An Etymological Dictionary of Astronomy and Astrophysics

The process whereby a system of gravitationally interacting particles attains stability. The comparable mass components interact with each other, but the whole system does not expand or collapse. Virialization occurs when the → potential energy is twice the negative → kinetic energy:

• W_vir = 2 K_vir (→ virial theorem). In the case of a → galaxy cluster,
  when the cluster is virialized the merging process and the collapse of matter have finished and the formation process of the galaxy cluster is considered to be 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. A cluster is virialized when it satisfies the condition:

R_vir ~ R_max/2,

where R_vir is the radius when the cluster is virialized and
R_max is the radius when the collapse starts. From this condition it follows that the object is 8 times denser at virialization than when the collapse started.

See also: Verbal noun of → virialize.