Astronomy & Celestial Mechanics
the sky, computed
Concept

Compton parameter — where it appears

A dimensionless measure of how much hot gas changes the energy of photons passing through it, the integral of electron pressure along the line of sight. It sets the strength of the thermal Sunyaev–Zel'dovich effect. In the middle of a rich cluster it is about one part in ten thousand.

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

A path length recovered from two integrals of one cluster. The two line-of-sight integrands through an isothermal β = 0.67 cluster, each normalised to its own centre, against distance along the line of sight in core radii. The upper curve is electron density, which the Compton parameter integrates; the lower is density squared, which the X-ray surface brightness integrates. They are integrals of the same gas along the same line and they weight it differently — the half-width is 1.00 core radii for the linear one and 0.64 for the quadratic, and one core radius either side of the centre holds 51 per cent of the pressure signal against 82 per cent of the X-ray. That difference is the whole method. Two integrals with different powers of one unknown density, down one unknown path, are two equations in two unknowns: y₀ = 1.5·10⁻⁴ and a central X-ray surface brightness of 1.63·10⁻⁵ erg cm⁻² s⁻¹ sr⁻¹ give back a central density of 0.006 cm⁻³ and a physical core radius of 0.250 Mpc. Divide that length by the angular core radius the same cluster subtends, 54.2 arcseconds, and the answer is an angular-diameter distance of 952 Mpc — against the 952 Mpc the cluster was built at, which is the round trip this figure exists to close. Nothing in that chain is calibrated on a Cepheid, a supernova or a parallax. It is a length in centimetres measured against an angle.

A length in centimetres, measured against an angle

A cluster's hot gas offers two line integrals of the same electrons — one linear in density, one quadratic. Two equations in two unknowns give back the path length in centimetres, and a length divided by the angle it subtends is a distance that leans on no other distance measurement.

cosmology · Sunyaev zeldovich One curve for every cluster, if the background cooled on schedule. The thermal Sunyaev–Zel'dovich distortion against observed frequency. With a background temperature proportional to one plus redshift, clusters at redshift 0, 0.5, 1 and 2 share one curve, crossing zero at 217.5 GHz. If the temperature instead scaled as the 1 − 0.1 power, the null of a cluster at redshift 1 would fall at 203 GHz and at redshift 2 at 195 GHz.

A null that stays put only if the sky cooled on schedule

A hot cluster dims the microwave background below 217 gigahertz and brightens it above, and that crossing falls at the same observed frequency for a cluster at any distance. It does so for one reason: the background's temperature has to have fallen exactly as one plus redshift. Nothing guarantees that. A molecule had already measured the temperature in 1941, and the crossing itself is a thermometer placed anywhere a cluster stands.

cosmology · Sunyaev zeldovich

Named alongside it

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

The Sunyaev–Zel'dovich effectAngular-diameter distanceBeta modelBremsstrahlungDistance dualityElectron densityExcitation temperatureGas clumpingHubble constantIntracluster mediumLine of sight integralMicrowave background

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