Department of Particle Physics and Astrophysics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev Lett. 2012 Dec 21;109(25):251103. doi: 10.1103/PhysRevLett.109.251103.
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.
不同形式的修正牛顿动力学对相同的质量分布预测出略有不同的旋转曲线。在这里，我考虑了旋转曲线的一个全局属性，当应用于处于修正牛顿动力学区域深处的孤立、纯盘星系时，它可能为理论之间提供一个方便的判别标准。这个参数是 Q≡V(2)/V(∞)(2)，其中 V(2)≡M(-1)∫2πrΣ(r)V(2)(r)dr，Σ(r)是盘的面密度，M 是其总质量，V∞是渐近（常数）旋转速度。Q 的观测值与预测值的比较忽略了距离、倾斜、质量和盘的大小以及插值函数的形式。对于已知的修正引力理论，Q 被预测为一个普遍常数[与 Σ(r)无关]：Q=2/3。修正惯性理论的预测 Q 值确实取决于 Σ 的形式。然而，令人惊讶的是，我在这里发现，它在非常广泛的质量分布范围内变化很小，Q≈0.73±0.01。虽然理论之间的差异在预测的 rms 速度中仅占约 5%，但足够多的星系样本可能为这两类理论提供首次有辨别力的测试。
