## Wednesday, November 25, 2015

### Does dark matter clump to radial filaments?

Earth's dark matter hair?

Lots of media including The Washington Post, Popular Science, Space Daily, Christian Science Monitor, Russia Today, and Fox News bring us the happy news that Nude Socialist already hyped in August.

The Earth is sprouting hair – radial filaments of dark matter.

This claim is taken from the July 2015 paper by Gary Prézeau, an experimenter at JPL NASA in Pasadena and a member of Planck,
Dense Dark Matter Hairs Spreading Out from Earth, Jupiter and Other Compact Bodies (arXiv)
which has just appeared in the Astrophysical Journal (which produced the new wave of interest). He claims that the ordinary cold dark matter (CDM) is organizing itself in such a way that compact objects including the Earth or other planets develop radial thick enough filaments of dark matter, the hair.

Does it make any sense? I spent about 5 minutes by efforts to understand why would such an anthropomorphic structure completely differing from the usual distributions develop. After some failed attempts to understand what this guy is talking about, I looked at the citation count and it remains at zero at this point. So I am surely not the only one who has problems.

Prézeau claims to have used some computer models but one shouldn't need computer models to explain the qualitative character of the "shape of ordinary dark matter", should he? After 10 minutes, I finally began to understand why he would believe such a thing. It's an interesting point but I still don't believe the conclusion.

A priori, you could think that for the dark matter to organize to well-defined filaments like that, it would need to be rather strongly interacting. After all, powerful molecular forces boiling down to electromagnetism have to act within the human hair for the hair to remain compact. There are no strong forces like that in CDM. So what is responsible for the clumping?

But as I understood, his reasoning is exactly the opposite one. The dark matter is supposed to be clumped into these filaments because it has almost no interactions. And interactions are needed for thermalization etc. So Prézeau claims that at the last scattering surface, the dark matter particles only live at/near a 3-dimensional submanifold of the 6-dimensional phase space.

And the subsequent evolution preserves the regularity and peaky character of the distribution. Only if the dark matter manages to orbit around the galaxy several times, the position and momentum became "chaotic" – more or less Maxwell-Boltzmann-distributed – as the particles are perturbed by various local gravitational fields. But the WIMPs are only flying at 220 kilometers per second. With a circumference over $$10^{18}$$ kilometers, it may take some $$10^{16}$$ seconds or 0.3 billion years to orbit the galaxy. Those numbers say some 50 orbits since the Big Bang which seems enough to randomize but maybe it is not.

So he claims – while referring to the authority of some computers – that because of the concentrated character at the last scattering surface and "too short and simple" evolution of the phase space in the subsequent 14 billion years, there will be easy to detect clumps. And because of the Earth's or other planetary gravitational fields, there will be hair that starts at a "root" with a very high density and goes outwards.

I seem to have problems with too many statements in the paper. First, I don't really see why the dark matter particle should start at a 3-dimensional manifold in the phase space only. It was spatially everywhere and only the magnitude of the momentum could have been constrained, approximately, right? And the kinetic energy was nonzero so it's still a 5-dimensional space.

Also, he talks about the general relativistic metric. I don't see why he would need general relativity to discuss the hypothetical clumping of matter particles near the weak Earth's gravitational field. Also, he admits that the focal points are $$2\times 10^{15}$$ meters, some 10 AU, away from the Earth for the dark matter speed. But why doesn't he agree that this huge distance means that the Earth's gravity is way too weak to modify the distribution of the dark matter at nearby distances – thousands or tens of thousands of kilometers from our planet?

And where does the hypothetical clumping to "preferred angular locations" of the hair come from? The thickness of these filaments is supposed to be vastly smaller than the Earth's radius. Where would such a hugely accurate localization come from? He even proposes these "soon-to-be-discovered" filaments as probes to study geological layers of the Earth!

Also, even his claims about the Kepler problem seem to be wrong to me. When an "unbound" particle moves in the Earth's gravitational field, the trajectory is a hyperbola. At infinity, the hyperbola approaches two lines – in a plane that crosses the center of the Earth. But he seems to claim that the lines themselves go through the Earth's center but they don't. Well, the asymptotic lines are become "close" to lines through the center visually, in the spherical coordinates, but the distance remains nonzero (and much greater than the Earth's radius) in the absolute sense. Prézeau seems to use his wrong idea about the asymptotics to claim that there is some focusing that doesn't actually exist.

And so on and so on. The paper offers lots of technically sounding claims and even elegant equations but it does seem to do almost nothing to explain the extraordinary claim about the shape of the dark matter. At this point, the paper seems to make almost no sense to me. Obviously, this detail doesn't prevent the journalists from selling this 0-citation paper as a scientific fact. For example, Forbes used the title "Strange But True: Dark Matter Grows Hair Around Stars And Planets".

Oh really? Wow, this text is actually by Ethan Siegel.

Does someone understand the paper more well than I do so that she could make me think that the paper is less nonsensical than I thought?