Astronomy & Celestial Mechanics
the sky, computed
Concept

Colour magnitude diagram — where it appears

Brightness plotted against colour for a whole population, in which how densely a region is occupied measures how long objects take to cross it. A gap in it is a phase stars pass through quickly rather than a mass that is missing, which is how the Hertzsprung gap and the instability strip are read.

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

The mirror: an envelope 62 times larger around a core 1.48 times smaller. Envelope radius and core radius against helium-core mass for a 1 solar-mass star, both in solar radii on one logarithmic axis. Two curves with opposite slopes at every point: the envelope grows from 2.0 to 122 solar radii — 0.57 astronomical units — while the degenerate core contracts from 13,848 to 9,368 kilometres, and the two are separated by a factor of 364 in the middle of the range. The figure is drawn from two stated relations rather than from a stellar model: a core-mass–luminosity law of the sixth power, calibrated to 2,500 solar luminosities at 0.48 solar masses of core, and a Hayashi temperature falling from 5000 to 3700 kelvin across the range. Everything else follows exactly — the radius by the Stefan–Boltzmann law, the core radius by the cold degenerate relation R ∝ M⁻¹ᐟ³. Note what the tip radius is and is not: it is the red-giant branch, and the later asymptotic-giant tip is a different and larger number.

The star that swells because its centre shrank

A helium core contracts, and the envelope around it expands by a factor of sixty. The central density rises at the same time as the radius, which is the opposite of what a self-gravitating body is expected to do, and a burning shell between the two is the whole reason it happens.

stars · Stellar evolution Two populations, and the valley between them. 420 model galaxies, 42 per cent of them drawn from a tight red sequence tilted by -0.08 magnitudes of colour per magnitude of brightness, the rest from a broad blue cloud. Only 3.3 per cent land in the band of width 0.20 magnitudes midway between the two sequences, against 17 per cent in the same band laid on the blue cloud and 27 per cent on the red sequence. The bimodality is the strongest statement the galaxy census makes: a galaxy is usually forming stars or has stopped, rarely in between, and since colour tracks the age of the newest stars, the emptiness of the middle is a statement about a timescale — whatever ends star formation does it in a few hundred million years, not a few billion.

Two colours, and almost nothing between

Plot a few hundred thousand galaxies by colour and brightness and they do not fill the plane. They pile into a tight red sequence and a broad blue cloud with a near-empty gap between, and an empty gap is a statement about how fast something happens.

galaxies · Galaxy populations Three colours watching one galaxy stop. One star-formation history — steady, then shut off with an e-folding time of 0.4 billion years — followed in three colour indices, each plotted as a fraction of the gap its own sequences actually span. The three curves are the same galaxy. Each band's luminosity is the history convolved with that band's own decline after a burst: NUV at 0.1 Gyr, u at 0.35 Gyr, g at 0.9 Gyr, r at 3 Gyr, because the ultraviolet comes from stars that live a hundred million years and the red from stars that live ten billion. In the first three hundred million years the ultraviolet index reddens at 1.56 magnitudes per billion years and the optical one at 0.10 — a factor of 15 — so a galaxy that has just stopped is already conspicuous in one and indistinguishable from a star-forming one in the other. That is what an ultraviolet band buys: not a better measurement of the same thing, but sensitivity to a phase the optical colours arrive too late to see.

A crossing time that is the filter's

The emptiness of the gap between the two galaxy populations was read as a timescale, and the reading used one colour. Each passband remembers star formation for a different length of time, so the same galaxies give a crossing time of one billion years in the ultraviolet and three in the optical — and the disagreement between two filters is the measurement the single filter could not make.

galaxies · Galaxy populations The most pressure a core can supply, and what its envelope asks for. The pressure at the boundary of a star's isothermal core, on a logarithmic scale, against the fraction of the star's mass the core holds. The coloured curves are the most pressure a core of that mass can supply at its edge — the maximum of the isothermal sphere, 1.40 c⁸/(G³M²) for a core of mass M — for cores of mean molecular weight 0.6, 1.0, 4/3; the flat grey line is the pressure the envelope, of molecular weight 0.6, exerts on the core at the same temperature. The core's ceiling falls as the square of its mass, and it can hold the envelope up only while it lies above the line. The curves cross it at core fractions of 0.370, 0.133, 0.075: a core of the same molecular weight as its envelope could hold 37 per cent of the star, and a fully ionised helium core, μ = 4/3, under this envelope only 7.5 per cent. The limit exists because the core is heavier per particle than the gas it has to hold up.

A core too heavy for the gas around it

When a star's centre runs out of hydrogen, the helium left behind stops making energy, settles to one temperature, and becomes the one member of the polytrope family with no surface of its own. It can hold up the envelope around it only while it is less than about a tenth of the star. Past that there is no balance to be had, and the star crosses to the giant branch in a few per cent of its lifetime — which is why that part of the diagram is empty.

stars · Polytropes One population, two period–luminosity relations. The period–luminosity relation of 400 synthetic Cepheids spread across the instability strip, each behind a random amount of dust up to E(B − V) = 0.6: absolute magnitude in V (upper scatter) and in the Wesenheit index W = V − 2.44(V − I) (lower). In V the scatter about the fitted line is 0.57 magnitudes — 0.20 from the strip's width alone, the rest from the dust. In W it is 0.07: the dust is gone by construction, and most of the strip's width has gone with it, because a star that is hotter at a given period is bluer by about as much as dust would make it redder. That leftover 0.07 magnitudes is 3 per cent in distance per star.

A scatter that points the way dust does

A Cepheid's period fixes its luminosity only to within the width of the instability strip, and at a given period the hotter stars are the brighter ones. Dust moves stars in the colour–magnitude diagram along a line too, and the two lines point nearly the same way. A magnitude built to cancel the dust — the Wesenheit index — therefore cancels most of the strip's width as well, which is why the tightest period–luminosity relations are the ones that ignore the extinction law's own advice.

stars · Variable stars

Named alongside it

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

Degeneracy pressureGreen valleyHydrostatic equilibriumQuenchingShell burningStar formation historyStellar evolutionStellar populationBimodalityBlue cloudCepheid variableDegeneracy

All concepts