Astronomy & Celestial Mechanics
the sky, computed
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Fusion — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Energy generation against core temperature. The proton–proton chain and the CNO cycle, in solar units, against core temperature on logarithmic axes. The CNO curve is far steeper, so the two cross at 18.8 million kelvin — above that temperature a star runs mostly on CNO, and below it mostly on pp.

    The furnace that runs cooler than a compost heap

    The Sun's core produces 276 watts per cubic metre. A human body produces more. The Sun is bright because it is enormous, and its fusion is astonishingly slow — which is exactly why it lasts.

    part 1 · stars
  2. A furnace with the thermostat taken out. Left, the two pressures in a red giant's helium core at 10⁶ g/cm³. The ideal-gas pressure rises with temperature, as the whole regulation of a star depends on it doing; the degenerate electron pressure is a horizontal line, because the exclusion principle does not know the temperature. At the ignition point near 10⁸ K the degenerate term is 5.1 times the gas term, so a temperature rise there raises the total pressure by almost nothing and the core does not expand. Right, what that costs. Both curves start at the same temperature with the same triple-alpha rate, whose logarithmic slope is 41 — the famous T⁴⁰, differentiated here rather than quoted. The regulated core settles; the degenerate one, with nowhere to put the extra energy, goes vertical. The flash reaches 10¹⁰ solar luminosities for a few seconds and not one photon of it is seen: every erg goes into lifting the degeneracy, and the star's visible response is to become fainter and settle on the horizontal branch.

    The resonance that had to exist

    Three alpha particles cannot meet at once, and the two-body intermediate falls apart in 8×10⁻¹⁷ seconds. That is a hundred thousand times longer than a crossing time, which is just enough — provided a nuclear level sits at 7.65 MeV. Hoyle argued from the existence of carbon to the existence of the level, and it was found where he said.

    part 2 · stars

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