Astronomy & Celestial Mechanics
the sky, computed
Concept

Instability strip — where it appears

The narrow, nearly vertical band on the colour-magnitude diagram within which a star pulsates radially. Its blue edge is where the driving zone has too little mass above it and its red edge is where convection short-circuits the valve, and only the first is straightforwardly computable.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The Hertzsprung–Russell diagram. Luminosity against surface temperature, both in solar units and on logarithmic axes, with temperature increasing to the left. The main sequence is computed from the mass–luminosity and mass–radius relations; the dashed diagonals are lines of constant radius.

The main sequence is a place stars sit, not a track they travel

The commonest misreading of the Hertzsprung–Russell diagram is that stars slide down the band as they age. They do not. They sit at one point for ninety percent of their lives and then leave sideways.

stars · The HR diagram 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 The period spans 492× and the pulsation constant 2.1×. The pulsation constant Q = P√(ρ̄/ρ̄_⊙) for 7 radial pulsators, against their periods. A radial pulsation is a standing sound wave across a star and the sound speed in a self-gravitating body is set by its own gravity, so the period should go as (Gρ̄)^−1/2 and Q should be the same for every star pulsating in the same mode. Across a factor of 492 in period — from 1.3 hours to 27 days — Q varies by 2.07, with a mean of 0.0393 days. That is the whole reason a period–luminosity relation can exist: a period is a density, a density is a mass and a radius, and a radius with a temperature is a luminosity. The masses here are the weak link and the caption should say so — for the Cepheids they come from evolutionary models rather than from a dynamical measurement, and the drift of Q with period is where that assumption is showing.

The valve that has to sit at the right depth

A period–luminosity relation only exists because a period is a density in disguise. Which stars have a period at all is decided by whether a partial ionisation zone sits deep enough to have mass behind it and shallow enough that convection has not taken it over.

stars · Variable stars

Named alongside it

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

Main sequenceAbsolute magnitudeBlue edgeConvectionDistance ladderEvolutionary trackGiant branchHeat engineHelium ionisationInitial mass functionIonisationIsochrone

All concepts