Astronomy & Celestial Mechanics
the sky, computed
Concept

Pressure support — where it appears

Resistance to gravity supplied by random motions, thermal or turbulent, rather than by ordered rotation. In a galaxy disc it thickens the gas and makes the rotation curve fall below the circular speed the gravitational field would demand.

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

Mass from a velocity dispersion, across nine decades. The virial estimate M = 5 σ²R_e/G, drawn for half-light radii from 0.2 to 20 kpc, with four systems placed on it: M32 at σ = 75 km/s and R_e = 0.1 kpc, giving 6.5e+8 M☉; the Milky Way's bulge at σ = 105 km/s and R_e = 1 kpc, giving 1.3e+10 M☉; M87 at σ = 320 km/s and R_e = 7 kpc, giving 8.3e+11 M☉; the Coma cluster at σ = 1000 km/s and R_e = 1500 kpc, giving 1.7e+15 M☉. The same expression spans from a dwarf elliptical to a cluster of galaxies — nine decades of mass — because the virial theorem does not care what the moving objects are. In the last case they are whole galaxies, and the estimate exceeds everything visible in the cluster by a factor of about fifty, which is where the problem was first noticed.

A galaxy held up by disorder

An elliptical galaxy barely rotates. What holds it up against its own gravity is the randomness of its stars' motions, and the virial theorem turns that randomness into a mass by exactly the reasoning that turns a rotation speed into one.

galaxies · Velocity dispersion Turbulence against star formation, driven two ways. Gas velocity dispersion against star-formation rate per unit area, both on logarithmic scales, for model discs of increasing gas surface density: a nearby spiral (circular speed 200 km/s at 8 kpc, gas a fifth of the disc's mass) and a disc at redshift two (the same speed at 4 kpc, gas half). Dashed: turbulence driven by supernovae alone, a tenth of their energy staying in the gas — it settles between 11 and 13 km/s however fast the disc forms stars, because more gas means both more stars and faster dissipation. Solid: the same discs when gravity can also stir them, holding the gas at marginal stability once supernovae fall short — which in the redshift-two disc happens above a gas surface density of 72 M☉ pc⁻², after which the dispersion climbs with the star-formation rate to 76 km/s. The shaded boxes are the approximate ranges in which nearby spirals and redshift-two discs are observed. Feedback alone reaches the first and not the second; with gravity the model reaches the second at its lower edge in star formation, a sign that its simple star-formation law, one per cent of the gas per free-fall time of the whole layer, is slow for the clumpy gas of those discs.

A stirring supernovae cannot pay for

The gas in a disc forming stars at redshift two moves at fifty kilometres a second in random directions, five times faster than in a spiral today, and turbulence that fast decays in a few tens of millions of years. Supernovae are the obvious source of the energy, and they run out at about thirteen kilometres a second however fast the disc forms stars. What holds the discs up is gravity — gas stirring itself by falling inward — and a disc stirred that way is also a disc pouring its gas into its own centre.

galaxies · Tully–Fisher

Named alongside it

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

Velocity dispersionAnisotropyDe vaucouleurs lawDynamical massEffective radiusElliptical galaxyGravitational instabilityLine-broadeningRadial inflowSersic profileStar formation efficiencyStellar feedback

All concepts