## Wednesday, 2 May 2012

### The Dark Matter Problem

One big and as-yet unanswered problem in modern physics is the dark matter problem.  The problem is astrophysical: a number of observations, from galactic to universal scales, show a difference between the mass distributions observed directly (in visible stars, galaxies etc) and indirectly (through its gravitational effects).  As the name of the problem suggests, it looks as though there is a lot of extra matter that we can't see (because it's dark).

The canonical example of such an observation is also the first one made (by the brilliant but prickly Zwicky), that of galactic rotation curves.  In particular, let us focus on objects (stars, globular clusters) orbiting a galaxy but not really part of it.  We are in the limit of weak gravitational fields and small speeds, so Newtonian mechanics is adequate.  The gravitational force due to the galaxy drops off with the standard inverse-squared law:
$F = \frac{G M m}{R^2}$
Here, G is Newton's constant; M and m are the masses of the galaxy and the object orbiting it, respectively; R is the distance between them and F the force.  Using Newton's second law of motion gives us the acceleration:
$a = \frac{G M}{R^2}$
Lastly, we use the relation between acceleration and velocity for objects moving in a circle:
$a = \frac{V^2}{R} ; \therefore V = \sqrt{\frac{G M}{R}}$
The main point is that we expect the speeds of objects orbiting a galaxy to decrease as they get further away from it.  We can extend this for objects within the galaxy itself, but then we need to take the finite size of the galaxy into account.  The result is that we expect the orbital speed to increase with distance within the galaxy, then decrease with distance outside it.

What we see looks like this:

Instead of decreasing, the speed seems to be roughly constant once you get outside the galaxy.  Further, if we compare the magnitudes of the speeds measured to the values of M from the number of stars we can see, they are much to large.

There are a number of other observations that have similar problems, from similar velocity distributions around galactic clusters; to gravitational lensing (the bending of light by massive objects); to studies of the oldest light in the Universe, the Cosmic Microwave Background.  All taken together, they seem to suggest one of two things:

1. Either about 80% of the matter in the Universe is quite different to the atoms that make up everything visible (the Dark Matter solution);
2. Our understanding of gravity on galactic scales and up is wrong (the Modified Newtonian Dynamics, or MOND, solution).
There are scientists in both camps, and both perspectives have particular advantages and weaknesses.  As a particle physicist, I tend to fall into the Dark Matter camp.  The reason for this is that many conjectured solutions to the hierarchy problem introduce new stable particles that would look just like Dark Matter.

Indeed, any stable particle with a mass close to the W and Z boson masses, with W- and Z-mediated interactions, would automatically be as abundant in the Universe as Dark Matter is observed to be.  This is known as the WIMP miracle, where WIMP stands for `Weakly Interacting Massive Particle'.  The most famous example of a WIMP is the neutralino of supersymmetry, but many alternatives exist.

The popularity of the Dark Matter paradigm has lead to a widespread effort to find it.  So far, these efforts have been unsuccessful.  However, there are a lot of difficulties involved with many of these searches.  The cleanest, hardest to fake signals are only just beginning to be probed for the most likely models.  For more ambiguous searches, there are already several discovery claims, but they are not widely accepted.  I will discuss a very recent claim in a follow up to this post later this week.