# A dark matter thought experiment

My colleague from OSU, Annika Peter, and I just put out a fairly massive paper, thinking about all the ways we can learn about the particle physics of dark matter by looking at its gravitational effects on astrophysical systems. We open the paper with a thought experiment (largely the brainchild of Prof. Peter), and it's too good to leave as a footnote for the main blog post on the paper, so I split it out here.

We're interested in thinking about the question

What can you learn about the particle physics properties of dark matter from measuring the gravitational imprint of the location and evolution of dark matter?

That is, we want to know if we can learn about the existence of non-trivial interactions in the "dark sector:" that is, does dark matter have internal forces beyond gravity? Does it decay? Is dark matter just one particle, or many? Do they interact? Many of the most popular models of dark matter (for example, Weakly Interacting Massive Particles from supersymmetry) are just one particle without significant interactions, and so have somewhat "boring" answers to these questions. But it doesn't have to be this way, and it is worth checking the data to see whether evidence exists suggesting complicate physics for dark matter.

To think about what sort of measurements we should be looking at, we can look at the Standard Model of particle physics. There are many particles (3 generations, each with two quark and two leptons). There are multiple forces beyond gravity (electromagnetism, strong nuclear, weak nuclear). The stuff that makes up the Standard Model component in the Universe (the stuff we are made out of) is multiple particles: protons, neutrons, electrons, neutrinos, and photons. This non-trivial physics is what allows there to be all sorts of complicated interactions, that lead to stars, planets, galaxies, and, ultimately, us. So the Standard Model is the perfect example of something that is way more complicated and un-boring than it needs to be.

So, to get our minds in the right place to think about finding non-gravitational physics in dark matter, let's ask if it would be possible to find any of the complexity of the Standard Model via gravity alone. Specifically, let's imagine the following thought experiment:

If you were made of and could "see" dark matter but had no non-gravitational interactions with the Standard Model, what could you learn about Standard Model particle physics from the gravitational imprint of the Standard Model particles on the dark matter?

Spiral Galaxy NGC 1232 - Credit: ESO

Simulated Dark Matter cluster - Credit: Benedikt Diemer, Philip Mansfield

### So, imagine you're made of dark matter.

Imagine you can see dark matter, just as we can see "regular" matter (I'll be referring to the matter that you and I and everything you can see as "baryons" for the rest of this post. This follows the usual astrophysics convention). The fact that you can see dark matter means that there is some photon-analogue, the presence of which is actually constrained by existing data - we'll assume that these "dark photons" evade all the constraints while still allowing you to perceive dark matter. So you look up at the night sky, and you see the 80% of the matter in the Universe that we baryonic beings cannot see. Where we see the beautiful spiral of the Milky Way galaxy, you see the halo of dark matter around it (and can't see the spiral). What we baryonic beings see is shown above, while your dark-matter vision (on intergalactic scales) is shown in comparison.

Let's imagine that there's an equivalent of the Cosmic Microwave Background (CMB) for the dark photons. Our CMB consists of the redshifted photons that have been traveling for the last 13.8 billion years, since the Universe was a mere 360,000 years old. At that time, the Universe finally cooled enough so that electrons could combine with protons and the Universe became mostly electrically neutral atoms, rather than a mixed plasma of positive and negative charges. Before that, photons were continually being scattered, absorbed, and reemitted by free charge. When the Universe became electrically neutral, whatever photons were traveling just soared off on a straight line, and we see them today (in microwave wavelengths). The CMB is important because it is a snapshot of the Universe at a particular moment in time; by comparing with particle physics we know today, we can determine how the Universe had expanded up til that time, and then how it expanded since then. This is one of the most critical pieces of information that tells us about the existence of dark matter. So we give the dark sector its own Dark CMB. Now you as a dark matter physicist know that there is 5% of the Universe you cannot account for: the baryons.

Great, now you know there is a problem that needs to be solved, namely:

What is this missing 5% of the Universe?

This is basically the situation we baryonic beings find ourselves in.

### What else can you learn?

Well, from the Dark CMB, you'd be able to determine how many "relativistic degrees of freedom" there were. The CMB (and our imagined Dark CMB) tells you how the Universe expands. If the Universe is filled with things like photons, things with small or zero mass which carry all their energy as kinetic energy rather than as mass-energy (via $E=mc^2$), then it expands differently than if it is filled with massive particles that have low kinetic energies (relative to their mass). The snapshot of the Universe provided by the CMB (and presumably the Dark CMB) gives you a measure of the number of these low-mass particles (at least, the number active at times not too far removed from the CMB decoupling). We baryonic observers know that the CMB is consistent with the known Standard Model relativistic particles, so you dark observers will see that your own dark photon must be accompanied by many more similar particles, none of which you can identify in your Dark Standard Model. So: you learn that there are very light particles out there in the Universe. Maybe these are the same as missing baryonic mass, maybe they are related, or maybe they are totally unconnected. I'd expect that you, as a "reasonable" dark scientist, would want to at least speculate that these unknown relativistic particles are at least connected to the missing 5% of the Universe.

The correct answer is that they are not the same but they are related, but you can't know that yet. But you've already learned something really interesting, and all from the expansion history of the Universe, encoded in the Dark CMB. That is, you learned about particle physics from gravity.

Now what? Well, we baryonic beings look for our missing 26% of the Universe in three main ways:

1. Via direct detection, where we look for dark matter scattering off low-background detectors.
2. Via indirect detection, where we look for dark matter annihilating with itself in deep space and giving off Standard Model particles we can see in our telescopes.
3. Collider production, where we smash protons together and hope we can pair-produce dark matter.

Of these, only option 3 is going to be a reasonable hope for you, dark scientist. Direct detection assumes that there's a relatively smooth background of particles moving through space around you. But baryons clump: they form stars and planets, and dust grains. That clumping means that, unless your dark direct detection experiment drifts through a baryonic planet or star, your scattering rate will be much lower than you'd expect, even if scattering could occur between dark matter and baryons. Furthermore, dark matter halos are much "fluffier" than baryonic galaxies, so it is rather unlikely that you as a dark matter observer are even co-local with significant baryonic material. Indirect detection requires baryons to annihilate with itself: but baryons are not their own antiparticles, and there is very little antimatter around with which to annihilate. That leaves only collider production, which is likely to be as difficult for dark scientists are we baryonic ones have found it.

Video of N-body simulations of galaxy formation from Andrew Pontzen (homepage). Simulation shows both dark matter (green) and baryonic material (blue) See http://youtu.be/77ZoF7Y1pNk for a more digested version of this video. These are the full versions of the BBC Stargazing Live galaxy formation animations (from series 2, January 2012). There are five clips in total. There is no sound.

But let's return to this point about the fluffiness of dark matter halos, because as a dark matter observer, you can get a huge amount of information from this. Compared to a spiral galaxies, the dark matter halos in which we are embedded are enormous (interestingly, we don't know what small dark matter halos look like, or even if they exist. This is one of the things that the rest of our paper is concerned with). A Milky Way-like galaxy has a baryonic disk maybe 20 kiloparsecs in radius, and a few hundred parsecs in width. The dark matter halo extends for a hundred kiloparsecs. That disk is much less massive in total than the halo, but it is very dense, comparatively.

Since you can see dark matter directly, it will be easy for you to see that, in the center of your dark matter halo, there is some dense invisible object that is exercising a significant gravitational pull on any dark matter that nears it. Tidal forces (the differential pull of gravity on different parts of extended objects, such as dark matter structures) will be at play, and from this you will likely be able to deduce the existence of the baryonic disk.

This tells you something hugely important about the particle physics of baryons. What is that?

Let's think about how a baryonic galaxy forms. Originally, there was some overdensity of material: more stuff here and not there. That pulled in, via gravity, other stuff. You might think that the natural result of all of this is a big pile of stuff all in one place. But that's not what necessarily happens. Remember, this is astrophysics: the distances involved are enormous, and there isn't enough stuff for pieces to directly collide and stick together. Instead, what should happen is that things get pulled in to a gravitational well, speed up, and then zip through without hitting anything else. That material will pass without losing energy, and thus escape out the other side. To stick together, gravitational systems must lose energy somehow.

In baryons this happens because of those relativistic particles that you, as a dark scientist, got a hint about from the Dark CMB. As charged particles fall into the growing proto-galaxy, they heat up. This allows them to radiate away energy in the form of photons. Thus, the baryons cool and lack enough energy to escape the gravitational well into which they have fallen. Thus, the existence of a compact, dense baryonic object in the center of your dark matter halo tells you, as a dark matter observer, that the baryons efficiently cool, and thus must have some force akin to electromagnetism. Now, there are a number of ways you could try to implement this (if you didn't know about the Standard Model); however, as we discuss in the paper, many of the simple options will require multiple types of baryonic material coupled to something like a photon, that form complicated bound states (the real cooling of galaxies is non-trivial, and involves the existence of the rich structure of electron orbitals in hydrogen and other elements).

What's more, most of the options that will give you consistent cooling will require you to assume that the baryons consist of at least two types of particles. The reason basically is that the temperature of the baryons will be set by the heavier particle (the proton), but that particle is too heavy to radiate away enough energy, requiring a second, lighter particle (the electron) to effectively "dump" the energy as required to form a disk. Amusingly, we show in our paper that you as a dark scientist could get approximately the correct fine-structure constant (the coupling of photons to charge), though you probably wouldn't be able to know for sure that you'd hit upon the right answer.

(You might at this point be asking how dark matter gets bound together, given that it doesn't -- apparently -- cool efficiently. The answer appears to be "dynamical friction" where dark matter with significant kinetic energy exchanges some of it with low energy dark matter via gravitational interactions. This heats dark matter already bound into a galaxy while cooling and trapping dark matter that isn't captured. The result is a much more extended and less dense "halo" as compared to a dense disk. Though I note that there are ways for non-trivial cooling mechanisms to exist in dark matter, allowing the formation of complicated "galaxy-like" structures, just at scales we haven't measured yet. This was the topic of my paper with my postdoc Anthony DiFranzo. And yes, working on this paper with Annika Peter helped spark that other idea.)

So now you know that baryons exist, that they have light degrees of freedom, that at least some of these light degrees of freedom allow at least some of the material to cool and collapse into dense disks, and you'll have an estimate for combinations of these particle's masses and couplings. You'll probably then notice that the combination of couplings and masses would imply that, if baryons were their own antiparticles, then all of it should have annihilated away by now. That would suggest that baryons are not their own antiparticles, which requires Charge-Parity violation in the Standard Model.

If you're lucky, and there are dark matter sources of dark photons that allow you to do strong gravitational lensing observations, you might even discover the existence of baryonic stars. Which would then make it apparent that there are structures that require significant energy production to be pressure supported. You're unlikely to hit upon the right model of the Strong Nuclear force, but at least you'd be aware of the problem and thinking about possible solutions.

So you're not going to nail the correct model of baryons. Which we baryonic beings can sympathize with -- we haven't gotten answers to all our questions yet either, and we have a much easier time than a dark scientist would. But maybe somewhere are Dark arXiv, there's a poorly-cited paper with the right insanely complicated model for the missing 5% of the Universe.

### So what's the point of the thought experiment?

We are not arguing in this paper or in this thought experiment that there are observers made of dark matter, that there are dark photons, or that the hypothesized observers could get the "right" model of baryons. All we wanted to think about was how much of our own, crazily complicated, Standard Model of particle physics would "bleed through" to invisible observers who could only detect us through gravity. Hopefully, in this thought experiment, we'll gain some spark of inspiration about what properties of dark matter we baryonic scientists can test through gravity.

Such dark matter observers would have a few advantages over us, since baryons apparently have many more relativistic degrees of freedom and cool much more effectively than dark matter. But right now all we have are limits on dark matter. Our job for the future will be to push those limits down, probing more of the possible particle physics. As I hope this little thought experiment demonstrates, you can do a lot of that using only gravity.