Hypothetical trans-Neptunian planets orbiting the Sun The planet HD 106906 b was found at 650 AU from its home star, a star not so different from the Sun. Fomalhaut b is also a young planet that is orbiting very far away from its star.

These two planets were discovered mainly because they are young enough to still be hot enough to be seen in the infrared. I think that old planets in very high orbits would have temperatures below 10K, and thus be black and invisible.

Some people agree with the hypothesis that, in our Solar System, somewhere out beyond Neptune, some non-dwarf planets might be orbiting the Sun. The existence of HD 106906 b and Fomalhaut b suggests that this is possible. What are the odds that we could find at least one of these planets in our Solar System? If they do exist, how could we find them?
If such a planet exists, WISE should observe it. WISE is an infrared satellite that imaged the entire sky. In particular:


it was able to detect anything with a temperature above 70-100 K, whereas the coolest known exoplanets are in the 100 K range (see histogram below, taken from the Exoplanets Catalogue);
it was able to detect objects larger than 1km up to 3 AU from the Sun, or objects of 2-3 Jupiter masses in a distance up to 7-10 light-years (so roughly up to 440,000 to 630,000 AU, see here and here);


so I would say that its existence is quite ruled out now.