Astronomy & Celestial Mechanics
the sky, computed
Concept

Continuum normalisation — where it appears

Dividing an observed spectrum by an estimate of the light that would reach the observer with no absorption lines present. Where lines crowd together the true continuum is never seen, and the estimate biases every line depth measured against it.

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

A continuum drawn 4.3 per cent below the real one. A short stretch of spectrum with one strong line in it and 150 weak ones scattered across the same interval. The upper dashed line is the true continuum — the flux the star would emit with no lines at all — and it is not observable. The lower one is what a fit through the highest points of the spectrum returns, which is 4.3 per cent lower, because the weak lines have depressed the gaps between the strong ones. Measuring the strong line's equivalent width against the apparent continuum instead of the real one makes it 11.2 per cent too small. The error has a sign, it is worse in spectra with more lines, and it therefore correlates with metallicity — which is exactly the quantity being measured.

A continuum that was never observed

An equivalent width is an area measured relative to the continuum, and the continuum is not in the data. It is drawn — a curve through the highest points of the spectrum — and in any spectrum with many weak lines those highest points are already below the true continuum, because the weak lines have eaten the gaps.

starlight · Line formation 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.

Equivalent widthSystematic errorAbundanceAbundance analysisBlendingCurve of growthDifferential analysisLine blanketingLine listMetallicityOscillator strengthPseudo continuum

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