Astronomy & Celestial Mechanics
the sky, computed
Concept

H minus opacity — where it appears

Absorption by the negative hydrogen ion, which binds a second electron by 0.754 electronvolts and has no line spectrum at all. It dominates the continuous opacity of cool stars, and its abundance follows the electron pressure the metals supply.

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

Also named here as ionisation equilibrium — the same set of essays touches all of them, so they are one junction rather than several.

742 kelvin between a dwarf and a supergiant, at the same ionisation. The fraction of calcium still neutral against temperature, for three surface gravities: a dwarf, a giant and a supergiant. The three curves are the same curve slid sideways. The Saha equation carries the electron pressure in its denominator, and the photospheric pressure follows the surface gravity as its square root — hydrostatic equilibrium gives a gas pressure of order g over the opacity, and the opacity in a cool star is set by the electrons themselves. So the pressure runs from 19 newtons a square metre in the dwarf down to 0.48 in the supergiant, a factor of 40, and the half-ionisation point moves from 4427 kelvin to 3685 — 742 kelvin apart. At fixed temperature the ionisation ratio goes as g^-0.50, exactly the square root the algebra requires. A star's luminosity class is a measurement of the density of its photosphere, read off which stage of an element the lines belong to.

A luminosity class is a density measurement

The Saha equation has an electron pressure in its denominator, and a supergiant's photosphere is forty times less dense than a dwarf's at the same temperature. So the same element sits in different ionisation stages in the two, the spectrum says which, and the second axis of stellar classification is a barometer.

starlight · Ionisation Where a photosphere's free electrons come from. The share of the free electrons donated by metals rather than by hydrogen, against temperature, at a gas pressure of 12000 N/m² and at solar abundance, 1 dex below solar, 2 dex below solar. The electron pressure is not assumed here — it is solved for, as the value at which the ionisation of the gas supplies exactly the electrons the gas contains. Below about 5897 K at solar abundance every free electron in the gas comes from an element present at one part in ten thousand, because hydrogen's 13.6 eV keeps it neutral while magnesium's 7.6 does not. The handover is fast: solar crosses a half at 5897 K, 1 dex down crosses a half at 5088 K, 2 dex down crosses a half at 4467 K. At 5,772 K and this pressure the solved electron pressure is 1.78 N/m².

The continuum is made by one atom in ten thousand

The Sun's light leaves through an ion that exists only because a hydrogen atom will hold a second electron by three-quarters of an electronvolt. The electrons it holds come almost entirely from magnesium, silicon and iron — so the level against which every solar line depth is measured is rationed by elements present at one part in ten thousand.

starlight · Ionisation

Named alongside it

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

Electron pressureIonisation equilibriumSaha equationBound-free absorptionContinuous opacityElectron donorFree free absorptionHydrostatic equilibriumLuminosity classMetallicityMK classificationPartition function

All concepts