The Virial Theorem is
a theorem relating the kinetic and potential energies of
a stable system as averaged over time.
2<T> = - Sum(over k=1..N) < F(k) * r(k) >
- <X> - X averaged over time
- T - Kinetic Energy
- F(k) - force on the kth object
- r(k) - position of the kth object
In a Gravity-bound system, this amounts to the time-averaged
kinetic energy equaling the negative of the time-averaged
potential energy of the objects.
The theorem helps calculation of the average total kinetic energy
in complex systems.
The terms virial radius and virial mass are used in astrophysics
in a couple of ways in regards to a system such as a Galaxy or
Galaxy Cluster (CL):
- The radius and mass within that radius at which the Velocity Dispersion (σ) is maximal.
- The radius and mass within that radius within which virial equilibrium holds.
Carbon Monoxide (CO)
Velocity Dispersion (σ)