Astronomy & Celestial Mechanics
the sky, computed
Concept

Hubble diagram — where it appears

A plot of recession velocity or redshift against distance for galaxies or supernovae. Its slope near the origin is the Hubble constant, and its curvature at large distance records how the expansion rate has changed.

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

Residuals of 112 per cent nearby and 2.2 far out. Deviations from a pure Hubble flow, in per cent, against distance. Each galaxy carries a peculiar velocity of a few hundred kilometres a second — part a coherent bulk flow shared with its neighbours and part a random dispersion — and that velocity is added to its recession. Since the recession grows with distance and the peculiar velocity does not, the fractional error falls as one over the distance: it is 112 per cent at 5 megaparsecs and 2.2 at 250. The practical consequence is a lower cut-off on any Hubble-constant measurement: below about 40 megaparsecs the motions dominate, and the coherent part does not average away over a sample because neighbouring galaxies share it. Choosing that cut-off is one of the analysis decisions a local expansion rate depends on.

A residual that is somebody else's velocity

A redshift is not a distance until the galaxy's own motion has been removed, and galaxies move at a few hundred kilometres a second. Nearby that is comparable to the expansion itself, so the local Hubble diagram's scatter is motions rather than measurement — and the motions are shared between neighbours, so they do not average away.

cosmology · Dark energy The flow round the Local Group, shell by shell. Radial velocity against distance from the Local Group's centre today, for spherical shells of matter in a standard expanding background with the cosmological constant, round a group whose mass inside the zero-velocity surface is 1×10¹² M☉, 2×10¹² M☉, 4×10¹² M☉. Inside the zero-velocity radius — 0.79 Mpc, 1.00 Mpc, 1.26 Mpc — the shells are falling in; outside it they recede, slowly at first and then at the Hubble rate (dashed, 67.7 km/s per Mpc). At 1.5 Mpc the three groups give 75, 57, 30 km/s against 102 for an undisturbed flow; by 5 Mpc the curves differ by 10 km/s and have nearly rejoined the line. The group's pull is written into the first two or three megaparsecs of the flow, and only there.

A flow too quiet for the lumps it runs between

The galaxies within ten megaparsecs of the Milky Way recede almost exactly as the Hubble law says, scattering about it by a few tens of kilometres a second. The matter they move through is lumpy at the factor-of-several level, and elsewhere galaxies move relative to their neighbours at three hundred. The quiet is a measurement, it limits what the group's own pull can be read from, and it says something about the place rather than about the law.

cosmology · Hubble constant

Named alongside it

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

Bulk flowPeculiar velocityCorrelated errorCosmic varianceCosmological constantHubble constantLinear theoryLocal groupLow redshift cutRedshiftSelection effectSpherical collapse

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