After glancing back through Niven’s A World Out of Time recently (which takes place in the future and mentions, in passing, the existence of one or two massive gas giants beyond Neptune’s orbit) and then reading the thread on the Oort cloud here, I started thinking again about trans-Neptunian planets: an idea that has sort of fallen out of favor recently, esp. in light of Pluto’s demotion from Planet to mere Object.
The area of the sky where a planet is likely to be (the ecliptic) has been combed pretty thoroughly, mostly looking for additional KBOs. It’s not impossible, but if there’s a large object out there it would have to be either very far away or very dark.
There is one possible sign of something big out there. The Kuiper Belt extends from about 30 AU to 50 AU, then mysteriously cuts off. There’s no reason why it shouldn’t gradually taper off instead of suddenly ending. It could be due to the disturbance of a massive object out there.
Some solar system models also show that it’s possible there was a 5th giant planet that was ejected during its early years. Maybe it didn’t completely leave the solar system, maybe it’s still out there, waiting…
At most, we might find another Pluto/Eris-sized object. Eris is far away (3 times as far as Pluto), but its albedo is .96, which means it reflects all but 4% of the light hitting it. So it’s unusually bright. There could be a closer object of a similar size which could have escaped detection if it has a very low albedo.
As for why it’s not likely we’ll find a real planet out there, you have to look at how we think the outer Solar System got to be the way it is. All four large planets out there are thought to have migrated to their current locations from areas closer to the Sun. There was not sufficient density in the protoplanetary disk out in the Saturn-to-Neptune region for the planets to have accumulated where they are now. As they migrated, they scattered some of the planetisimals in the disk to areas where there are no planets (i.e. the asteroid and Kuiper belts). And in the process, they spaced themselves out so they didn’t interfere with each other’s orbits.
So if there were another planet, to survive to this day, it would have had to be somewhere it didn’t perturb or be perturbed by the other planets. So it most likely would have ended up where the Kuiper belt is. But if it were there, it would have scattered those objects even further away from the Sun.
The cut-off of the Kuiper belt at 50 AU is unlikely to be an indicator of a planet. Yes, it could be. But for a planet to get out that far, it would have had to traverse the Kuiper belt and would have scattered those objects. That didn’t happen.
My guess as to the cause of the cut-off is that there are objects out there, but for some reason, most of them have very low albedos, so they’ve escaped detection so far. There’s something similar to this in the asteroid belt where the ones closer in generally have a different composition than those further out. This is the result of the two sets of objects having somewhat different origins (I’ve forgotten the details of what those were, but it was basically two different scattering “events”).
There may be a large number of Plutoids (large KBOs, or Pluto like dwarf planets). Estimates of how many vary, but up to 1,000 or so seems possible. And if you include much smaller objects, then in total there seem to be easily at least 100,000 Kuiper Belt Objects.
But a big planet? That seems unlikely. Anything big enough to be considered a planet should have been found by now. We’ve seen enough KBOs to easily be able to categorize them. A large portion of them fall into some sort of resonant orbit with Neptune. If there were another planet out there. We would expect to see some sort of resonant pattern to develop among the others. And there is just no such pattern.