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Vera Rubin Sticker

Galaxy Rotation? She Saw the Dark Side. | Physics

\[v(r)^{2} = \frac{G M(r)}{r}\]
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The outer stars of galaxies move too fast for what we can see. Vera Rubin and Kent Ford’s 1970s galaxy rotation curves showed outer stars orbit too fast for the visible mass: key dark matter evidence. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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3″ × 3″ kiss-cut sticker.

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The physics

If most of a galaxy's mass were in its bright centre, stars far out would orbit more slowly. Vera Rubin found the speeds stay roughly constant far out, which means the enclosed mass keeps growing with radius: unseen matter.

The sticker says She Saw the Dark Side. What she saw first was a flat line where a falling curve should have been.

Nearly all the solar system's mass sits in the Sun, so the farther out a planet is, the slower it moves: speed falls as one over the square root of distance. Neptune, thirty times farther out than Earth, travels at less than a fifth of Earth's speed. The first formula on this page turns that rule around: measure how fast something orbits at radius r, and you can work out how much mass lies inside r.

In 1965 Vera Rubin began work at the Carnegie Institution's Department of Terrestrial Magnetism in Washington, with the astronomer W. Kent Ford and his sensitive new spectrograph. They measured the Doppler shifts of glowing gas clouds across the Andromeda galaxy and published in 1970, and through the following decade Rubin and colleagues measured many more spiral galaxies. Far out, past most of the visible starlight, the speeds did not fall. They stayed flat. By the second formula, a flat speed means the enclosed mass keeps growing in proportion to radius, long after the light has thinned out. Most of each galaxy's mass is something that does not shine.

She was not first. Fritz Zwicky argued in the 1930s that the Coma cluster held far more mass than its galaxies showed, and radio astronomers were finding fast-moving hydrogen at the edges of galaxies in the same years Rubin worked. Her measurements across many galaxies are a large part of why astronomers came to accept it.

What dark matter is remains unknown. No particle has been detected directly, and a minority of physicists prefer to change the law of gravity instead.

Rubin clocked the edges. The dark side was what they told her.

Equations

\[v(r)^{2} = \frac{G M(r)}{r}\]
\[v(r) \approx \text{const} \;\Rightarrow\; M(r) \propto r\]
Symbols
SymbolMeaningUnit
\(v(r)\) circular orbital speed \(\mathrm{m/s}\)
\(M(r)\) enclosed mass \(\mathrm{kg}\)
\(r\) radius \(\mathrm{m}\)
\(G\) gravitational constant \(\mathrm{m³·kg⁻¹·s⁻²}\)

Source Rubin, V. C.; Ford, W. K., Jr. (1970). Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions. The Astrophysical Journal 159, 379.doi.org/10.1086/150317 (opens in a new tab)