They don't explain it in detail, but the reason it's consistent with Planet IX [1] is its orbit has specific properties that require a near pass with a large body in the outer solar system (basically the definition of Planet XI). That seems like it may be easy to do by other means, but if you've played Kerbal Space Program you know how difficult it can be to change all six orbital elements in the way you want to. For example, a close pass to Jupiter could launch something extremely far our, but it would not change it's perihelion or closest approach to the Sun. Like a Homann transfer, going to a larger orbit requires at least two "kicks": one to kick it into an ellipse and a second at the outer point. Planet XI would give the kick at a far distance to get many of these curious Trans-Neptunian Objects out to crazy perihelion distances like 65 au. There's also a specific effect to the inclination and argument of perihelion, but I don't understand how these work as well.
The amount of sky we have to look for Planet IX is enormous (and given how faint it is likely to be), and the evidence so consists of about ten of these TNOs with these orbits (not many, but it's very hard to make these orbits). But there are potentially hundreds of bodies with orbits like these waiting to be found by a the soon to be constructed LSST, which is an 8 meter telescope that will survey its entire sky every 3 days. With many more of these orbits to predict from, we may really narrow down the search space to look for it, and ultimately test its existence.
[1] Predicted by Konstantin Batygin and Mike Brown, the latter of which played a big part in helping to disqualify Pluto as a planet by discovering Eris. I know from a lunch-talk that he greatly relishs the thought of both demoting the former Planet XI and predicting the new one.
>> There's also a specific effect to the inclination and argument of perihelion.
To get a significant inclination (ie away from the low inclinations of the inner planets) and a drop in the perihelion (ie highly oval rather than the round orbits of the inner planets) you need a close pass of a large body. As the little think comes close to the big thing it is thrown randomly, away from the nicely round orbits of most things in the early solar system. So if you find a body with those two features, you know it passed close to something big somewhere our near the highest part of its orbit. That is the evidence of a large object out beyond pluto.
Yes, I agree, it's a combination of high inclination, perihelion, and eccentricity that point point to scattering.
The clustering of the arguments of perihelia is less straight forward (you can see it in Figure 4 of the linked pre-print PDF in another comment) and my limited understanding is that they are shepherded into that configuration over time by the large body. That is more clear when you see the results of the numerical simulations I suppose.
The number of potential encounters is also a factor. Objects in orbits this large, with periods measurable in thousands of years, won't have many periodic encounters. There isn't enough time since the formation of our solar system for them to get close enough together. The lower the number of potential encounters, the more significant must those be that do happen. That too points to a larger body out there.
So, just using a 1/r relation for potential energy, and the ratio of perhelion to aphelion, this thing has only ~3% of the potential energy at the outermost point in is orbit compared to the innermost point. That's practically miraculous on its own, isn't it?
The paper authors are actually arguing for a Planet X which has had periodic encounters much weaker than that at a distance of a few hundred au.
Quite the change in distance from the sun. Btw, kinetic energy is proportional to 1/r, and is at a peak at the perihelion. Potential energy is highest at the aphelion.
The amount of sky we have to look for Planet IX is enormous (and given how faint it is likely to be), and the evidence so consists of about ten of these TNOs with these orbits (not many, but it's very hard to make these orbits). But there are potentially hundreds of bodies with orbits like these waiting to be found by a the soon to be constructed LSST, which is an 8 meter telescope that will survey its entire sky every 3 days. With many more of these orbits to predict from, we may really narrow down the search space to look for it, and ultimately test its existence.
[1] Predicted by Konstantin Batygin and Mike Brown, the latter of which played a big part in helping to disqualify Pluto as a planet by discovering Eris. I know from a lunch-talk that he greatly relishs the thought of both demoting the former Planet XI and predicting the new one.