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.

———————————————————————–

The post It Is Dark. You Are Likely To Be Eaten By A WIMP. appeared first on The Scientific Gamer.

(Click on that for the full picture. DO IT. DO IT NOW.)

This question plopped into my inbox like a month ago now.

Name: Justin M.
Question: How can physicists determine the shape of the universe, and what implications might the different speculated shapes of the universe have?

And I’ve been avoiding it ever since, because if you mean what I think you mean it’s an insanely hard subject to try to explain to somebody who hasn’t done, say, three years of an undergraduate physics degree course.

Now, if I’m lucky you just want to know about the old open/closed/flat conundrum. That I can do. We will start with this picture, swiped from the usual source:

These are the three possible candidates for the general shape of the fabric of the universe: football, pringle or bedsheet. Other scientists call these closed, open and flat respectively. I call them boring. Exactly what is going on here is quite easy to visualise in my head but as soon as I try to put it into words bad things happen, but I’ll have a go just for you.

When Einstein first worked out the fundamental concept of general relativity he also came up with a bunch of equations – called the Einstein field equations – which describe how gravity works in a universe where the fabric of spacetime is warped and curved by the presence of matter and energy. Einstein did his general relativity work before Edwin Hubble showed that the universe was expanding through galactic redshift measurements and the Big Bang had yet to be accepted as common scientific orthodoxy, so he assumed we lived in a static universe (i.e. one that is not expanding or contracting) just like the rest of the scientific establishment. The problem with this was that if you start off with a universe that is in perfect static equilibrium, general relativity says that that universe will inevitably start to contract due to the mutual gravitational attraction of everything in it. As it stood general relativity simply didn’t allow for the concept of a static universe, so in order to make his field equations work he fudged them slightly by adding in something called the cosmological constant which provided the universe with a fundamental internal pressure that resisted the contraction due to gravity.

This may have made Einstein’s equations balance and allowed him to model his static universe, but it was bad science and he knew it. After the expansion of the universe was proven he famously referred to the cosmological constant as the biggest blunder of his life; if he’d had faith in the robustness of his theory he could have predicted an expanding universe long before it was confirmed experimentally. Anyway, in an expanding universe the cosmological constant was nothing more than a curio, a simple artefact of the maths. It didn’t have any relevance to anything that was actually physically happening and a lot of people simply ignored it.

That was up until 1998, when it was discovered through redshift measurements of Type 1a supernovae in distant galaxies (have I talked about standard candles before? I’m sure I must have) that those galaxies were actually moving away from us far faster than a simple model of a continually expanding universe would seem to imply, and that the most distant parts of the universe were accelerating in their rate of expansion. This accelerating universe model has since been confirmed by, amongst other things, observations of fluctuations in the cosmic background radiation by the Wilkinson Microwave Anisotropy Probe (WMAP) in the 2000s. An imperfect way of describing this CMB anisotropy is as an “echo” of the Big Bang – the CMB is leftover radiation from the formation of the universe, and the fluctuations in its structure essentially make up a record of the distribution of matter in the universe just after the Big Bang. Circumstances have changed a bit since then, of course, and by comparing the positions and velocities of galaxies now to the CMB rest frame we can get the closest thing possible to an “absolute” measure of galactic velocity. These velocity measurements appear to show that the universe is indeed accelerating in its expansion.

This is interesting for a number of reasons, but the one we’re mainly concerned about is that in the basic expanding universe model without a cosmological constant there are two factors governing the rate of expansion: the inertia of expansion provided by the Big Bang, and the gravitational attraction of all the matter inside the universe counteracting that. Depending on how much stuff there is in the universe and how closely it’s packed together (density), there are three possible outcomes for this basic model.

1)     There is enough gravity to overcome the expansion inertia. The expansion of the universe will gradually stop and reverse itself, and everything will collapse into a Big Crunch. This is a closed universe.

2)     There isn’t enough gravity to overcome the expansion inertia. The universe continues to expand, everything becomes more and more spread out and diffuse, and things inevitably end in widespread entropy and heat death. This is an open universe.

3)     There is just enough gravity to counterbalance the expansion inertia. The expansion rate of the universe will continually slow, gradually approaching zero without ever quite getting there. This is a flat universe.

Note that in none of these three models is there any room for the expansion of the universe accelerating somehow. Clearly there’s something up with it that needs fixing. Serendipitously, though, if you drop Einstein’s previously-defunct cosmological constant back into the cosmological model, it turns out that you can model the accelerating expansion of the universe. The acceleration is driven by the outwards pressure that the cosmological constant represents. And by fiddling with the parameters of the cosmological constant, we can describe something approximating the universe we see today.

What is the cosmological constant, though? Where is this outwards pressure it describes coming from in physical terms? The short answer is: dark energy. Exactly what that is nobody really knows; all we know for sure is that there must be some sort of intrinsic energy permeating all of space (sometimes called vacuum energy if you’re particularly into sci-fi) that counterbalances gravity and causes this acceleration in expansion. I can’t give you a great explanation of dark energy since it really is at the cutting edge of theoretical cosmology, so if you want to find out about it I recommend you read this bit on Wikipedia and then go from there. All I can tell you is that while we cannot perceive the dark energy itself, we can certainly perceive its effects: accelerating expansion, which requires some tinkering with the basic cosmological model I described above in order to accommodate it.

When you dump the cosmological constant back into the model you end up with what is today called the Lambda-CDM model of the universe, which is the currently-accepted model of How Things Are. It’s called Lambda-CDM because lambda is the mathematical symbol representing the cosmological constant, while CDM stands for Cold Dark Matter. Both of these things are needed to explain inadequacies in the previously-accepted model of the universe, the FLRW metric. Lambda-CDM is FLRW on steroids; it doesn’t replace FLRW so much as it supplements it and makes it work with the current observational evidence. The expansion of the universe is governed by lambda, the cosmological constant, as well as baryonic and dark matter (for gravity). The idea is that you add the shit out of all these subcomponents and you get a final number, omega, which tells you what is going to happen to the universe at the end of time, and also incidentally what it happens to be shaped like.

Hey, I knew we’d get back here eventually. That number to the bottom left of each possible universe shape is omega, or Ω. Omega is the observed density of all the stuff in the universe divided by the theoretical critical density required for a perfectly flat universe. If Ω adds up to be bigger than one, then you get the closed beachball universe. If it’s less than one then you get an open pringle universe. If it happens to be exactly one, then you get a flat bathtowel universe. The outcomes are roughly the same as described above, except with the addition of the cosmological constant the pressure due to dark energy eventually overcomes gravitational attraction in the flat model, causing the universe to first slow down in its expansion and then speed back up again once gravity has been smacked down sufficiently, and things end up just like an open universe: in entropy and heat death. The role this shape — or geometry — plays beyond being linked to the expansion and fate of the universe is somewhat explained here if you read the bits about triangles and angles and parallel lines.

As it happens the WMAP probe also measured the overall geometry of the universe (if you want a “how?” then you can start with this), and it came back with the answer that Ω was equal to 1 with less than 0.5% error. In other words the part of the universe that we can see appears to be almost perfectly flat with very little local curvature. However, since we don’t know how much of the universe we can see it could be that this only holds true for our little corner of it. Saying that the universe is flat now would be like ancient civilisations saying that the world was flat; it certainly looked flat, but that was just because they could only see part of it and it was actually way bigger than they thought.

So yes. After like a hundred years of modern astronomy and cosmology, we can finally say that the bit of the universe we live in is probably mostly flat. QED.

(Christ I just realised I managed to get all the way through this post without mentioning Friedmann at all. That’s a massive fault on my part.)

PS – I’m out of questions now so feel free to send more in. I mean, you don’t have to if you don’t want to. But it would be nice.

The post The Shape Of The Universe. appeared first on The Scientific Gamer.