Astronomy & Celestial Mechanics
the sky, computed
Concept

Period luminosity relation — where it appears

The tight line between how slowly a variable star pulsates and how bright it intrinsically is, which turns a clock into a ruler. It exists because a pulsation period is a mean density, and a mean density with a temperature is a luminosity.

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

Leavitt's law, through the Milky Way calibrators. Mean absolute magnitude against the logarithm of the pulsation period, for classical Cepheids with independently known distances, and RR Lyrae itself for comparison. The line is M = −2.81 log P − 1.43: a tenfold longer period is 2.81 magnitudes brighter, a factor of 13 in luminosity. The vertical axis runs the astronomers' way, with brighter upward.

A star that tells its distance by how slowly it blinks

Some stars pulsate, and the slow ones are the bright ones. That single correlation turns a clock into a ruler, and it is how the size of the universe was first measured.

stars · Variable stars H₀: nine determinations in two families. Published determinations of H₀, each with its quoted one-sigma interval, sorted into two families — measured locally, calibrated by a ladder, against inferred from z ≈ 1100 through a model. The shaded band behind each family is that family's inverse-variance weighted mean: 72.66 ± 0.75 across 5 of them, against 67.40 ± 0.41 across 4. The difference is 5.26 ± 0.85 km/s/Mpc, which is 6.2 standard deviations, computed here from the quoted errors alone. That number is an upper bound on the significance rather than the significance: the determinations within each family share calibrations, samples and in two cases the same supernovae, so they are not independent, and a correlated pair combines to something wider than the formula used here gives. What the figure does establish is that the split is not one discrepant measurement against a consensus — it is two internally consistent groups, and the grouping is by method rather than by result.

The same constant, measured twice, five sigma apart

The distance ladder gives an expansion rate of about 73 kilometres per second per megaparsec. The microwave background gives 67.4. Both quote errors near one per cent, both have been rebuilt from scratch by rival teams, and the gap between them has grown as the measurements have improved.

cosmology · Hubble constant

Named alongside it

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

Distance ladderAbsolute magnitudeEarly dark energyHubble constantHubble tensionInstability stripInverse distance ladderIonisationMain sequenceRadial velocitySound horizonStellar radius

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