Astronomy & Celestial Mechanics
the sky, computed
Concept

Excitation — where it appears

The event that starts an oscillation. Because a free libration damps in far less than the age of the solar system, detecting one is a statement that something disturbed the body recently rather than a property of its shape.

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

The Balmer maximum is at 9,870 K, and it is a maximum in temperature. What two absorption lines actually count, each normalised to its own maximum. The first curve is the fraction of all hydrogen sitting in n = 2 — the only hydrogen a Balmer line can absorb — which is a Boltzmann factor climbing with temperature multiplied by the neutral fraction falling with it. The product peaks at 9,870 K, where 35.2% of the hydrogen is still neutral and only 8.73·10⁻⁶ of all of it is in n = 2 at all. Below the peak there is plenty of hydrogen and almost none of it excited; above it there is plenty excited and almost none of it neutral. The second curve is the fraction of calcium that is singly ionised, which is what the Ca II K line counts, and it peaks at 6,335 K — cooler, because calcium gives up its first electron at 6.113 eV. At 6,000 K the Balmer curve is at 0.1% of its own maximum while Ca II is near its peak, and calcium is 4.5·10⁵ times rarer than hydrogen in the same gas. A spectrum in which Ca II K is the strongest line is not a spectrum of a calcium star. Reading it as one is precisely the error that had the Sun made of iron until 1925.

Why hydrogen's lines are strongest where hydrogen is not

A Balmer line counts the hydrogen atoms sitting in one particular excited state, and that population peaks near 10,000 K — where a third of the hydrogen has already been ionised away. The strength of a line is a thermometer, and reading it as an abundance put hydrogen at one per cent of the Sun until 1925.

starlight · Ionisation A free libration does not last. How long a free libration survives before tidal dissipation removes it, against the tidal quality factor, for four locked bodies — with the age of the solar system marked. A lightly damped oscillator loses its amplitude in about Q of its own periods, and a free libration's period is years, so the decay time is thousands to hundreds of thousands of years for any plausible Q. Against 4.5 billion years that is instantaneous. A free libration that is observed today was excited within the last geological instant, and one that is not observed bounds how much has happened. The Moon's is detected, at a few arcseconds, and requires something recent — an impact, a core–mantle interaction, or a resonance passage. Mercury's has been searched for and not found, and the upper limit is the constraint.

A rocking nobody started

A locked body is a pendulum, and a pendulum has a period of its own. That free libration is damped by tides in thousands of years, so any body still oscillating at its own frequency was disturbed in the last geological instant — and the Moon is, while Mercury is not.

sky · Libration

Named alongside it

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

AbundanceBalmer seriesBoltzmann distributionCore mantle boundaryForced librationFree librationIonisationLine formationLunar laser rangingPartition functionQuality factorSaha equation

All concepts