Astronomy & Celestial Mechanics
the sky, computed
Concept

Main-sequence turnoff — where it appears

The point on a cluster's colour–magnitude diagram where its stars are leaving the main sequence because their central hydrogen is used up. Its mass falls as the cluster ages, so it is the clock from which cluster ages are read, once composition and distance are known.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

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.

stars · The HR diagram Brighter by mass, fainter by temperature. Main sequences from 0.5 to 1.3 solar masses in luminosity against effective temperature, hotter to the left, for solar composition, [Fe/H] = −1.5, from homology applied to the solar-composition relation. The dots join stars of the same mass: lowering the metals moves each one up and to the left, so a 0.8 solar-mass star goes from 0.41 to 0.66 solar luminosities and from 5049 to 5879 K. The main sequence is steep, so a move of that size to the left carries a star past solar stars much brighter than itself: at a fixed temperature of 5800 K the metal-poor sequences lie 0.59 magnitudes below the solar one. A metal-poor star is brighter than a solar one of the same mass and fainter than a solar one of the same temperature — which is why such stars were called subdwarfs.

Brighter for its mass and fainter for its colour

Two stars of the same mass are almost the same star only if they are made of the same material. Take most of the metals out and the opacity falls, the radiation leaks out faster and the star settles brighter and much hotter — so far hotter that, at a given colour, it sits below the ordinary main sequence. The relation between mass and light has composition inside it, and every mass, age and distance read off it inherits that.

stars · The mass–luminosity relation Isochrones that crowd on the main sequence and fan out above it. Isochrones for stars of solar metallicity at 1, 2, 4, 6, 8, 10, 12 billion years, luminosity against temperature with temperature falling to the right. On the main sequence they lie almost on top of one another — a star brightens and barely changes colour as it ages — and only where they turn off and cross towards the giants do they separate. Two boxes show the measurement errors of a star with a good parallax and spectrum (twice 70 K and 3 per cent): one around a Sun-like star of 4.6 billion years, whose age they allow anywhere in 4.53 (3.38–5.63) billion years; one around a subgiant of the same mass at 10.5, allowed only 10.5 (10.3–10.7).

A lone star is dated only as it leaves

A star in a cluster is dated by the bend its neighbours trace. A star alone has one position on the Hertzsprung–Russell diagram, and an age for it means finding which isochrone passes through that point. On the main sequence they almost all do: a Sun-like star measured as well as a parallax and a spectrum allow is anywhere from three and a half to five and a half billion years old. A star the same mass on its way off the main sequence is dated to two per cent.

stars · The HR diagram

Named alongside it

The objects these essays reach for when they reach for this one.

MetallicityGlobular clusterIsochroneMain-sequenceSubgiant branchCoeval populationDistance modulusHertzsprung–Russell diagramHomologyThe HR diagramKramers opacityMass luminosity relation

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