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.
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
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
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
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