The merging process won't go on for ever, it stops when a cluster is virialized. Virialized means a system of gravitationaly interacting particles that is stable. The small structures interact with each other, but the cluster doesn't expand or collapse. A system is virialized when de the potential energy is twice the negative kinetic energy. This is shown is the following equation with Wvir the potential energy and Kvir the kinetic energy.

virialization 1

When the cluster is virialized the merging process and the collapse of matter have finished and the formation process of the galaxy cluster is done. A cluster has formed by hierarchical clustering. Virialized clusters, in other words finished clusters, can be found by looking at their radius and density. From the definition of virialization, the potential energy is twice the negative kinetic energy, the next condition can be found. A cluster is virialized when it satisfies this condition.


Rvir is the radius when te cluster is virialized, Rmax is the radius at turnaround, the moment that the object collapses. From this condition it follows that the object is 8 times denser at virialization than it was at turnauround. So looking at the radius and the density of a cluster gives information about if a cluster is virialized and finished or not.

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