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Henrietta Swan Leavitt Sticker

The Blink Is the Ruler | Physics

\[M_V = -2.43\,(\log_{10} P - 1) - 4.05\]
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How do you measure the distance to a galaxy? At Harvard in 1908–1912, Henrietta Swan Leavitt found that Cepheid variable stars in the Small Magellanic Cloud which pulse more slowly are brighter. Time a Cepheid’s blink, infer its true brightness, compare with how faint it looks, and you have its distance. A 3" pixel-art physicist sticker; equation, symbols and sources in the physics panel below.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Leavitt found that the longer a Cepheid variable star takes to pulse, the brighter it really is. Comparing that true brightness with how bright it looks gives its distance, which made Cepheids a cosmic ruler.

Henrietta Swan Leavitt worked at Harvard College Observatory measuring stars on glass photographic plates.

Studying variable stars in the Small Magellanic Cloud, she found that the Cepheids which take longer to brighten and dim are brighter. Because all of those stars are at about the same distance, the pattern had to be real. She published it in 1908 and gave periods for 25 of them in 1912.

That turns a Cepheid into a ruler. Time its blink, read off how bright it really is, compare with how bright it looks, and the difference gives the distance. The chart on the sticker plots five Cepheids on a modern calibration of the relation, M_V = −2.43 (log P − 1) − 4.05, from Hubble parallaxes (Benedict et al. 2007). Higher on the chart means brighter.

Edwin Hubble used Cepheids in 1924–25 to show that the Andromeda nebula is a galaxy far outside our own.

The blink is the ruler.

Equations

\[M_V = -2.43\,(\log_{10} P - 1) - 4.05\]
\[m - M = 5\log_{10}\frac{d}{10\,\mathrm{pc}}\]
SymbolMeaningUnit
\(M_V\) absolute visual magnitude: how bright the star really is (more negative = brighter) \(\mathrm{mag}\)
\(P\) pulsation period of the Cepheid \(\mathrm{days}\)
\(m\) apparent magnitude: how bright it looks from here \(\mathrm{mag}\)
\(d\) distance to the star (ignoring dust) \(\mathrm{pc}\)

Sources

  1. Leavitt (1908) 1777 variables in the Magellanic Clouds, Annals of Harvard College Observatory 60, 87
  2. Leavitt & Pickering (1912) Periods of 25 Variable Stars in the Small Magellanic Cloud, Harvard College Observatory Circular 173, 1
  3. Benedict et al. (2007) HST Fine Guidance Sensor parallaxes of Galactic Cepheid variable stars: period-luminosity relations, AJ 133, 1810

Source Leavitt, H. S.; Pickering, E. C. (1912). Periods of 25 Variable Stars in the Small Magellanic Cloud. Harvard College Observatory Circular, 173, 1–3.

Field notes

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