Astronomy & Celestial Mechanics
the sky, computed
Series

Clusters — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · galaxies
  2. Gas outweighs stars 6:1, and the baryons come to 15%. Above: enclosed mass against radius for a 7-keV cluster with a beta-model gas profile, β = 0.65 and a 250-kpc core. The total is from hydrostatic equilibrium — the same equation that holds up a star, with the mass following from the density and temperature gradients and from nothing else — and comes to 9.98·10¹⁴ solar masses inside 2 megaparsecs. The gas, integrated from the same profile, is 1.6·10¹⁴; the stars in all the galaxies are 2.5·10¹³, 6 times less. Most of a cluster's ordinary matter is not in anything anybody would call an object. The two total-mass curves differ by the 15 per cent hydrostatic bias: some of the pressure holding the gas up is turbulence left from the last merger rather than heat, and a mass computed from the thermal pressure alone is low by about that — the assumption that makes the measurement possible is the one that biases it. With the correction, the baryons come to 15 per cent of the total, against the 15.7 per cent the microwave background gives for the universe as a whole. A cluster is large enough to have kept everything it started with, so its own accounting is a cosmological measurement. Below: the same gas seen two ways. X-ray surface brightness falls as (1+z)⁻⁴, so a cluster at redshift one is 16 times fainter per unit sky than the same cluster nearby; the Sunyaev–Zel'dovich distortion of the microwave background does not fall at all, because it is a fraction of a background whose own brightness rises by exactly the same factor. That is why a millimetre survey finds clusters at any distance and an X-ray survey finds the near ones.

    The baryons that are not in the galaxies

    The stars in a cluster are about a seventh of its ordinary matter. The rest is ten-million-kelvin gas that is invisible optically and dominant in X-rays — and weighing it with hydrostatic equilibrium biases the answer low by exactly the amount the assumption is wrong by.

    part 2 · galaxies
  3. Gas kept inside 3.6 to 6.8 kiloparsecs, depending only on the speed of the fall. The pressure holding a disc galaxy's gas down, against radius, with the ram pressure of the cluster gas it is falling through drawn as three levels. The restoring pressure is two pi times the gravitational constant times the product of the stellar and gaseous surface densities, both exponential with scale lengths of 3 and 5 kiloparsecs, so it falls steeply outward; the ram pressure is the intracluster density times the square of the infall speed and does not depend on radius at all. Where the level crosses the curve, the gas goes. A galaxy entering at 700 kilometres a second keeps everything inside 6.8 kiloparsecs; at 1600 it keeps only 3.6. Nothing in this touches the stars, which are not a fluid and feel no pressure at all, so the galaxy emerges with its stellar disc and its rotation curve intact and its star formation stopped from the outside in. That is the mechanism behind the most conspicuous fact about clusters: their spirals are red, gas-poor and still spiral-shaped, which no process acting on the stars could produce.

    Red, gas-poor, and still spiral-shaped

    A galaxy falling into a cluster meets a headwind of hot gas at two thousand kilometres a second. Where that ram pressure exceeds the disc's own grip on its gas, the gas goes; the stars, which are not a fluid and feel no pressure, do not. The result is a spiral with no fuel, and it is the commonest kind of galaxy in a cluster.

    part 3 · galaxies
  4. The middle of a cluster cools faster than the universe ages. The time the gas of a cool-core cluster, of central electron density 0.05 per cubic centimetre, would take to radiate its heat at constant pressure, against radius, both logarithmic. Inside 76 kiloparsecs it is less than 7.7 billion years, the time since a redshift of about one when the cluster's core is thought to have settled, and at 10 kiloparsecs it is 0.8 billion years. Beyond a few hundred kiloparsecs it is longer than the age of the universe, and the gas is simply hot.

    A cooling flow that never arrives

    The gas at the centre of a rich cluster radiates its heat in under a billion years, so it should be sinking inward and turning into stars at hundreds of solar masses a year. For two decades that was the accepted picture and it was treated as a measurement. Then X-ray spectra looked for the gas on its way down and found that it stops at a third of the temperature it began with, while the galaxy in the middle forms stars a hundred times too slowly. Something pays the radiative bill, and bubbles of the right size are visible in the X-ray images.

    part 4 · galaxies

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