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 ≡ V(2)/V(∞)(2), where V(2) ≡ M(-1)∫ 2πrΣ(r)V(2)(r)dr, with Σ(r) the disk's surface density, M its total mass, and V∞ 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 Σ(r)]: Q = 2/3. The predicted Q value for modified-inertia theories does depend on the form of Σ. 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% in the predicted rms velocity, a good enough sample of galaxies may provide the first discerning test between the two classes of theories.