic orbit. By testing different plausible physical models of a sub-Neptune class planet, we estimated the regions of stability and destruction versus rotational breakup in the radius-rotational period plane. In this plane the shortest rotational period is constrained by the possible size range of P9 and the separation curves. We applied quantitative measures of the stability domain of possible satellites orbiting P9 to quantify the search region in which to find possible satellite companions of the putative trans-Neptunian giant planet of our solar system.
Results. Its predicted apparent magnitude even near aphelion allows discovering P9 with eight-meter class telescopes. P9 is stable against rotational breakup for stronger material if the period is longer than ∼6h, and for weaker material if the period is longer than ∼13h. The Szebehely stability domain for possible satellites of the hypothetical P9 is very large: for a small satellite it extents to ∼1.7au from the planet, and the longest orbital period of the satellite in this orbit is ∼396yr. For a possible twin planet configuration, the radius of the Szebehely stability domain is 1.3au and the corresponding orbital period is ∼280yr. A twin planet would be brighter by about 0.25mag than a single planet.