Astronomy & Celestial Mechanics
the sky, computed
Concept

X-ray temperature — where it appears

The temperature of a cluster's hot gas read from the shape of its X-ray spectrum. Because the emission goes as density squared it is weighted towards the dense core, and so can differ from a temperature weighted by pressure along the whole line of sight.

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

A cluster weighed three ways, and its stars weighed once. A cluster of galaxies with a velocity dispersion of 1000 km/s, gas at 8 keV and a strong-lensing Einstein radius of 25 arcseconds, each turned into a mass inside 1.5 Mpc by its own relation and nothing else: 7.0, 8.9 and 15.2 × 10¹⁴ M☉. The three assume, respectively, that the galaxies are in equilibrium, that the gas is, and nothing whatever — so their agreement to within a factor of 2.2 is not three restatements of one assumption. The lensing bar is the loosest of the three and is drawn that way deliberately: it measures the mass inside a cylinder of radius 109 kpc, 1.11×10¹⁴ M☉, and carrying that out to 1.5 Mpc as though it were a sphere overstates it. The stars are 2.9 per cent of it.

A cluster weighed three ways

The speeds of a cluster's galaxies, the temperature of its gas and the bending of light behind it are three measurements with almost nothing in common. They agree within a factor of two, and all three exceed the mass of the stars by about a hundred.

galaxies · Clusters At 15 keV the decrement is 9 per cent shallower and the null has moved to 224.4 GHz. The thermal Sunyaev–Zel'dovich distortion at one fixed Compton parameter, 10⁻⁴, computed with the relativistic kinetic equation expanded to second order in kTₑ/mₑc² for gas at 5, 10, 15 keV, against the non-relativistic shape that is the same for every temperature. All are scaled to the non-relativistic curve's largest excursion. Heating the gas at fixed y does two things to the spectrum. The decrement becomes shallower — by 9.3 per cent at its deepest point for 15 keV — and the increment becomes lower and broader, by 17.3 per cent at its peak, because fast electrons scatter photons over a wider spread of frequencies than slow ones and some of the boost is carried to frequencies above the drawn range. The crossing moves up, from 217.5 GHz to 224.4 GHz. A cluster's temperature is therefore written into the shape of its distortion and not only its amplitude, which is what a thermometer needs; and a Compton parameter read off one frequency with the non-relativistic shape is biased low by the drawn amount, which is what a mass estimate does not need. The expansion is good to well under a per cent below 15 keV; above 20 it has to be replaced by the exact integral.

A null that moves with the temperature

The frequency at which a cluster's hot gas vanishes from the microwave sky was derived for slow electrons. The electrons in a massive cluster move at a quarter of the speed of light, the null drifts half a gigahertz per keV, and what is left at the old frequency reads as a velocity as large as the ones being sought.

cosmology · Sunyaev zeldovich

Named alongside it

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

Intracluster mediumBaryon fractionBremsstrahlungCompton y parameterDark matterGalaxy clusterGravitational lensingHydrostatic biasHydrostatic equilibriumInverse Compton scatteringKinematic sunyaev zeldovich effectOptical depth

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