Axions as Cold Dark Matter

WIMP (weakly interacting massive particle) searches have been getting more frustrating. The LHC, as of yet, has found no evidence for supersymmetric extensions to the Standard Model for particle physics. The least massive supersymmetric particle, if it exists, is a favored WIMP candidate. But detection limits on WIMPs from several experiments are becoming more severe, and are in conflict with other possible or claimed detections. One way out of this quandary may be that there is more than one type of WIMP particle responsible for dark matter (prior blog).

Or perhaps the dominant dark matter constituent is not a WIMP at all. Baryons (ordinary matter) only contribute 1/5 of the total mass, and only 5% of the total mass-energy of the universe. The dark matter component cannot be baryons – this is ruled out by the abundances of deuterium, helium, and lithium generated via nucleosynthesis during the first few minutes of the Big Bang.

Dark matter must be “cold” that is, moving at low to moderate speeds, based on the way galaxies are distributed and cluster together. If dark matter is not due to baryons and not due to WIMPs, what other alternative is there? Neutrinos and other known light particles are ruled out by observations.

But there is another light particle, the axion, which has not been observed, yet is a good candidate as a “weakly interacting light particle” explanation for dark matter. Axions do not require the existence of supersymmetry. They have a strong theoretical basis in the Standard Model as an outgrowth of the necessity to have charge conjugation plus parity conserved in the strong nuclear force (quantum chromodynamics of quarks, gluons). This conservation property is known as CP-invariance. (While CP-invariance holds for the strong force, the weak force is CP violating).

The neutron, composed of three quarks, is observed to have no electric dipole moment, to very high accuracy, indicating CP-invariance holds for the strong force. An additional mechanism (field) is required to “enforce” the invariance. Initial theoretical work was done by Nobel winning physicists Weinberg and Wilczek in the 1970s. The axion is the corresponding particle for this field, providing the favored explanation for allowing the preservation of CP-invariance.

The axion, if it exists, has a very low mass, in the range of over 1 micro-eV to as much as 10 milli-eV. (One eV, or electron-Volt is the energy from moving one electron through a potential of one Volt). By comparison, electron neutrino masses are less than 2 eV, but axions are probably a thousand or more times lighter than the elusive neutrino.


Installation of the insert chamber into the magnet of the ADMX, October 4, 2013.

The Axion Dark Matter Experiment (ADMX) at the University of Washington is the best known experiment searching for axions as a principal component of dark matter. It relies on the prediction that axions can be converted to photons in the presence of a magnetic field. A well-designed experiment requires a large microwave cavity at very low temperature to minimize noise, and with a strong magnetic field. ADMX consists of a microwave cavity surrounded by an 8 Tesla magnet and cooled to liquid helium temperatures.

ADMX has not yet detected axions, but it has placed limits on their interaction cross-section for masses in the range of about 2 to 3 micro-eV. These limits are consistent with the two most popular theoretical models. The ADMX team is in the process of upgrading the apparatus to a sensitivity that would allow them to detect axions if they adhere to one of the two main axion dark matter models, and have mass less than 10 micro-eV. They are scheduled to be able to reach this goal by the end of 2015.

Another interesting possibility is that 110 micro-eV axions may explain an anomalous signal seen in an experiment with Josephson junctions, and thus are already detected. Josephson junctions consist of two superconducting elements separated by an insulating layer. If the axion mass is resonant with the junction frequency, a current spike would occur. An exceptionally high noise spike in one such prior experiment could conceivably be due to an axion resonance signal. We await further experiments to see if the behavior can be repeated at the same frequency.

And for fun, here’s an historical perspective on the axion, from the 1960s, featuring Arthur Godfrey:


References: - ADMX web site – talk by Gray Rybka from the ADMX team – Josephson junction anomaly



2013 in review

The stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

A New York City subway train holds 1,200 people. This blog was viewed about 4,900 times in 2013. If it were a NYC subway train, it would take about 4 trips to carry that many people.

Click here to see the complete report.

Dark Matter Eludes LUX

The LUX (Large Underground Xenon) experiment has just announced results from their first run, which gathered data for 85 days between April and August of this year. LUX is located a mile underground (to shield from cosmic rays and other interference) in an old mine in South Dakota, and employs a liquid Xenon detector with total mass of 370 kg. LUX is searching for WIMP dark matter particles which recoil directly off the nucleus of Xenon atoms in the detector.


Large Underground Xenon detector, Photo by Carlos Faham, CC Attribution 3.0 license

They have two important findings from this first swath of data. First, to within the sensitivity of their experiment, they detected no weakly interacting massive dark particles (WIMPs). And second, their experiment has much greater sensitivity than other experiments in the low mass range from about 5 GeV to 100 GeV (the proton rest mass is a bit less than 1 GeV). Thus it is placing much tighter constrains on the cross-section for dark matter to interact with a nucleus, and the density of dark matter at the Earth’s orbit. The previous largest Xenon-based experiment was XENON100 (for 100 kg total detector mass). With LUX, the sensitivity has improved over the results of that earlier experiment by around a factor of 20 for a possible 10 GeV WIMP mass, due to the larger target and better rejection of background events.


This chart is the most interesting portion of Fig. 5 from the LUX first results paper (reference below). The blue line shows the upper limit on the cross section dropping from 10^-40 cm² to less than 10-44 cm² as a function of WIMP mass, as the mass increases from about 5 to 12 GeV (X-axis above the chart). Note the Y-axis is logarithmic, so the new limit is orders of magnitude below other limits (various colored curves) and claimed possible detections (shaded areas).

These new LUX results are in direct conflict with possible detections from CoGeNT (small red-shaded area on chart), CRESST (yellow-shaded), CDMS- II (green-shaded area), and DAMA/LIBRA (grey-shaded area), all of which were suggesting detections with a WIMP dark matter mass around 10 GeV. Now certain assumptions are made about the astrophysical parameters such as the density of dark matter at the Earth being the same as the average in our part of the galaxy. But other experimental results are based on similar assumptions, so this does not explain the discrepancy.

Both CoGeNT and CDMS-II sit in the same Soudan Laboratory in Minnesota, one state over from where the LUX experiment resides. However different experiments use different atoms as targets: CoGeNT uses germanium, CDMS uses silicon, CRESST uses calcium tungstate crystals and DAMA/LIBRA uses thallium doped sodium iodide. These latter two experiments are both located in Italy, in a mountain tunnel. All of these experiments are attempting to discern a very faint signal against significant backgrounds. And perhaps earn a Nobel Prize in Physics as well. So it’s natural for the researchers on the associated teams to lean toward optimism It remains quite possible, and now seems more and more probable, that the experiments other than LUX are observing some unexplained non-dark matter background effect, so this is a very significant result.

LUX is not finished, of course. It’s just getting going. So we await their further results, with either a possible WIMP detection in the future, or even tighter limits on the existence of lower mass WIMPs.

References: – LUX consortium home page – D.S. Akerib et. al., 2013,  “First results from the LUX dark matter experiment at the Sanford Underground Research Facility” – LUX results are constraining WIMP parameter space – on the LUX results

Higgs Boson and Dark Matter, Part 1

The discovery of the Higgs boson at the Large Hadron Collider (the LHC, at CERN, near Geneva) was announced on the 4th of July, 2012. This new particle was the important missing component of the Standard Model of particle physics; the Standard Model has had great success in describing the three non-gravitational forces: electromagnetism, the weak nuclear force, and the strong nuclear force.

The mass of the Higgs is about 126 GeV (giga electron-Volts) and by way of comparison the proton mass is a bit under 1 GeV.  The Higgs particle is highly unstable, with a decay lifetime of only about one tenth of one billionth of one trillionth of a second (10^-22 seconds). While the  Higgs field pervades all of space, the particle requires very high energy conditions to “pop out” of the field for a very short while. The only place where these conditions exist on Earth is at the LHC.

The Higgs boson is not detected directly at LHC, but inferred (with high confidence) through the detection of its decay products. The main decay channels are shown in the pie chart below, and include bottom quarks, W vector bosons (which mediate the weak force), gluons (which mediate the strong force holding quarks inside protons and neutrons), tau leptons (very heavy members of the electron family), Z vector bosons (also weak force mediators), and even some photon decay channels. While the two photon channel is rare, much less than 1% of the decays, it is the most important channel used for the Higgs detection because of the “clean” signal provided.


What is the relationship between the Higgs and dark matter? In an earlier blog, , I discussed why the Higgs particle itself cannot be the explanation for dark matter. Dark matter must be stable; it must persist over the nearly 14 billion year lifetime of the universe. In today’s universe it’s very difficult and expensive to create a Higgs particle and it vanishes immediately.

But in the very early universe, at a tiny fraction of a second after its creation (less than the present-day Higgs boson lifetime!), the “temperature” and energy levels were so high that the Higgs particle (or more than one type of Higgs particle) would have been abundant, and as today it would have decayed to many other, lighter, particles. Could it be the source of dark matter? It’s quite plausible, if dark matter is due to WIMPs – an undiscovered, stable, weakly interacting massive particle. That dark matter is due to some type of WIMP is currently a favored explanation among physicists and cosmologists. WIMPs are expected from extensions to the Standard Model, especially supersymmetry models.

One possible decay channel would be for the Higgs boson to decay to two dark matter WIMPs. In such a decay to two particles (a WIMP of some sort and its anti-particle), each would have to have a rest mass energy equivalent of less than half of the 126 GeV Higgs boson mass; that is, the dark matter particle mass would have to be 63 GeV or less.

There may be more than one type of Higgs boson, and another Higgs family particle could be the main source of decays to dark matter. In supersymmetric extensions to the Standard Model, there is more than one Higgs boson expected to exist. In fact the simplest supersymmetric model has 5 Higgs particles! 

Interestingly, there are 3 experiments which are claiming statistically significant detections of dark matter, these are DAMA/LIBRA, COGENT,  and CDMS-II. And they are all suggesting a dark matter particle mass in the neighborhood of just 10 GeV. Heavy, compared to a proton, but quite acceptable in mass to be decay products from the Higgs in the early universe. It’s not a problem that such a mass might be much less than 63 GeV as the energy in the decay could also be carried off by additional particles, or as kinetic energy (momentum) of the dark matter decay products.

At the LHC the search is underway for dark matter as a result of Higgs boson decays, but none has been found. The limits on the cross-section for production of dark matter from Higgs decay do not conflict with the possible direct detection experiments mentioned above.

The search for dark matter at the LHC will actively continue in 2015, after the collision energy for the accelerator is upgraded from 8 TeV to 14 TeV (trillion electron-Volts). The hope is that the chances of detecting dark matter will increase as well. It’s a very difficult search because dark matter would not interact with the detectors directly. Rather its presence must be inferred from extra energy and momentum not accounted for by known particles seen in the LHC’s detectors.


Multi-component Dark Matter: Let there be Heavy and Let there be Light

Around 27% of the universe’s mass-energy is due to dark matter, according to the latest Planck satellite results; this finding is consistent with a number of other experiments as well. This is approximately 6 times more than the total mass due to ordinary matter (dominated by protons and neutrons) that makes up the visible parts of galaxies, stars, planets, and all of our familiar world.
The most likely explanation for dark matter is some kind of WIMP – Weakly Interacting Massive Particle. The amount of deuterium (heavy hydrogen) produced in the very early universe rules out ordinary matter as the primary explanation for the various “excess” gravitational effects we see in galaxies, groups and clusters of galaxies and at the largest distance scales in our observable universe.

WIMPs are thought to be a class of new, exotic particles, beyond the Standard Model. A favored candidate for dark matter is the lightest supersymmetric particle, although supersymmetry is as of yet unproven. The lightest such particle would be very stable, having nothing into which it could decay readily. A mass range of 5 to 300 GeV or so is the range in which most of the direct detection experiments looking for dark matter are focused (1 GeV = 1 giga-volt is a little more than the mass of a proton).

But there would certainly be more than one kind of such WIMP formed in the very early universe. These would be heavier particles, and most would quickly decay into lighter products, but there might still be some heavier WIMPs remaining, provided their lifetime was sufficiently long. Particle physicists are actively working on models with more than one component for dark matter, typically two-component models with a heavy particle above 100 GeV mass, and a lighter component with mass of order 10 GeV (more or less).

In fact there are observational hints of the possibility of both a light dark matter particle and a heavier one. The SuperCDMS team has announced a possible detection around 8 or 9 GeV. The COGENT experiment has a possible detection in the neighborhood of 10 GeV, and in general agreement with the SuperCDMS results.

ImageFermi satellite payload, photo credit: NASA/Kim Shiflett

At the heavier end, the Fermi LAT gamma-ray experiment has made a possible detection of an emission line at 130 GeV which might result from dark matter decay. A pair of such gamma rays could be decay products from annihilation of a heavier dark matter particle with mass around 260 GeV. Or a particle of that mass could decay into some other particle plus a photon with about half of the heavy dark matter mass, e.g. 130 GeV.

Kajiyama, Okada and Toda have built one such model with a light particle around 10 GeV and a heavier one in the 100 to 1000 GeV region. They claim their model is consistent with the observational limits on dark matter placed by the XENON 100 experiment.

Gu has developed a model with 2 dark matter components with magnetic moments. Representative values of the heavy dark matter particle mass at 262 GeV and the lighter particle mass at 20 GeV can reproduce the observed overall dark matter density. He also finds the decay lifetime for the heavier particle state to be very long, in excess of 10^20 years, or 10 billion times the age of the universe, thus in this model the heavy dark matter particle easily persists to the present day. In fact, he finds that the heavy particle dominates with over 99% of the total mass contribution to dark matter. And a heavy dark matter particle with the chosen mass can decay into the lighter dark matter particle plus an energetic 130 GeV gamma ray (photon). This might explain the Fermi LAT results.

Furthermore, the existence of two highly stable dark matter particles of different masses would help explain some astrophysical issues related to the formation of galaxies and their observed density profiles. Mikhail Medvedev has numerically simulated galaxy formation using supercomputers, with a model incorporating two dark matter components. This model results in a better fit to the observed velocities of dwarf galaxies in the Local Group than does a model with a single dark matter component. (The Local Group includes our Milky Way, the Andromeda galaxy, the Magellanic Clouds and a number of dwarf galaxies.) His model also helps to explain the more flattened density profiles in galaxies and the smaller numbers of dwarf galaxies actually observed relative to what would be predicted by single dark matter component models.

Occam’s razor says one should adopt the simplest model that can explain observational results, suggesting one should add a second component to dark matter only if needed. It seems like a second dark matter component might be necessary to fully explain all the results, but we will require more observations to know if this is the case.

References: Y. Kajiyama, H. Okada and T. Toda 2013, “Multicomponent dark matter particles in a two-loop neutrino model”
P. Gu 2013, “Multi-component dark matter with magnetic moments for Fermi-LAT gamma-ray line” M. Medvedev 2013, “Cosmological Simulations of Multi-Component Cold Dark Matter”




Dark Matter in the Solar System: Does it Matter?

Dark matter is the dominant form of matter in the universe. Measurements from supernovae, the cosmic microwave background, galaxy clusters, galaxy rotation and other techniques indicate that it is approximately 5 or 6 times as abundant by mass density as ordinary matter. By particle number, it is probably less abundant, as long as the dark matter particle has mass greater than 6 GeV (giga-electron Volts) as seems likely (actually mass is in units of GeV/c², but physicists like to use the shorthand of “GeV”). The ordinary matter mass component is dominated by protons and neutrons with approximately 1 GeV mass. So if the dark matter particle turns out to be 6 GeV, which is near the lower bound of expected mass, then just as many dark matter particles as protons and neutrons combined would explain the nearly 6 times as much dark matter mass density on average, as compared to ordinary matter density. Otherwise, if the dark matter particle mass is larger, fewer would suffice.

Dark matter clumps, under its own gravitational influence, into large scale structures including superclusters of galaxies, clusters and groups of galaxies, and individual galaxies and dwarf galaxies. Within our own Milky Way galaxy, the dark matter is more diffuse, more spread out, than ordinary matter. As one moves away from the center of the galaxy, and above the spiral disk that contains most of the ordinary, luminous matter, the dark matter to ordinary matter ratio increases. Ordinary matter clumps to a much greater degree since it feels electromagnetic forces, and these result in friction and shock waves that heat up the ordinary matter, but also cooling via radiative processes – emission of photons. Cold ordinary matter will clump due to mutual gravitational infall as it cools, and this is how we end up with molecular clouds (stellar nurseries), stars, and planets, moons, asteroids, and comets. In these structures, which are at much smaller distance scales, ordinary matter dominates over dark matter. Dark matter doesn’t feel electromagnetic forces, so it remains more spread out, influenced primarily by gravitational forces.


Nevertheless, one can ask the question, to what extent does dark matter influence our Solar System? For example, are the orbits of the Earth or other planets perturbed due to the gravitational effect of dark matter found in the Solar System? Surely there is some dark matter within the Solar System, assuming the most favored explanation, that it is some sort of new particle, a WIMP – weakly interacting massive particle, or perhaps an axion. This is why direct detection efforts looking for dark matter passing through Earth-bound laboratories are worthwhile.

The amount of dark matter in the galactic plane in the vicinity of the Solar neighborhood is estimated by looking at the dynamics of stars nearby and above and below the Milky Way’s disk. By looking at their velocity distribution we can measure the total mass density and subtract out the ordinary matter component. The favored value in the Solar neighborhood for the galactic background is usually taken to be 0.3 GeV/cc and equates to the equivalent of 1 proton per every 3 cubic centimeters. Thus, with this value, if the dark matter particle has mass 10 GeV, there would need to be 1 of these particles for each 30 cc of space. This is not a significant amount; within Earth’s orbit it would amount to about 8 billion tons. Out to the orbit of Saturn, the total amount would be around 9 trillion tons. This is not much in Solar System terms.

However, there’s more to the story than just this quick estimate. Let’s look at the observational constraints first; one can look for perturbations in the orbits of the major Solar System bodies to place some constraints on the amount of dark matter. Then we will look at the possibility that the  Solar System’s complement of dark matter is significantly higher than the value inferred from stellar dynamics within the Milky Way, due to gravitational capture of some of the dark matter encountered over billions of years as the Sun (and the rest of the Solar System) orbits the center of our galaxy at over 200 kilometers per second. The idea is that the average in the Solar “suburban” neighborhood is close to the estimate above, but in the “urban” neighborhood closer to the Sun the dark matter is more concentrated, due to being gravitationally swept up by the Sun and larger planets.

Russian researchers Pitjev and Pitjeva have studied hundreds of thousands of observations – over a nearly 50 year period – of the planets, a number of their moons, and spacecraft in the Solar System, looking for orbital perturbations. They find no measurable deviations which could be ascribed to dark matter. They have found that the density is less than 1.1 x 10^-20 grams/cc at the orbit of Saturn, 1.4 x 10^-20 g/cc at Mars, and less than 1.4 x 10^-19 g/cc at Earth. We can convert this to GeV/cc by noting that the proton mass is .938 GeV, which is equivalent to 1.67 x 10^-24 grams. So their upper limit on density at Saturn is then equivalent to 6000 GeV/cc. This is a much looser constraint. In other words, even at several thousand GeV/cc for the dark matter density near to the Sun, no apparent orbital perturbations would be expected for the 8 planets and several moons and spacecraft studied.

Thus one can conclude that even if the dark matter density in the Solar neighborhood were 10 or even 100 times larger than expected from stellar dynamics observations, that its gravitational effects on the precisely measured orbits of the major planets and major moons in the Solar system would be of no consequence.

In fact the authors note that the aggregate dark matter within Saturn’s orbit should be less than 1/6th of 1 billionth of the Sun’s mass, which is 2 x 10^27 metric tons. We’re talking at most 3 x 10^17 metric tons, which is a lot, but not in Solar system terms. The mass of the Moon is 7 x 10^19 metric tons, so this is an amount over 200 times smaller than the Moon’s mass spread out over the volume within Saturn’s orbit.

Another research team, at the University of Arizona, used a different technique five years ago. They modeled how much dark matter would be swept up into and gravitationally captured, by the Solar System over its 4.5 billion year history as it moves around the galactic center. Drs. Xu and Siegel calculate that about 10^17 metric tons of dark matter have been captured, out to the outer reaches of the Solar system. This amount is just 0.14% of the Moon’s mass and 0.0018% the mass of the Earth. This is consistent with the less than 1/3 x 10^18 metric tons within Saturn’s orbit from the orbital study above.

One of the important consequences of the Xu and Siegel results is that direct searches for dark matter need to consider in their models for data analysis not only the flux of the high velocity component as the Earth and Solar System move around the galactic center at over 200 km/sec, but also the lower velocity component. This applies to the more abundant dark matter that is bound within the Solar System and through which the Earth moves at a rate of 30 km/sec. At the Earth’s location their model implies a density 2000 times higher, or 600 GeV/cc, for this low velocity, bound component so despite the lower velocity, it could well dominate in dark matter detection experiments.

References: – N. P. Pitjev and E. V. Pitjeva, 2013, “Constraints on Dark Matter in the Solar System” – describes Solar System dark matter capture model of Ethan Siegel and Xiaoying Xu of the University of Arizona – E. Siegel and X. Xu, 2008, “Dark Matter in the Solar System”

More Dark Matter: First Planck Results


Credit: European Space Agency and Planck Collaboration -

Map of CMB temperature fluctuations with slightly colder areas in blue, and hotter areas in red.


The first results from the European Space Agency’s Planck satellite have provided excellent confirmation for the Lambda-CDM (Dark Energy and Cold Dark Matter) model. The results also indicate somewhat more dark matter, and somewhat less dark energy, than previously thought. These are the most sensitive and accurate measurements of fluctuations in the cosmic microwave background (CMB) radiation to date.

Results from Planck’s first 1 year and 3 months of observations were released in March, 2013. The new proportions for mass-energy density in the current universe are:

  • Ordinary matter 5%
  • Dark matter 27%
  • Dark energy 68%


Credit: European Space Agency and Planck Collaboration

The prior best estimate for dark matter primarily from the NASA WMAP satellite observations, was 23%. So the dark matter fraction is higher, and the dark energy fraction correspondingly lower, than WMAP measurements had indicated.

Dark energy still dominates by a very considerable degree, although somewhat less than had been thought prior to the Planck results. This dark energy – Lambda – drives the universe’s expansion to speed up, which is known as the runaway universe. At one time dark matter dominated, but for the last 5 billion years, dark energy has been dominant, and it grows in importance as the universe continues to expand.

The Planck results also added a little bit to the age of the universe, which is measured to be about 13.8 billion years, about 3 times the age of the earth. The CMB radiation itself, was emitted when the universe was only 380,000 years old. It was originally in the infrared and optical portions of the spectrum, but has been massively red-shifted, by around 1500 times, due to the expansion of the universe.

There are many other science results from the Planck Science team in cosmology and astrophysics. These include initial support indicated for relatively simple models of “slow roll” inflation in the extremely early universe. You can find details at the ESA web sites referenced below, and in the large collection of papers from the 47th ESlab Conference link.

References: – news article at ESA site – runaway universe blog – Planck Science Team site – 47th ESlab Conference presentations on Planck science results


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