The theory behind MOND?

Rotation curve dynamics in low surface brightness spiral galaxies.

All of the following dynamical description (full details in 2004GRG) has its roots in the hard-line interpretation of Mach's Principle developed in the paper 2002GRG.

We present the results arising from the modelling of the rotation curves of a set of eight low surface brightness (LSB) galaxies, the data for which was given by Stacy McGaugh. LSB galaxies provide a critical test for theory because they are the ones which present the greatest difficulties for the CDM models - which fail comprehensively in this context. By contrast, the theory discussed here and the MOND algorithm (MOND pages) are unique in being the only methods (so far as we are aware) which have modelled the details of LSB rotation curves exactly to within the observational error bars.

The major distinction between the theory discussed here and MOND is that the presented theory is exactly that - a theoretical development based upon a particular quantitative interpretation of what Mach's Principle means - whilst MOND is simply an ad-hoc computational algorithm, albeit an enormously successful one.

There is also an important difference of detail: MOND requires an estimate of the mass distribution within the disc which is obtained from the disc photometry and then assuming that light traces mass in a simple way. By contrast, the theory being discussed here (2004GRG) requires only an estimate of the total disc mass. Given this, the theory is able to recover the mass distribution from an internal mass distribution equation.

In figure 1, the red solid lines are the computed rotation curves whilst the blue filled circles (with error bars) are the observations. The green crosses are the estimated densities (from photometry) whilst the black dashed lines are the computed densities. Figure 2 is similar, except that there is no colour coding. In all eight cases, we see a remarkable conjunction between theory and observation. MOND is equally successful (except that it requires far more mass information) whilst the CDM models fail comprehensively here.

The success is so total that it is tempting to think that this theory, immersed so deeply in Machian ideas, is the theory which underlies the MOND algorithm - the only other successful modeller of LSBs. However, the connection - if it exists - is by no means obvious!

LSB rotation curves

Figure 1:


Figure 2: