Astronomy & Celestial Mechanics
the sky, computed
Concept

Distance modulus — where it appears

The difference between apparent and absolute magnitude, which is a logarithmic distance and turns a brightness comparison into a length. Five magnitudes of it is a factor of ten in distance, and an error of a tenth of a magnitude is a five per cent error in the length that comes out.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The magnitude scale, plotted. The logarithm of the received light against magnitude from -27 to 32, with the vertical scale left unlabelled because only its slope matters. The relation is a straight line of slope −0.4, which is what makes five magnitudes exactly a hundredfold — and the numbers run backwards, so brighter is smaller. 9 landmarks are marked, from the Sun to the deepest exposures, spanning a factor of 1.2·10²³ in received light.

A scale that runs backwards, multiplies, and works

Brighter stars have smaller magnitudes, and five steps is a factor of a hundred. A scale invented by eye in the second century BC turned out to be logarithmic, because eyes are.

starlight · Magnitudes The fractional distance error, rung by rung. Cumulative fractional uncertainty in a measured distance against the distance itself, both on logarithmic axes. Each rung of the ladder is calibrated against the one below it, so its scatter adds in quadrature to everything already inherited, and the total can only rise: radar to the planets 10⁻⁵%, parallax 1.0%, main-sequence fitting 5.1%, Cepheids 6.5%, Type Ia supernovae 8.2%.

Every distance is measured with the last one

No single method reaches from a planet to a distant galaxy. The ladder is built rung by rung, each calibrated on the one below, and the errors multiply all the way up.

starlight · Distance ladder The distance modulus. The difference between apparent and absolute magnitude against distance, on a logarithmic distance axis. It is a straight line of slope five per decade, passing through zero at ten parsecs — the definition of the absolute magnitude. Reading a distance off it requires the absolute magnitude, which is never measured and always inferred.

A brightness is a distance only if something is known

The inverse square law turns a brightness into a distance in one line. The line contains a quantity that has never been measured for any object outside the solar system.

starlight · Magnitudes The extinction law, for three kinds of dust. How much of a star's light dust removes, against inverse wavelength, normalised to one at the V band. Blue light is extinguished more than red, which is why reddening and extinction are the same measurement — and the hump at 4.6 inverse microns is a feature of the grains themselves, present on almost every sight line and still without an agreed carrier. Larger grains give a flatter law and a larger R_V.

Dust makes everything look further away

A star behind dust is fainter, so a distance taken from its brightness comes out too large. The same dust also makes it redder, and the reddening is measurable where the dimming is not — which is the only reason the correction can be applied at all.

starlight · Extinction Three clusters, three ages, one diagram. Isochrones for populations of 100 Myr, 1 Gyr, 12 Gyr, each drawn as the main sequence up to its own turnoff and then the post-main-sequence track of the turnoff mass. The turnoffs are at 5.52 M☉, 2.20 M☉, 0.94 M☉, from t = 10¹⁰ M/L with this file's own mass–luminosity relation. Nothing here is a track along which a star moves. Every point is a different star of a different mass, all the same age, and the bend is simply where the population runs out of stars that have had time to leave. That is why a cluster has an age and a field star does not: the bend needs a population, and one star is not one. The oldest globular clusters sit near the 12 Gyr line, and in the 1990s the same construction gave them ages of 16 to 18 Gyr against a universe measured at 10 — a two-standard-deviation contradiction that was resolved from the distance side, by Hipparcos, and not from this one.

An age read off a bend

A cluster is a population of one age and many masses, so the place where its stars leave the main sequence is a clock. The bend needs a population — which is why a cluster has an age and a single star does not.

stars · The HR diagram

Named alongside it

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

PhotometryMetallicityParsecAbsolute magnitudeApparent magnitudeAstronomical unit (AU)Colour indexDistance ladderInverse square lawCluster turnoffCoeval populationColour excess

All concepts