Friday Lunchtime Talks - MOdified Gravity

On Friday we had the latest of the Durham Astronomy groups Friday Lunchtime Talks, these usually consist of two members of the group (which consists of over 50 members including students) giving a half hour talk, either about their own work or a paper that has appeared recently in which they have some interest. Last Fridays was something different however, it was an hour long talk by Professor Emeritus John Moffat of the Perimeter Institute on the subject of his own version of modified gravity, MOG.

I always have a lot of respect to someone that comes to Durham to talk about modified gravity, it really can be like entering the Lions den. Tinkering with gravity is usually done in an attempt to explain astrophysical phenomena without the need to demand that most of the mass in the Universe is invisible and can only be detected through its gravitational influence (the so called Dark Matter). Durham is world renowned as a centre of research into Dark Matter, as such some members of the group could be expected to be particularly partisan on the issue. I think its a great credit to the people involved that things never seem to get too heated, in fact in this Fridays talk, most of the difficult questions were directed from the one Professor in the group who has never been too happy with the current Cosmological Paradigm. He's generally good value for entertainment, and important in keeping everything honest.

Anyway, onto the talk itself. John Moffat has been working on modifying the gravitational laws for many years and has produced several different models. These models differ from most of the work on MOND (MOdified Netwonian Dynamics) in that from the beginning they were specifically chosen to be relativistic, that is that they are modifications to Einsteins General Relativity and not Newtons law of gravity. Essentially in MOdified Gravity (or if you prefer, MOffat Gravity, MOG) the gravitational constant G (also called Newtons Constant) is not in fact a constant, but can vary both in time and in space, so that the G that relates the force between two masses separated by one distance R1 is not the same G that relates the force between the same masses if they are separated by distance R2, similarly for time T1 and T2. These changes in G have to be negligible for objects within the solar system otherwise we should be able to detect deviations from the GR predictions which so far have not been observed, but they can become significant over galactic scales.

The speaker showed several examples of where his proposed changes would allow us to fit astronomical observations without the need to invoke Dark Matter. In particular he mentioned fitting the rotation curves of dwarf galaxies, spiral galaxies and clusters of galaxies (for clusters its technically not a rotation curve but the principle is the same). This in particular interested me as rotation curves are something I have personal experience with, both in my MSci project and the first paper I have published. Below is an example of a spiral galaxy rotation curve, it simply measures the speed at which stars at different radii in the disk orbit the galaxy, the data is the black circles (with error bars) the various dashed lines show the amount of velocity provided by the mass of various components of the galaxy including a DM halo. MOG allows you to explain the observed rotation of the galaxy without this DM component, by assuming the influence of the other two components is stronger than you would naively expect using Newtonian (or GR) gravity.

For me the first and largest problem that appeared during the talk appeared when JM was talking about these fits to the rotation curves. It seems it is possible using his model to fit all spiral galaxies using the same values for two parameters, as far as I could tell these parameters deal with the scale over which G begins to diverge from a constant value and some sort of normalisation of the size of the divergence. The problem was that when he fit the rotation curves of dwarf galaxies, or of clusters of galaxies the values of these two free parameters were different, all dwarfs had the same values, all clusters had the same values but different from the dwarfs or the spirals. This would appear to mean that there has to be yet another effect going on, meaning we need more free parameters to explain everything in terms of one unified gravitational theory. If this is true it would seem to be a problem. I have to go and look at the actual papers and see if in fact this is the case, or if I simply misunderstood something, it could be that the values he was quoting were actually telling you something about the scales involved, i.e that dwarf galaxies are smaller than spirals which are smaller than clusters.

The second major part of the talk dealt with JM's attempts to explain the results from the Bullet Cluster without the need for Dark Matter. This cluster is so far unique and very exiting. Its unique because it is actually two clusters, one of which has passed through the other, during this interaction the hot gas that resides in the clusters hit each other and slowed down, the gas from the smaller cluster having shocked and formed a bullet like shape as seen as the red triangle on the right of the image below. In the image below you can see the hot intracluster gas as the red regions. This is interesting because the hot intracluster gas has been separated from the galaxies of the clusters (seen in the blue regions), normally there is around 10x as much mass in this hot gas as there is in the galaxies of a cluster. By crashing through each other the two clusters have managed to separate the collisional material (the gas) from the collision less material (the galaxies and any Dark Matter).


It is possible to use gravitational lensing of background galaxies by the clusters of galaxies to work out the mass that must be contained within the galaxy clusters. This cluster is so important because it can be convincingly shown that even though the vast majority of the visible mass (the intracluster gas) has been removed the effect of gravity is still very strong, considerably stronger than can possibly be explained by the visible mass contained in the galaxies in the cluster. The traditional explanation is therefore that there must be some invisible mass (DM), which from this cluster we can see must be collision less, otherwise it would have piled up where the intracluster gas is. In MOG the explanation for the extra lensing, above what is predicted by GR for just the normal mass is that the gravity from the galaxies is stronger at larger distances, and also I believe that there is some lensing caused by the gravity from the intracluster gas.

If this is the case then there is happily a way to test which approach is correct, MOG or DM, the intracluster gas is much more massive than the mass contained in the luminous matter of the galaxies, but it is also located on one side of the cluster. Therefore it would seem that if MOG is correct there should be an increase in lensing on the side of the cluster nearest to the gas, of course the size of the effect would depend on many factors, but may in principle be measurable. If MOG is incorrect and DM is really at work, then the lensing should be more symmetric around the cluster, both because the DM is by far the largest mass contribution but also because the gravity of the gas is much less at larger distances than predicted by MOG.

Whatever the result of work such as this, we are really going to learn something fundamental about the Universe. Either most of the mass of the Universe is in some really exotic form, or else the force of gravity is even stranger than we have ever dreamt.

Unfortunately time caught up with us and we didn't get to find out much on the implications of this modified gravity on Cosmology, for example whether it could explain the mysterious Dark Energy at the same time that does away with Dark Matter. Many other interesting questions were raised however, it appears that MOG doesn't allow for singularities, so no black holes, though objects observationally indistinguishable from them probably can exist. This led one prominent member of the group to spend the time to see if the Metric for MOG is compatible with these condensed objects having a "last stable orbit", apparently it doesn't seem like it can, and as these are thought to be observed around BHs this is probably a problem for the theory.

All in all a very interesting talk, a perfect example of the kind of research that is ongoing in Astronomy. I don't think anyone is going to be packing in the DM work anytime soon, but if the DM particles continue to remain so illusive, its good to see that there are concrete alternatives being formulated.