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The Galaxy Rotation Curve

If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s inverse square law, matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics.

The Gradient of the Rotation Curve

In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic.

According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes, with superposed the gradient (dashed) calculated from local stars.

Conflict with CDM and MOND

The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al. found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is also distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.

The Local Slope of the Rotation Curve ↑ Radial Velocity Test →