Thanks to
Clifford and
Robert, I came to realize the
awesome power of theoretical physics, and that a
grocery store is an excellent place to look for it.
| This of course justifies uninhibited shopping in every brain downtime. For instance yesterday, I heard a talk by Sean Carroll, after which I was so confused about the direction of time that I went to get some chocolate as antidote. And that's how I found a model of the universe. It came in a bar of aero chocolate, one of the numerous children from the Nestlé family. It basically consists of: |
 |
- An high amount of emptiness which puffs up the volume. As I learned from Wikipedia, exactly how this works is one of the best kept secrets on earth. ( "The exact procedure [...] is a closely guarded secret. A spokesperson for Nestlé provided some clues but there has been no definitive answer." )
- Since it's a Nestlé product, the actual solid part of the bar consists of an almost negligible amount of the real thing (that is in this case cacao), which leads us to the conclusion that...
- ... the rest is a pretty mysterious dark matter, which (ALLERGY ALERT) might contain traces of this or that.
And isn't that a nice way to model our universe, where the present day cosmological data lets us conclude that
- 73% of the universe's content is dark energy, responsible for the observed accelerated expansion, exactly how this works is one of the best kept secrets of the universe ("A spokesperson from Super Zing-Zong provided some clues...")
- Only 4% is baryonic matter, or the real thing that we are made of...
- ... and 23% is non-baryonic dark matter, a mysterious but apparently unavoidable ingredient which makes out a disturbingly high fraction of the matter content.
On Wednesday we had a very interesting colloquium by Stefan Hofmann about the small scale structure of dark matter. It was one of these talks that succeed to capture the fascination of understanding a part of how the universe works, a talk that reminded me why I studied physics - and convinced me that the end of physics is nowhere close by.
1. Evidence for Dark Matter
a) Rotation Curves
Stars and other objects that are bound to spiral galaxies rotate around a common center. The rotation velocity of the stars is such that the orbits are stable. The required velocity for this depends on the attractive force acting on the star, which results from the matter content in the galaxy. The larger the force, the higher the velocity has to be to allow for a stable orbit.
Measuring the velocities of stars as a function of their distance to the galaxy's center therefore allows to draw conclusions about the matter distribution inside the galaxy. As it turns out, the visible amount of matter is not remotely sufficient to explain the observations, which in the outer regions of galaxies show larger velocities than expected (its square remains constant instead of dropping inverse to the distance). The observations can be explained by assuming a significant amount of non-visible (dark) matter which is distributed in the galaxy.
The challenge here is that the ratio of dark matter to visible matter (the mass-to-light ratio, commonly denoted M/L) depends on the type of galaxy. E.g. globular clusters show little or no evidence for dark energy.
b) Virilization of Galaxy Clusters
In a similar way, clusters of galaxies have a dynamics that is related to the total mass of the cluster, a relation which can be estimated using the virial theorem. Again, one finds that the visible matter is not remotely sufficient to explain the observations. Measurements indicate a mass-to-light ratio of M/L~300. Though there is some uncertainty as to whether clusters of galaxies have had sufficient time to properly virialize their internal motion, this evidence is pretty strong.
c) Weak Gravitational Lensing
General Relativity predicts that travelling light is bent by mass distributions. If a large amount of mass lies between us and objects that we are looking at, the image of the object can be noticeably distorted. This is known as gravitational lensing.
If the light bending is strong, it can result in multiple images of the source (examples here), or change a point-like shape into arcs. In case the bending is not strong enough to actually produce multiple images, as is typically the case when the matter that causes it is not cleanly localized, one can still measure resulting fuzzy distortions of the background image. In this case, which is known as weak gravitational lensing, the significance for the observed effect has to be enhanced by accumulating sufficient statistics.
Dark matter, though not visible on its own, causes gravitational lensing as every other stuff. In this way, gravitational lensing provides evidence for Dark Matter, which has been reported e.g. by the Canada-France-Hawaii Telescope:
"Using a series of deep images obtained at the Canada-France-Hawaii Telescope over the past two years, the French team analyzed the shapes of some 200,000 faint galaxies spread over two square degrees of the sky (an area approximately 10 times greater than that of the full moon). They have determined that the galaxies appear to be elongated in a coherent manner over large regions of the sky. The measured effect is small, a percent or so deviation from a purely random distribution of shapes, but the accuracy of the results leaves no doubt that the signal is due to the gravitational lensing effect of the dark matter distribution. These results have been partially confirmed by subsequent reports from two teams, one English and the other American, who have studied different patches of the sky."
Recently, researchers have been able to use weak lensing data to produce a three-dimensional map of how dark matter is distributed.
d) Large Scale Structure
The stuff that builds up everything we sit on, live from, and can order at amazon.com fails disastrously when it comes to explain what we see at the night sky. Ordinary matter, also called 'baryonic matter', just doesn't clump enough during the evolution of the universe. To be more precise, it does not clump on small enough scales. To explain the observed density contrast and fluctuations, it requires a non-baryonic type of matter (non-baryonic meaning it is not something from the standard model of particle physics, or a synonym for we-don't-know-what). Moreover, this type of matter has to be rather cold, otherwise its temperature also wouldn't allow sufficient clumping. So, what we really need is non-baryonic cold dark matter (CDM).
The best evidence for this comes from the WMAP data, where the third peak in the distribution of temperature fluctuations (Delta T, the vertical axis) over angular momenta (l, the horizontal axis) is the indicator for a large fraction of dark matter. This is very nicely to see in the animation below (borrowed from this website). It shows how the peaks in the WMAP data change with turning up and down the fraction of CDM, denoted with Omega_m, displayed in the pink bar on the right.
As one sees, the height of the third peak is the thing to look for. In the measured distribution, the third peak is almost as high as the second. For details, see astro-ph/0603451.
2. Candidates for Dark Matter
The model we use to describe the universe on large scales is classical General Relativity (GR), its ingredients being the background metric which describes space-time, and source terms from the matter that cause the background to be curved. There are then basically two ways to explain the above deviations from this model: either our understanding of GR or that of the sources is incomplete.
The first possibility sounds tempting at first but faces severe challenges. GR on distances of the solar system is extremely well confirmed, so any modification could only set in at larger distances. A modification becoming important at a fixed distance however could never explain the observed rotation velocities for spiral galaxies, whose constant asymptotic value depends on the luminosity of the galaxy, a relation which is known as the Tully-Fisher relation.
A way to escape this was provided by modified Newtonian dynamics (MOND), where the modification of GR sets in, not at a fixed distance, but at a certain acceleration. This worked very well for explaining the rotation velocities, and there have been some attempts to also approach structure formation. However, recent observations of the bullet cluster strongly disfavor MOND. Even if MOND is realized in nature, it doesn't seem to work without the additional assumption of dark matter particles. For more details on the bullet cluster observations, see Sean Carroll's excellent post Dark Matter exists on CV, or the discussion here.
This then leaves us with the second possibility of finding source terms with the right properties to explain the observations. Candidates that fulfill the requirements for CDM luckily appear more or less naturally in various extensions of the standard model. These candidates can be characterized as a) being weakly interacting (via gravity and weak interactions only) with each other as well as with baryonic matter and b) being more massive than the common particles of the standard model. Both points are necessary for a sufficient clumpiness as well as to explain why we haven't yet seen these particles.
The term used for these candidates is therefore WIMP - weakly interacting massive particles. The most common candidates are axions, heavy sterile neutrinos, and supersymmetric particles like the neutralino or the bino. (Side remark for the Germans around here.)
3. Experimental Detection
The problem with the above mentioned CDM candidates is that their exact nature doesn't play a role for the observed rotation curves or the large scale structure. Though these particle differ in their microscopic properties, these have no imprint on the above mentioned observations. The present concordance model of cosmology (Lambda-CDM) is basically a parametrization of our ignorance about the nature of the universe's ingredients.
There are ways to examine the nature of CDM directly. There is of course the possibility that the WIMPs will be found in high energy experiments on earth if the collision energy exceeds the necessary production energy. And even though the WIMPs are weakly interacting, it still happens every now and then that they do interact. Decay products of such reactions can in principle be detected. The neutralino for example, is its own anti-particle, and it can annihilate into photons. The probability for this to happen depends on the density of the CDM (the rate is proportional to the squared density) and is typically very low. This makes experiments a very challenging task: The expected flux of photons on earth is approximately the same 'as we would receive from a single candle placed on Pluto' (source: astro-ph/0501589).
For more details about experiments on direct detection, see e.g.
 |
And then there are the imprints of the nature of CDM in the structure of our universe. Structure formation is a very involved topic, a big part of which is typically performed numerically, with just stunningly beautiful results.
If you have DivX, and a fast internet connection, look at these movies from the millenium simulation in low resolution (10.8 MB), med resolution(13.4 MB), high resolution (48.6 MB), -- more info on this website.
Wow, what a trip!
But here's the point: each point in this simulation corresponds to 106 solar masses. All smaller structures are not resolved. What Stefan Hofmann and collaborators showed in their work though was that CDM's smallest structures are 12 orders of magnitude smaller than that! This applies generally for those types of CDM that have been in thermal and chemical equilibrium with the radiation in the early universe. This is typically the case for neutralinos and binos, but not for axions, in which case the small scale structure would look differently (he says work is in progress).
|
Starting with a primordial initial power spectrum, they calculated the evolution of this spectrum, for the first time including collisional damping and free-streaming. As Stefan said in his talk, in principle there is a third contribution from heat conduction
'but heat is a pretty boring thing for cold stuff, so we drop this term'. In their work they showed that the spectrum has a sharp cut-off at about 10
-6 solar masses, below which there are no smaller substructures. You find a very readable summary on the arxiv
The first WIMPy halos
Anne M. Green, Stefan Hofmann amd Dominik J. Schwarz
astro-ph/0503387
Cosmologists measure time in redshift, commonly denoted with
z. We are today at
z=0. The larger
z, the further in the past an event was. Hofmann's analytical calculations hold down to
z approximately 60, where the linear perturbation theory can no longer be applied because the density contrast has become too large. These analytical results however, can then be used as input for numerical calculations. This has been reported in a Nature article
where the numerical calculation goes down to approximately z=20. Results of this simulation are shown in the picture below, where the small structures are magnified
(If you have no access to Nature, the same article is also available at astro-ph/0501589)These smallest CDM halos without further substructure are distributed over a size of roughly the solar system, which means they are extremely diluted. Their average velocity is approximately 1 meter per second. They are estimated to propagate through galaxies without being disrupted, which means that these CDM substructures could travel through our solar system and render the background we live in time-dependent!
To summarize: the microscopic nature of CDM
has an imprint on the small scale structure of our universe. The examination of these small scale fluctuations therefore would allow us to distinguish between different candidates for CDM.
Update Nov. 14th: See also the
PS on Dark Matter.
4. Further Reading
5. EpilogueIn the October Issue of Physics Today,
Burton Richter - an experimentalist and Nobel laureate - commented on
'Theory in particle physics'. About cosmology he wrote that it is in
"[...] a kind of intermediate state in which all that is missing to make it practical knowledge is a mathematically sound microscopic realization."
Well, yes, that is ' all ' that is missing ;-)
But as a theoretical physicist in the 21st century, I have to give credits to the experimental achievements. We have plenty of evidence for physics beyond the standard model. Astrophysics and cosmology provide us with numerous puzzles to keep our days busy. In case someone got the impression, we theoretical physicists are not sitting around being depressed about the trouble with physics. We just don't have the time! The universe is waiting to be explored. And if you aren't yet convinced of the beauty of it all, go get some chocolate.
(Some comments on Richter's article, see here and here)
Updated on Jan. 14th 2007.TAGS: SCIENCE, PHYSICS, ASTROPHYSICS,
COSMOLOGY, DARK MATTER
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