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Cecilia Payne-Gaposchkin Sticker

Almost Certainly Real. | Physics

\[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]
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What are stars made of? Her thesis had the answer before anyone believed it. Payne’s 1925 thesis found huge hydrogen and helium abundances in stars and called them “almost certainly not real.” They were real. 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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The physics

Saha's equation gives how much of each element is ionized in a hot gas at a given temperature and density. Cecilia Payne used it to correct for ionization in stellar spectra, and showed that stars are made mostly of hydrogen and helium.

The sticker says Almost Certainly Real. It answers one sentence in a 1925 thesis.

That year, at Harvard College Observatory, Cecilia Payne finished Stellar Atmospheres. Using Meghnad Saha's new theory of how atoms ionise with temperature, she showed that the great differences between stellar spectra are mostly differences of temperature, not ingredients, and that stars look strikingly uniform in composition.

Her own numbers said something stranger: hydrogen and helium vastly outnumbered everything else. On page 188 she wrote: “The enormous abundance derived for these elements in the stellar atmosphere is almost certainly not real.” She suggested hydrogen's figure might be another aspect of its abnormal behaviour rather than a true abundance.

Henry Norris Russell, the leading authority, had written to her that it was “clearly impossible that hydrogen should be a million times more abundant than the metals”, and her caution echoes and cites him. The historian David DeVorkin reads it as a standard of evidence rather than suppression, since Russell approved the thesis, abundance table and all. How much pressure she felt is still argued over. By 1929 Russell had found hydrogen dominant by other routes, and he called her thesis “the most important previous determination of the abundance of the elements by astrophysical means.”

The label on this Sun gives today's best estimates for its surface, by mass: about 74 percent hydrogen, 25 percent helium and everything heavier in the last one percent or so. The helium figure comes from helioseismology, because the Sun's visible surface shows no usable helium lines. These are modern values, not her 1925 numbers.

Almost certainly real.

Equations

\[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]
\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
Symbols
SymbolMeaningUnit
\(n_i, n_{i+1}\) number densities of ionisation stages i and i+1 \(\mathrm{m⁻³}\)
\(n_e\) electron number density \(\mathrm{m⁻³}\)
\(g_i\) statistical weight of stage i \(\mathrm{1}\)
\(\chi_i\) ionisation energy from stage i \(\mathrm{J}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(m_e\) electron mass \(\mathrm{kg}\)
\(\Lambda\) thermal de Broglie wavelength \(\mathrm{m}\)
\(X, Y, Z\) mass fractions of hydrogen, helium, everything heavier \(\mathrm{1}\)

Source Saha, M. N. (1920). Ionization in the solar chromosphere. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 40, 472–488.doi.org/10.1080/14786441008636148 (opens in a new tab)