K^2

You'll have to explain that one.

I very much doubt that pressure will ever get high enough for solid Hydrogen, and temperature will only increase as you go deeper. Even if it has all of its original Hydrogen, you'll run out of that, before you're deep enough for it to solidify. Next layer bellow liquid Hydrogen will be solid Methane. Likely in Methane I state, which is a Plastic Crystal. Temperature matters, but a large planet works like a pressure cooker. As you increase the temperature, instead of liquids starting to boil, pressure rises.

This isn't quite how phases work. Relevant values are the melting point, which varies with pressure, but not much. We can just take it at 14K. The triple point, which is about the same 14K, but at 7kPa, so we don't care about it. And the critical point, which is 12 bar and 32K. Between these 14K and 32K, actual boiling point is going to vary with pressure. It's only 20K at 1 bar. At this point, it becomes very important that Nine's atmosphere is almost pure Hydrogen. It's going to have some Helium in it, but not too much. So lets picture what happens to 30 bar atmosphere at 25K. We look at the phase diagram, and at 25K, the vapor pressure of Hydrogen is 3.5 bar. That means, at anything above 3.5 bar, Hydrogen from atmosphere is going to condense into liquid. It's going to keep condensing, until pressure drops to 3.5 bar. There is absolutely no mechanism to stop it. Which means that at 25K, atmospheric pressure on Nine would be 3.5 bar. It can't get any higher. It can't really be lower, either, at least, until all Hydrogen from all the lakes boils off. That's a possibility, but I think there is enough H2 there to maintain pressure at 3.5 bar and have enough left over for lakes or oceans. Helium in atmosphere would provide a touch of buffering. Technically, it's partial pressure of H2 that's going to be at 3.5 bar, and total pressure would be slightly higher, because partial pressure of He would add to it. That would prevent things from being constantly at the threshold of boiling. It would also allow for things like cloud formation and weather. Though, I suspect, not particularly exciting weather, since the Solar power input is pretty low. There are essentially two possibilities here. First, Nine maintained most of the Hydrogen an Ice Giant would start out with. Given a thin atmosphere of 3.5 bar, most of that Hydrogen would end up on the surface, certainly flooding it all. That would result in an ocean world. Constant overcast, perpetual drizzle. Liquid Hydrogen from horizon to horizon. Not very exciting at all. Second possibility is much more fun. A catastrophic event, such as impact with one of the moons, could have knocked out a huge chunk of that atmosphere when Nine got ejected from the System. This could lead to a world with very little Hydrogen on its surface. The surface of such a world would be dominated by solid Methane, which forms Plastic Crystal at the above temperature and pressure. Which means surface will be solid, but soft. Hard to say just how much plasticity it will have at 25K, though. In either case, significant elevations are not possible, even if there is some tectonics. This means that entire planet would be lowlands, either resembling Titan with its lakes, or an endless marsh. Weather on a world like this could have more familiar patterns with partial cloud cover and actual weather systems. Second version being more exciting also happens to be less likely, unfortunately. An ocean world seems like the most likely possibility.

It can depend on internal composition, of course, and these things do vary planet to planet, but if we assume that it's a Fifth Giant, I would not expect its initial composition to vary wildly in composition from the Ice Giants. And internal heating ramps up really quickly with size. You don't expect a 10M⊕ to be anywhere close to 60% heat production of 15M⊕. I don't get where you are getting the 40K from. Equilibrium temperature at Neptune's orbit is about 50K. Equilibrium temperature at 200AU, the closest Nine gets to Sun, is about 20K. Triple point of Hydrogen is at 32K and 12 bar.

This isn't a guessing game. Take a look at phase and vapor pressure diagrams for relevant substances. Given Nine's distance from the Sun, it's much too cold to be anything like Uranus or Neptune.

There is no such thing as "can't be a coincidence," in physics, unfortunately, but when odds are less than a tenth of a percent, the safe bet is on there being some sort of a mechanism involved. And of known mechanisms that could account for it, a planetary body is the most plausible. Very far from certainty, but between that and Nice Model suggesting there was another giant in the early Solar System, it seems more likely that Planet Nine is there than that it isn't. Certainly enough of a reason to put an effort in finding it visually.

Atmospheric pressure is limited by vapor pressure of constituents. Methane is going to be frozen out, and Helium won't be sufficiently abundant. That leaves a Hydrogen-dominated atmosphere. And in plausible temperature ranges, that gives us upper limits on pressure in 1-10 bar, perhaps as high as 100 bar if there is a strong greenhouse effect, but that's a stretch already. Anything else will condense and rain down as Liquid Hydrogen. These are very low pressures. Conditions much closer to what we see on rocky worlds than gas giants. I'll grant you, that this is very unusual for a Gas/Ice Giant, or even a large Super-Earth, but only because our study is focused on much warmer worlds. We tend to see the smaller worlds have a solid surface, and large worlds have layers. But the boundary depends on size and temperature of the world. A good example, once again, is Venus. It's an Earth-sized world, but due to its temperature, it already starts exhibiting some of the features we expect of a large Super-Earth. Likewise, Nine should be an ice giant. And had it remained in the outer system, it would certainly be one of these layered planets with no well-defined surface. But with temperatures as lows they should be on that world, I expect an environment that at the first glance looks very terrestrial. A well-defined surface, either icy with lakes of Hydrogen, or a global Hydrogen ocean, and above it, an atmosphere of a few bar with clouds of Hydrogen mist. All on a world with a surface gravity 30%-50% higher than that on Earth. If it weren't for temperatures, I'd say it'd make a good world for a colony.

Unless there is a system of moons there, it doesn't. Circular orbits are a result of many, many interactions between multiple objects orbiting the same parent body.

It'd be a total speculation, and pushing the plausible range from the data so far, but for a KSP mod, it'd be fun to build an ice Super-Earth version of Nine. 10M⊕ is right there at the edge of Super-Earth definition, but in principle, this could allow for a hard surface made up primarily of Methane ice, with lakes of liquid Hydrogen and a Hydrogen-Helium atmosphere. The atmospheric pressure would be within a few bar limit, and surface gravity would be within tolerable for a landing. I'd also throw in a few moons. Could make for some really interesting challenges, and it'd be different. Edit: So here are some numbers to go along with that. Assuming Nine has a rocky core, but still covered by a lot of ice, I would guess that it'd be rather dense for an ice giant, and rather fluffy for a rocky world. So I went with 3g/cm³. That might be a little high, but we're stretching things here to make it fun for the game. That puts radius at a little under 17,000km. Almost 3x the Earth's. The neat thing about that is that the surface gravity, ends up being mere 13.8m/s². About 40% higher than Earth's! You'd be able to survive on that world, provided sufficient heat insulation. The orbital velocity would be rather high, at about 15km/s, which is about twice that for Earth, but it's nothing insane. Finally, the atmosphere. Depending on typical temperature, it could be anywhere from 1 to 10 bar. On the plus side, scale height should be comparatively small, making it a little easier to escape. Scaling that to KSP, I'd do basically the same thing they did with Kerbin. Take radius at 1/10th and keep the surface gravity. That would put radius of KSP Nine at 1,700km and surface gravity at 1.4g. That puts orbital velocity in KSP at 4,834 m/s. Then I would set surface pressure at 4 atm and scale height at 4km. That will make ascent from Nine about as challenging as ascent from Eve, especially since there won't be any significant mountains on the surface to help you along.

That's not possible. It's too large to have lost its Hydrogen, which basically guarantees a substantial atmosphere and either liquid on its surface or slush of various ices. Either way, it'd be nothing like a comet.

That's due to numerical errors in KSP. It's a well known "bug", if you will. Real physics doesn't work that way. While it's possible for a very tiny momentum transfer to take place in a two-body encounter, in practice, it never leads to a lasting capture, since the tiniest perturbation from an outside source will knock the would-be-moon loose again. So you need a three body interaction to actually result in a capture.

It's a Nice giant, which makes it an ice giant. Unless it's a capture, but then we're just guessing.

Capture always requires a three-body interaction. There are two typical scenarios. Either an object enters a system and gets a gravity assist from one of the bodies already orbiting in that system, or a pair of bodies enter the system, one of them gets ejected, and the other captured. Either way, a lone planet cannot capture a moon. It must get help from another object.

It is. But if it's the Fifth Giant, we are likely looking on the smaller end of that estimate. So it'd still be the smallest of the Ice Giants.

It's also significantly smaller than either of these ice giants, with far weaker greenhouse effect, due to lower illumination. Expecting it to be only 20K colder than Uranus or Neptune is unfounded. RuBisCO's estimate of 40K upper bound is much more plausible. Lower mass also means significantly less Hydrogen, and methane freezes at 90K. So unlike the ice giants, which are basically huge methane slushies, Planet Nine actually has a pretty good chance to have solid methane "land". All depends on just how much Hydrogen it has.

Hubble has main mirror of 2.4m and is diffraction limited in its 300nm UV band. From 500 AU, a single pixel would be about 9,000 km. So in the best case scenario, we are looking at a spot 4-5 pixels in diameter as seen by Hubble. If Planet Nine turns out to be on the smaller end of the scale and further out, we'd be barely able to tell that it's not a point source object. James Webb would be able to do a tiny bit better, because of the larger mirror. But since it's shortest wavelength is 600nm, it'd only have about 50% better resolution.

Even for liquid Methane, which is an absolute minimum requirement for any sort of life, you need to go deep enough to where pressures would be too extreme. Moons... well, yeah, there could be a Titan-like moon in theory, but I can't think of any remotely plausible energy source for life there. Lets check on actual Titan first.

I wouldn't say that that's the most-plausible way. We could do interesting things with ion propulsion, or even direct nuclear propulsion if we were dead-set on it. We could, but we won't, because of how absurdly expensive it'd be. EM drive, even if it was delivering as advertised, would still require a very impressive nuclear reactor that we'd have to launch on an escape trajectory for it to make it out there in a couple of decades. In terms of what we realistically could do, I can come up with a maneuver that puts a probe 200AU out in 125 years. As I've indicated above, it'd take many centuries to get to the likely location of Planet Nine. Might still be worth it, if we can build a probe that can survive the voyage.

No, it's the other way around. The trajectories of objects it boosted must still intersect original trajectory, which puts the periapsis of Planet Nine on the same side as apoapsides of observed objects. Since they all seem to point in one direction, the apoapsis of Planet Nine is in the exact opposite direction, giving a very close estimate to where it must pass. However, the only parameter this establishes precisely is the inclination. The semi-major axis and argument of periapsis would be slightly less restricted, but still in the ballpark. And the worst information is on eccentricity, other than it's pretty eccentric. We can also put some lower limit on the periapsis, which is estimated to be about 200AU. Likely significantly higher, however.

Looking at vapor pressure of H2, even at 20K, it will have a 1bar atmo. And the melting point for it is 14K. In contrast, the longest wavelength WISE was looking at was 22 microns, which corresponds to something like 100K peak. Which means that Planet Nine can still have a Hydrogen ocean and a substantial Hydrogen atmosphere without being detectable to WISE. Anything like Methane will, of course, be frozen. Given the pressure and feasible temperature ranges, it's entirely possible that there is not enough Hydrogen to cover the entire surface, and we'd be looking at something that resembles Titan, with lakes of liquid Hydrogen on terrain made up of frozen Methane. Could be a very interesting world. P.S. In either case, I expect Hydrogen clouds, and it'd be exciting to see for that alone. Shame it's so far away.

What does that have to do with discoverers' names? These are Shakespearean characters. And being fictional characters, it's not much different from naming planets after Gods. Well, someone's an optimist... With periapsis of 200AU, and it might be significantly higher, we could get a probe to periapsis in a few decades, yes. But this orbit has a period of 10-20ky. So it's very unlikely to be anywhere near periapsis right now. Given the kind of rockets we can realistically build, we might be able to make a probe that gets to it in a few centuries.

Ejection could have been pretty soft, given that it stayed in the system. Anything tightly bound could have survived it. That does still put some limits, but it could have retained at least one sizable moon. On the other hand, given that it had to interact with a whole lot of debris for its orbit to be entirely beyond Neptune, I would definitely expect an entire system of tiny little moonlets made up of various captures.

That's why I'm saying, it'd be totally fine if it's not classified as a planet. But if it actually turns out to be in the 10 M⊕ range, IAU will be under a lot of pressure to classify it as a planet, and odds are, they'll warp definitions (again) to make it work.

That works if it's not given a planet status. But if it is actually classified as a planet, IAU will require it to be a deity in Roman Mythology.

I haven't read the paper yet, but I'd like to think the sort of people who can build the model necessary to show the correlation would also do the work necessary to distinguish between a transit and periodic source. It's basically going to be the first thing that pops into anyone's head, so not doing the legwork to check for it before announcing that there is a planet there would be quite irresponsible. Not to mention, make it very hard for the paper to pass peer review. But I reserve the right to flip on this once I actually get the time to read the paper in full.