Dark matter cropped up in the news again recently (scientists think they might have detected something which may or may not be produced by dark matter; this happens every four or five years or so with no conclusive result so I wouldn’t hold your breath), so I thought now might be a good time to write something about it on the blog. This is particularly difficult — or easy, depending on how you look at it — since we currently know next to sod-all about dark matter and its even more mysterious counterpart, dark energy. It’s even been said that our calling it dark matter reflects more on our total and utter lack of understanding of what it actually is than any intrinsic properties on the part of the dark matter itself. Still, while we’ve never been able to directly observe dark matter (indeed, this may not ever be possible depending on what the dark matter eventually turns out to be) we have  been able to infer its existence from certain odd phenomena that don’t make any sense without something that fits the rather broad description we have of it, so we can at least have an interesting discussion about that.

(Well, I say discussion. Mostly this is going to consist of me writing at you, and you hopefully taking it all in.)

There’s a word that’s going to crop up a lot in this post. That word is baryonic, which is a term used to describe the overwhelming majority of visible matter in the universe. A baryon is a particle made up of three quarks — the quark is what’s called an elementary particle, which means that it is a particle with no known substructure and which is effectively a base building block from which you construct other particles — and which is subject to the four fundamental forces: electromagnetism, strong nuclear, weak nuclear and gravity. The protons and neutrons that give atoms most of their mass are baryonic particles, and so anything made up of atoms is called baryonic matter. Literally everything we can see (and quite a few things that we can’t, except with very high-tech observing equipment) is made of baryonic matter — you, me, the Earth, stars, galaxies, the whole works. So when a scientist is throwing around the term “baryonic” in the context of dark matter, what they mean is that it’s something that behaves rather conventionally according the laws of the physics: we can see it, we can detect it, we can predict how it will behave and what properties it will have.

There are also an apparent minority of things in the universe that are non-baryonic in nature. Most familiar to us are the electrons which orbit atomic nucleii in a fuzzy cloud, which are members of a family of particles called leptons. Like quarks, leptons are also elementary particles, but with the crucial difference that — for reasons that I’m not going to go into here for the very good reason that I barely understand them — they are not subject to the strong nuclear force which binds atomic nucleii together. This means that if you have a lepton which carries no charge and is electrically neutral you wind up with something that isn’t subject to electromagnetism either; the resulting particle is called a neutrino and it is, famously, a complete bastard to detect thanks to it ignoring two of the four fundamental forces. The other two aren’t much help either; we cannot use gravitational interaction to detect neutrinos because they have next to no mass, and the weak interaction is an incredibly short range force that is only really relevant if your neutrino is in physical contact with another particle. This is why the only way we can spot neutrinos is by detecting the aftereffects of them ramming into other particles and exchanging charge, resulting in the creation of a muon/electron which moves faster than light in water (not the same thing as faster than light in a vacuum) and an associated burst of Cherenkov radiation. And even then dedicated neutrino detectors hundreds of metres underground with billions of neutrinos sleeting through them every second will spot only a few of these.

Still, despite the difficulty we have finding it we’ve seen enough of it to know that all this non-baryonic stuff tends to have next to no mass, and that the total mass of estimated non-baryonic matter inside a given galaxy is going to be negligible in comparison to all the heavy baryonic stuff like stars and planets. This is why this graph is such a big problem for modern physics.

This is a graph of the rotation curve of a typical galaxy. The way this works is that the rotation velocity of individual stars as they orbit the galactic core is dictated by the distribution of mass throughout the galaxy. With much of a typical galaxy’s visible mass concentrated within the galactic core we would expect to see a rotation curve broadly similar to that of a solar system’s planets orbiting the central star: this is described by Kepler’s third law, which says that orbital velocity will decrease exponentially as you get further away from the star, and which is the reason why Mercury has an orbital period of 88 days and Neptune has an orbital period of 165 years — not only is Neptune covering a larger distance thanks to the increased orbital radius, but it’s doing it more slowly¹ to boot.

Now, the problem here is that this expected behaviour is represented on the above graph by the dashed line. What’s actually happening is represented by the red one, which is that the orbital velocity of matter within a galaxy remains constant no matter how far you travel out from the galactic core. This is patently absurd considering the distribution of visible mass within a typical galaxy, and yet it’s a relationship (or lack of one) that’s been proven to hold firm no matter how many galaxies we look at. There are only two ways that we can make this flat rotation curve fit in with our established laws of physics. One is to rewrite the laws of physics, which is what a vocal minority of physicists are attempting with Modified Newtonian Dynamics (or MOND). The other is to accept the existence of a hitherto unsuspected and almost completely invisible collection of matter within every galaxy that can distort the galactic mass distribution to the point where the flat rotation curve becomes possible. There are substantial issues with each approach, but since this is a post about dark matter — and because MOND is having difficulty getting traction in mainstream scientific consensus — I’ll be talking about the second one here.

As I said earlier, the name “dark matter” reflects both the fact that it’s next to impossible to detect conventionally as well as the almost total paucity of information we have about the nature of the dark matter itself. What little we know is inferred from the effect it has on the stuff we can see, like the galactic rotation curve. We know that it’s subject to gravity, since without its gravitational interactions with baryonic matter we wouldn’t know it was there in the first place. We know that there must be a staggering amount of it present in every galaxy in order to distort the curve away from its expected shape to the degree that it does, to the point that the baryonic matter component of a galaxy — all those stars, planets, and dust clouds — comprises only 15% of its actual mass. The other 85% is dark matter, coexisting in the same place (and possibly even in the same space) but otherwise eerily beyond our perception. And despite the idea being around for a good seventy years now, those two facts are just about all we know about the stuff.

Not that that stops scientists from speculating about what it might be, of course. The two major candidates for dark matter are referred to — and you’ll have to imagine me gritting my teeth as I say this — as MACHOs and WIMPs. MACHO stands for MAssive Compact Halo Object, and represents the idea that the galactic halo (the bit just outside the visible rim) might be full of extremely small, dense and dark objects like neutron stars and black holes. These MACHOs would be composed of regular baryonic matter, but they’d be impossible to spot directly thanks to being situated in a region of the galaxy with very little ambient radiation to make them show up, not to mention being distinctly non-luminous themselves. Unfortunately there are a couple of drawbacks to this idea: first, you’d need a truly ridiculous number of MACHOs in order to multiply the galaxy’s known mass by seven, and second… well, it’s complicated, but let’s just say that our current models of the Big Bang indicate that it created X amount of baryonic matter. Adding these MACHOs to the mix takes the amount of baryonic matter present in the universe to quite some way above X. There’s simply not enough regular matter around to create the required number of MACHOs.

So MACHOs are falling out of favour as potential candidates for dark matter. This leaves WIMPs, or Weakly Interacting Massive Particles. These are hypothetical non-baryonic particles somewhat like neutrinos — they are not subject to the strong nuclear force, which means they barely ever interact with other particles/atomic nucleii, and their absence of charge means they are also unaffected by electromagnetism. However, they do differ from neutrinos in that a WIMP — as its name implies — is a relatively heavy particle. It has to be in order to inject enough mass into a galaxy to produce that distorted rotation curve. There is no known particle in the Standard Model² that combines this hard-to-detect nature with a heavy mass, so if scientists ever do manage to find one the Standard Model is going to need a fair bit of rewriting. They haven’t yet, despite a number of seemingly-promising signs that they might exist; this is largely because in addition to being immune to the two major forces used to detect regular particles our hypothetical WIMPs are also very, very slow, which means we can’t use the same method we use to find neutrinos. Still, you should never underestimate the ingenuity of scientists when faced with a seemingly-impossible challenge; here’s just one of the proposed detection methods cribbed from Wikipedia:

Halo WIMPs may, as they pass through the Sun, interact with solar protons and helium nuclei. Such an interaction would cause a WIMP to lose energy. The resulting slower WIMP would not have enough energy to escape the gravitational pull of the sun and thus would be “captured” by the Sun. As more and more WIMPs thermalize inside the Sun, they begin to annihilate with each other, forming a variety of particles including high-energy neutrinos. These neutrinos may then travel to the Earth to be detected in one of the many neutrino telescopes.

Which seems to be saying that if WIMPs exist we should be seeing an excess of neutrinos being emitted from the Sun. Exactly how many extra neutrinos we see is going to depend both on the properties of the WIMPs and the mass of the Higgs boson, another scientific puzzle that has yet to be satisfactorily resolved. So it’s not just a matter of building better instruments; we need to nail down a couple of other crucial discoveries before we can properly get to work on finding WIMPs. And that’s if they even exist at all; both the MACHO and WIMP theories might be completely wrong for all we know. Maybe MOND actually has some legs. Maybe it’s one of the more obscure theories, like RAMBOs. Maybe it’s none of these things. Dark matter is one of those intriguing glimpses into the future of physics that’s just out of our grasp because we lack the necessary framework to properly describe it, much like all the not-so-minor discrepancies in our theory of the universe before general relativity and quantum mechanics came along. I suspect unravelling its exact nature is going to be one of the great scientific mysteries of the 21st century, and the one thing you can be sure of is that it’s going to take a lot more than a single experiment on board the ISS to do it. Keep that in mind when the next round of “Dark matter detected” stories hits the news in a couple of years’ time.

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Blah blah blah transit of Venus blah blah blah once in a lifetime event blah blah astonishing photographs blah. Screw that astronomy shit, let’s do some real science.

Why is the transit of Venus important? It’s less so than it was, but in the 18^th century it was very important because it provided astronomers with the first practical method of measuring the distance separating the Earth from the Sun. This is a much bigger deal than it sounds; until this measurement was taken we were in the situation of not knowing for sure how far away anything in the Solar System was, because while we knew a lot of relative distances – i.e. we know planet X is twice as far away from the Sun as we are, and we know planet Y is three times as far away from the Sun as we are – we had nothing absolute. There was nothing we could point to and say “Yes, we know for sure that this distance is X number of metres,” or whatever. Getting the distance between the Earth and the Sun would allow us to easily figure out the distance between the Sun and all the other planets, not to mention eventually allowing us to determine the distance separating us from the nearest stars, but measuring out the length of that first cosmic yardstick with which to scale everything else is an incredibly big deal because it’s so goddamn hard.

The problems are similar to the ones I mentioned in my post on stellar measurement; without doing something very clever there’s no real way of determining how big something is in space. It could be a big thing far away or a small thing close up, and telling the difference is nigh-impossible making it very very difficult to measure even interplanetary distances without modern technology like radar. Not knowing the numbers behind the basic structure of the Solar System kind of puts a crimp on our properly understanding it, so getting this one measurement of the Earth-Sun distance – and by inference, all other planet-Sun distances – was very important. Happily there was a way of doing it in the eighteenth century without having to wait two hundred years for radar, and the methodology was similar to the parallax method used to measure the distance to the nearest stars.

The idea is that at its closest point of approach (i.e. between the Earth and the Sun) Venus will be close enough that, if observed from different points on the Earth’s surface, it will appear to be located in different positions in the sky due to the difference in viewing angle between the observers. Most of the time this isn’t that useful because you need a fixed background against which to track Venus’ movement; however, during a transit Venus is silhouetted against the Sun, which acts as a reference point and allows us to do this:

Send out lots of different observers to locations all over the world and get them to note down what they see when Venus transits the Sun. Gather together all their information. Compare the differences in the observed position of Venus with the differences in position of the observer. Work out the parallax angle α from the shift in the apparent position of Venus. Use the parallax angle α and known distance d separating the observers to work out the distance between the Earth and Venus.

This sort of thing took an incredible amount of effort to pull off in the eighteenth century (especially since the Seven Years’ War was going on at the time) and the story of the attempt to measure the 1761 and 1769 transits is littered with tragic-comical failures like this guy. However, after nearly a decade of work astronomers did eventually get some good measurements of the transit and calculated the distance separating the Earth and Venus. Unfortunately, this on its own isn’t that useful. Because the Earth and Venus aren’t gravitationally bound at all we can’t use that information to infer anything else about the rest of the Solar System. What we need to do is somehow use the Earth-Venus separation to figure out either the Earth-Sun distance or the Venus-Sun distance, since those actually are useful.

Enter Kepler’s third law. Kepler’s laws are a set of relationships governing the behaviour of orbiting bodies, and the third law states that

The square of the orbital period of any planet is proportional to the cube of the semimajor axis of its orbit.

What the hell does this mean? The orbital period of a planet is the amount of time it takes to go around the Sun once – i.e. one year for that planet. The semimajor axis is… basically it’s the distance separating the planet and the Sun, although it’s a little more complicated than that. Expressed mathematically Kepler’s third law is

where P is the period, a is the semimajor axis and the funny thing separating them is a mathematical operator meaning “proportional to”. In other words, P² is equal to a³ multiplied by some constant of proportionality k – if k is 2, then P² is always twice a³, and so on.

(This graph expresses Kepler’s third law visually and may help to give some idea of what the hell I’m jabbering on about here.)

Now, while the orbital periods of all the planets were known in the 18^th century (we could see the damn things, after all) astronomers had no idea what the constant of proportionality k was. It could have been anything, and without knowing what that constant was we were unable to determine the semi-major axes from the period alone. However, we did know that the constant of proportionality — whatever it actually turned out to be — was the same for all planets. Or in other words

Where P_e is the orbital period of the Earth, P_v is the orbital period of Venus etc. etc. No matter what planet you’re dealing with k doesn’t change, and this lets us do some really convoluted rearranging to get

Where T is the distance between the Earth and Venus as measured from the transit. This looks awful, but since T, P_e and P_v are all known quantities it all boils down to

We can figure out the semi-major axis of the Earth based on the distance between the Earth and Venus. Furthermore, we can use this number to work out the constant of proportionality k mentioned in Kepler’s third law above, and from that and their orbital periods we can work out the distance separating the Sun and every other planet in the solar system, not to mention eventually being able to use the astronomical unit derived from this to determine the distance to the nearest stars. Not bad for a decade’s work.

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