Astronomy & Celestial Mechanics
the sky, computed
Concept

Spherical collapse — where it appears

A model of a spherical overdensity in an expanding universe that expands more slowly than its surroundings, turns around and collapses. It gives the thresholds used throughout structure formation, and run in reverse for an underdensity it describes how voids expand faster than the universe around them.

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

Two galaxies that stopped moving apart, and the mass that did it. The separation of two galaxies on a radial orbit that began together at the big bang, against cosmic time, solved so that after 13.797 Gyr they are 770 kpc apart and approaching at 110 km/s — the present separation and approach speed of the Milky Way and the Andromeda galaxy. The curve is a cycloid, r = A(1 − cos θ) and t = B(θ − sin θ), and only one cycloid passes through that point with that slope. It rose to 1037 kpc, turned round when the universe was 8.5 Gyr old, and on this purely radial orbit the two meet 3.3 Gyr from now. Its period fixes the mass: A³/(GB²) = 4.2·10¹² solar masses. The dashed curve is the same calculation with the cosmological constant's outward push included, integrated rather than solved; to arrive at the same place at the same speed against that push it needs 4.76·10¹² solar masses, 13 per cent more. Far more than the stars of the two galaxies, it is the timing argument's measurement of the Local Group's dark matter.

The age of the universe weighs the Local Group

The Andromeda galaxy is approaching the Milky Way, and in an expanding universe that means the two once moved apart, stopped and turned round. One radial orbit passes through their present separation with their present speed after exactly the age of the universe, and its period fixes the mass that turned them — four trillion suns, twenty-five times what their stars can account for.

cosmology · Expansion A void: a deficit of matter, and the outflow it drives. The density contrast of a typical cosmic void against distance from its centre in units of its radius (solid), from the profile fitted to stacked voids in simulations, with a central density 15 per cent of the mean and a compensating overdense ridge just outside the edge. The dashed curve is the excess expansion rate the deficit drives, v/(Hr) = −(f/3)Δ(r), for a growth rate f = 0.75: the centre expands 21 per cent faster than the universe around it, and the outflow speed, which is this rate times the radius, peaks near 0.7 void radii. Beyond the ridge the flow reverses: matter at the ridge is pulled back towards the denser wall. A void is a small open universe expanding inside a flat one, and every galaxy in it is moving outward.

An emptiness that expands faster

A cosmic void is not a hole in the universe but a region with a fifth of the average density, and gravity makes it behave like a small open universe: it expands faster than its surroundings, every galaxy in it streams outward, and in a redshift survey it is stretched along the line of sight — the opposite of what the same gravity does around a cluster. The stretch measures how fast structure grows, and the average void's roundness measures the geometry of the universe.

cosmology · Large-scale structure Haloes at the centre of a void, and in an average place. The number of dark matter haloes per unit volume and per factor e in mass, against halo mass in solar masses per h, in the universe on average (dashed) and inside a sphere of 5 Mpc/h radius at the centre of a void whose density there is 20 per cent of the mean (solid), from the excursion-set theory at redshift zero. The void's sphere holds 9.2e+12 solar masses per h of matter altogether, and no halo can be heavier than that. At the dwarf end the void holds 38 per cent of the average abundance per unit volume — more than its 20 per cent share of the matter. At the mass of the Milky Way's halo, 10¹² M☉/h, it holds 1.62 per cent. An emptiness of galaxies like the Milky Way is guaranteed by the theory; an emptiness of dwarfs is not.

A void is not short of dwarf haloes

The centre of a large void holds a fifth of the average density of matter and almost no galaxies, and it is natural to read the two facts as one. They are not. The theory of how haloes form says a void turns its matter into dwarf-sized haloes at least as readily as anywhere else — it is short of big haloes, not small ones — so a void empty of dwarf galaxies is a statement about which haloes were allowed to light up.

cosmology · Large-scale structure The number of lit dwarfs at a void's centre, against the date it was reionised. The number of haloes heavier than 3.2·10⁹ M☉/h that had collapsed from the matter of a 5 Mpc/h sphere by the redshift at which that sphere was reionised, on a logarithmic axis, against that redshift — for a sphere at the centre of a void with 20 per cent of the mean density today (solid) and an average sphere of the same size (dashed). If only those haloes could make stars, they are the sphere's dwarf galaxies. Reionised at 5.3: 4.3 in the void sphere, 195 in the average one; reionised at 6: 2.0 in the void sphere, 121 in the average one; reionised at 7.7: 0.22 in the void sphere, 29 in the average one. Each unit of delay in the date multiplies the void's count by 3.2 and the average sphere's by 2.1: the void's dwarfs sit further out in the tail of the distribution, and a tail is steep. A count of a few galaxies at a void centre is a statement about when that void's gas was heated, to within a fraction of a unit of redshift — provided the threshold is known.

A void dated by the dwarfs that lit in time

Reionisation did not heat the universe all at once, and the centres of the large voids were among the last places it reached. A dwarf halo there could make stars only if it had grown heavy enough before its own gas was heated — so the number that did is a clock for one void, and a clock that runs faster the emptier the void.

cosmology · Large-scale structure 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.

Cosmic voidPeculiar velocityCosmological constantDark matter haloDwarf galaxyGalaxy biasHalo mass functionLocal groupPress schechterReionisationStructure growthTurnaround

All concepts