An Etymological Dictionary of Astronomy and Astrophysics
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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.