What’s the Matter?

I couldn’t resist a quick comment today on a news article to which my attention was drawn at the weekend. The piece concerns the nature of the dark matter that is thought to pervade the Universe. Most cosmologists believe that this is cold, which means that it is made of slow-moving particles (the temperature of  a gas being related to the speed of its constituent particles).  They also believe that it is not the sort of stuff that atoms are made of, i.e. protons, neutrons and electrons. In particular, it isn’t charged and therefore can’t interact with electromagnetic radiation, thus it is not only dark in the sense that it doesn’t shine but also transparent.

Cold Dark Matter (CDM) particles could be very massive, which would make them much more sluggish than lighter ones such as neutrinos (which would be hot dark matter), but there are other, more complicated, ways in which some exotic particles can end up in a slow-motion state without being massive.

So why do so many of us think the dark matter is cold? The answer to that is threefold. First, this is by far the simplest hypothesis to work on. In other words, good old Occam’s Razor. It’s simple because if the dark matter is cold there is no relevant physical scale associated with the speed of the particles. Everything is just dominated by the gravity, which means there are fewer equations to solve. Not that it’s exactly easy even in this case: huge supercomputers are needed to crunch the numbers.

The second reason is that particle physics has suggested a number of plausible candidates for non-baryonic candidates which could be cold dark matter particles. A favourite theoretical idea is supersymmetry, which predicts that standard model particles have counterparts that could be interesting from a cosmological point of view, such as the fermionic counterparts of standard model bosons. Some of these candidates could even be produced experimentally by the Large Hadron Collider.

The final reason is that CDM seems to work, at least on large scales. The pattern of galaxy clustering on large scales as measured by galaxy redshift surveys seems to fit very well with predictions of the theory, as do the observed properties of the cosmic microwave background.

However, one place where CDM is known to have a problem is on small scales. By small of course I mean in cosmological terms; we’re still talking about many thousands of light-years! There’s been a niggling worry for some time that the internal structure of galaxies, especially in their central regions,  isn’t quite what we expect on the basis of the CDM theory. Neither do the properties of the small satellite galaxies (“dwarfs”) seen orbiting the Milky Way seem to match what what we’d expect theoretically.

The above picture is taken from the BBC website. I’ve included it partly for a bit of decoration, but also to point out that the pictures are both computer simulations, not actual astronomical observations.

Anyway, the mismatch between the properties of dwarf galaxies and the predictions of CDM theory, while not being exactly new, is certainly a potential Achilles’ Heel for the otherwise successful model. Calculating the matter distribution on small scales however is a fearsome computational challenge requiring enormously high resolution. The disagreement may therefore be simply because the simulations are not good enough; “sub-grid” physics may be confusing us.

On the other hand, one should certainly not dismiss the possibility that CDM might actually be wrong. If the dark matter were not cold, but warm (or perhaps merely tepid), then it would produce less small-scale structure whilst not messing up the good fit to large-scale structure that we get with CDM.

So is the Dark Matter Cold or Warm or something else altogether? The correct answer is that we don’t know for sure, and as a matter of fact I think CDM is still favourite. But if the LHC rules out supersymmetric CDM candidates and the astronomical measurements continue to defy the theoretical predictions then the case for cold dark matter would be very much weakened. That might annoy some of its advocates in the cosmological community, such as Carlos Frenk (who is extensively quoted in the article), but it would at least mean that the hunt for the true nature of dark matter would be getting warmer.


26 Responses to “What’s the Matter?”

  1. Interesting post – but is the proposal of WDM to get rid of the dwarf problem a new result? (don’t think so)

    • No, it’s not new…WDM has in fact been around as long as CDM, i.e. about 30 years!

      There are other ways of fixing the problem than WDM too. A very light scalar boson might do it, for example.

  2. If somebody asked me why dark matter must be cold, I would myself use the argument that there is evidence from galaxy redshift surveys that dark matter and visible baryonic matter are distributed in similar ways. I would also add that weak gravitational lensing suggests the same on the scale of galaxies and galaxy clusters. What information we have from the distribution of dark matter within galaxies (based on dynamical observations) also shows that dark matter is regularly found localised within and around visible galaxies. Hot dark matter would not be localised within galaxy haloes: it would leak out, with a consequent strong change in the gravitational potential of the galaxy.

    The Ockham’s Razor argument, though true, seems a bit philosophical and slightly weak.

    What would happen if dark matter were slightly collisional? Wouldn’t that suppress the formation of small structures? (But that would also affect the formation of cusps in the cores of massive galaxies.)

    Of course, observers do have severe trouble in identifying the lowest luminosity galaxies: they are very difficult to find because of their low surface brightnesses. So the observational data are not quite as conclusive about the numbers of very low mass satellite galaxies as some people might think.

    • Just to be contrary I’d say that the Ockham’s Razor argument is a pretty good one in this context. Once you start assigning additional parameters to the dark matter particles then the space you have to explore rapidly becomes enormous. It’s a good scientific principle to do as much as possible with as little as possible until forced to do otherwise.

    • Perhaps the term “cold” is a bit vague. Let’s try to be a bit more precise.

      The speeds of the fastest stars in the solar neighbourhood can provide a limit on the escape velocity from the Galaxy in the vicinity of the Sun, and they provide a figure of roughly 550 km/s. (I would argue that the infall of dwarf galaxies should feed the halo of the Galaxy with stars with high velocities, and so the real escape velocity is likely to be close to this limit.)

      So dark matter is likely to be moving with velocities <~ 550 km/s in the solar neighbourhood (in the rest frame of the Galaxy, assuming that dark matter is composed of particles – which I would say is very likely). So dark matter r.m.s. velocities are likely to be a few hundred km/s around the Sun.

      Perhaps one important issue here is how much of the kinetic energy of the dark matter particles was produced by gravitational collapse: all, or just some. That is to say, what were the kinetic energies of the dark matter particles in the early Universe before gravitational collapse became important, and how these energies compare with the kinetic energies today.

    • Actually it’s not their current velocity dispersion that relates to the name “cold”. It’s what the particle velocities were like in the early Universe when the initial perturbation spectrum was generated. In the case of hot dark matter – which probably does exist in the form of neutrinos but does not dominate things – the particles are relativistic when they decouple from the radiation background which damps small scale structure. Cold dark matter is born non-relativistic so it doesn’t stream about like neutrinos do.

      Cold dark matter acquires a large velocity disperson at late times after gravitational clustering has amplified the density and velocity perturbations, but it’s what it was like at early times that really counts.

    • Some kind of constraint, though much less direct, on the dynamics of dark matter today comes from the motions of stars in dwarf spheroidal galaxies. The stars have velocity dispersions as little as 5 – 10 km/s. These systems are dark matter dominated, often with very high mass-to-light ratios.

      This, of course, provides information on the gradient of the potential, rather than on the depth of the potential. With lots of imagination, we could construct some very odd model where dark matter produced a deep potential with a flat core where the stars are found, allowing dark matter with a high velocity dispersion to remain trapped in its own potential today, while stars in the core could have very low velocities. However, such a situation would seem very contrived, and there is a strong plausibility argument that the low velocities of stars in dwarf spheroidal galaxies imply a shallow dark matter potential, and consequently cold dark matter today (otherwise the dark matter would have escaped), and therefore cold dark matter in the early Universe.

      There. I’ve just used dwarf galaxies to argue in favour of cold dark matter, contrary to the spirit of the BBC article.

      (By the way, WordPress doesn’t notify me of updates here, even though I asked it to do so.)

    • And, of course, though dominated by cold (probably) dark matter, dwarf spheroidal galaxies do not have Navarro-Frenk-White density profiles.

  3. RE: Dark Matter in general:

    It seems more likely to the (non-expert) popular science reader, that while the maths is surely right, it’s based somewhere on big assumptions that might be wrong.

    For example, could the distribution of space-time itself be very uneven in certain places, (e.g due to forces outside of the familiar four dimensions) ? Then it would be the very shape of space-time itself having the otherwise unexplained large-scale effects on clustering of matter.

    While we know from Einstein that mass affects the density of spacetime, perhaps there are forces outside of our universe that affect its shape on a much larger scale. Like a thick rubber sheet lying across bumpy rocks.

    Far-fetched speculation, yes. But do we know for sure that this is impossible? We are, after all, like those 2D flat-landers trying to understand the Earth.

    • All these models are based on general relativity, which describes gravity as an effect of the curvature of space-time. That seems to be precisely what you’re advocating.

      Also if the “universe” is everything that exists – which is what I generally take it to mean – then what could be existing outside our universe to exert forces on it?

      • re: “what could be existing outside our universe to exert forces on it”

        Perhaps what we see with our blinkered view (and amazing instruments) as “the universe” is just a kind of shadow of what is *really* the whole universe. A bit like me assuming that the surface of my skin is the entirety of my body, because the surface is the only bit I can see. And then labelling that surface “the universe”.

        It just seems highly likely to me that there are some big unknowns that we’re a long way from knowing (and which we may, by their nature, be unable to measure).

        Anyway, pointless conjecture…

  4. There’s more than meets the eye to dark matter.

    Or is it less ?

  5. Has a preprint appeared anywhere yet? I couldn’t find anything searching for Frenk at the arXiv. It’s a bit tough to interpret this if the only available source is a BBC article…

    • As I said in the piece, it’s not a new result so I don’t think there is really a paper to go with it. The BBC article seems to simply be a response to a talk by Carlos Frenk that their reporter attended.

      • Hmm. It sounded like there were some new simulation results from the Virgo Consortium. But then one should know better than to trust BBC science journalism.

  6. Ben Maughan Says:

    I saw Carlos present this work last week at the Nottingham workshop, and there is (of course) a little more to it than you get from the BBC article.

    If I recall correctly, the point was not that the cold dark matter simulations predict too many small haloes associated with the Milky Way compared to observations, as the estimated luminosity function of the simulated haloes matches the observed luminosity function.

    Neither was the problem that simulations predict cuspier cores in haloes than are observed, as you can flatten the dark matter cores in some subhaloes by the influence of the baryons (my memory is patchy here).

    The problem was that the cold dark matter simulations can’t give you both together – they put the brightest satellites in the most concentrated subhaloes. This seemed to be a refinement of the previously recognised problems with the numbers of satellites and shapes of the density profiles – at least it was new to me.

    Carlos said it was just the second time he’s lost sleep over cosmology – the first was apparently when it became clear that Omega_M < 1!

    Apologies for the vagueness of my notes – Carlos gave references for most of the above, but I don't seem to have written them down!

    • I rarely lose sleep over cosmological matters. And if I do I usually make up for it by attending a seminar about Cold Dark Matter…

  7. The paper by Mark Lovell et al is at arXiv:1104.2929. The problem is that the sub-haloes that are identified in the CDM Milky Way simulation as having the right luminosity turn out to have the wrong mass. In the paper its not that significant. But in the interview at least, Carlos seem to be agreeing with Pavel Kroupa that dwarf galaxies rule out CDM. The neutralino as a cold DM particle was looking shaky anyway at the LHC but the dwarf galaxy constraint would rule out other CDM candidates like axions too. Another (warm) DM particle eg the sterile neutrino, is then needed but it has to have a mass lower than ~10keV or the dwarf galaxy problem reappears and higher than ~2keV due to other constraints. Maybe this is finely tuned to fit the MW subhalo problem. Other issues – if WDM replaces CDM what happens to all those papers on feedback? And can the Milky Way and smaller galaxies now be said to form in monolithic collapse? Let’s hope WDM doesnt go the same way as WMD (or CDM)!

  8. Anton Garrett Says:

    Award yourself the CDM…

    • Monica Grady Says:

      Anton – is this, by any chance, a reference to the Cadbury’s advertising campaign of about 40 years ago?

    • Anton Garrett Says:


      CDM = Cadbury’s Dairy Milk.

      Many old adverts are on YouTube, and I looked for this one before posting. It isn’t there, but it quickly became clear that Cadbury’s are currently using ‘CDM’ as a marketing slogan in India.

      Is the universe really constructed of chocolate?

  9. “Calculating the matter distribution on small scales however is a fearsome computational challenge requiring enormously high resolution. The disagreement may therefore be simply because the simulations are not good enough; “sub-grid” physics may be confusing us.”

    A few months ago, Eva Grebel gave a popular talk in Frankfurt where she mentioned the problem in the first sentence quoted above. I asked her whether the idea in the second sentence could be the (rather obvious) solution. Her response was that more detailed simulations make the problem worse.

  10. “Carlos said it was just the second time he’s lost sleep over cosmology – the first was apparently when it became clear that Omega_M < 1!"

    At least Carlos lost sleep over it. Rocky Kolb still hadn’t woken up a few years after essentially the entire community finally became convinced of what observers had found all along [add pithy reference to Coles and Ellis here]. Or has he finally conceded that Omega_M < 1?

    • I suppose it was an observation that pushed CDM-ers away from Omega_m=1 in the mid 1990’s – it was the “baryon catastrophe” in rich clusters like Coma. If Omega_cdm~0.95 and Omega_baryon~0.05 at the start then they couldn’t get CDM simulations of Coma to produce its observed 20-25% baryon-CDM fraction. Their solution was to go to Omega_cdm~0.25. But then you need Omega_lambda~0.7. Think some CDM-ers still regret this step to this day. But it means that anyone who wants to ditch the troublesome lambda has to ditch CDM as well. This is actually close to my solution but that’s a different story…

      • So what’s the Hubble constant this week? 🙂

        Yes, it was the observations which convinced people like Carlberg that Omega<1. At the same time, Kolb remained unconvinced. I remember them battling it out at a conference (and IIRC Rocky used to be a boxer!).

  11. Am still attracted by solving the above baryon catastrophe issue by lowering H_0. The lower H_0 goes the more the X-ray gas explains the dark matter in Coma. A low H_0 also helps you get round nucleosynthesis limits on Omega_baryon~1 so you can have inflation and dark matter without needing undetected exotic particles or dark energy.

    Of course, you then have to explain why the distance scale is currently giving ~2x too high a value of H_0, although it has already come down by ~7x. My simple model also has a problem with the 1st acoustic peak in the CMB. But life wasnt meant to be easy!

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