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Witten and colleagues favor an ultralight axion as dark matter

...it's not a new idea at all but it's described and analyzed by clear thinkers who know the standard state-of-the-art toolkit to determine the basic consequences...

Edward Witten is often painted as a "basically mathematician".

In fact, it's a description that you may have heard not only from the postmodern critics of science but perhaps even from your humble correspondent (especially whenever I found the number of homotopies and other things excessive for a given physical purpose in a paper he wrote). But I have always appreciated how much he understands both mathematics and physics – including physics that is very close to experiments. I was amazed by his knowledge of deeply technical, experiment-oriented particle physics phenomenology more than once.

Well, a week ago, along with Lam Hui (Columbia), Jeremiah P. Ostriker (Columbia + Princeton U.), and Scott Tremaine (Princeton IAS), Witten co-wrote a paper on cosmology (astro-ph.CO) which was submitted to PRD (the acronym means FART in Czech)

On the hypothesis that cosmological dark matter is composed of ultra-light bosons
I don't follow astro-ph abstracts on a daily basis so I had to learn about the paper from a big fan of Edward Witten who religiously digests every letter that Witten writes anywhere and who went to a vacation – and declared a hiatus in his blogging – because he needs to read the paper in detail. Well, this fan is also a big fan of supersymmetry and string theory whenever he's not drunk. His name is Tommaso Dorigo. Well, the Italian wine is good – I mean good enough for the Italians.




The WIMP, or the "weakly interacting massive particle", has been the #1 popular candidate for the composition of the dark matter. It was probably my #1 choice as well although I have never been a warrior in this particular battle.

By definition, a WIMP is a particle with a similar mass and a similar interaction strength as the "lightest superpartner" (LSP) in supersymmetric theories. The masses were supposed to be around or beneath \(1\TeV\) and the values of the coupling constants are dictated by the supersymmetry – in some fundamental counting, they are equal to those of their known superpartners in the Standard Model. The "number of LSPs" is typically conserved modulo two – because of the R-parity – so these particles may annihilate in pairs and that's often assumed to be the property of the WIMP, too.

Exactly with these natural masses and couplings, cosmological models including the enhanced particle physics give you a realistic cosmological evolution including a pretty successful prediction of the amount of dark matter for today. This a priori unexpected success is known as the "cosmic coincidence" and it was – and it still mostly is – an important reason to take the theory that dark matter is made of WIMPs seriously.

(But it's just mostly an order-of-magnitude agreement in a single number so you shouldn't overstate the certainty that this "consistency checks" offers you.)




WIMP is still a likely enough possibility but it has never been a near-certain possibility. Its competitors were always comparably likely. Because the LHC as well as the direct search experiments – which operate under the ground – could have found a WIMP in recent years but haven't (despite the preliminary hopes that several experiments have ignited), the odds have shifted.



There are at least five subtypes of axions. Concerning the first one, don't overlook the claims that all these antibacterial ones are probably more dangerous than helpful for your health. Picture via David Saltzberg of UCLA, the science advisor behind Sheldon Cooper and pals, and the idea not only behind the name is due to Frank Wilczek.

If you were assigning the probability 70% to the WIMP and 25% to the second most likely explanation for dark matter's beef, an axion (you're 95% certain that it's one of those), some 5 years ago, it's rather likely that by now, you already think that the axion is more likely than a WIMP. Why? Because over 2/3 of the "reasonable parameter space" of the WIMP's parameter. So 70% got reduced to some 23% and the axions' 25% already beat the WIMPs' 23%. Note that you need to renormalize the percentages if you reduce one. (The numerical values of the probabilities are arbitrary – perhaps my subjective ones – but I am confident that most cosmologists and particle physicists would okay them as "vaguely compatible with their guesses".)

(In the remaining 5%, I could say that 3% is "dark matter is made of black holes similar to the LIGO-detected ones", 1% is some MOND-like modified gravity without zillions of excitations of new particle species, and 1% is something else including the possibility that the people will decide that "nothing like dark matter or corresponding new physical phenomena exists at all" for some reasons I don't understand now. Also note that if you replaced 70% by 99.999%, like I do with the validity of SUSY as a principle, the number would stay way above 99% even after the reduction of 2/3 of the parameter space.)

In recent years, the axions haven't been weakened (almost) as a theory of dark matter at all because the axions are hard to directly produce or detect because of their interaction constants. (I say "almost" because some cosmological observations do constrain axions and those observations got a little bit better, too.) Note that axions are usually very light scalar particles that play several roles in physics and may come from many sources. The key role they were designed for is to solve the strong CP-problem i.e. explain why the coefficient of the topological term \({\rm Tr}(F\wedge F)\) in the QCD part of the Standard Model – a term that could contribute a lot to the violation of the CP-symmetry but contributes very little if not nothing – is so tiny.

Concerning the origins, string theory may normally produce lots of axions, perhaps even hundreds of them. It's because the 10- or 11-dimensional effective theory for string/M-theory contains \(p\)-form fields such as \(C_{\lambda\mu\nu}\). When integrated via \(\oint_C\) over \(p\)-cycles (noncontractible or topologically nontrivial \(p\)-dimensional submanifolds) of the compactification manifold (such as a Calabi-Yau or a \(G_2\) holonomy manifold), they reduce to one of the scalars (a \(0\)-form is a way to call a scalar in the \(p\)-form language). There may be hundreds of inequivalent cycles, so you may get hundreds of scalars. It may be shown that their masses are naturally low and "exponentially small" while the exponents may take very diverse values. General ideas like that are known as the "axiverse".

The recent paper by Witten et al. describes the stringy ancestry of the axions as follows:
For example, all models of particle physics derived from string theory have at least several periodic scalar fields such as \(a\), and typical models have many of them (dozens or even hundreds). Various possible applications of these fields have been considered (see for example [23]). With different assumptions about their masses, they have been proposed as candidates for the inflaton field of inflationary cosmology; as potential QCD axions, whose existence may explain CP conservation by nuclear forces; and as contributors to dark energy or the cosmological constant and/or ingredients in a mechanism to explain its smallness. For our present purposes, we are interested in these fields as candidates for FDM.
A paragraph later, they also mention an estimate from heterotic string theory. I am mentioning these things to assure you that Witten hasn't forgotten that he is a string theorist.

OK, let's return to the new claims in the paper by Witten and co-authors.

They just point out – a not completely new but nicely and concisely phrased and supplemented with some new ideas that thicken the picture – that a massive but ultralight axion seems compatible with everything we know and demand from dark matter. In particular \[

M \gtrapprox 10^{-31}\GeV

\] seems to be a great value for the axion mass. This is a tiny mass relatively to the LHC particles, indeed, which is why I used the high-energy unit, one \({\rm GeV}\). (Witten and pals used \({\rm eV}\) to show how much grounded to the Earth, lithium-ion batteries, and the Milky Way they are.) This tiny mass is equivalent to the de Broglie wavelength\[

\lambda\lessapprox 3,000\,\,\text{light years}

\] which the authors describe as one kiloparsec, for Edward Witten to remind us that he wanted to be an astronomer and how often he looks into a real telescope (where one may see some angles and those are the only possible justification for medieval units such as one parsec which I would ban if I became an EU commissar).

Because of this ultralong de Broglie wavelength, something is "different" when you try to squeeze these particles too much. That's much like trying to compress things to too small areas in the phase space. And that's why this model of dark matter is called "fuzzy dark matter" or FDM for short. It may be considered a competing alternative of the CDM or cold dark matter paradigm.

At these astronomical distances – which are still safely smaller than our galaxy – new effects appear. The authors argue that the FDM dark matter halos cannot be too small because they always have a "minimum size object" somewhere inside – which is described as nothing else than a soliton. There is an envelope around the soliton core and they discuss the relaxation process in between them. They also discuss the evaporation of the soliton through tunneling.

Finally, they mention the Fornax dwarf galaxy – a low-luminosity satellite galaxy of our Milky Way (i.e. with a high ratio of dark and visible matter; it also contains globular clusters) – as a possible smoking gun that seems compatible with their preferred FDM picture while it apparently contradicts the CDM paradigm. Why does it contradict? Because it should have spiralled to the center, much like the classical hydrogen atom. The fuzzy FDM picture makes the dwarf galaxy stable much like quantum mechanics makes the atoms stable against the spiraling inwards.

It's a refreshing paper to read because the required science is arguably more basic than (even) the science needed to read and understand Witten's papers on condensed matter physics and other disciplines studied by the mortals. And the four authors – don't forget that there are four – just write sufficiently clearly.

So with the FDM as a possibility, there is clearly no "catastrophic contradiction" in current physics when it comes to dark matter. At the same moment, if some ultralight axions like that play such an important role in cosmology, it will only deepen the thirst for the new groundbreaking terrestrial discoveries. Just to be sure, their ultralight FDM axion has observable consequences, especially if the axion mass is at most 10 times heavier than the lower bound (after all, there is already a slight tension with the Lyman-\(\alpha\) forest), but all these observational consequences require astronomers and telescopes to be tested rather than experimenters standing on our blue, not green, planet.

Some people may find it irritating and less scientific but Nature doesn't care. If the particle of dark matter may only be studied through the telescopes, well, then it's what Nature wanted. If you're dissatisfied, apply for the political asylum in a different Universe (or in Saudi Arabia where the Earth is still flat).

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