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Jocelyn Bell Burnell Sticker

She Found Pulsars. They Gave Her Silence. | Physics

\[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]
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A strange, regular blip in a chart of radio noise. In 1967 Jocelyn Bell Burnell spotted the first pulsar in radio data: a rapidly spinning neutron star. 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

A pulsar's very regular pulses mean it must be extremely dense to spin that fast without flying apart, which points to a neutron star. Radio pulses at lower frequencies arrive later after passing through interstellar electrons, and that delay measures how many electrons lie along the way.

The sticker says She Found Pulsars. They Gave Her Silence. The first half is exactly right. The second is more complicated, as she has said herself.

In 1967 Jocelyn Bell, a Cambridge graduate student who had helped build a large radio telescope, was reading its chart-paper output for twinkling quasars when she noticed a signal that did not belong: pulses, extremely regular, a little more than a second apart. She took it to her supervisor, Antony Hewish. The team spent months ruling out interference, half-jokingly calling it LGM, for little green men. Then she found a second, elsewhere, at a different rate. The paper appeared in Nature in February 1968, her name second of five. It suggested the pulses might come from white dwarfs or neutron stars.

The first formula on this page is how that was settled. Anything that spins and holds together needs its own gravity to beat the spin, which puts a floor under its average density: about 3π divided by G times the period squared. A pulsar reported in 2006 spins 716 times a second, so its density must exceed about 7 × 10¹⁶ kilograms per cubic metre, far beyond any white dwarf. Only a neutron star, as dense as an atomic nucleus, survives. The second formula weighs the space between: lower radio frequencies arrive later, delayed by free electrons.

The 1974 Nobel Prize in Physics went to Hewish and Martin Ryle. Prominent scientists protested her omission; she has said leaving out a student was appropriate. Recognition followed: the 2018 Special Breakthrough Prize in Fundamental Physics, whose $3 million she gave away to help under-represented students become physics researchers, and in 2021 the Royal Society's Copley Medal.

Silence is the wrong word. The pulses were never silent, and neither was she.

Equations

\[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]
\[\Delta t = \frac{e^{2}}{8\pi^{2}\varepsilon_0 m_e c}\,\mathrm{DM}\left(f_1^{-2} - f_2^{-2}\right)\]
Symbols
SymbolMeaningUnit
\(\bar\rho\) minimum mean density for a body spinning with period P not to fly apart \(\mathrm{kg/m³}\)
\(G\) gravitational constant \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(P\) rotation period \(\mathrm{s}\)
\(\Delta t\) arrival-time delay between frequencies f₁ < f₂ \(\mathrm{s}\)
\(\mathrm{DM}\) dispersion measure, ∫ nₑ dl (free electrons per area along the line of sight) \(\mathrm{m⁻²}\)
\(f_1, f_2\) observing frequencies \(\mathrm{Hz}\)
\(e, \varepsilon_0, m_e, c\) constants \(\mathrm{C, F/m, kg, m/s}\)

Source Hewish, A. et al. (1968). Observation of a Rapidly Pulsating Radio Source. Nature 217, 709–713.doi.org/10.1038/217709a0 (opens in a new tab)