An Etymological Dictionary of Astronomy and Astrophysics

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).

See also: → virial; → temperature.