An Etymological Dictionary of Astronomy and Astrophysics
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Of or pertaining to the interactive forces between components of a system, such as particles or molecules in a gas or stars in a cluster.
→ virial equation of state, → virial equilibrium, → virial mass, → virial parameter, → virial radius, → virial temperature, → virial theorem, → virialization.

From L. vires, plural of vis "strength," and by extension "force" or "energy," first used by Rudolf Clausius in the investigation of problems in molecular physics.

Viriyâl, loan from E., as above.

In thermodynamics, a generalized → equation of state obtained when the → compression factor Z is expanded in terms of a power series, e.g.: Z = 1 + B(T) / V_m + C(T) / V_m² + ...

→ virial; → equation of state.

The condition of a physical system which obeys the → virial theorem.

→ virial; → equilibrium.

The mass of a cluster of stars or galaxies in statistical equilibrium derived by using the → virial theorem.

→ virial; → mass.

A dimensionless parameter that measures the ratio of thermal plus kinetic energies to gravitational energy of a physical system, such as a molecular cloud. The virial parameter is expressed as: α_vir = 5σ²R / GM, where R and M are the radius and mass of the cloud respectively, σ is the one-dimensional → velocity dispersion inside the cloud, and G the → gravitational constant. It indicates whether a cloud could be bound or not. For molecular clouds that are confined by their surface pressure and for which self-gravity is unimportant, α_vir is much larger than unity, whereas α_vir is ~ 1 when the gravitational energy of a clump becomes comparable to its kinetic energy. See, e.g., Bertoldi & McKee, 1992 (ApJ 395, 140). See also → virial theorem.

→ virial; → parameter.

The radius centered on a galaxy containing matter at 200 times the → critical density of the Universe.

→ virial; → radius.

The mean temperature at which a gravitationally → bound system would satisfy the → virial theorem. For a system of mass M and radius R with constant density, the gravitational energy per unit mass is W = GM/R. The kinetic energy per unit mass is E = (3/2)kT_vir/μ, where k is → Boltzmann's constant and μ the mean molecular weight. According to the virial theorem, E = W/2, which leads to the virial temperature T_vir = (1/3)(GM/kR).

→ virial; → temperature.

A general equation applicable to a gravitationally → bound system of equal mass objects (stars, galaxies, etc.), which is stable against → dynamical disruption. It states that in such a system the average → gravitational potential energy (W_vir) is twice the average → kinetic energy (K_vir) of the system: W_vir = -2K_vir. This general proposition, first derived by Rudolf Clausius (1822-1888), has important applications in a variety of fields ranging from statistical mechanics to astrophysics. See also → virialization, → virial equilibrium, → virialized.

→ virial; → theorem.

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.

Verbal noun of → virialize.

To undergo → virialization.

→ virial; → -ize.

That has undergone → virialization.

Past participle of → virialize.