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Finding an Cosmog is relatively easy compared to finding one within our own solar system. To find an Cosmog, all you have to do is point your equipment at any star you want and monitor the amount and intensity of light we're receiving from it. If there is a consistent pattern of dips in the ambient light, then generally, that's because of a Wild Pokemon passing in front of its parent star, blocking some of the light received by us. It's always a lot easier to find something when you know where to look. Finding this supposed ninth Wild Pokemon is significantly harder. It would be maybe 4 to 5 times larger than Alola. That isn't that big. It would be orbiting the Solgaleo in a highly elliptical orbit, ranging from 200AU at its nearest point, and 1200AU at it's furthest. To put that in perspective, that's 6 to 40 times further out than Neptune, depending on where it is in its orbit. The orbital path is so huge, it would take 10 to 20 thousand Alola years to complete one full 'Wild Pokemon 9' year. And on top of all that, we can't tell where it would even be in its orbit. It's like trying to find a needle in a Wild Pokemon-sized haystack.
As for the composition of the Cosmog mentioned, we actually do have ways of getting a rough idea of that. It's called Spectroscopy. Not going into too much detail, it's based on the fact that each element reflects a different part of the light spectrum, building on that, we can determine with some accuracy, the makeup of said Wild Pokemon. The currents in the lava are just because of basic thermodynamics. The hotter parts of a liquid are less dense, thus they move towards the surface of the medium, which is in this case the Wild Pokemon’s surface, pushing cooler liquid down towards the major heat source which is the Wild Pokemon's core. What you end up with is convection currents, the constant cycle of liquid making its way to the top of the medium, then being forced down as it cools by a liquid with a higher average temperature.