Astronomy & Celestial Mechanics
the sky, computed
Concept

Cluster turnoff — where it appears

The point on a star cluster's colour-magnitude diagram where the main sequence bends away towards the giants. It marks the mass whose main-sequence lifetime equals the cluster's age, which turns a bend in a diagram into a date.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The fractional distance error, rung by rung. Cumulative fractional uncertainty in a measured distance against the distance itself, both on logarithmic axes. Each rung of the ladder is calibrated against the one below it, so its scatter adds in quadrature to everything already inherited, and the total can only rise: radar to the planets 10⁻⁵%, parallax 1.0%, main-sequence fitting 5.1%, Cepheids 6.5%, Type Ia supernovae 8.2%.

Every distance is measured with the last one

No single method reaches from a planet to a distant galaxy. The ladder is built rung by rung, each calibrated on the one below, and the errors multiply all the way up.

starlight · Distance ladder How long a star lasts, against its mass. Main-sequence lifetime against mass, on logarithmic axes. Fuel grows in proportion to mass and consumption grows as its three-and-a-half power, so the lifetime falls steeply — a star of thirty solar masses lives for a few million years.

Why the biggest stars die first, and take the galaxy with them

A star thirty times the Sun's mass has thirty times the fuel and burns it forty thousand times faster. It lasts a few million years, and everything heavier than iron exists because of it.

stars · Stellar lifetimes Mestel cooling for white dwarfs of 0.4 to 1 solar masses. Luminosity against age for white dwarfs of 0.4, 0.6, 0.8, 1 solar masses, both axes logarithmic. Each line is the whole of the star's later life: there is no nuclear source, so what is radiated is the thermal energy the ions had when the star was made, leaking out through a thin envelope whose opacity is Kramers'. That one sentence gives L ∝ t^(−7/5), and the lines are straight here because a power law is straight on these axes — the slope is the exponent and can be measured off the picture. Two features are worth more than the numbers. The first is how flat the sequence becomes: a factor of ten in luminosity costs a factor of 5.2 in age, so a white dwarf spends most of its existence faint, and any population of them piles up at the bottom. The second is that the heavier tracks lie above the lighter ones. A heavier white dwarf is smaller, so it has more ions to cool and less surface to lose them through, and at a given age it is the brighter object. The picture does not show what happens at the faint end, where the ions crystallise and the heat capacity stops being constant; that is a separate figure, and it is where this law stops being enough.

A clock with no fuel in it

A white dwarf has nothing left to burn, so its brightness is a record of how long it has been cooling. The faintest ones in the Galaxy are not faint because they are small — they are as faint as anything has had time to become, and the place where they stop is a date.

stars · White dwarf cooling

Named alongside it

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

Initial mass functionSupernovaWhite dwarfAstronomical unit (AU)Black holeCrystallisationDebye coolingDegeneracy pressureDistance ladderDistance modulusGiant branchGlobular cluster

All concepts