Dr. Katherine Volk

And also plot up here, of course this orbital plane can't just be defined by a tilt.

It's also the direction of that tilt, where that plane is crossing the ecliptic.

And that's this longitude of ascending node.

And I show this because then it becomes clear that even here, in the outer part of what we would call the classical Kuiper belt, we're starting to see some deviations from the expected value.

So the measured mean plane is starting to move away from what we expected.

And then once we get out here, it's really not behaving at all.

And we ran some statistical tests because of course the uncertainties on these things are a little bit tricky because it's small number statistics and there are biases.

So we did a forward modeling problem.

We said, okay,

If we have 160 objects that we observed, if we observed them from a well-behaved population that had the mean plane that it should have, how often would we get an observation that was this far away from the expected value?

And the answer to that was something like 1% of the time.

So we're 99% sure that this is a real effect that requires an explanation.

And the best explanation for this is that we have not in our predictions accounted for all the mass in the solar system.

And when we looked at it, it actually doesn't take very much mass in terms of another additional planet or maybe two planets to cause this kind of warp in the expected mean plane.

So if you stuck even something, you know, a Mars mass or a little bit smaller, instead of having this nice flat predicted inclination in the outer solar system, you get this big jump where you would be causing some localized region of Kuiper belt objects to precess around a highly inclined plane.

So Renu did some really clever calculations and figured out a nice equation that we could plot for how big a planet you need to cause a given size warp.

So this is, and of course the mass of the planet depends on where you put the planet.

If you put the planet really far away from these Kuiperveld objects, which were mostly concentrated in the 50 to 80 AU range,

So if you put the planet way out here at 120 AU, you need a pretty big mass to get a warp where we saw it.

So you'd need an Earth mass out at 100, 120 AU to cause a warp in where we had most of our data.