Astronomy & Celestial Mechanics
the sky, computed
Concept

Coulomb coupling — where it appears

The ratio of the electrostatic energy between neighbouring ions to their thermal energy, written Γ. A plasma with Γ near 175 crystallises into a lattice, which is how the interior of a cooling white dwarf freezes from the centre outward.

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

A 1.1 solar-mass white dwarf held up for 2.8 extra billion years. The time a white dwarf takes to reach the crystallisation luminosity, and the two delays that follow, against mass. The lower band is bare Mestel cooling — thermal energy of the ions leaking out through an envelope whose opacity is Kramers'. On top of it sits the latent heat of crystallisation, 0.85 kT per ion released when the liquid interior freezes into a lattice; and on top of that the gravitational energy of ²²Ne settling through what is left, taken here as 0.6 kT per ion. Neither is fuel: both are energy the star already had, released late and radiated at the low luminosity it has by then, which is why so little of it buys so much time. The delay rises from 1.88 billion years at 0.5 solar masses to 2.81 at 1.1 — 58 per cent of the cooling already done. A white dwarf age computed from the bare law is too young, and it is too young by more the heavier the star is, which is exactly the direction that matters, because the massive white dwarfs are the ones used to date the oldest populations.

A clock that stops while its interior freezes

A white dwarf has nothing left to burn, so its brightness is a record of how long it has been cooling — until the interior crystallises. The latent heat of that phase change, and the settling of a heavy isotope through what is left, hold a massive white dwarf up for nearly three extra billion years.

stars · White dwarf cooling Only the massive pulsators freeze while they ring. The crystallised fraction of a white dwarf's mass against its surface temperature, for 0.6, 0.9, 1.1 solar masses, with the instability strip of the hydrogen pulsators shaded. The 0.6 M☉ star begins to freeze at 6,000 K, long after it has stopped pulsating; the 0.9 M☉ star begins near 10,900 K; the 1.1 M☉ star near 17,100 K, and it crosses the strip 58–75% frozen. A massive pulsator is a star whose interior is solidifying while its clock is running.

A pulsating star that freezes while it rings

An ordinary white dwarf pulsates long before its interior begins to crystallise. A heavy one does not: above about nine-tenths of a solar mass the core starts freezing while the star is still hot enough to ring, and a 1.1-solar-mass pulsator crosses the instability strip with more than half its mass already solid. The heat released by the freezing slows its cooling, and so slows the lengthening of its pulsation periods by about a fifth — the only way to measure the latent heat of a star directly, and one that takes half a century of timing to see.

stars · White dwarf cooling

Named alongside it

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

Cooling ageCrystallisationLatent heatWhite dwarf coolingAsteroseismologyDebye coolingLuminosity functionNeon-22 sedimentationNumber densityPhase transitionWhite dwarf

All concepts