Clusters of Galaxies:

Historically, this was the first set of observations that hinted at dark matter. This is the subject of problem 3 in the homework.

However, substructure can fool you.

The case of the Cancer cluster:

Cancer is a spiral rich cluster of about 100 bright galaxies. Below is the velocity distribution of galaxies in the Cancer cluster:

IF you treat the above distribution as belonging to one system and just apply the virial theorem you determine that the Cancer Cluster has M/L = 1000 (!). If this value is representative of clusters of galaxies then

• Clusters have significantly more dark matter in them than individual galaxies. Individual galaxies have M/L in the range 10--100. This implies that the Intracluster Medium has quite massive.

• But, any gas in the ICM feels the effect of the potential and is heated to some virial temperature:
  (1/2)mv² = (3/2)kT

  where v is the velocity dispersion. For dispersions greater than 300 km/s, the emission is in X-rays. Most clusters of galaxies have a characteristic Temperature of 1--5 keV. But, for Cancer, there was no substantial X-ray emission observed.

• M/L = 1000 is close to the value needed to close the Universe.

Plotting contours of Galaxy density in Cancer suggested that the distribution of galaxies was not relaxed; that is secondary density maxima appeared. These are labelled A thru E below:

This brought up the issue if redshift and position were correlated in this cluster. That is, do galaxies in Group A have different velcoities than galaxies in Group B or C? After a thorough analysis it was shown that these two were highly correlated and that the Cancer cluster could in fact be decomposed into individual groups. In redshift space these groups are shown here:

There is a clear separation of these components in mean velocity and each component has an internal velocity dispersion of about 300 km/s. The M/L of these individual components is 200--300. Furthermore, the components themselves are not gravitationally bound. That is, the Cancer cluster is really an unbound collection of groups:

While Cancer is an extreme case, most all clusters do show some evidence of substructure. Hence, the measured velocity dispersion in these cases does not apply to one dynamical system but to, perhaps, several. Failure to adequately account for substructure in clusters of glaxies leads to systematic overestimates of M/L.

The observation that most clusters have significant substructure implies that cluster formation is still, in essence, occurring as small groups are assimilated into the cluster core. This has implications regarding structure formation scenarios.

Observations of galaxy rotation curves and cluster velocity dispersions suggest that M/L associated with these structures is in the range 10--500; where 500 is fairly extreme. At most, these structures then contribute 20% of the closure mass density. Hence we are driven to the following inescapable conclusion:

If the Universe has a critical density, then the dominant mass constituent is not contained in galaxies or in clusters of galaxies but must be distributed in intergalactic space as well. This requires an isotropic particle background of unknown origin or content. This means accelerator physics is really the same as cosmology.