Today I'd like to talk about the highly publicised bullet cluster which has convincingly given us the first direct empirical proof of the existence of dark matter on galaxy cluster scales independent of your preferred theory of gravity. I’d like to talk about the bullet cluster’s implications for Modified Newtonian Dynamics because I think many believe this is the final nail in the coffin of MOND and although it may well come to be A nail, I don’t think it is the final one. Nevertheless, the entire analysis is independent of a gravity theory and I leave it up to you to draw your own conclusions.
Before getting to the bullet cluster I need just three quick slides of background information which will be well known to most. The first being the mass budget of galaxy clusters and second being a brief recap of MOND and what we already know about its predictions in galaxy clusters. 

Galaxy clusters like the coma cluster shown here in optical and x-ray light are the largest gravitationally bound systems in the universe. The Coma cluster was of course where Fritz Zwicky inferred the existence of DM from the radial velocities of 7 galaxies. But rich clusters like Coma can have thousands of large elliptical galaxies within the Abel Radius, but these galaxies with the stars, and hydrogen and helium gas contribute only 10-20% of the detected baryon budget of the system. The remaining 80-90% of the detected baryons are in the form of x-ray emitting gas which has fallen through the cluster potential and has been superheated to many 10's or 100's of millions degree Kelvin. These temperatures ionise the gas and allow bremstahlung emission. Of course, in the CDM universe these baryons only form something like 11% of the total matter and the rest is cold dark matter. Most probably neutralinos or some other supersymmetric wimp.

The long and short of MOND is that gravity becomes stronger than Newtonian in the weak field limit of gravity below the acceleration constant a_0 which is around an angstrom per sec ^2.

It has some very wonderful successes such as it’s fits to rotation curves, the dearth of DM in ellipticals, the freeman value and the Tully-Fisher relation to name but a few. It has recently been cast into a fully covariant theory by Bekenstein and many people here like Pedro Ferreira, Constantino Skordis and Tom Zlosnik are working very successfully on theories like this.

But it also has some curious failures, the most obvious of these was pointed out by Aguirre in 2001 and confirmed by Sanders in 2003 and Pointecouteau & Silk in 2005. This was that without a large amount of DM, MOND still cannot explain the large radial velocities shown in this dynamical mass vs observed mass plot and the temperature profiles of the x-ray gas shown here.

However, this isn’t a falsification because MOND never made predictions of no DM on cluster scales. After all, it was postulated to negate the need for DM in galaxies which it does very well. If it had underpredicted the mass then it would have been doomed.

Another important thing is that massive neutrinos are required for MOND/TeVeS fits to the CMB  because 2eV neutrinos contribute around 15% to the critical density of the universe helping to fix the locations of the peaks of the CMB power spectrum.

The annoying thing thus far of making strong arguments for or against CDM or MOND is that wherever we infer DM, we see baryons and so there is the potential for degeneracy. Luckily in 1995 Tucker discovered the bullet cluster.

200 million years ago, the bullet cluster looked like the first frame shown here. There is a large cluster on the right and a small cluster on the left and they are on a collision course with a relative velocity of ~4500km/s which is enormous but not unprecedented from CDM simulations shown by Hyashi & White 2006. You can see the DM and galaxies in blue and the x-ray gas in purple. During the collision, the DM and galaxies pass through each other, whereas the gas is stripped by ram pressure.

Clearly we need a test to exploit this unique set up. And that technique was spoken about last week so I needn’t go into too much details of weak lensing reconstruction except to say it’s a robust technique that measures the convergence kappa i.e. the amplification and the shearing of a statistical sample of background galaxies. Put more clearly, the matter in the bullet cluster is a lense and as a lense it distorts the background galaxies. It streches the galaxies in the direction of the gravitational field without diminishing the surface brightness. Now although we can’t say anything definitive about a single galaxy’s shape or brightness, we can for instance be sure the major axes don’t all line up with the gravitational field.

What we clearly see in the bullet cluster is that the contours of convergence, or surface density in GR are centred around the position we would expect the collisionless matter to be and not where the dominant component of known baryons are. So the bullet cluster shows conclusive proof of DM whatever that may be. Although to be consistent with the CMB and LSS in GR or MOND it is most likely CDM or massive neutrinos, the bullet cluster does not a priori show evidence for weakly interacting matter only that it must be collisionless. This means it could be cold gas or MACHOS or planets or spaceships whatever… but its probably not. It could also be neutrinos in GR giving us a mixture of hot and cold dark matter.

Without performing a full analysis in MOND we cannot know how serious the mass discrepancy is and whether or not MOND is falsified.

Our approach was to read off the coordinates of the convergence contours in a simple coordinate system and place 4 potentials at the four mass centres. These potentials with two free parameters each, the asymptotic velocity and the scale length, correspond to cored isothermal spheres because we found Hernquist profiles were not a good fit.

Then we used the fact that there is a linear chain in any gravity between the potential which gives gravity which gives the deflection of light which gives the convergence kappa and amplification. It only becomes non-linear when we calculate the underlying matter density in MOND.

We performed a chi^2 fit of the 8 free parameters in order to find the best match whilst keeping in mind certain constraints such as gas mass which is fixed in any gravity from the free-free emission.

From this fit we wanted to calculate the DM:baryon ratio in the system because CLowe's figure was around 10:1, which is inconsistent with MOND. In this table we've compared our mass estimates for 3 apertures for Newtonian gravity and MOND. The first row is the total mass within a 250kpc radius centred on the DM of the main cluster. We estimate this by performing a surface integral given by this formula. In Newtonian gravity, mu = 1, in MOND it can be slightly different everywhere in the system

Where is all this leading? Well, while cosmologists have been working extremely hard to put together a cohesive theory of the universe, particle physicists haven’t been sitting on their hands. They’ve been working hard on reducing the experimental upper limit on the neutrino mass. The upper limit currently sits at around 2.2eV from the Mainz-Troitz exp.