Global Deep-MOND Parameter as a Theory Discriminant

Different formulations of modified Newtonian dynamics predict somewhat different rotation curves for the same mass distribution. Here I consider a global attribute of the rotation curve that might provide a convenient discriminant between theories when applied to isolated, pure-disk galaxies that are everywhere deep in the modified Newtonian dynamics regime. This parameter is Q equivalent to < V-2 >/V-infinity(2), where < V-2 > equivalent to M-1 integral 2 pi r Sigma(r)V-2(r)dr, with Sigma(r) the disk's surface density, M its total mass, and V-infinity the asymptotic (constant) rotational speed. The comparison between the observed and predicted values of Q is oblivious to the distance, the inclination, the mass, and the size of the disk, and to the form of the interpolating function. For the known modified-gravity theories Q is predicted to be a universal constant [independent of Sigma(r)]: Q = 2/3. The predicted Q value for modified-inertia theories does depend on the form of Sigma. However, surprisingly, I find here that it varies only little among a very wide range of mass distributions, Q approximate to 0: 73 +/- 0.01. While the difference between the theories amounts to only about 5% in the predicted rms velocity, a good enough sample of galaxies may provide the first discerning test between the two classes of theories. DOI: 10.1103/PhysRevLett.109.251103