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Stellar Core

Nuclear Fusion Physics

\[4\,{}^{1}\mathrm{H} \to {}^{4}\mathrm{He} + 2e^{+} + 2\nu_e\]
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The Sun doesn’t burn. It fuses, and loses weight doing it. In the core, at about 15.7 million kelvin, four protons become one helium-4 nucleus, releasing 26.73 MeV. The Sun turns about 4.3 million tonnes of mass into energy every second. Hans Bethe worked out the reactions in 1939. Stellar Core on a pixel-art unisex tee; equation, symbols and sources in the panel below.

Color
Size

Size guide S–5XL · inches

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

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The physics

Stellar Core does not burn. They fuse, and they lose weight doing it.

In the Sun's core, at about 15.7 million kelvin, hydrogen nuclei are slowly turned into helium. The first formula on this page is the net result of the proton–proton chain: four protons in; one helium-4 nucleus, two positrons and two neutrinos out. The second formula weighs the books. Four protons and two electrons, which the positrons will annihilate, outweigh the helium nucleus they become by 26.73 MeV, using CODATA masses. A few percent of that leaves with the neutrinos; the rest heats the Sun. Arthur Eddington suggested in 1920 that this kind of conversion powers the stars, and Hans Bethe worked out the reactions in 1939, including the CNO cycle, a minor source in the Sun that supplies most of the energy of hotter, more massive stars. Bethe received the 1967 Nobel Prize.

The weight loss is measurable on paper. The Sun radiates about 3.8 × 10²⁶ watts. Divided by c², that is about 4.3 million tonnes of mass converted to energy every second. The Sun is large enough to keep this up for billions of years.

Not every star is doing this. A star fuses hydrogen in its core for most of its life, but when the core hydrogen runs out it changes: a red giant can fuse helium into carbon in its core instead. White dwarfs and neutron stars, the remnants, fuse nothing in their interiors; they are cooling down. Brown dwarfs never get hot enough to sustain hydrogen fusion at all. And the very heaviest stars run through successive fuels until an iron core forms, which cannot release energy by fusing, and the core collapses.

Stellar Core endures because they are balanced: gravity squeezing in, fusion heat pushing out.

Equations

\[4\,{}^{1}\mathrm{H} \to {}^{4}\mathrm{He} + 2e^{+} + 2\nu_e\]
\[Q = \left(4m_p + 2m_e - m_\alpha\right)c^{2} \approx 26.73\ \text{MeV}\]
Symbols
SymbolMeaningUnit
\(m_p\) proton mass \(\mathrm{kg}\)
\(m_e\) electron mass \(\mathrm{kg}\)
\(m_\alpha\) helium-4 nucleus (alpha) mass \(\mathrm{kg}\)
\(Q\) total energy released incl. positron annihilation (a few % carried off by neutrinos; quoted in MeV) \(\mathrm{J}\)