Thread by @plutokiller

1/
Clustering in the outer solar system. A thread, which is really a discussion of tinyurl.com/p9cluster

Three years ago @kbatygin and I proposed the existence of Planet Nine because we noticed two strange things about the most distant objects in the solar system.

@kbatygin 2/
First, Kuiper belt objects with distant, very eccentric orbits are predominantly aligned in one direction. They should be more or less randomly oriented in space. Something has to cause that.

Second, the orbits of these bodies are mainly tilted in one direction. Also odd.

@kbatygin 3/
A distant massive planet on an inclined eccentric orbit very simply and naturally provides an explanation to these two key observations and to a slew of observations we weren't even trying to explain at the time. The Planet Nine hypothesis was born.

@kbatygin 4/
The Planet Nine hypothesis relies on the the clustering in alignment and tilt of the distant objects to be real and not some statistical fluke or observational artifact. Three years did some simple calculations, and decided that the clusterings were real.

@kbatygin 5/ In the intervening years, the biggest question for the reality of Planet Nine was: are those clusters real? This is a critically important question to answer correctly, and the subject of today's paper.

@kbatygin 6/
First, are the orbits aligned? Check out Figure 1. In the left panel, each of the black dots shows the direction of elongation of one of the distant KBOs. Does it look random to you? Def. not. The fat red dot is the average of all of the data. Random would be in the center.

@kbatygin 7/
But maybe that's a random fluke? In the right panel we simulated 100,000 observations of non-clustered KBOs and calculated the average. Each of the little black dots is one of those averages. They mostly fall near zero but ~4% of the time they are as extreme as the red dot.

@kbatygin 8/
Statistically, we would say that we can rule out a uniform distribution of objects at the 96% confidence level. That's good but I don't like the 1-in-25 chance that we're seeing a fluke. I'd like to be more confident.

@kbatygin 9/
We repeat the entire analysis with the tilts. In FIg 2 here each dot shows, on a polar plot, the direction of the north pole of the orbit. Orbits in the plane of the solar system are in the center, tilted orbits move away from the center.

@kbatygin 10/
An analogous analysis shows that such tilting only occurs 3.5% of the time for orbits aligned with the plane of the solar system. That's 97.5% significant, which is even better! If these two numbers were independent we could multiply them together, but they're not.

@kbatygin 11/
So we do a final analysis where we rigorously calculate the combined probabilities by doing both the alignment and the tilt at the same time. The final answer?
[drum roll please......]

@kbatygin 12/
OK, you probably already read the abstract so you know that it says:

" we calculate that the probability that these distant Kuiper belt objects would be clustered as strongly as observed in both longitude of perihelion and in orbital pole position
is only 0.2%"

@kbatygin 13/
Yay! I'm pretty happy believing that something is going on out there when there is only a 1-in-500 chance that it is a statistical fluke.

Great.

BUT WAIT. there's more.

@kbatygin 14/
There is a frequently mentioned result from the OSSOS KBO survey that people often say shows that there IS NO clustering. How could this also be true?

We looked into it.

@kbatygin 15/
Basically we show that even if the clustering is as strong as we think, the OSSOS survey was statistically incapable of confidently detecting it. The survey was designed for other purposes which turned out to make it particularly bad at detecting these clusterings.

@kbatygin 16/
Or, to quote the paper:
Because of the limited survey region and small number of detected distant objects, ... [N]o conclusions on clustering of longitude of perihelion observed in the complete dataset can be drawn from the OSSOS data.

@kbatygin 17/
I'm pretty sure that this is the most complete analysis that can be done on these data. And the results are pretty conclusive: the cluster is nearly certainly real, and we now understand the smaller and limited OSSOS observations couldn't detect the clustering.

@kbatygin 18/ To paraphrase the final sentence of the abstract: the cluster is real. Something that we have not yet observed must be causing it. What is it? Planet Nine is a simple and elegant solution. Let's go find it.
/fin

@kbatygin p.s./
should have linked to the article in the Astronomical Journal. iopscience.iop.org/article/10.384…

It's paywalled though. So feel free to use the link at the top to the pdf. Or wait until Wednesday for arXiv.