Velocity Curves for Spiral Galaxies

The first and perhaps most direct evidence for dark matter in the universe is found in the measurement of rotational velocities for objects in spiral galaxies as a function of distance from the nucleus. When you reach the outside of the matter of a rotating galaxy, the rotational velocity for an orbit about the galactic center should drop off proportionately to the inverse square root of the distance from the galactic center.

宇宙中暗物质的最直接证据之一是通过测量螺旋星系中物体相对于星系中心的距离的旋转速度得到的。当到达旋转星系的边缘时，围绕星系中心的轨道速度应与到星系中心的距离的平方根成反比而下降。

The Sun lies about 8.5 kpc from the galactic center of the Milky Way galaxy, and the visible spiral arms and globular clusters extend out to about 15 kpc. But the rotational velocity does not drop off, as shown in the above illustration. This indicates the presence of gravitational mass beyond 15 kpc, but it cannot be detected by any mechanism which has been tried.

太阳位于银河系中心约8.5 kpc处，可见的螺旋臂和球状星团延伸到约15 kpc。但如上图所示，旋转速度并未下降，这表明在15 kpc之外存在引力质量，但无法通过任何已尝试的机制检测到。

It is important to note that this non-Keplarian behavior is not unique to the Milky Way, but has been observed for other spiral galaxies. The data for the other spiral galaxies in the above illustration is from Rubin, Ford, and Thonnard, Ap. J. Lett., 225, L107, 1978 and is discussed in Chapter 24 of Carroll and Ostlie.

需要注意的是，这种非开普勒行为并非仅存在于银河系，其他旋涡星系中也观察到了这种现象。上述示意图中其他旋涡星系的数据来源于Rubin, Ford, and Thonnard, Ap. J. Lett., 225, L107, 1978，相关内容详见Carroll和Ostlie的第24章。