Observational constraints on the existence of a KBP based on our best models. The apparent visual magnitudes were estimated for a KBP with m = 1.5 M _⊕ (blue curves) and m = 3 M _⊕ (cyan curves). The results are shown for an assumed albedo of 0.1 (straight curves) and 0.3 (dashed curves). In all cases, a mean density of 2 g cm⁻³ was assumed for the KBP (assuming that 3 g cm⁻³ leads to ∼0.°3 darker magnitudes). The variation in heliocentric distance is also indicated by gray bars at the bottom for three hypothetical orbits with q _P = 195 au and a _P = 250, 350, and 500 au. Finally, the apparent sky motion is indicated by the brown curve. See Section 3. for details.