Imagine the Universe!

Galaxy Clusters and How they Live their Lives

One of the most basic areas of investigation in astrophysics today is in cosmology. Theorists and observationalists are working together to try and answer questions like, "How did the Universe evolve after the Big Bang?" and "How did galaxies form?" These are big questions, and they are not easy to answer: after all, these things occurred billions of years ago. Galaxy clusters provide one window into the very early Universe. They are the largest gravitationally bound objects in the Universe, and the properties of clusters can be used to place strong limits on cosmological theories of structure formation and evolution.

A Measure of how Clusters Evolve (the Mass Function)

The mass function (MF) of a galaxy cluster is a measure of the number of galaxies with a given mass. If you know the shape and amplitude of the MF and how it changes with time you can distinguish cosmological models of the evolution of the Universe. For example, in most standard cosmological models most massive clusters form from successive mergers of smaller, less massive (and more common) poor clusters and groups. Therefore, if you compare the MF now (i.e. locally in space) with the MF in the past (i.e. at higher redshifts), you would expect to see fewer massive clusters in the past.

Difficulties with Observations

Most theories of how the Universe evolved make a prediction for the mass function of galaxy clusters. However, the mass function is only poorly determined by observations. This is especially true at high redshifts. Part of the problem is that it is hard to define the large statistical samples needed. Such large samples are needed to draw conclusions about cluster evolution in general, rather than about several individual clusters. Optical surveys suffer from contamination - galaxies in front of and behind the cluster (but not part of the gravitationally bound group) can look like part of the cluster. This makes it difficult to detect rich clusters at high redshifts and poor clusters or groups at any redshifts.

These problems can be avoided by using X-ray based surveys. X-ray surveys detect clusters based on emission from the hot gas in between the galaxies of the cluster. Observing the clusters in this way has several advantages: the X-ray emitting intracluster gas is much brighter than the background and is easily distinguished from the unresolved X-ray background. The presence of the X-ray gas guarantees the cluster is bound, and the observations are only limited by the exposure time, and not by the number of galaxies visible in the cluster.

Direct Measurements

Using X-ray emission, then, it is easier to find statistical samples of clusters. However, even with statistical samples of clusters, a major problem is that cluster masses are difficult to accurately measure. The main method of measuring cluster masses via their X-ray emission, the hydrostatic isothermal beta-model, requires both the average X-ray temperature (from the X-ray spectrum) and density profile (from a fit to the surface brightness distribution). These quantities are difficult to measure for all but the brightest clusters, and practically impossible for many distant clusters which are very faint (to get an X-ray spectrum requires lots of photons).

Indirect Measurements

Since we cannot directly measure mass, we must rely on secondary but related indicators to tell us about the evolution of clusters. The easiest quantity to measure for clusters (and in many cases the only quantity which can be measured for distant clusters) is their X-ray luminosity. Observationally, we can then construct the X-ray luminosity function (XLF) of galaxy clusters, the number of clusters at a given luminosity. Unfortunately, the luminosity of a cluster is determined not only by the mass (i.e. higher mass clusters have higher luminosity) but also hydrodynamics and other effects which are difficult to take into account, like energy injection by early supernovae. Therefore, interpreting results of evolution of the XLF is much more complicated than that of the MF.

Types of Surveys

Currently there are two basic categories of X-ray selected cluster surveys which aim to measure the XLF. One type covers large areas on the sky but has a high flux limit and is mainly limited to optically rich systems with high luminosities. The surveys of this type are the Einstein Extended Medium Sensitivity Survey (EMSS), the only survey so far that has measured the highest luminosity end of the XLF at high redshifts, and the ROSAT All Sky Survey Brightest Cluster Survey (BCS). The BCS has determined the high luminosity XLF very well (because it has contains many clusters) but only at low redshifts.

Until recently the form of the XLF at low X-ray luminosities has not been well determined even at low redshifts. It was with this aim in mind that a second type of survey was begun at Goddard Space Flight Center. The Wide Angle ROSAT Pointed Survey (WARPS) is based on serendipitously detected clusters in archival ROSAT PSPC (Position Sensitive Proportional Counter) observations. The EMSS survey also uses such serendipitously discovered sources, but there are important differences. WARPS analyzes only the central part of the PSPC field, and sticks to the deepest fields (longest exposure times). This means that WARPS and other surveys like it (e.g. the RDCS and SHARC surveys which use the same PSPC archival data but different detection methods) cover much smaller areas than the BCS and EMSS and consequently contain fewer rich clusters. However, they have lower flux limits and contain many more lower luminosity clusters (i.e. poor clusters and groups). We can now determine the XLF at low luminosities at low and high redshifts.

What do these surveys tell us about the XLF and its evolution? The current surveys allows us to divide clusters into low and high redshift subsets divided at a redshift of 0.3. The XLFs for z > 0.3 and z < 0.3 are almost the same. The WARPS and surveys like it show no evolution for lower luminosity clusters, and there is only a hint of a difference (at about 3 sigma level or lower) at the highest luminosity end of the XLF, which has only been well sampled by the EMSS. The trend is towards fewer high luminosity clusters at redshifts above 0.3.

What does this mean in terms of cosmological theories? Analytic theories allow the relationships of luminosity, temperature, size and mass to be determined for the gas in clusters. However, the simplest 'self-similar' model, in which the cluster population at any one time is just a scaled version of the population at any other time and where gravity is the only process affecting the hot gas, seems to fail to explain the observed evolution of the XLF. It predicts a change in the relationship between the mass and luminosity of clusters as a function of redshift and that there should be more high luminosity clusters at earlier times in the XLF (strong evolution if Omega=1, i.e. the Universe is at the "critical density").

A solution to this disagreement between observations and theory is to invoke an epoch of 'pre-heating' in the clusters history, where the gas is heated by some astrophysical source (e.g. supernovae). In this case the scaling laws predict little evolution at the low luminosity end of the XLF and negative evolution for high luminosity clusters, which is what is observed. However, for Omega=1, you would still expect more evolution than is currently seen in the high end of the XLF. The small amount of negative evolution seen suggests both pre-heating and low omega.

Future Work

What does the future hold? WARPS is only partially completed and will be better able to quantify the evolution or lack thereof in the XLF. Eventually, surveys like WARPS will be able to check the EMSS results of evolution in the high luminosity XLF at high redshifts. WARPS and surveys like it also provide a sample of clusters to use as input for studies by future X-ray mission like the Chandra X-ray Observatory and XMM. These mission will be able to measure the X-ray temperatures of clusters even at high redshift. Measuring the temperature of clusters will allow determination of the temperature function (TF) of clusters. Temperature is much more simply related to mass than luminosity and avoids many complications like pre-heating of the gas. Comparing evolution of the high and low redshift TFs will allow for a much better constrains on cosmological quantities like Omega.

Thank you to Don Horner ( for contributing to this article

Imagine the Universe is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center.

The Imagine Team
Acting Project Leader: Dr. Barbara Mattson
All material on this site has been created and updated between 1997-2012.

DVD Table of Contents
Educator's Index