Observational Astronomy

X-Rays from Galaxy Clusters

In our universe we see bound gravitational systems on all scales. At the lowest scales we have the moons orbiting their parent planets. Outside of our solar system we have binary stars and stars cluster. The highest easily recognized bound system is the galaxy. But we have one higher level to consider, and this is the cluster of galaxies.

Galaxy clusters contain from several hundred to several thousand galaxies in a volume of around 1 Mpc. These galaxies are bound together by their mutual gravitational attraction. The amount of mass tied up in these systems is generally between 10¹⁴ to 10¹⁵ solar masses; in comparison, our Galaxy, which counts as a large galaxy, is about 10¹² solar masses in size. The typical velocity of a galaxy in a galaxy cluster is around 10³ km s^-1, which is about five times the typical velocity of a star around the center of a spiral galaxy. This high velocity is set by the mass of the cluster; the average kinetic energy of a galaxy in a cluster is equal to the magnitude of the average potential energy, so that a galaxy's velocity is proportional to the square-root of the cluster's mass.

Galaxy clusters, however, are not just composed of galaxies, for they also contain hot gas. This gas, which constitutes about 15% of a cluster's mass, forms a sphere sitting at the center of the cluster The temperature of the gas is very high, ranging from 0.2 keV to 10 keV. With such a high temperature, the gas is almost fully ionized, with the few electrons that are bound clinging to heavier ions such as iron. The dominant radiative process is bremsstrahlung emission, which is the emission of electromagnetic radiation by a free electron passing by an ion. This radiation has a characteristic energy that is set by the temperature of the electrons. For a temperature of several keV, this energy is in the x-ray band. Galaxy clusters are therefore x-ray sources.

The temperature of the x-ray gas is set by the same principle that sets the galaxy velocity: the thermal energy of the gas equals the magnitude of the potential energy. For hydrogen at 1 Mpc from the center of a 10¹⁵ solar mass cluster, this relationship between temperature and potential energy gives a maximum possible temperature of around 45 keV. A smaller mass or a larger cluster radius will make this value smaller, but more important, a gas cloud radius that is much smaller than the radius of the cluster also makes this temperature smaller. For these reasons, the temperature that is measured is smaller than the maximum temperature that is possible.

The hot gas in a cluster is in hydrostatic equilibrium, so that the pressure at any point within the sphere must fully supports the weight of the overlying layers. Because the gas is almost fully ionized, the relationship between pressure, temperature, and density is very simple: the ideal gas law (P = nkT, where the pressure P equals the total number density of particles n times the Boltzmann constant k times the temperature T). When one calculates this very simple model, one finds that the the mass of the cluster is directly given by the density and the temperature of the hot gas. The temperature can be measured with an x-ray telescope from the shape of the x-ray spectrum. The density of the gas in the cluster requires more imagination, because the x-ray flux from the cluster is set by both the square of the density of the gas (the rate at which bremsstrahlung creates x-rays is proportional to the density squared) and the radius of the sphere. If we know the distance from redshift measurements, we can derive the mass of the cluster by measuring the angular size of the cluster on the sky. Alternatively, if we can measure the effect of the hot gas in the cluster on the microwave background (the Sunyaev-Zeldovich effect), we can derive the density of the gas independent of a redshift measure.

While the hot gas in the cluster is in static equilibrium, it is still slowly shrinking. This happens because the gas is cooling. Because bremsstrahlung cooling is proportional to the density squared, and because it is weakly dependent on the temperature, most of the cooling occurs at the core, where the density is highest. This cooling causes the gas sphere to shrink. This process is called a cooling flow, with hot, tenuous gas maintaining a fixed temperature until it flows to the core, where the cooling can efficiently remove energy from the gas. At the very center of the sphere, the cooling is so rapid that the gas precipitates into cool gas clouds. The timescale for this process to cause total precipitation of the hot gas in a cluster is much shorter than the age of the universe, so the gas in the cluster is being replenished. Much of this new gas comes from outside the cluster; it free-falls into the cluster and is heated by a shockwave when it strikes the hot gas in the cluster. Other sources of gas and energy appear to be supernovae shockwaves and the wind and energy expelled by AGNs within a galaxy cluster.

All of this makes for an interesting x-ray source that can tell us something about how the universe evolved. The first issue in observing galactic clusters with the current imaging x-ray telescopes is to accurately model this gas cloud. Already these telescopes have shown the structure of the hot gas to be spatially more complicated than a simple sphere; the gas can have two central concentrations, and it can have a somewhat complicated structure. Much of the x-ray work centers on the types of atomic lines produced at the center of the cluster. Expectations were that the areas of high density, where gas would be precipitating into cool clouds, would produce strong line emission in the x-ray from heavy elements; this expectation turned out to be mistaken.

Because clusters of galaxies emit x-rays, they can be found by their x-ray emission. For this reason, current x-ray telescopes are conducting surveys to find clusters. The value of these surveys is that they tell us how much of the universe's mass is tied up in galaxy clusters, and it gives us a measure of how clumped matter is on the 10 Mpc length. These measurements therefore improve our understanding of cosmology.