Astronomy & Celestial Mechanics
the sky, computed
Concept

Phase transition — where it appears

A change of state at which a substance releases or absorbs latent heat without changing temperature. In a white dwarf's interior it is the freezing of the ion plasma into a lattice, and the latent heat has to be radiated before cooling resumes.

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

Thirty e-foldings erase the memory of a seed. Field strength against time for three seed fields 8 orders of magnitude apart, amplified at one e-folding every 3·10⁸ years — a galactic dynamo's measured turnover rate — and stopped at the 3·10⁻⁶ gauss the disc actually has. In 10 billion years the budget is 33 e-foldings, which is a factor of 3·10¹⁴. That is the finding: the three tracks reach the same ceiling within 5.5 billion years of one another, so the field a galaxy has today carries essentially no information about the field it started with. Any seed above about 10⁻²⁰ gauss will do, and mechanisms that produce far less than that are the only ones ruled out. The measurement that does constrain a seed has to be made where no dynamo ever ran, which means the voids between clusters — and the limit there comes from gamma rays that never arrived.

The seed that cannot be remembered

A galactic dynamo affords something like thirty e-foldings over the age of a galaxy, which multiplies any seed field above a ten-thousandth of a billionth of a microgauss up to the microgauss actually observed. The field a galaxy has today therefore says nothing about the field it started with, and the only place a seed survives unamplified is the emptiness between clusters.

cosmology · Primordial fields 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 An electroweak field decays toward one line, and helicity decides where it meets it. The comoving strength of a magnetic field against its coherence length, both on logarithmic scales. A field made at the electroweak transition, at 100 GeV, starts on a hundredth of the Hubble length then (1 AU today) with a tenth of the radiation's energy density (1 × 10⁻⁶ G), and decays as its turbulence is processed until the largest eddy is the one an Alfvén wave can cross by recombination — the straight line, 10⁻⁸ G at 1 Mpc. With no net helicity it falls as λ^−5/2 and stops at 0.038 pc and 4 × 10⁻¹⁶ G. Maximally helical, it falls only as λ^−½ and stops at 4.7 kpc and 5 × 10⁻¹¹ G. The shaded floor is what the missing gamma-ray halos exclude: a field coherent over more than a megaparsec must exceed 9 × 10⁻¹⁷ G, and the bound rises as the inverse square root of the coherence length below the leptons' cooling length of 0.6 Mpc. The non-helical field ends 3.0 decades below it; the helical one 4.6 decades above it. Above 10⁻⁹ G at a megaparsec the microwave background excludes the field.

A twist that decides where the field ends

A magnetic field made in the first trillionth of a second starts strong and absurdly small, and its turbulence spends the next three hundred thousand years trading strength for size. How far it gets depends on one conserved quantity — how twisted its field lines are — and for a field made at the electroweak transition, that twist is the difference between failing the void bound by three decades and clearing it by five.

cosmology · Primordial fields

Named alongside it

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

BlazarMagnetogenesisPair cascadePrimordial fieldsAlfven speedBiermann batteryCoherence lengthCooling ageCoulomb couplingCrystallisationDebye coolingDynamo

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