Astronomy & Celestial Mechanics
the sky, computed
Concept

Oscillator strength — where it appears

The dimensionless factor giving the probability of an atomic transition relative to a classical oscillator. It multiplies the optical depth of a spectral line, so climbing a series to weaker lines is how a saturated column density is measured.

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

The curve of growth. The equivalent width of an absorption line against the number of absorbers along the sight line, both logarithmic, computed by integrating a Voigt profile with damping parameter 0.005. Three regimes: the width grows in proportion to the abundance while the line is weak, then almost not at all for two decades once the core saturates, then as the square root once the damping wings dominate. A line measured in the middle stretch carries almost no information about the abundance, and most strong lines in a stellar spectrum are there.

How much of a line is not in its depth

An absorption line stops getting deeper long before it stops getting stronger. What keeps growing is its area, and the way the area depends on the number of absorbers has three distinct regimes over five decades — one of which carries almost no information at all.

starlight · Line formation The deuterium burning rate against the expansion, at three baryon densities. The rate at which a deuteron is destroyed, divided by the expansion rate, against temperature. Temperature falls to the right, so the picture reads left to right as time, and the horizontal line at one is where the burning stops mattering: above it a deuteron is destroyed many times over before the universe doubles in size, below it the reaction has effectively ceased. The rate drawn is D(p,γ)³He at the NACRE parameterisation, multiplied by the free-proton density — three quarters of the baryons by number once ⁴He has taken the rest — and the expansion rate is the same 1.66√g* T²/mPl the freeze-out calculation raced the weak interactions against. The three curves differ in one number and one only: the baryons per photon, 3, 6, 12 in units of 10⁻¹⁰. They are therefore vertical translations of each other, exactly in proportion to η, because the reaction is two-body and the expansion is not. That is the entire mechanism by which an abundance measures a density. A denser universe crosses the line later — 21.4 keV at η₁₀ = 3, 16.0 keV at η₁₀ = 6, 12.3 keV at η₁₀ = 12 — and every extra second below the crossing is deuterium that does not survive. What the figure does not do is predict the abundance itself: the residue depends on the whole reaction network and on the ⁷Be and ³He channels that feed back into it, and the curve the abundance is read off is a fit to that network rather than to this.

The residue that failed to burn

Deuterium's abundance is not a measure of what the first three minutes made. It is a measure of what escaped being used — a two-body destruction rate losing a race to a one-body expansion, which is why its curve against the baryon density is steep and helium's is flat.

cosmology · Nucleosynthesis A synthetic spectrum fitted with a line list that is missing the weak lines. Four ångströms of a simulated metal-line spectrum near 5000 Å at resolving power 20,000 and a signal-to-noise ratio of 200 (thin, noisy line), and the best-fitting synthesis (heavy line) computed from a line list that omits every line with a central optical depth below 0.15 — 137 of the 160 lines in the ten-ångström window, carrying 32 per cent of its total absorption. The fit adjusts one abundance for all the listed lines, with the continuum held at its true level; it returns an abundance 0.188 dex too high: the missing lines' absorption has nowhere to go but into the parameters the synthesis has. The residuals (below, offset) show the missing lines as dips that no parameter of the synthesis can fill — which is how an incomplete list announces itself at high resolution, and why it does not at low.

The lines a synthesis keeps pay for the ones it lacks

Modern abundance work fits a computed spectrum to a whole stretch of the observed one rather than measuring lines one at a time, and it averages away the errors in each line's laboratory data as it does so. It cannot average away a line that is not in its list. The absorption of the missing lines has to be put somewhere, and the fit puts it into the parameters it has — the abundance of the lines it knows, or the level of the continuum — in a direction set by which of the two it was allowed to move.

starlight · Line formation

Named alongside it

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

AbundanceCurve of growthEquivalent widthVoigt profileBaryon densityBaryon-to-photon ratioBig bang nucleosynthesisBlendingColumn densityContinuum normalisationDamping wingsDeuterium abundance

All concepts