Dark Photons

It’s humbling to think that ordinary matter, including all of the elementary particles we’ve ever detected in laboratory experiments, only makes up about 5% of the energy density of the universe. The rest, of course, comes in the form of a dark sector: some form of energy density that can be reliably inferred through the gravitational fields it creates, but which we haven’t been able to make or touch directly ourselves.

It’s irresistible to imagine that the dark sector might be interesting. In other words, thinking like a physicist, it’s natural to wonder whether the dark sector might be complicated, with a rich phenomenology all its own. And in fact there is something interesting going on: over the last 15 years we’ve established that the dark sector comes in at least two different pieces! There is dark matter, 25% of the universe, which we know is like “matter” because it behaves that way — in particular, it clumps together under the force of gravity, and its energy density dilutes away as the universe expands. And then there is dark energy, 70% of the universe, which seems to be eerily uniform — smoothly distributed through space, and persistent (non-diluting) through time. So, there is at least that much structure in the dark sector.

But so far, there’s no evidence of anything interesting beyond that. Indeed, the individual components of dark matter and dark energy seem relatively vanilla and featureless; more precisely, taking them to be “minimal” provides an extremely good fit to the data. For dark matter, “minimal” means that the particles are cold (slowly moving) and basically non-interacting with each other. For dark energy, “minimal” means that it is perfectly constant throughout space and time — a pure vacuum energy, rather than something more lively.

Still — all we have are upper limits, not firm conclusions. It’s certainly possible that there is a bushel of interesting physics going on in the dark sector, but it’s just too subtle for us to have noticed yet. So it’s important for we theorists to propose specific, testable models of non-minimal dark sectors, so that observers have targets to shoot for when we try to constrain just how interesting the darkness really is.

Along those lines, Lotty Ackerman, Matt Buckley, Marc Kamionkowski and I have just submitted a paper that explores what I think is a particularly provocative possibility: that, just like ordinary matter couples to a long-range force known as “electromagnetism” mediated by particles called “photons,” dark matter couples to a new long-range force known (henceforth) as “dark electromagnetism,” mediated by particles known (from now on) as “dark photons.”

Dark Matter and Dark Radiation
Authors: Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, Marc Kamionkowski

We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (“dark electromagnetism”) that couples only to dark matter, not to the Standard Model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine-structure constant $hatalpha$ is sufficiently small. The correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions, and we verify that this is consistent with particle-physics constraints. The primary limit on $hatalpha$ comes from the demand that the dark matter be effectively collisionless in galactic dynamics, which implies $hatalpha$ < 10-3 for TeV-scale dark matter. These values are easily compatible with constraints from structure formation and primordial nucleosynthesis. We raise the prospect of interesting new plasma effects in dark matter dynamics, which remain to be explored.

Just to translate that a bit, here is the idea. We’re imagining there is a completely new kind of photon, which couples to dark matter but not to ordinary matter. So there can be dark electric fields, dark magnetic fields, dark radiation, etc. The dark matter itself consists half of particles with dark charge +1, and half with antiparticles with dark charge -1. Now you might say to yourself, “Why don’t the particles and antiparticles all just annihilate into dark photons?” That kind of thinking is probably why ideas like this weren’t explored twenty years ago (as far as we know). But if you think about it, there is clearly a range of possibilities for which the dark matter doesn’t annihilate very efficiently; for example, if the mass of the individual dark matter particles was sufficiently large, their density would be very low, and they just wouldn’t ever bump into each other. Alternatively, if the strength of the new force was extremely weak, it just wouldn’t be that effective in bringing particles and antiparticles together.

None of that is surprising; the interesting bit is that when you run the numbers, they turn out to be pretty darn reasonable, as far as particle physics is concerned. For DM particles weighing several hundred times the mass of the proton, there should be about one DM particle per coffee-cup-sized volume of space. The strength of the dark electromagnetic force is characterized, naturally, by the dark fine-structure constant; remember that ordinary electromagnetism is characterized by the ordinary fine-structure constant α = 1/137. It turns out that the upper limit on the dark fine-structure constant required to stop the dark matter particles from annihilating away is — about the same! I was expecting it to be 10-15 or something like that, and it was remarkable that such large values were allowed.

However, we know a little more about the dark matter than “it doesn’t annhilate.” We also know that it is close to collisionless — dark matter particles don’t bump into each other very often. If they did, all sorts of things would happen to the shape of galaxies and clusters that we don’t actually observe. So there is another limit on the strength of dark electromagnetism: interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters. That turns into a more stringent bound on the dark fine-structure constant: about an order of magnitude smaller, at $hatalpha$ < 10-3. Still, not so bad.

More interestingly, we can’t say with perfect confidence that the dark matter really is effectively non-interacting. If a model like ours is right, and the strength of dark electromagnetism is near the upper bound of its allowed value, there might be very important consequences for the evolution of large-scale structure. At the moment, it’s a little bit hard to figure out what those consequences actually are, for mundane calculational reasons. What we are proposing is that the dark matter is really a plasma, and to understand how structure forms, one needs to consider dark magnetohydrodynamics. That’s a non-trivial task, but we’re hoping it will keep a generation of graduate students cheerfully occupied.

The idea of new forces acting on dark matter is by no means new; I’ve worked on it recently myself, and so have certain co-bloggers. (Strong, silent types who are too proud to blog about their own papers.) What’s exciting about dark photons is that they are much more natural from a particle-physics perspective. Typical models of quintessence and long-range fifth forces invoke scalar fields, which are easy and fun to work with, but which by all rights should have huge masses, and therefore not be very long-range at all. The dark photon comes from a gauge symmetry, just like the ordinary photon, and its masslessness is therefore completely natural.

Even the dark photon is not new. In a recent paper, Feng, Tu, and Yu proposed not just dark photons, but a barrelful of new dark fields and interactions:

Thermal Relics in Hidden Sectors
Authors: Jonathan L. Feng, Huitzu Tu, Hai-Bo Yu

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter’s thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated…

They show that these models manage to evade all sorts of limits you might be worried about, from getting the right relic abundance to fitting in with constraints from primordial nucleosynthesis and the cosmic microwave background.

Our model is actually simpler, because we have a different flavor of fish to fry: the possible impacts of this new long-range force in the dark sector on observable cosmological dynamics. We’re not sure yet what all of those impacts are, but they are fun to contemplate. And of course, another difference between dark electromagnetism and a boring scalar force is that electromagnetism has both positive and negative charges — thus, both attractive and repulsive forces. (Scalar forces tend to be simply attractive, and get all mixed up with gravity.) So we can imagine much more than a single species of dark matter; what if you had two different types of stable particles that carried dark charge? Then we’d be able to make dark atoms, and could start writing papers on dark chemistry.

You know that dark biology is not far behind. Someday perhaps we’ll be exchanging signals with the dark internet.

  1. Quoted from Marshall:

    “If a dark matter clump comes through the solar system, and it gravitationally interacts with one of the planets, there is a chance that some of the clumps, or some portion of the clumps, will become gravitationally bound to the solar system, and thus detectable. (The same 3 body interactions will apply to individual dark matter particles if there is no clumping of dark matter.) Even if the rms velocity of the clumps is too high to make this very probable, 4.5 billion years is a long time and there will be a dark matter halo around the Sun, and maybe individual planets as well; this should be considered tests of dark matter.”

    There’d be an easy way to detect a dark matter halo around the Sun, in the orbits of the outer planets. Suppose it were uniform in density; then by Newton’s shell theorem, you should get a sunward force linearly increasing with distance from sun, then dropping off at some boundary. Now clearly, the density is likely to be higher closer to the sun, that was just an illustrative model. But that might show up, say, in the trajectories of the Pioneer and Voyager probes, accounting for some of the sunward acceleration.

    I like Alsee’s idea, too. Having interactions on the scale of ours would be exciting, suggesting there could be dark life, but I’d be curious as to what sort of chemistry could develop with a very low fine structure constant.

    Just one point. What about a dark colour force? It’s difficult enough as it is to make QCD calculations where we know what the answer should be; is it possible to exclude this based on astrophysical data? Because if you’re having strongly radiant bodies, either it’s going to be thermal, with pockets of very hot dark matter contracting, say, under their own gravity, or you’ve got to have nuclear or chemical reactions.

  2. If dark matter clusters around stars or stellar systems then we might get some F = -kr type of force inwards for bodies in the DM cloud and assuming a more or less constant density. If there is a dark matter particle in a coffee cup volume, as stated by Sean, then this is one particle per ~10cm^3. A spherical volume containing the solar system is about 10^{30}km^3 = 10^{45}cm^3. So that would amount to about 10^{22} moles of DM particles in the whole solar system. If the mass of DM particles is assumed to be ~ 1 TeV then this is about 10^{25} grams of the stuff within a sphere of 10^{10}km around the sun. This is a bit, but considering that the Earth is 10^{30}g in mass the total DM mass in the solar system is then comparable to one of the larger asteroids in the solar system.

    Of course we can play with the mass of DM particles and their distrubutions. I am also not sure whether this works for the Pioneer anomaly, which appears “device dependent,” as the Voyager crafts don’t appear to have this effect.

    Lawrence B. Crowell

  3. If there is a dark matter particle in a coffee cup volume, as stated by Sean, then this is one particle per ~10cm^3. A spherical volume containing the solar system is about 10^{30}km^3 = 10^{45}cm^3. So that would amount to about 10^{22} moles of DM particles in the whole solar system. If the mass of DM particles is assumed to be ~ 1 TeV then this is about 10^{25} grams of the stuff within a sphere of 10^{10}km around the sun.

    This should understand the effect, as this is the background density, not the density of a solar DM halo. However, 10^22 Kg is about 5 x 10^-9 Msun or about 10 times the Mass of Ceres. Ceres can be detected at the few percent level in Earth-Mars ranging (the Ceres mass formal error is 7 x 10^-13 Msun in the EPM2004 ephemeris – see http://iau-comm4.jpl.nasa.gov/EPM2004.pdf). Note that 10^10 km ~ 67 AU, so there should be about 5 x 10^-12 Msun within 6.7 AU in this model.

    So, there is at least a potential for detectability – the real question IMHO is how concentrated a dark matter halo would be. Best for detectability would be a scale height of a few AU, but it would clearly be good to estimate that in a parameterized fashion.

    There are similar considerations with binary pulsars, of course.

  4. Lawrence,

    Calculating very roughly, I get a density of about 3 x 10^-13 kilograms per cubic metre (assuming the Pioneer spacecraft to be at 71 AU; assuming 90, you get about 2.3 x 10^-13). This is about five orders of magnitude more dense than your calculation would have it. Though I couldn’t find any data with more than one or two significant figures freely available, I was working mainly from press fact sheets, which is never very good and could easily have made the calculation meaningless.

    The real problem I see is that the two spacecraft are quite far apart, so you’d tend to have noticed the force being higher for the one further away. The difference would be smaller if the density of the dark matter halo decreases as you get further away from the sun.

    At least it should only show up at long distances, as the effect on the Earth would be tens of times smaller.

  5. Benjamin: I am not sure how you got that figure of 10^{-13}kg/m^3. That would be 10^{-10}g/m^3 or 10^{-16}g/cm^3. A proton at m ~ 10^{-27}g means a TeV DM particle is ~ 10^{-26}g, so your DM particles would be very hefty! I just worked directly with moles, which is easier IMO.

    Marshall: I agree that the gravitational effect of DM might be detectable in the solar system, even though it would be small. It is not clear to me that the Pioneer craft reflect this physics. That this anomaly is absent from the Voyager craft makes me suspect this is due to a leak or some differential cold gas to solid deposition or sublimation of atoms on the surfaces of the craft.

    Lawrence B. Crowell

  6. I did a rough calculation of what density would be required to produce the observed acceleration at a distance of 71 AU, which was the only figure I could find data for. It had nothing to do with the particles themselves.

  7. Ok, got you. I think this suggests that the Pioneer anomaly may not likely be due to DM. That is unless DM particles are very hefty, or much more abundant that one particle per “coffee cup.” We’d also have to sum this up over intergalactic volumes to see if this can reproduce the gravitational effects attributed to DM.

    Lawrence B. Crowell

  8. The individual masses of the particles might not necessarily have to be that high, but they’d have to be quite clumpy, and I think that’s pretty much ruled out by our observation that dark matter tends to be vastly less clumpy than normal matter.

  9. The rational for DM as very weakly interacting with itself is that DM regions don’t exhibt much clumpiness. As far as I know the relative paucity of clumps is seen in the absence of localized Einstein lensing in DM regions.

    Lawrence B. Crowell

  10. Hi Sean,

    From what I understand, Matti Pitkanen’s work also directly discusses the possibilities of dark photons, dark chemistry, and dark biology.

    A brief Letter to the Editor, Foundations of Physics is at: http://cavekitty.ca/db_origin.pdf

    I’m hoping that they’ll publish it, since these are all very good ideas. I’d just hate to see Pitkanen’s hard work go unnoticed, etc, etc, etc.

  11. Since bridge sales are down a bit this month and bills are mounting up, would anyone be interested in purchasing one of several small dark worlds I happen to have on hand? Would be a great place to experiment with dark chemistry and dark biology. Be the first in your department to have one! String theorists are welcome–we speak branes fluctuationently. Wholesale prices, retail quality! (Shipping & handling extra)

  12. ” Imagine there is a space with only one charge on it. Suppose the space is a sphere. Then in a classical picture the lines of force leave all these charges and have “nowhere to go.” ”

    Why is this not true of gravity?

  13. I went to an interesting lecture at J-Lab today by Andrei Afanasev.


    “Search for Dark-Matter Particles in Photon-Photon Interaction at Optical Frequencies”

    He went over the basics of DM, including evidence from the Bullet Cluster (since approaching clumps of DM blew past each other and their formerly associated clumps of matter, I guess that close to rules out regular matter (RM) bases of DM such as MACHOs?) Andrei considers axions (of some sort) to be a good choice of what DM consists of, curiously not mentioned here. He discussed the LIPSS experiment, interesting to me as offbeat physics but also since I know and got to brainstorm with one of the main experimenters (K Beard.) I had already heard how hard it was to do right. Briefly: Take advantage of photon-photon coupling to produce some axions A or other DM particle by shining powerful laser through magnetic field. Stop conventional photons with a wall, and convert A back into photons with magnetic field on other side. It would be a tiny effect, much noise from cosmic rays, and the experiment turned out negative. That doesn’t mean “no DM can be produced from photon-photon reactions” but the mass must be even less (“milli-eV”)

    Another idea was directly relevant to “dark photons”, and that was the creation through the same means of what Andrei and some others call “paraphotons” which is presumably the same sort of idea. I told Andrei that should mean an equivalent para-charge analogy for the DM particles, which seemed odd to me and would maybe have prevented DM in the Bullet collision from cross-passing like that – he said, it weakly couples even to itself. He appreciates that we wouldn’t just have “four forces” in the universe any more.

    I forgot to bring up, that paracharged particles seem to imply an analogous “anti-dark matter” regime, and then the same question as for RM of why it didn’t all mutually disintegrate etc. (Also, they would be stable, not with 10^10 s half-life decay even into paraphotons, since paracharge presumably is conserved. BTW axions are thought to decay into ordinary photons.) There are other odd issues, like what role to virtual paraphotons play in the scheme of things? Maybe if virtual photons give the wrong vacuum energy level for DE, then VPPs do it right?

  14. Neil,

    Well, structure formation arguments basically rule out MACHO’s, as we see the evidence of dark matter even within the CMB, which was long before any compact objects had a chance to form. The Bullet Cluster does not, because MACHO’s are just as non-interacting as the stars and galaxies: they’re few and far between, so they mostly just miss one another in a collision like that.

    The difficulty with axions is that they have very low mass, which makes them a candidate for “warm” dark matter, which seems to not fit well with our current observations of structure formation. But, more observations are necessary to really say this with confidence, and perhaps the 21cm and cosmic shear observations will weigh in here to say something definitive.

  15. (I hope this is OK to do, I got this “lost” comment from Sean using my browser cache of the old CV site):

    Sean on Nov 10th, 2008 at 12:32 pm

    Actually, axions are (usually) very much cold dark matter, not warm. It’s true that their masses are small — small enough to make them hot dark matter, if they were produced in thermal equilibrium. But they’re not; they come into existence at zero momentum as part of a Bose condensate. The energy per axion is enormously smaller than the energy per CMB photon.

  16. Robert, if anti-light traveled at 10c as you suggest, it would make causality troubles in our universe if it could ever be detected (read about special theory of relativity.) However, such alternate photons might go slower than our light.

    Also, “dark photons” as imagined by Sean and others are not like negative energy that can cancel out ordinary light or energy, they are “dark” because we can’t see them (i.e., they don’t interact with ordinary matter-energy enough.)

  17. Negative energy is of course unlikely. In this case the eigen-numbers or spectrum of quantum field theory is not bounded below. This has serious pathological consequences.

    L. C.

  18. Neil B,

    Interesting. Guess that shows that I haven’t been following axions very closely.

    Robert Bast,

    Anti-light is a really bad name. It can only cause confusion as it evokes anti-matter, which is a completely different phenomenon. In fact, there is an anti-particle to the photon: it’s called the photon (so yes, this means that just as an electron and a positron can annihilate with one another to produce all sorts of things, a photon can annihilate with another photon, if the pair have enough energy between them to produce anything).

    I honestly don’t see how the speed of dark photons could be any different from normal photons unless they have some mass, which would cause the force to be short range, which would be something other than what Sean is proposing.

  19. This guy, Jay Alfred, has written a lot about “dark plasma” since 2006 in his books. He argues in his article “Dark Matter – Plasma of Super Particles” (June 2008) that “…dark matter consists of non-standard (or super) plasma which radiates energetic waves. These postulated “super” waves or “S-Waves” are currently not directly measurable by our scientific instruments.” See http://ezinearticles.com/?Dark-Matter—Plasma-of-Super-Particles&id=1240357.

  20. Sean, I’m trying to understand what you said: “Yes, I forgot to mention: our DM candidate is certainly not some superpartner of any of the particles in the Standard Model, since we don’t want any of them to carry dark charge.”

    Did you not argue in your paper that the DM candidate could be a WIMP (which is a linear combination of super partners)? Furthermore, it is stated in your paper that the particles have a dark U(1) charge (but there is overall charge neutrality). Puzzled…

    By the way the link to Jay Alfred’s article should be:


    (without the full-stop at the end … hope it works this time)

  21. Brane Matter … Could dark matter be evidence for parallel branes? Matter in our brane and other(s) would only interact via the gravitational force.

  22. Pingback: Dark Atoms | Cosmic Variance | Discover Magazine