Astronomy & Celestial Mechanics
the sky, computed
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The HR diagram — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The Hertzsprung–Russell diagram. Luminosity against surface temperature, both in solar units and on logarithmic axes, with temperature increasing to the left. The main sequence is computed from the mass–luminosity and mass–radius relations; the dashed diagonals are lines of constant radius.

    The diagram that sorted the stars, by plotting two things against each other

    Plot brightness against colour for a few thousand stars and they do not scatter. They fall on a narrow band with two islands off it, and explaining that structure is most of stellar astronomy.

    part 1 · stars
  2. The Hertzsprung–Russell diagram. Luminosity against surface temperature, both in solar units and on logarithmic axes, with temperature increasing to the left. The main sequence is computed from the mass–luminosity and mass–radius relations; the dashed diagonals are lines of constant radius.

    The main sequence is a place stars sit, not a track they travel

    The commonest misreading of the Hertzsprung–Russell diagram is that stars slide down the band as they age. They do not. They sit at one point for ninety percent of their lives and then leave sideways.

    part 2 · stars
  3. Three clusters, three ages, one diagram. Isochrones for populations of 100 Myr, 1 Gyr, 12 Gyr, each drawn as the main sequence up to its own turnoff and then the post-main-sequence track of the turnoff mass. The turnoffs are at 5.52 M☉, 2.20 M☉, 0.94 M☉, from t = 10¹⁰ M/L with this file's own mass–luminosity relation. Nothing here is a track along which a star moves. Every point is a different star of a different mass, all the same age, and the bend is simply where the population runs out of stars that have had time to leave. That is why a cluster has an age and a field star does not: the bend needs a population, and one star is not one. The oldest globular clusters sit near the 12 Gyr line, and in the 1990s the same construction gave them ages of 16 to 18 Gyr against a universe measured at 10 — a two-standard-deviation contradiction that was resolved from the distance side, by Hipparcos, and not from this one.

    An age read off a bend

    A cluster is a population of one age and many masses, so the place where its stars leave the main sequence is a clock. The bend needs a population — which is why a cluster has an age and a single star does not.

    part 3 · stars

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