Astronomy & Celestial Mechanics
the sky, computed
Generator

The absorption-spectrum generator

An absorption spectrum at 5772 K
An absorption spectrum at 5772 K. A blackbody continuum at 5772 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.

A blackbody continuum at 5772 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.

5 essays call absorption-spectrum. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.

An absorption spectrum at 5772 K. A blackbody continuum at 5772 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence. Starlight

Composition, read from what is missing

The dark lines in a stellar spectrum are wavelengths that never arrived. Which ones are absent names the elements present — and the strength of a line says more about temperature than about abundance.

 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. Starlight

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.

 A strong line at three gravities, 6000 K. Left, one strong absorption line of Fe computed at three surface gravities and drawn on the same wavelength scale — no normalisation to each profile's own width, which is exactly what the comparison is about. The thermal core is identical in all three, because the Doppler width is 0.00223 nm at 6000 K whatever the star's size. The wings are not: collisional damping is proportional to the density of perturbers, that density is proportional to the gas pressure, and in a grey atmosphere the pressure at the photosphere is proportional to g — so log g = 4.4 carries a damping parameter 794 times that of log g = 1.5. Right, the width at a tenth of the core depth against gravity, measured off those curves: a slope of 0.499, against the half a Lorentzian wing forces. That is the second dimension of a spectral classification. The first is the temperature, read from which lines are present; this one is the pressure, read from how wide they are, and it is the whole reason a spectrum can be turned into an absolute magnitude and then into a distance. Starlight

The second thing a spectrum says

Two stars of the same colour can differ in luminosity by ten magnitudes, and the difference shows in the widths of their lines rather than in which lines are present. That width is a pressure, the pressure is a gravity, and the gravity is a distance.

 Four kinds of explosion, told apart by which line is missing. Spectra of 4 supernova types — Ia, II, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 10,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 614.0 nanometres, which recovers 10,131 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too. Stars

Two explosions told apart by a missing line

The classification of supernovae is a decision tree on absences — is hydrogen there, is silicon there, is helium there — and it was drawn up decades before anybody knew what any of these events were. It nevertheless separates a detonating white dwarf from a collapsing stellar core almost perfectly, and the reason it does is worth the essay.

 A radius that depends on the colour it is measured in. Transit depth against wavelength for a planet of 1.38 Jupiter radii at 1400 K, whose atmosphere has a scale height of 538 km — computed from H = kT/µg, not assumed. One scale height of extra opacity adds 153 parts per million to a transit of 1.40 per cent, so the whole spectral signal is 862 ppm at its strongest: one part in 16 of the transit that carries it. The features are at real band centres — sodium at 0.589 µm, water at 1.4 µm, carbon dioxide at 4.3 µm — with the rise at the blue end the Rayleigh slope of scattering off the smallest particles. Exoplanets

A radius that depends on the colour it is measured in

Measure a transit in one colour and then another, and the planet is a different size. The difference is a few atmospheric scale heights, which is a few hundred parts per million of an already tiny signal.

The whole library · All essays