19

THE SPEED OF DARK

Both casual observers of science and scientists themselves frequently employ Occam’s Razor for guidance when evaluating scientific proposals. This oft-cited principle says that the simplest theory that explains a phenomenon is most likely to be the best one. Its sensible-sounding logic dictates that it is probably a bad idea to build complicated structures when a leaner one will do.

Yet two factors undermine the authority of Occam’s Razor, or at least suggest caution when using it as a crutch. I’ve learned the hard way to be wary of crutches—both intellectual and physical. Once when I used the tangible kind to heal a broken ankle, I leaned on them incorrectly and caused nerve damage in my arms. Theories that conform to the dictates of Occam’s Razor sometimes similarly address one outstanding problem while creating issues elsewhere—usually in some other aspect of the theory that embraces it.

The best science should always encompass, or at the very least be consistent with, the broadest possible range of observations. The real question is what most effectively solves the entire set of unexplained phenomena. A proposed explanation that seems simple at first might devolve into a Rube Goldberg contraption when confronted with a larger set of issues. On the other hand, an explanation that seemed unduly cumbersome when applied to the original problem might, when seen through the lens of scientific peripheral vision, come to reveal its underlying elegance.

My second concern about Occam’s Razor is just a matter of fact. The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter—at least according to what we’ve deduced so far. Yet they exist. Sometimes the simplest model just isn’t the correct one.

Discussions on this topic emerged many times at the “Dark Matter Debates” conference mentioned in the previous chapter. In her talk about experimental constraints on unnecessary but testable particles, the particle physicist Natalia Toro argued that a more appropriate guide than Occam’s Razor would be a principle she called “Wilson’s Scalpel.” She named it after the physicist Ken Wilson, who developed a general framework for understanding how to do science by keeping track only of those elements that are testable. Natalia proposed that a scalpel in his name should be used to shape, rather than shave, a theory, leaving all testable elements intact—whether or not we can attribute an underlying purpose. When I spoke next, I jokingly suggested that the principle of “Martha’s Table” was a better idea still. After all, you don’t set a table with just knives. You set it with everything necessary to eat a meal in a dignified fashion. With the talent of a Martha Stewart, you will retain an organizing principle—no matter how many dishes and silverware you arrange.

Science too should have a properly set table—one that allows us to address the many phenomena that we observe. Although scientists tend to prefer simple ideas, they are rarely the whole story.

This discussion is all by way of prelude to my introducing what my collaborators and I called “partially interacting dark matter,” which led to the “double-disk dark matter” category of models, which I will also now present. Both classes of models acknowledge that the makeup of dark matter might not be so simple. Just as is true of particles of ordinary matter, dark matter particles might not all be the same. New types of dark matter with different types of interactions might exist and furthermore have observable, previously unforeseen consequences. Even if the interacting component turns out to be only a small fraction of the dark matter, it could have important implications for the Solar System and the galaxy. It might have had some significance for the dinosaurs too.

ORDINARY-MATTER CHAUVINISTS

Even though we know that ordinary matter accounts for only about one-twentieth of the Universe’s energy and a sixth of the total energy carried by matter (with dark energy constituting the remaining portion), we nonetheless consider ordinary matter to be the truly important constituent. With the exception of cosmologists, almost everyone’s attention is focused on the ordinary matter component, which you might have thought to be largely insignificant according to the energy accounting.

We of course care more about ordinary matter because we are made of the stuff—as is the tangible world in which we live. But we also pay attention because of the richness of its interactions. Ordinary matter interacts through the electromagnetic, the weak, and the strong nuclear forces—helping the visible matter of our world to form complex, dense systems. Not only stars, but also rocks, oceans, plants, and animals owe their very existence to the nongravitational forces of nature through which ordinary matter interacts. Just as a beer’s small-percentage alcohol content affects carousers far more than the rest of the drink, ordinary matter, though carrying a small percentage of the energy density, influences itself and its surroundings much more noticeably than something that just passes through.

Familiar visible matter can be thought of as the privileged percent—actually more like 15 percent—of matter. In business and politics, the interacting one percent dominates decision making and policy, while the remaining 99 percent of the population provides less widely acknowledged infrastructure and support—maintaining buildings, keeping cities operational, and getting food to people’s tables. Similarly, ordinary matter dominates almost everything we notice, whereas dark matter, in its abundance and ubiquity, helped create clusters and galaxies and facilitated star formation, but has only limited influence on our immediate surroundings today.

For nearby structure, ordinary matter is in charge. It is responsible for the motion of our bodies, the energy sources that drive our economy, the computer screen or paper on which you are reading this book, and basically anything else you can think of or care about. If something has measurable interactions, it is worth paying attention to, as it will have far more immediate effects on whatever is around.

In the usual scenario, dark matter lacks this type of interesting influence and structure. The common assumption is that dark matter is the “glue” that holds together galaxies and galaxy clusters, but resides only in amorphous clouds around them. But what if this assumption isn’t true and it is only our prejudice—and ignorance, which is after all the root of most prejudice—that led us down this potentially misleading path? What if, like ordinary matter, a fraction of the dark matter interacted too?

The Standard Model contains six types of quarks, three types of charged leptons including the electron, three species of neutrinos, all the particles responsible for forces, as well as the newly discovered Higgs boson. What if the world of dark matter—if not equally rich—is reasonably wealthy too? In this case, most dark matter interacts only negligibly, but a small component of dark matter would interact under forces reminiscent of those in ordinary matter. The rich and complex structure of the Standard Model’s particles and forces gives rise to many of the world’s interesting phenomena. If dark matter has an interacting component, this fraction might be influential too.

If we were creatures made of dark matter, we would be very wrong to assume that the particles in our ordinary matter sector were all of the same type. Perhaps we ordinary matter people are making a similar mistake. Given the complexity of the Standard Model of particle physics, which describes the most basic components of matter we know of, it seems very odd to assume that all of dark matter is composed of only one type of particle. Why not suppose instead that some fraction of the dark matter experiences its own forces?

In that case, just as ordinary matter consists of different types of particles and these fundamental building blocks interact through different combinations of charges, dark matter would also have different building blocks—and at least one of those distinct new particle types would experience nongravitational interactions. Neutrinos in the Standard Model don’t interact under the strong or electric force yet the six types of quarks do. In a similar fashion, maybe one type of dark matter particle experiences feeble or no interactions aside from gravity, but a fraction of it—perhaps five percent—does. Based on what we’ve seen in the world of ordinary matter, perhaps this scenario is even more likely than the usual assumption of a single very feebly or non-interacting dark matter particle.

People in foreign relations make a mistake when they lump together another country’s cultures—assuming they don’t exhibit the diversity of societies that is evident in our own. Just as a good negotiator doesn’t assume the primacy of one sector of society over another when attempting to place the different cultures on equal footing, an unbiased scientist shouldn’t assume that dark matter isn’t as interesting as ordinary matter and necessarily lacks a diversity of matter similar to our own.

The science writer Corey Powell, when reporting on our research in Discover magazine, started his piece by announcing that he was a “light-matter chauvinist”—and pointing out that virtually everyone else is too. By this he meant that we view the type of matter we are familiar with as by far the most significant and therefore the most complex and interesting. It’s the type of belief that you might have thought was upended by the Copernican Revolution. Yet most people persist in assuming that their perspective and their conviction of our importance are in keeping with the external world.

Ordinary matter’s many components have different interactions and contribute to the world in different ways. So too might dark matter have different particles with different behaviors that might influence the Universe’s structure in a measurable fashion.

THE INTERACTING MINORITY

My collaborators and I called the scenario with a small component of dark matter that interacts through nongravitational forces “partially interacting dark matter.” We first investigated the simplest such model, which involves only two components. The dominant component interacts only gravitationally and is the conventional cold dark matter that resides in spherical haloes around galaxies and galaxy clusters. The second component interacts gravitationally too, but also through an additional force very similar to electromagnetism.

This two-tiered dark matter scenario might sound exotic, but keep in mind that similar statements can be made about ordinary matter. Quarks experience the strong nuclear force but particles like electrons don’t. That is why quarks get bound into protons and neutrons but electrons do not. Similarly, electrons experience the electromagnetic force to which neutrinos are oblivious. So if we go against our usual chauvinism and allow for similar diversity in the dark world, it shouldn’t be impossible to imagine that a portion of the dark sector interacts through forces similar to—but distinct from—the ones through which the stuff we are made of interacts.

However, bear in mind that partially interacting dark matter is a little different from Standard Model matter in that although electrons don’t experience the strong force directly, they do interact with quarks and therefore experience indirect effects. The newly proposed form of dark matter might instead be entirely isolated in its interactions, with the bulk of dark matter not even experiencing indirect effects of the newly introduced dark force. Since we don’t yet know whether components of dark matter should interact—or whether dark matter is even composed of different types of particles—the first and simplest assumption would be that there are no other new interactions aside from the new form of electromagnetism and only the newly introduced charged particles experience this force. In this scenario, the bulk of the dark matter wouldn’t experience the new force at all.

For fun, I’ll call the force that is experienced by the interacting dark matter component dark light, or more generally I’ll call it dark electromagnetism. The names are chosen to remind us that the new type of dark matter experiences a force like electromagnetism—but one that is invisible to the ordinary matter of our world. Whereas ordinary matter carries charge so that it emits and absorbs photons, the newly introduced component of dark matter would emit and absorb only this new type of light, which ordinary matter simply doesn’t experience.

This dark electromagnetic force would be analogous to the usual electromagnetic force. But it would be an entirely different influence acting on particles charged under a distinct additional force that is communicated by an entirely new type of particle—a dark photon if you will. Though the new component of dark matter wouldn’t interact with ordinary matter, it would have self-interactions that would make it behave similarly to familiar matter, which, after all, doesn’t interact with dark matter either.

Both ordinary matter and dark matter would carry charge and experience forces, but those charges and forces would be distinct. The particles that carry charge under the new dark force would be attracted or repelled by each other in a way that is similar to the behavior of ordinary charged particles. But the dark sector’s interactions would be transparent to ordinary matter since dark matter interacts through its own unique form of light—not through the light with which we are familiar. Only dark matter particles would experience the new force’s influence.

Even while obeying similar laws of physics and maybe being in close proximity in space, dark matter and normal matter would each occupy their own worlds. Ordinary matter and dark matter could even physically overlap without ever interacting. Because they would interact with each other through distinct forces—aside from their extremely feeble gravitational influence, the charged ordinary matter and charged dark matter would be oblivious to each other’s presence.

Two types of electrically charged particles in the same place that don’t interact with each other is really not so mysterious. It’s a bit like ordinary matter interacts via Facebook whereas the charged matter of the partially interacting dark matter model interacts on Google+. Their interactions are similar, but they have contact only with those on their own social network. Interactions proceed on one network or the other—but usually not on both.

Going further afield to make an analogy, it’s like left-wing and right-wing TV shows, which follow more or less the same rules of programming and can both be broadcast on a single television, but which are entirely different entities—each reinforcing their own confirmation biases. Though they have similar formats, with interview hosts, guest “experts,” graphic displays illustrating their points, and running news alerts on random unrelated topics underneath, the actual content and outcomes as well as the advertisers for the two types of shows are nonetheless very different. Very few if any guests or issues will appear on both types of show and the products and candidates they advocate will be different too.

Just as it’s only rare individuals who both watch Fox News and listen to NPR, most, or perhaps all, particles interact via one force or the other. The model—like the media—encourages sticking to one point of view. Though in principle there can be intermediary particles that interact via forces of both types, most particles carry either one type of charge or the other and therefore don’t communicate with each other.

To be fair, it wasn’t only prejudice that discouraged physicists from thinking about a new type of electromagnetism that dark matter would experience. Interactions have consequences that often can be tested. Physicists shied away from the idea of dark forces and self-interacting dark matter because they thought such scenarios were constrained or even ruled out. However, as explained in Chapter 18, even if all of dark matter experiences those forces, those constraints are not so severe. But interactions are allowed only within prescribed limits based on observations.

However, the situation is much less constrained if only a small portion of the dark matter self-interacts. Recall the two types of limits on self-interactions. The first had to do with the structure of halos themselves: they had to be spherical—with a little non-uniformity known as triaxial structure. The second concerned galaxy cluster mergers, such as the most famous one, known as the Bullet Cluster, which was the result of merging clusters. The gas visibly remains in the central region, but dark matter, observed through gravitational lensing, passed through unhindered to create two external bulbous structures—a bit like Mickey Mouse’s ears.

Both constraints are most significant when all of the dark matter interacts. But neither tells us much if the interacting component constitutes only a small fraction of the dark matter. If only a small component interacts, most of the halo will be spherical. The interactions won’t wipe out the triaxial structure either unless it is the dominant component or scatters more than can be expected.

Similarly, the fractions of gas and dark matter in the Bullet Cluster are not nearly sufficiently well measured to register a tiny component of dark matter, which, after all, comprises only a small fraction of the galaxy cluster. That component might interact and remain in the central region along with the gas—and no one would be any the wiser for it. Perhaps eventually measurements such as those of the Bullet Cluster will become sufficiently precise to constrain the partially interacting scenario I’m describing. Certainly now, partially interacting dark matter remains a viable and promising possibility.

THE SPARK

My impetus for considering this idea—along with Matthew Reece, a recent young addition to the Harvard physics faculty, and two postdoctoral fellows, JiJi Fan and Andrey Katz—was not entirely direct. As with many other research projects that turn out to be the most interesting, we weren’t aiming to study what ultimately became our major focus. Rather we were trying to understand some intriguing data from the Fermi satellite—the NASA space observatory that scans the sky for gamma rays, which are a more energetic version of light than visible light or even X-rays.

Most astrophysical processes produce radiation with a smooth distribution over a broad range of frequencies, meaning the number of photons doesn’t change dramatically at any particular wavelength. So when Christoph Weniger from the University of Amsterdam and his collaborators noticed an excess of radiation in the Fermi data all concentrated at a single frequency, it sparked our interest—and that of many others in the physics and astronomy communities.

The spike in the density of radiation (here radiation just means photons or light) that Weniger and his collaborators had identified appeared to emerge from the center of the galaxy, where dark matter is more highly concentrated, but where no such signal from ordinary astrophysical sources should arise. In the absence of a more conventional explanation—or a mistake—a spike in the photon number could only represent something new.

The most intriguing suggestion was that the signal could be the result of dark matter annihilating into photons—an indirect detection signal of the sort that was described in Chapter 17. Maybe dark matter particles collided with each other and through the “magic” of E = mc2, turned into photons that the Fermi satellite could then detect. Further support for this suggestion was that the energy of the photons at which the excess was observed was in the range expected for dark matter. It was also close in value to that of the Higgs boson mass—the mass of the recently discovered missing piece of the particle physics Standard Model—perhaps indicating an even deeper connection. The third intriguing aspect of the measurement was that the interaction rate agreed with what it takes to get the right dark matter relic density. Just about the right amount of dark matter would remain today if dark matter annihilated at the rate that had been measured.

Despite these rosy signs, however, a few things seemed badly off if indeed the signal originated in dark matter. Dark matter doesn’t produce photons directly since it doesn’t interact with light. Maybe dark matter interacts with some heavy charged particle that we haven’t yet observed and those particles in turn interact with light. But if that were the case, we would have expected that when dark matter annihilates and turns into energy, that energy would produce charged particles too. But the Fermi satellite detected no sign of such a process.

The other problem was that although the total amount of dark matter depends on how much it annihilates to anything, the signal depends only on the amount it annihilates to photons. Given the dark matter density in the Universe, the annihilation rate to photons turned out to be too small in all but the most finely-tuned models. This meant that this particular dark matter explanation of the signal could only even possibly be consistent in a very narrow range of parameters that would permit a large enough rate of annihilation to photons but no measurable annihilation into charged particles. No credible scenario seemed to make this happen.

JiJi, Andrey, Matt, and I viewed this as an interesting opportunity to explore the range of permissible dark matter models. We wanted to know if there was any reasonable example in which all the rates agree with their measured values. We began by focusing on the Fermi result and asking whether we could think of a way that nature could do better than the models other physicists had already suggested. We were fully aware that the data might turn out to have been misleading. The Fermi results were tantalizing, but were not sufficiently strong to make a decisive case for a new signal—with an origin in dark matter or otherwise. The observations might have simply reflected some statistical fluke or a misunderstanding of the apparatus, rather than a true signal of a new physical process, which—to stem any overly high expectations as you read this—turned out to be the case.

But the observation was sufficiently interesting that, especially early on, it warranted asking whether any reasonable physical process could have created it. After all, looking for exotic new forms of matter is tough. We want to be aware of every possible way of finding them. Whether or not this signal would prove to be correct, we might learn something that could be useful in the future.

The four of us worked at my blackboard, trying out a number of ideas designed to cleverly escape the problems while preserving the desirable features of the signal. But none of our proposals worked well enough to be worth pursuing. The ones that succeeded in satisfying all the constraints were inconsistent with the spirit of Occam’s Razor. Worse still, they wouldn’t be allowed anywhere in the vicinity of a properly set table of ideas.

However, one of the models that we rejected triggered a line of thinking that was ultimately much more interesting than anything we had set out to do. Our initial inquiries were all based on trying to find a particular model that we could shoehorn into existing constraints. But we took a step back and asked ourselves: What if the local dark matter was denser than we thought so that we were in fact misinterpreting the implications? What if dark matter could annihilate much more than expected because of this greater density?

With higher density, dark matter particles could find and interact with each other much more efficiently. This in turn would create a bigger signal that would more readily stand up to observations. Just as you are more likely to bump into someone in New York’s Penn Station at rush hour than you are in the Waterbury, Vermont train station at 9 A.M. on a Sunday, one dark matter particle is more likely to interact with another dark matter particle in a dense matter environment than in the usual diffuse environment of the amorphous halo. If some dark matter were more concentrated than the matter in the halo, all the other constraints could be much more readily satisfied.

The question then is the underlying reason. Why would dark matter—or at least some of the dark matter—be denser than we thought? This is where the idea of partially interacting dark matter came about—together with the dark-disk idea that closely follows. In fact, even though we now are pretty sure the Fermi signal is spurious, this new idea has so many unexplored implications that we soon realized it was independently worth pursuing. One of these consequences is a disk of dark matter with far greater density than is usually assumed.

THE DARK DISK

Once when I was cleaning my house (well, letting my Roomba robotic vacuum cleaner do its thing), I emptied the dust tray and found an old fortune cookie paper I had saved. The paper asked an enigmatic question, “What is the speed of dark?” I didn’t know then that the words were indeed a sort of fortune, in that they more or less prophesied the research project I was about to commence.

Chapter 5 explained that ordinary matter is found in a thin dense disk because it sheds energy, which it does by emitting photons that efficiently carry energy away. The consequence of dissipation of energy is slower, cooler matter particles that don’t make the kind of big excursions that would be expected from hotter, more energetic, higher-velocity ones. Matter collapse happens because with less energy, it has less velocity with which to spread out. Ordinary matter, which dissipates energy and thereby lowers its speed, collapses into a disk—like the disk of the Milky Way—which you can see on a clear, dry night.

After my collaborators and I had unleashed the notion of partially interacting dark matter, we pursued its potential consequences for the Milky Way galaxy and beyond. We assumed that interacting dark matter is present, and that it behaves similarly to ordinary charged matter, which we know in the galaxy cools, slows down, and thereby forms a disk.

Only a small fraction of the dark matter interacts in our scenario. So the bulk of the dark matter would still form a spherical halo, consistent with what astronomers have so far observed. However, the new component of interacting dark matter could dissipate energy so it—like ordinary matter—could cool down and form a disk too. The interacting dark matter component would—via dark photon interactions—radiate away energy and lower its velocity. In this respect it would behave very much like ordinary matter. Just as ordinary matter cools and collapses, the interacting component of dark matter would as well. And because of conserved angular momentum, which prevents collapse in all but the vertical direction, the interacting dark matter would collapse into a disk.

Furthermore, just as ordinary atoms are composed of protons and electrons with opposite charges, this component of dark matter would also contain oppositely charged particles. The charged particles would continue to radiate energy until they became cool enough to get bound into dark atoms. The cooling would then become much slower and the dark matter atoms, like the atoms of normal matter, would reside in a disk whose thickness would be related to the temperature at which atomic binding occurred. With reasonable assumptions, the temperatures of the ordinary and dark components after cooling stops should turn out to be comparable. So we would be left with a disk of dark matter and a disk of ordinary matter whose temperatures would be about the same.

However, the dark disk wouldn’t have exactly the same structure as the usual Milky Way disk. In fact, it might even be more interesting. The remarkable property of the dark disk is that if a dark matter particle is heavier than a proton but has the same temperature, the dark disk will be thinner—narrower in width than that of the Milky Way. The energy a particle carries is associated with its temperature. But kinetic energy is also related to mass and velocity. Heavier particles with the same temperature will have lower velocity in order for the energy to be about the same, so bigger masses lead to thinner disks. For a dark matter particle with mass about one hundred times heavier than the proton—a commonly assumed value for dark matter masses—the disk could be about one hundred times thinner even than the narrow disk of the Milky Way—a remarkable possibility, which, as we will see in the next couple of chapters, can give rise to many interesting observational consequences. (See Figure 38.)

[FIGURE 38] A small interacting component of dark matter can lead to a very thin dark disk in the midplane of the Milky Way, indicated in the picture by the solid black line.

Also important is that the two disks, though different, should nonetheless be aligned—with the dark disk embedded inside the wider disk of the Milky Way plane. That’s because the ordinary matter and dark matter disks, which interact via gravity, are not entirely independent. Reflecting one flaw in my earlier Fox News–NPR analogy, the gravitational pull that both the dark disk and the ordinary disk experience would actually make the two entities want to orient themselves in the same direction. Though left- and right-wing TV are not entirely independent either since they do influence each other through the collective effects of their constant and often repeated broadcasts, most reactions are negative, which makes their mutual interaction repulsive. The dark matter and normal matter disks, on the other hand, interact via gravity and therefore align.

The remarkable and surprising outcome of our research was that there can be a thin disk of dark matter that exists along with our ordinary disk—and that this newly proposed dark matter disk can be embedded inside the well-known one of the Milky Way. My collaborators and I were rather excited about our proposal and were eager to share it with other physicists. My colleague Howard Georgi at Harvard very much liked the idea too, but wisely thought this scenario merited a catchier name than anything we had suggested. He did us the further favor of proposing the alternative name “double disk dark matter” (DDDM), which served our purpose well and which we have since employed. The name is appropriate since according to our assumptions, the galaxy indeed contains two types of disks, with one embedded inside the other.

Star observations indicate that we left the center of the plane less than a couple of million years ago—a short time on cosmological scales. This tells us that if double-disk dark matter exists, the Solar System oscillated through the dark disk around that time too, so we aren’t very far away (in astrophysical terms). In fact, if the disk turns out to be a little thicker, we might even be inside it—perhaps with observable consequences. And, as we will soon see, the disk would also influence the dynamics of the Solar System—possibly with some very dramatic effects, albeit on very long time scales. The small component of interacting dark matter that we proposed can also create disks inside other galaxies—possibly explaining some of their properties too.

Of course, the big question is whether an interacting component of dark matter and dark matter disks truly exist. Discovering a dark disk by measuring its consequences would help establish the significance of any of the above suggestions. Fortunately, as with ordinary matter, even if it is only a small fraction of the total dark matter in the Universe, the interacting component’s enhanced density might make it easier to find and identify than the usual diffuse dark matter in the halo. The many potential particle physics and astronomical signals of this enhanced dark matter density that the next chapter will discuss should tell us if the dark disk is viable or perhaps even preferred.

If I am truly lucky—as the fortune hiding in my Roomba might have me believe—perhaps one or more of these observations will ultimately reveal a dark matter disk’s existence.