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Global Deep-MOND Parameter as a Theory Discriminant

Different formulations of MOND 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 MOND regime. This parameter is Q=<V^2>/V0^2, where <V^2> is the mean squared rotational speed of the galaxy, and V0 is 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 the mass distribution in the disk): Q=2/3. The predicted Q value for modified-inertia theories does depend on the mass distribution. However, surprisingly, I find here that it varies only little among a very wide range of mass distributions, Q=0.73+-0.01. While the difference between the theories amounts to only about 5 percent in the predicted RMS velocity, a good enough sample of galaxies may provide the first discerning test between the two classes of theories.