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.
Department of Particle Physics and Astrophysics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Mordehai
M
Milgrom