Astronomy & Celestial Mechanics
the sky, computed
Concept

Spectrograph — where it appears

An instrument that spreads light into its component wavelengths and records the result. Its resolving power, stability and throughput decide which spectral lines can be measured, how precisely their shifts are known, and how faint a star can be.

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

The wobble of a star with a circular companion. The star's velocity along the line of sight, over two orbits, computed from the companion's orbit. A circular orbit gives a sine wave; an eccentric one gives a skewed curve whose shape encodes the eccentricity.

The star moves, and the mass is a lower bound

A planet is found by watching its star fall towards it. The wobble gives a mass multiplied by the sine of an angle nobody has measured — and the shortfall is not a rounding error.

exoplanets · Reflex velocity Where the velocity information in a spectrum lies. Above: a 600 km/s stretch of two synthetic spectra with the same continuum of 10000 photons per pixel at a resolving power of 100,000 — a cool, slowly rotating star, with 12 lines per nanometre, and a hot star rotating at 25 km/s, with 3 lines per nanometre. Below: the velocity information each pixel carries, (dA/dv)²/A, which is zero in the continuum and at line centres and largest on the steep flanks of deep, narrow lines. Summed over 100 nanometres of spectrum, the first star measures its velocity to 1.61 m/s and the second to 39.17 m/s — 24 times worse from the same number of photons. The photons that measure a velocity are the ones on the sides of lines; the continuum, however bright, contributes nothing.

The photons on the sides of the lines

A spectrum measures a star's velocity only through the slopes of its absorption lines. The continuum, however bright, carries no information at all, and a star with many deep, narrow lines gives a velocity twenty times more precise than a hot, fast-rotating one from the same number of photons.

starlight · The Doppler effect

Named alongside it

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

Radial-velocityBarycentreCross-correlation functionDoppler shiftFisher informationHot jupiterInclinationMinimum massPhoton noiseQuality factorReflex motionRotational broadening

All concepts