Astronomy & Celestial Mechanics
the sky, computed
Concept

Cooling age — where it appears

The time a white dwarf has spent radiating away the thermal energy of its ions, inferred from its luminosity through a cooling model. It is not the star's total age, which also includes however long the progenitor spent on the main sequence.

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

7 solar masses of progenitor become 0.56 of white dwarf. Above: the initial–final mass relation. The steep line is what a star would leave if it kept everything; the shallow one is what it actually leaves, M_f = 0.08M_i + 0.489, fitted to white dwarfs in open clusters. Everything between 1 and 8 solar masses ends up between 0.57 and 1.13 — a range of 7 compressed by a factor of 12 — and the fraction thrown away rises from 43% at the bottom to 86% at the top. A star spends most of its mass in the last per cent of its life, at rates no theory predicts from first principles, and this relation is measured by running stellar evolution backwards: a cluster's turn-off gives the age, a white dwarf's temperature gives its cooling time, the difference gives how long its progenitor lived, and a model turns that into the mass it was born with. Below: the white dwarf mass distribution that follows, from a Salpeter initial mass function pushed through the relation above. It peaks at 0.61 solar masses, which is what every survey of white dwarfs measures. Two things make that peak and the flatness of the relation is only one of them: the unsmoothed distribution (the stepped curve) falls monotonically and is largest at its low-mass edge, because the initial mass function is steep. The edge is where it is because no star lighter than about 1.0 solar masses has had time to die yet, and the scatter of the measurement rounds that cliff into a maximum a little above it. A flat relation produces a narrow range; it takes the age of the Galaxy to produce a peak.

The mass a star does not keep

The initial–final mass relation is nearly flat, so everything from one to eight solar masses ends as a white dwarf between 0.57 and 1.13 — and the observed distribution piles up at 0.6 almost regardless of what went in. The relation is measured by running stellar evolution backwards, because nothing predicts the loss.

stars · Stellar evolution 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

Named alongside it

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

Asymptotic giant branchChandrasekhar limitCoulomb couplingCrystallisationDebye coolingDredge upInitial final mass relationLatent heatLuminosity functionMass lossMass loss rateNeon-22 sedimentation

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