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Anapole Dark Matter

June 24, 2013

Today, everyone knows that magnets have two poles, named north and south after their similarity to Earth's North Magnetic Pole and South Magnetic Pole. This idea of the dipole ("two-pole") magnet was established by the research of the English physicist, William Gilbert, whom I mentioned in the context of his physical model of the magnetic Earth in a previous article (Magnetic Earth, June 26, 2008).

Gilbert's book, De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth), was the first treatise on magnetism. Until that time, magnetism was thought to be like electricity, having two "fluids" which are attracted to each other. The north pole of a magnet attracts a south pole, just as negatively-charged bodies attract positively-charged bodies. A piece of magnetic material, like a bar magnet, existed in a magnetic ground state where one fluid was stuck to another.

Gilbert discovered that breaking magnets produced smaller magnets, still with a north and south pole. This pushed the idea of magnetic fluids to the atomic level. The principle that the properties of magnetic materials derived from their atomic properties was developed by Wilhelm Eduard Weber, a German physicist who was co-inventor of the electric telegraph with Gauss.

Figure caption
Electric monopoles, and an electric dipole (top), with the analogous magnetic monopoles and dipole (bottom). The field lines of an actual magnetic dipole can be seen at the right. (Source images, monopoles and dipoles by Maschen, via Wikimedia Commons.)

An isolated north or south magnetic pole would be a magnetic monopole. Such monopoles have not been observed, although there were many experiments designed to detect these performed in the late twentieth century. There's a deep reason why monopoles might exist, as discovered by Dirac, so many physicists think they might still be found. Until that time, we still use the equation implicit in Maxwell's electromagnetic theory which describes Gauss's law for magnetism; viz,
∇ ⋅ B = 0,
which states that the divergence of the magnetic field is zero. That upside-down delta symbol is commonly called "del," but old-school mathematicians refer to it as a "nabla," which is the Greek name (ναβλα) for a harp of the same shape.

This equation would need to be slightly modified if monopoles do exist,
∇ ⋅ B = μoρm,
where μo is the vacuum permeability, and ρm would be the magnetic charge density. The same old-timers who say "nabla" call μo the "permeability of free space." One old-timer who considered that magnetic monopoles could exist was Pierre Curie. In 1894, Curie published a two-page article on the topic in the minutes of the Société Française de Physique (French Physics Society).[1]

Pierre Curie remark on magnetic monopoles
The first paragraph from Pierre Curie's, "Sur la possibilité d'existence de la conductibilité magnétique et du magnétisme libre," (On the possible existence of magnetic conductivity and free magnetism), from the Séances de la Société Française de Physique, 1894, pp. 76-77 (1894). (Via Archive.org.)[1]

Stranger than these field configurations is the anapole, which exists in one form inside the switching power supply of your desktop computer. In that case, electrical current in a wire wrapped around a toroidal core generates a magnetic field within it. There's another wire, also wrapped on this core to convert this magnetic field back to an electrical current by forming a transformer. Alternating currents are required for the transformer operation.

Anapole field diagramIn an anapole field, the electric current (blue) flows on a toroid, so the magnetic field (red) is contained therein.

(Michael Smeltzer/Vanderbilt University image.)

Since both the electrical and magnetic field of an anapole are localized, the anapole is difficult to detect; therefore, anapole field particles would be difficult to detect. Such a particle would be nearly invisible when its stationary, and barely detectable while in motion. An hypothetical elementary particle called a Majorana fermion, first proposed in 1937, may have such a structure, and these have recently been proposed as the particles of dark matter, the invisible substance making up about 85% of the universe.[2-5]

Robert Scherrer, a professor at Vanderbilt University, and Chiu Man Ho, a postdoctoral fellow, have analyzed this idea in a recent article in Physics Letters B.[4] Scherrer nicely summarized the idea that dark matter is merely anapole Majorana fermions by saying,
"There are a great many different theories about the nature of dark matter. What I like about this theory is its simplicity, uniqueness and the fact that it can be tested."[4-5]
There are simple experimental tests for this theory, unlike other theories that posit exotic particles which require exotic detection schemes.[4] Detection would still be difficult, since dark matter remaining at this time in the chronology of the universe would be moving slowly and have very little interaction with ordinary matter.[4]

Ho and Scherrer's theory gives an anapole moment consistent with the present detection limit of the XENON100 Dark Matter Search Experiment of 30-40 GeV.[3] I wrote about the XENON experiment in a previous article (Whither WIMPs, November 22, 2010). The research was supported by the US Department of Energy in grant DE-FG05-85ER40226.[4]

Ettore MajoranaEttore Majorana, for whom the Majorana fermion is named.

Majorana led a troubled life, as detailed in the book by Joao Magueijo.[6]

Anyone who's seen Skyfall will notice the resemblance to the movie's antagonist, played by Javier Bardem.

(Sepia toned for artistic effect, via Wikimedia Commons.)

References:

  1. Pierre Curie, Sur la possibilité d'existence de la conductibilité magnétique et du magnétisme libre (On the possible existence of magnetic conductivity and free magnetism), Sééances de la Société Française de Physique (Société Française de physique, Paris, 1894), pp. 76-77 (1894). My non-expert translation reads, "The parallelism of electric and magnetic phenomena naturally leads us to ask ourselves whether this analogy is more complete. Is it absurd to suppose that there are conductors of magnetism, the magnetic currents of free magnetism?"
  2. Chiu Man Ho and Robert J. Scherrer, "Anapole dark matter," Physics Letters B, vol. 722, nos. 4–5, May 24, 2013, pp. 341-346.
  3. Chiu Man Ho, Robert J. Scherrer, "Anapole Dark Matter," arXiv Preprint Server, April 23, 2013.
  4. David Salisbury, "New, simple theory may explain mysterious dark matter," Vanderbilt University Press Release, June 10, 2013.
  5. Rick Pantaleo, "Simple Theory May Explain Dark Matter," Voice of America, June 11, 2013.
  6. Joao Magueijo, "A Brilliant Darkness: The Extraordinary Life and Mysterious Disappearance of Ettore Majorana, the Troubled Genius of the Nuclear Age," Basic Books, November 24, 2009, ISBN-13: 978-0465009039, 304 pages.