Astronomy & Celestial Mechanics
the sky, computed
Concept

Thermal timescale — where it appears

The time a star or part of a star would take to radiate its stored heat at its present luminosity, also called the Kelvin–Helmholtz time. It is about thirty million years for the Sun as a whole. A star forced to change faster than this is driven out of its equilibrium size.

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

The core's neutrino luminosity against its temperature, and the star's light. The luminosity carried off by neutrinos from pair annihilation in a burning core of 3 solar masses, in erg per second on a logarithmic axis, against the core's temperature in billions of kelvin, along a rough track on which the density rises as the cube of the temperature, with each burning stage marked at its own published temperature, density and core mass. The horizontal line is the star's light, about 1.5 × 10⁵ times the Sun's, nearly constant through all the late stages. The neutrino luminosity rises roughly as the ninth power of the temperature and overtakes the light at about 0.60 billion kelvin — between helium and carbon burning. From carbon burning on, carbon 76, neon 3·10⁴, oxygen 10⁵, silicon 7·10⁵ times the light is lost as neutrinos. The core is no longer cooled by the surface it shines through; it is cooled directly, from inside, by particles that leave without interacting.

The last fuels burn for the neutrinos

A massive star burns hydrogen for millions of years and silicon for about a day. The collapse in duration is not because the late fuels are poorer; it is because, from carbon burning on, the core loses more energy to neutrinos than the whole star gives out as light, and the neutrino losses rise as the ninth power of the temperature.

stars · Fusion A binary that goes silent for part of its shrinking. The orbital period of a white dwarf of 0.8 M☉ and a donor from 0.5 M☉, in a one-zone evolution, against time. Mass transfer drives the period down fast while magnetic braking acts. At 3.17 hours the donor reaches 0.2 M☉ and loses its radiative core and with it the brake. Its radius, swollen by the fast transfer, relaxes and it falls inside its Roche lobe; transfer stops (dashed, no accretion, nothing to see). Gravitational waves alone close the orbit, until contact returns at 2.30 hours, 0.60 billion years later. The observed gap runs from 2.15 to 3.18 hours. The donor's thermal time at 0.2 M☉, set here to 3×10⁸ years, is chosen to place the upper edge, so that edge is fitted and the lower one is not. The period reaches a minimum of 68 minutes against an observed 80, a shortfall every model of this simplicity shares.

A binary that goes silent for an hour of period

Binaries of a white dwarf feeding off a small star can be found at almost any orbital period down to about eighty minutes, except between about two and three hours, where they are strikingly rare. They have not stopped existing there. They have stopped shining. The moment the donor loses its radiative core, the wind's magnetic brake appears to switch off. The star, swollen by the transfer it was being driven through, shrinks back inside its own Roche lobe, and the feeding stops. Only gravitational waves remain to close the orbit, and it takes them about half a billion years.

stars · Magnetic braking A reservoir so large that it does not notice. The fractional increase in the heat of the Sun's convective envelope if a fraction 0.001, 0.003, 0.01 of the surface is held under spots, against time. The envelope holds about 7×10⁴⁵ erg, 58 thousand years of the Sun's light. Spots covering 0.3% of the surface for an eleven-year cycle add 4.2e-7 of that, a temperature change of 0.4 parts per million at most, spread over the whole envelope. So the blocked heat simply remains in the star, and the surface flux shows the deficit. It levels off only after the envelope's thermal time, when the star has adjusted.

A spot whose missing heat goes nowhere

A sunspot blocks most of the energy trying to come up beneath it, and a large group visibly dims the whole Sun by a thousandth. Energy is conserved, so the blocked flux ought to come out somewhere else, and for a century observers looked for the bright ring around every spot. There is none to speak of. The heat has gone into the rest of the convection zone, spread so fast and so widely that the surface cannot notice, and it will stay there for longer than human history. For the time being the Sun simply is fainter, without any contradiction.

stars · Energy transport

Named alongside it

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

Bright ringCarbon burningCataclysmic variableConvection zoneCore collapse supernovaFaculaFully convective starMagnetic brakingNeutrino coolingNuclear fusionPair annihilationPeriod gap

All concepts